/*! * \defgroup VMSF vector/matrix support function * \defgroup SF support function * \defgroup SR support routine * \defgroup C canonical * \defgroup CM canonical model * \defgroup CT canonical transformation */ /*! \file a2af.c * \fn void iauA2af(int ndp, double angle, char *sign, int idmsf[4]) * \brief Decompose radians into degrees, arcminutes, arcseconds, fraction. * \ingroup VMSF * \details * 1) The argument ndp is interpreted as follows: * \verbatim ndp resolution : ...0000 00 00 -7 1000 00 00 -6 100 00 00 -5 10 00 00 -4 1 00 00 -3 0 10 00 -2 0 01 00 -1 0 00 10 0 0 00 01 1 0 00 00.1 2 0 00 00.01 3 0 00 00.001 : 0 00 00.000... * \endverbatim * 2) The largest positive useful value for ndp is determined by the * size of angle, the format of doubles on the target platform, and * the risk of overflowing idmsf[3]. On a typical platform, for * angle up to 2pi, the available floating-point precision might * correspond to ndp=12. However, the practical limit is typically * ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is * only 16 bits. * * 3) The absolute value of angle may exceed 2pi. In cases where it * does not, it is up to the caller to test for and handle the * case where angle is very nearly 2pi and rounds up to 360 degrees, * by testing for idmsf[0]=360 and setting idmsf[0-3] to zero. * * \param[in] ndp resolution * \param[in] angle angle in radians * \param[out] sign '+' or '-' * \param[out] idmsf degrees, arcminutes, arcseconds, fraction */ /*! \file a2tf.c * \fn void iauA2tf(int ndp, double angle, char *sign, int ihmsf[4]) * \brief Decompose radians into hours, minutes, seconds, fraction. * \ingroup VMSF * \details * * 1) The argument ndp is interpreted as follows: * \verbatim ndp resolution : ...0000 00 00 -7 1000 00 00 -6 100 00 00 -5 10 00 00 -4 1 00 00 -3 0 10 00 -2 0 01 00 -1 0 00 10 0 0 00 01 1 0 00 00.1 2 0 00 00.01 3 0 00 00.001 : 0 00 00.000... * \endverbatim * * 2) The largest positive useful value for ndp is determined by the * size of angle, the format of doubles on the target platform, and * the risk of overflowing ihmsf[3]. On a typical platform, for * angle up to 2pi, the available floating-point precision might * correspond to ndp=12. However, the practical limit is typically * ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is * only 16 bits. * * 3) The absolute value of angle may exceed 2pi. In cases where it * does not, it is up to the caller to test for and handle the * case where angle is very nearly 2pi and rounds up to 24 hours, * by testing for ihmsf[0]=24 and setting ihmsf[0-3] to zero. * * \param[in] ndp resolution * \param[in] angle angle in radians * \param[out] sign '+' or '-' * \param[out] ihmsf hours, minutes, seconds, fraction */ /*! \file ab.c * \fn void iauAb(double pnat[3], double v[3], double s, double bm1, double ppr[3]) * \brief Apply aberration to transform natural direction into proper direction. * \ingroup SF * \details * * 1) The algorithm is based on Expr. (7.40) in the Explanatory * Supplement (Urban & Seidelmann 2013), but with the following * changes: * * o Rigorous rather than approximate normalization is applied. * * o The gravitational potential term from Expr. (7) in * Klioner (2003) is added, taking into account only the Sun's * contribution. This has a maximum effect of about * 0.4 microarcsecond. * * 2) In almost all cases, the maximum accuracy will be limited by the * supplied velocity. For example, if the SOFA iauEpv00 function is * used, errors of up to 5 microarcseconds could occur. * * References: * * Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to * the Astronomical Almanac, 3rd ed., University Science Books * (2013). * * Klioner, Sergei A., "A practical relativistic model for micro- * arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003). * * * \param[in] pnat natural direction to the source (unit vector) * \param[in] v observer barycentric velocity in units of c * \param[in] s distance between the Sun and the observer (au) * \param[in] bm1 sqrt(1-|v|^2): reciprocal of Lorenz factor * \param[out] ppr proper direction to source (unit vector) */ /*! \file ae2hd.c * \fn int iauAe2hd(double az, double el, double phi, double *ha, double *dec) * \brief Horizon to equatorial coordinates: transform azimuth and altitude to hour angle and declination. * \ingroup SF * \details * 1) All the arguments are angles in radians. * * 2) The sign convention for azimuth is north zero, east +pi/2. * * 3) HA is returned in the range +/-pi. Declination is returned in * the range +/-pi/2. * * 4) The latitude phi is pi/2 minus the angle between the Earth's * rotation axis and the adopted zenith. In many applications it * will be sufficient to use the published geodetic latitude of the * site. In very precise (sub-arcsecond) applications, phi can be * corrected for polar motion. * * 5) The azimuth az must be with respect to the rotational north pole, * as opposed to the ITRS pole, and an azimuth with respect to north * on a map of the Earth's surface will need to be adjusted for * polar motion if sub-arcsecond accuracy is required. * * 6) Should the user wish to work with respect to the astronomical * zenith rather than the geodetic zenith, phi will need to be * adjusted for deflection of the vertical (often tens of * arcseconds), and the zero point of ha will also be affected. * * 7) The transformation is the same as Ve = Ry(phi-pi/2)*Rz(pi)*Vh, * where Ve and Vh are lefthanded unit vectors in the (ha,dec) and * (az,el) systems respectively and Rz and Ry are rotations about * first the z-axis and then the y-axis. (n.b. Rz(pi) simply * reverses the signs of the x and y components.) For efficiency, * the algorithm is written out rather than calling other utility * functions. For applications that require even greater * efficiency, additional savings are possible if constant terms * such as functions of latitude are computed once and for all. * * 8) Again for efficiency, no range checking of arguments is carried * out. * * \param[in] az azimuth * \param[in] el alittude (informally, elevation) * \param[in] phi site latitude * \param[out] ha hour angle (local) * \param[out] dec declination */ /*! \file af2a.c * \fn int iauAf2a(char s, int ideg, int iamin, double asec, double *rad) * \brief Convert degrees, arcminutes, arcseconds to radians. * \ingroup SF * \details * 1) The result is computed even if any of the range checks fail. * * 2) Negative ideg, iamin and/or asec produce a warning status, but * the absolute value is used in the conversion. * * 3) If there are multiple errors, the status value reflects only the * first, the smallest taking precedence. * * \param[in] s sign: '-' = negative, otherwise positive * \param[in] ideg degrees * \param[in] iamin arcminutes * \param[in] asec arcseconds * \param[out] rd angle in radians * \return 0 = OK * 1 = ideg outside range 0-359 * 2 = iamin outside range 0-59 * 3 = asec outside range 0-59.999... */ /*! \file anp.c * \fn double iauAnp(double a) * \brief Normalize angle into the range 0 <= a < 2pi. * \ingroup VMSF * * \param[in] a angle (radians) * \return angle in range 0-2pi */ /*! \file anpm.c * \fn double iauAnpm(double a) * \brief Normalize angle into the range -pi <= a < +pi. * \ingroup VMSF * \param[in] a angle (radians) * \return angle in range +/-pi * */ /*! \file apcg.c * \fn void iauApcg(double date1, double date2, double ebpv[2][3], double ehp[3], iauASTROM *astrom) * \brief prepare star-independent astrometry parameters * \ingroup SF * \details * For a geocentric observer, prepare star-independent astrometry * parameters for transformations between ICRS and GCRS coordinates. * The Earth ephemeris is supplied by the caller. * * The parameters produced by this function are required in the * parallax, light deflection and aberration parts of the astrometric * transformation chain. * * \param[in] date1 TDB as a 2-part Julian Date * \param[in] date2 TDB as a 2-part Julian Date * \param[in] ebpv Earth barycentric pos/vel (au, au/day) * \param[in] ehp Earth heliocentric position (au) * \param[out] astrom star-independent astrometry parameters: * \param[out] pmt PM time interval (SSB, Julian years) * \param[out] eb SSB to observer (vector, au) * \param[out] eh Sun to observer (unit vector) * \param[out] em distance from Sun to observer (au) * \param[out] v barycentric observer velocity (vector, c) * \param[out] bm1 sqrt(1-|v|^2): reciprocal of Lorenz factor * \param[out] bpn bias-precession-nutation matrix * \param[out] along unchanged * \param[out] xpl unchanged * \param[out] ypl unchanged * \param[out] sphi unchanged * \param[out] cphi unchanged * \param[out] diurab unchanged * \param[out] eral unchanged * \param[out] refa unchanged * \param[out] refb unchanged * * 1) The TDB date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TDB)=2450123.7 could be expressed in any of these ways, among * others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in cases * where the loss of several decimal digits of resolution is * acceptable. The J2000 method is best matched to the way the * argument is handled internally and will deliver the optimum * resolution. The MJD method and the date & time methods are both * good compromises between resolution and convenience. For most * applications of this function the choice will not be at all * critical. * * TT can be used instead of TDB without any significant impact on * accuracy. * * 2) All the vectors are with respect to BCRS axes. * * 3) This is one of several functions that inserts into the astrom * structure star-independent parameters needed for the chain of * astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. * * The various functions support different classes of observer and * portions of the transformation chain: * * functions observer transformation * * iauApcg iauApcg13 geocentric ICRS <-> GCRS * iauApci iauApci13 terrestrial ICRS <-> CIRS * iauApco iauApco13 terrestrial ICRS <-> observed * iauApcs iauApcs13 space ICRS <-> GCRS * iauAper iauAper13 terrestrial update Earth rotation * iauApio iauApio13 terrestrial CIRS <-> observed * * Those with names ending in "13" use contemporary SOFA models to * compute the various ephemerides. The others accept ephemerides * supplied by the caller. * * The transformation from ICRS to GCRS covers space motion, * parallax, light deflection, and aberration. From GCRS to CIRS * comprises frame bias and precession-nutation. From CIRS to * observed takes account of Earth rotation, polar motion, diurnal * aberration and parallax (unless subsumed into the ICRS <-> GCRS * transformation), and atmospheric refraction. * * 4) The context structure astrom produced by this function is used by * iauAtciq* and iauAticq*. * */ /*! \file apcg13.c * \fn void iauApcg13(double date1, double date2, iauASTROM *astrom) * \ingroup SF * \brief prepare star-independent astrometry parameters * \details * * For a geocentric observer, prepare star-independent astrometry * parameters for transformations between ICRS and GCRS coordinates. * The caller supplies the date, and SOFA models are used to predict * the Earth ephemeris. * * The parameters produced by this function are required in the * parallax, light deflection and aberration parts of the astrometric * transformation chain. * * \param[in] date1 TDB as a 2-part... * \param[in] date2 ...Julian Date (Note 1) * * \param[out] astrom * star-independent astrometry parameters: * \param[out] pmt PM time interval (SSB, Julian years) * \param[out] eb SSB to observer (vector, au) * \param[out] eh Sun to observer (unit vector) * \param[out] em distance from Sun to observer (au) * \param[out] v barycentric observer velocity (vector, c) * \param[out] bm1 sqrt(1-|v|^2): reciprocal of Lorenz factor * \param[out] bpn bias-precession-nutation matrix * \param[out] along unchanged * \param[out] xpl unchanged * \param[out] ypl unchanged * \param[out] sphi unchanged * \param[out] cphi unchanged * \param[out] diurab unchanged * \param[out] eral unchanged * \param[out] refa unchanged * \param[out] refb unchanged * * Notes: * * 1) The TDB date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TDB)=2450123.7 could be expressed in any of these ways, among * others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in cases * where the loss of several decimal digits of resolution is * acceptable. The J2000 method is best matched to the way the * argument is handled internally and will deliver the optimum * resolution. The MJD method and the date & time methods are both * good compromises between resolution and convenience. For most * applications of this function the choice will not be at all * critical. * * TT can be used instead of TDB without any significant impact on * accuracy. * * 2) All the vectors are with respect to BCRS axes. * * 3) In cases where the caller wishes to supply his own Earth * ephemeris, the function iauApcg can be used instead of the present * function. * * 4) This is one of several functions that inserts into the astrom * structure star-independent parameters needed for the chain of * astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. * * The various functions support different classes of observer and * portions of the transformation chain: * * functions observer transformation * * iauApcg iauApcg13 geocentric ICRS <-> GCRS * iauApci iauApci13 terrestrial ICRS <-> CIRS * iauApco iauApco13 terrestrial ICRS <-> observed * iauApcs iauApcs13 space ICRS <-> GCRS * iauAper iauAper13 terrestrial update Earth rotation * iauApio iauApio13 terrestrial CIRS <-> observed * * Those with names ending in "13" use contemporary SOFA models to * compute the various ephemerides. The others accept ephemerides * supplied by the caller. * * The transformation from ICRS to GCRS covers space motion, * parallax, light deflection, and aberration. From GCRS to CIRS * comprises frame bias and precession-nutation. From CIRS to * observed takes account of Earth rotation, polar motion, diurnal * aberration and parallax (unless subsumed into the ICRS <-> GCRS * transformation), and atmospheric refraction. * * 5) The context structure astrom produced by this function is used by * iauAtciq* and iauAticq*. */ /*! * \file apci.c \fn void iauApci(double date1, double date2, double ebpv[2][3], double ehp[3], double x, double y, double s, iauASTROM *astrom) \ingroup SF \brief prepare star-independent astrometry parameters * * For a terrestrial observer, prepare star-independent astrometry * parameters for transformations between ICRS and geocentric CIRS * coordinates. The Earth ephemeris and CIP/CIO are supplied by the * caller. * * The parameters produced by this function are required in the * parallax, light deflection, aberration, and bias-precession-nutation * parts of the astrometric transformation chain. * * * \param[in] date1 TDB as a 2-part Julian Date * \param[in] date2 TDB as a 2-part Julian Date (Note 1) * \param[in] ebpv Earth barycentric position/velocity (au, au/day) * \param[in] ehp Earth heliocentric position (au) * \param[in] x CIP X,Y (components of unit vector) * \param[in] y CIP X,Y (components of unit vector) * \param[in] s the CIO locator s (radians) * * \param[out] astrom star-independent astrometry parameters: * \param[out] pmt PM time interval (SSB, Julian years) * \param[out] eb SSB to observer (vector, au) * \param[out] eh Sun to observer (unit vector) * \param[out] em distance from Sun to observer (au) * \param[out] v barycentric observer velocity (vector, c) * \param[out] bm1 sqrt(1-|v|^2): reciprocal of Lorenz factor * \param[out] bpn bias-precession-nutation matrix * \param[out] along unchanged * \param[out] xpl unchanged * \param[out] ypl unchanged * \param[out] sphi unchanged * \param[out] cphi unchanged * \param[out] diurab unchanged * \param[out] eral unchanged * \param[out] refa unchanged * \param[out] refb unchanged * * Notes: * * 1) The TDB date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TDB)=2450123.7 could be expressed in any of these ways, among * others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in cases * where the loss of several decimal digits of resolution is * acceptable. The J2000 method is best matched to the way the * argument is handled internally and will deliver the optimum * resolution. The MJD method and the date & time methods are both * good compromises between resolution and convenience. For most * applications of this function the choice will not be at all * critical. * * TT can be used instead of TDB without any significant impact on * accuracy. * * 2) All the vectors are with respect to BCRS axes. * * 3) In cases where the caller does not wish to provide the Earth * ephemeris and CIP/CIO, the function iauApci13 can be used instead * of the present function. This computes the required quantities * using other SOFA functions. * * 4) This is one of several functions that inserts into the astrom * structure star-independent parameters needed for the chain of * astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. * * The various functions support different classes of observer and * portions of the transformation chain: * * functions observer transformation * * iauApcg iauApcg13 geocentric ICRS <-> GCRS * iauApci iauApci13 terrestrial ICRS <-> CIRS * iauApco iauApco13 terrestrial ICRS <-> observed * iauApcs iauApcs13 space ICRS <-> GCRS * iauAper iauAper13 terrestrial update Earth rotation * iauApio iauApio13 terrestrial CIRS <-> observed * * Those with names ending in "13" use contemporary SOFA models to * compute the various ephemerides. The others accept ephemerides * supplied by the caller. * * The transformation from ICRS to GCRS covers space motion, * parallax, light deflection, and aberration. From GCRS to CIRS * comprises frame bias and precession-nutation. From CIRS to * observed takes account of Earth rotation, polar motion, diurnal * aberration and parallax (unless subsumed into the ICRS <-> GCRS * transformation), and atmospheric refraction. * * 5) The context structure astrom produced by this function is used by * iauAtciq* and iauAticq*. */ /*!\file apci13.c \fn void iauApci13(double date1, double date2, iauASTROM *astrom, double *eo) \ingroup SF \brief prepare star-independent astrometry parameters * * For a terrestrial observer, prepare star-independent astrometry * parameters for transformations between ICRS and geocentric CIRS * coordinates. The caller supplies the date, and SOFA models are used * to predict the Earth ephemeris and CIP/CIO. * * The parameters produced by this function are required in the * parallax, light deflection, aberration, and bias-precession-nutation * parts of the astrometric transformation chain. * * * \param[in] date1 TDB as a 2-part Julian Date * \param[in] date2 TDB as 2 2-part Julian Date (Note 1) * * \param[out] astrom star-independent astrometry parameters: * \param[out] pmt PM time interval (SSB, Julian years) * \param[out] eb SSB to observer (vector, au) * \param[out] eh Sun to observer (unit vector) * \param[out] em distance from Sun to observer (au) * \param[out] v barycentric observer velocity (vector, c) * \param[out] bm1 sqrt(1-|v|^2): reciprocal of Lorenz factor * \param[out] bpn bias-precession-nutation matrix * \param[out] along unchanged * \param[out] xpl unchanged * \param[out] ypl unchanged * \param[out] sphi unchanged * \param[out] cphi unchanged * \param[out] diurab unchanged * \param[out] eral unchanged * \param[out] refa unchanged * \param[out] refb unchanged * \param[out] eo equation of the origins (ERA-GST) * * Notes: * * 1) The TDB date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TDB)=2450123.7 could be expressed in any of these ways, among * others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in cases * where the loss of several decimal digits of resolution is * acceptable. The J2000 method is best matched to the way the * argument is handled internally and will deliver the optimum * resolution. The MJD method and the date & time methods are both * good compromises between resolution and convenience. For most * applications of this function the choice will not be at all * critical. * * TT can be used instead of TDB without any significant impact on * accuracy. * * 2) All the vectors are with respect to BCRS axes. * * 3) In cases where the caller wishes to supply his own Earth * ephemeris and CIP/CIO, the function iauApci can be used instead * of the present function. * * 4) This is one of several functions that inserts into the astrom * structure star-independent parameters needed for the chain of * astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. * * The various functions support different classes of observer and * portions of the transformation chain: * * functions observer transformation * * iauApcg iauApcg13 geocentric ICRS <-> GCRS * iauApci iauApci13 terrestrial ICRS <-> CIRS * iauApco iauApco13 terrestrial ICRS <-> observed * iauApcs iauApcs13 space ICRS <-> GCRS * iauAper iauAper13 terrestrial update Earth rotation * iauApio iauApio13 terrestrial CIRS <-> observed * * Those with names ending in "13" use contemporary SOFA models to * compute the various ephemerides. The others accept ephemerides * supplied by the caller. * * The transformation from ICRS to GCRS covers space motion, * parallax, light deflection, and aberration. From GCRS to CIRS * comprises frame bias and precession-nutation. From CIRS to * observed takes account of Earth rotation, polar motion, diurnal * aberration and parallax (unless subsumed into the ICRS <-> GCRS * transformation), and atmospheric refraction. * * 5) The context structure astrom produced by this function is used by * iauAtciq* and iauAticq*. */ /*!\file apco.c \fn void iauApco(double date1, double date2, double ebpv[2][3], double ehp[3], double x, double y, double s, double theta, double elong, double phi, double hm, double xp, double yp, double sp, double refa, double refb, iauASTROM *astrom) \ingroup SF \brief prepare star-independent astrometry parameters * * For a terrestrial observer, prepare star-independent astrometry * parameters for transformations between ICRS and observed * coordinates. The caller supplies the Earth ephemeris, the Earth * rotation information and the refraction constants as well as the * site coordinates. * * \param[in] date1 TDB as a 2-part Julian Date * \param[in] date2 TDB as a 2-part Julian Date (Note 1) * \param[in] ebpv Earth barycentric PV (au, au/day, Note 2) * \param[in] ehp Earth heliocentric P (au, Note 2) * \param[in] x CIP X,Y (components of unit vector) * \param[in] y CIP X,Y (components of unit vector) * \param[in] s the CIO locator s (radians) * \param[in] theta Earth rotation angle (radians) * \param[in] elong longitude (radians, east +ve, Note 3) * \param[in] phi latitude (geodetic, radians, Note 3) * \param[in] hm height above ellipsoid (m, geodetic, Note 3) * \param[in] xp polar motion coordinates (radians, Note 4) * \param[in] yp polar motion coordinates (radians, Note 4) * \param[in] sp the TIO locator s' (radians, Note 4) * \param[in] refa refraction constant A (radians, Note 5) * \param[in] refb refraction constant B (radians, Note 5) * * \param[out] astrom star-independent astrometry parameters: * \param[out] pmt PM time interval (SSB, Julian years) * \param[out] eb SSB to observer (vector, au) * \param[out] eh Sun to observer (unit vector) * \param[out] em distance from Sun to observer (au) * \param[out] v barycentric observer velocity (vector, c) * \param[out] bm1 sqrt(1-|v|^2): reciprocal of Lorenz factor * \param[out] bpn bias-precession-nutation matrix * \param[out] along longitude + s' (radians) * \param[out] xpl polar motion xp wrt local meridian (radians) * \param[out] ypl polar motion yp wrt local meridian (radians) * \param[out] sphi sine of geodetic latitude * \param[out] cphi cosine of geodetic latitude * \param[out] diurab magnitude of diurnal aberration vector * \param[out] eral "local" Earth rotation angle (radians) * \param[out] refa refraction constant A (radians) * \param[out] refb refraction constant B (radians) * Notes: * * 1) The TDB date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TDB)=2450123.7 could be expressed in any of these ways, among * others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in cases * where the loss of several decimal digits of resolution is * acceptable. The J2000 method is best matched to the way the * argument is handled internally and will deliver the optimum * resolution. The MJD method and the date & time methods are both * good compromises between resolution and convenience. For most * applications of this function the choice will not be at all * critical. * * TT can be used instead of TDB without any significant impact on * accuracy. * * 2) The vectors eb, eh, and all the astrom vectors, are with respect * to BCRS axes. * * 3) The geographical coordinates are with respect to the WGS84 * reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN * CONVENTION: the longitude required by the present function is * right-handed, i.e. east-positive, in accordance with geographical * convention. * * 4) xp and yp are the coordinates (in radians) of the Celestial * Intermediate Pole with respect to the International Terrestrial * Reference System (see IERS Conventions), measured along the * meridians 0 and 90 deg west respectively. sp is the TIO locator * s', in radians, which positions the Terrestrial Intermediate * Origin on the equator. For many applications, xp, yp and * (especially) sp can be set to zero. * * Internally, the polar motion is stored in a form rotated onto the * local meridian. * * 5) The refraction constants refa and refb are for use in a * dZ = A*tan(Z)+B*tan^3(Z) model, where Z is the observed * (i.e. refracted) zenith distance and dZ is the amount of * refraction. * * 6) It is advisable to take great care with units, as even unlikely * values of the input parameters are accepted and processed in * accordance with the models used. * * 7) In cases where the caller does not wish to provide the Earth * Ephemeris, the Earth rotation information and refraction * constants, the function iauApco13 can be used instead of the * present function. This starts from UTC and weather readings etc. * and computes suitable values using other SOFA functions. * * 8) This is one of several functions that inserts into the astrom * structure star-independent parameters needed for the chain of * astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. * * The various functions support different classes of observer and * portions of the transformation chain: * * functions observer transformation * * iauApcg iauApcg13 geocentric ICRS <-> GCRS * iauApci iauApci13 terrestrial ICRS <-> CIRS * iauApco iauApco13 terrestrial ICRS <-> observed * iauApcs iauApcs13 space ICRS <-> GCRS * iauAper iauAper13 terrestrial update Earth rotation * iauApio iauApio13 terrestrial CIRS <-> observed * * Those with names ending in "13" use contemporary SOFA models to * compute the various ephemerides. The others accept ephemerides * supplied by the caller. * * The transformation from ICRS to GCRS covers space motion, * parallax, light deflection, and aberration. From GCRS to CIRS * comprises frame bias and precession-nutation. From CIRS to * observed takes account of Earth rotation, polar motion, diurnal * aberration and parallax (unless subsumed into the ICRS <-> GCRS * transformation), and atmospheric refraction. * * 9) The context structure astrom produced by this function is used by * iauAtioq, iauAtoiq, iauAtciq* and iauAticq*. */ /*!\file apco13.c \fn int iauApco13(double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, iauASTROM *astrom, double *eo) \ingroup SF \brief prepare star-independent astrometry parameters * * For a terrestrial observer, prepare star-independent astrometry * parameters for transformations between ICRS and observed * coordinates. The caller supplies UTC, site coordinates, ambient air * conditions and observing wavelength, and SOFA models are used to * obtain the Earth ephemeris, CIP/CIO and refraction constants. * * The parameters produced by this function are required in the * parallax, light deflection, aberration, and bias-precession-nutation * parts of the ICRS/CIRS transformations. * \param[in] utc1 UTC as a 2-part... * \param[in] utc2 ...quasi Julian Date (Notes 1,2) * \param[in] dut1 UT1-UTC (seconds, Note 3) * \param[in] elong longitude (radians, east +ve, Note 4) * \param[in] phi latitude (geodetic, radians, Note 4) * \param[in] hm height above ellipsoid (m, geodetic, Notes 4,6) * \param[in] xpp polar motion coordinates (radians, Note 5) * \param[in] yp polar motion coordinates (radians, Note 5) * \param[in] phpa pressure at the observer (hPa = mB, Note 6) * \param[in] tc ambient temperature at the observer (deg C) * \param[in] rh relative humidity at the observer (range 0-1) * \param[in] wl wavelength (micrometers, Note 7) * * \param[out] astrom star-independent astrometry parameters: * \param[out] pmt PM time interval (SSB, Julian years) * \param[out] eb SSB to observer (vector, au) * \param[out] eh Sun to observer (unit vector) * \param[out] em distance from Sun to observer (au) * \param[out] v barycentric observer velocity (vector, c) * \param[out] bm1 sqrt(1-|v|^2): reciprocal of Lorenz factor * \param[out] bpn bias-precession-nutation matrix * \param[out] along longitude + s' (radians) * \param[out] xpl polar motion xp wrt local meridian (radians) * \param[out] ypl polar motion yp wrt local meridian (radians) * \param[out] sphi sine of geodetic latitude * \param[out] cphi cosine of geodetic latitude * \param[out] diurab magnitude of diurnal aberration vector * \param[out] eral "local" Earth rotation angle (radians) * \param[out] refa refraction constant A (radians) * \param[out] refb refraction constant B (radians) * \param[out] eo equation of the origins (ERA-GST) * * \return * +1 = dubious year (Note 2) * 0 = OK * -1 = unacceptable date * Notes: * * 1) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any * convenient way between the two arguments, for example where utc1 * is the Julian Day Number and utc2 is the fraction of a day. * * However, JD cannot unambiguously represent UTC during a leap * second unless special measures are taken. The convention in the * present function is that the JD day represents UTC days whether * the length is 86399, 86400 or 86401 SI seconds. * * Applications should use the function iauDtf2d to convert from * calendar date and time of day into 2-part quasi Julian Date, as * it implements the leap-second-ambiguity convention just * described. * * 2) The warning status "dubious year" flags UTCs that predate the * introduction of the time scale or that are too far in the * future to be trusted. See iauDat for further details. * * 3) UT1-UTC is tabulated in IERS bulletins. It increases by exactly * one second at the end of each positive UTC leap second, * introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This * practice is under review, and in the future UT1-UTC may grow * essentially without limit. * * 4) The geographical coordinates are with respect to the WGS84 * reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the * longitude required by the present function is east-positive * (i.e. right-handed), in accordance with geographical convention. * * 5) The polar motion xp,yp can be obtained from IERS bulletins. The * values are the coordinates (in radians) of the Celestial * Intermediate Pole with respect to the International Terrestrial * Reference System (see IERS Conventions 2003), measured along the * meridians 0 and 90 deg west respectively. For many * applications, xp and yp can be set to zero. * * Internally, the polar motion is stored in a form rotated onto * the local meridian. * * 6) If hm, the height above the ellipsoid of the observing station * in meters, is not known but phpa, the pressure in hPa (=mB), is * available, an adequate estimate of hm can be obtained from the * expression * * hm = -29.3 * tsl * log ( phpa / 1013.25 ); * * where tsl is the approximate sea-level air temperature in K * (See Astrophysical Quantities, C.W.Allen, 3rd edition, section * 52). Similarly, if the pressure phpa is not known, it can be * estimated from the height of the observing station, hm, as * follows: * * phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) ); * * Note, however, that the refraction is nearly proportional to * the pressure and that an accurate phpa value is important for * precise work. * * 7) The argument wl specifies the observing wavelength in * micrometers. The transition from optical to radio is assumed to * occur at 100 micrometers (about 3000 GHz). * * 8) It is advisable to take great care with units, as even unlikely * values of the input parameters are accepted and processed in * accordance with the models used. * * 9) In cases where the caller wishes to supply his own Earth * ephemeris, Earth rotation information and refraction constants, * the function iauApco can be used instead of the present function. * * 10) This is one of several functions that inserts into the astrom * structure star-independent parameters needed for the chain of * astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. * * The various functions support different classes of observer and * portions of the transformation chain: * * functions observer transformation * * iauApcg iauApcg13 geocentric ICRS <-> GCRS * iauApci iauApci13 terrestrial ICRS <-> CIRS * iauApco iauApco13 terrestrial ICRS <-> observed * iauApcs iauApcs13 space ICRS <-> GCRS * iauAper iauAper13 terrestrial update Earth rotation * iauApio iauApio13 terrestrial CIRS <-> observed * * Those with names ending in "13" use contemporary SOFA models to * compute the various ephemerides. The others accept ephemerides * supplied by the caller. * * The transformation from ICRS to GCRS covers space motion, * parallax, light deflection, and aberration. From GCRS to CIRS * comprises frame bias and precession-nutation. From CIRS to * observed takes account of Earth rotation, polar motion, diurnal * aberration and parallax (unless subsumed into the ICRS <-> GCRS * transformation), and atmospheric refraction. * * 11) The context structure astrom produced by this function is used * by iauAtioq, iauAtoiq, iauAtciq* and iauAticq*. */ /*!file apcs.c \fn void iauApcs(double date1, double date2, double pv[2][3], double ebpv[2][3], double ehp[3], iauASTROM *astrom) \ingroup SF \brief prepare star-independent astrometry parameters * * For an observer whose geocentric position and velocity are known, * prepare star-independent astrometry parameters for transformations * between ICRS and GCRS. The Earth ephemeris is supplied by the * caller. * * The parameters produced by this function are required in the space * motion, parallax, light deflection and aberration parts of the * astrometric transformation chain. * * \param[in] date1 TDB as a 2-part Julian Date * \param[in] date2 TDB as a 2-part Julian Date (Note 1) * \param[in] pv observer's geocentric pos/vel (m, m/s) * \param[in] ebpv Earth barycentric PV (au, au/day) * \param[in] ehp Earth heliocentric P (au) * * \param[out] astrom star-independent astrometry parameters: * \param[out] pmt PM time interval (SSB, Julian years) * \param[out] eb SSB to observer (vector, au) * \param[out] eh Sun to observer (unit vector) * \param[out] em distance from Sun to observer (au) * \param[out] v barycentric observer velocity (vector, c) * \param[out] bm1 sqrt(1-|v|^2): reciprocal of Lorenz factor * \param[out] bpn bias-precession-nutation matrix * \param[out] along unchanged * \param[out] xpl unchanged * \param[out] ypl unchanged * \param[out] sphi unchanged * \param[out] cphi unchanged * \param[out] diurab unchanged * \param[out] eral unchanged * \param[out] refa unchanged * \param[out] refb unchanged * * Notes: * * 1) The TDB date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TDB)=2450123.7 could be expressed in any of these ways, among * others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in cases * where the loss of several decimal digits of resolution is * acceptable. The J2000 method is best matched to the way the * argument is handled internally and will deliver the optimum * resolution. The MJD method and the date & time methods are both * good compromises between resolution and convenience. For most * applications of this function the choice will not be at all * critical. * * TT can be used instead of TDB without any significant impact on * accuracy. * * 2) All the vectors are with respect to BCRS axes. * * 3) Providing separate arguments for (i) the observer's geocentric * position and velocity and (ii) the Earth ephemeris is done for * convenience in the geocentric, terrestrial and Earth orbit cases. * For deep space applications it maybe more convenient to specify * zero geocentric position and velocity and to supply the * observer's position and velocity information directly instead of * with respect to the Earth. However, note the different units: * m and m/s for the geocentric vectors, au and au/day for the * heliocentric and barycentric vectors. * * 4) In cases where the caller does not wish to provide the Earth * ephemeris, the function iauApcs13 can be used instead of the * present function. This computes the Earth ephemeris using the * SOFA function iauEpv00. * * 5) This is one of several functions that inserts into the astrom * structure star-independent parameters needed for the chain of * astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. * * The various functions support different classes of observer and * portions of the transformation chain: * * functions observer transformation * * iauApcg iauApcg13 geocentric ICRS <-> GCRS * iauApci iauApci13 terrestrial ICRS <-> CIRS * iauApco iauApco13 terrestrial ICRS <-> observed * iauApcs iauApcs13 space ICRS <-> GCRS * iauAper iauAper13 terrestrial update Earth rotation * iauApio iauApio13 terrestrial CIRS <-> observed * * Those with names ending in "13" use contemporary SOFA models to * compute the various ephemerides. The others accept ephemerides * supplied by the caller. * * The transformation from ICRS to GCRS covers space motion, * parallax, light deflection, and aberration. From GCRS to CIRS * comprises frame bias and precession-nutation. From CIRS to * observed takes account of Earth rotation, polar motion, diurnal * aberration and parallax (unless subsumed into the ICRS <-> GCRS * transformation), and atmospheric refraction. * * 6) The context structure astrom produced by this function is used by * iauAtciq* and iauAticq*. */ /*!\file apcs13.c \fn void iauApcs13(double date1, double date2, double pv[2][3], iauASTROM *astrom) \ingroup SF \brief prepare star-independent astrometry parameters * * For an observer whose geocentric position and velocity are known, * prepare star-independent astrometry parameters for transformations * between ICRS and GCRS. The Earth ephemeris is from SOFA models. * * The parameters produced by this function are required in the space * motion, parallax, light deflection and aberration parts of the * astrometric transformation chain. * * \param[in] date1 TDB as a 2-part Julian Date * \param[in] date2 TDB as a 2-part Julian Date (Note 1) * \param[in] pv observer's geocentric pos/vel (Note 3) * * \param[out] astrom star-independent astrometry parameters: * \param[out] pmt PM time interval (SSB, Julian years) * \param[out] eb SSB to observer (vector, au) * \param[out] eh Sun to observer (unit vector) * \param[out] em distance from Sun to observer (au) * \param[out] v barycentric observer velocity (vector, c) * \param[out] bm1 sqrt(1-|v|^2): reciprocal of Lorenz factor * \param[out] bpn bias-precession-nutation matrix * \param[out] along unchanged * \param[out] xpl unchanged * \param[out] ypl unchanged * \param[out] sphi unchanged * \param[out] cphi unchanged * \param[out] diurab unchanged * \param[out] eral unchanged * \param[out] refa unchanged * \param[out] refb unchanged * Notes: * * 1) The TDB date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TDB)=2450123.7 could be expressed in any of these ways, among * others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in cases * where the loss of several decimal digits of resolution is * acceptable. The J2000 method is best matched to the way the * argument is handled internally and will deliver the optimum * resolution. The MJD method and the date & time methods are both * good compromises between resolution and convenience. For most * applications of this function the choice will not be at all * critical. * * TT can be used instead of TDB without any significant impact on * accuracy. * * 2) All the vectors are with respect to BCRS axes. * * 3) The observer's position and velocity pv are geocentric but with * respect to BCRS axes, and in units of m and m/s. No assumptions * are made about proximity to the Earth, and the function can be * used for deep space applications as well as Earth orbit and * terrestrial. * * 4) In cases where the caller wishes to supply his own Earth * ephemeris, the function iauApcs can be used instead of the present * function. * * 5) This is one of several functions that inserts into the astrom * structure star-independent parameters needed for the chain of * astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. * * The various functions support different classes of observer and * portions of the transformation chain: * * functions observer transformation * * iauApcg iauApcg13 geocentric ICRS <-> GCRS * iauApci iauApci13 terrestrial ICRS <-> CIRS * iauApco iauApco13 terrestrial ICRS <-> observed * iauApcs iauApcs13 space ICRS <-> GCRS * iauAper iauAper13 terrestrial update Earth rotation * iauApio iauApio13 terrestrial CIRS <-> observed * * Those with names ending in "13" use contemporary SOFA models to * compute the various ephemerides. The others accept ephemerides * supplied by the caller. * * The transformation from ICRS to GCRS covers space motion, * parallax, light deflection, and aberration. From GCRS to CIRS * comprises frame bias and precession-nutation. From CIRS to * observed takes account of Earth rotation, polar motion, diurnal * aberration and parallax (unless subsumed into the ICRS <-> GCRS * transformation), and atmospheric refraction. * * 6) The context structure astrom produced by this function is used by * iauAtciq* and iauAticq*. */ /*!\file aper.c \fn void iauAper(double theta, iauASTROM *astrom) \ingroup SF \brief update the Earth rotation angle * * In the star-independent astrometry parameters, update only the * Earth rotation angle, supplied by the caller explicitly. * * \param[in] theta Earth rotation angle (radians, Note 2) * \param[in] astrom star-independent astrometry parameters: * \param[in] pmt not used * \param[in] eb not used * \param[in] eh not used * \param[in] em not used * \param[in] v not used * \param[in] bm1 not used * \param[in] bpn not used * \param[in] along longitude + s' (radians) * \param[in] xpl not used * \param[in] ypl not used * \param[in] sphi not used * \param[in] cphi not used * \param[in] diurab not used * \param[in] eral not used * \param[in] refa not used * \param[in] refb not used * * \param[out] astrom star-independent astrometry parameters: * \param[out] pmt unchanged * \param[out] eb unchanged * \param[out] eh unchanged * \param[out] em unchanged * \param[out] v unchanged * \param[out] bm1 unchanged * \param[out] bpn unchanged * \param[out] along unchanged * \param[out] xpl unchanged * \param[out] ypl unchanged * \param[out] sphi unchanged * \param[out] cphi unchanged * \param[out] diurab unchanged * \param[out] eral "local" Earth rotation angle (radians) * \param[out] refa unchanged * \param[out] refb unchanged * * Notes: * * 1) This function exists to enable sidereal-tracking applications to * avoid wasteful recomputation of the bulk of the astrometry * parameters: only the Earth rotation is updated. * * 2) For targets expressed as equinox based positions, such as * classical geocentric apparent (RA,Dec), the supplied theta can be * Greenwich apparent sidereal time rather than Earth rotation * angle. * * 3) The function iauAper13 can be used instead of the present * function, and starts from UT1 rather than ERA itself. * * 4) This is one of several functions that inserts into the astrom * structure star-independent parameters needed for the chain of * astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. * * The various functions support different classes of observer and * portions of the transformation chain: * * functions observer transformation * * iauApcg iauApcg13 geocentric ICRS <-> GCRS * iauApci iauApci13 terrestrial ICRS <-> CIRS * iauApco iauApco13 terrestrial ICRS <-> observed * iauApcs iauApcs13 space ICRS <-> GCRS * iauAper iauAper13 terrestrial update Earth rotation * iauApio iauApio13 terrestrial CIRS <-> observed * * Those with names ending in "13" use contemporary SOFA models to * compute the various ephemerides. The others accept ephemerides * supplied by the caller. * * The transformation from ICRS to GCRS covers space motion, * parallax, light deflection, and aberration. From GCRS to CIRS * comprises frame bias and precession-nutation. From CIRS to * observed takes account of Earth rotation, polar motion, diurnal * aberration and parallax (unless subsumed into the ICRS <-> GCRS * transformation), and atmospheric refraction. */ /*!\file aper13.c \fn void iauAper13(double ut11, double ut12, iauASTROM *astrom) \ingroup SF \brief update the Earth rotation angle * * * In the star-independent astrometry parameters, update only the * Earth rotation angle. The caller provides UT1, (n.b. not UTC). * * * \param[in] ut11 UT1 as a 2-part Julian Date * \param[in] ut12 UT1 as a 2-part Julian Date (Note 1) * \param[in] astrom star-independent astrometry parameters: * \param[in] pmt not used * \param[in] eb not used * \param[in] eh not used * \param[in] em not used * \param[in] v not used * \param[in] bm1 not used * \param[in] bpn not used * \param[in] along longitude + s' (radians) * \param[in] xpl not used * \param[in] ypl not used * \param[in] sphi not used * \param[in] cphi not used * \param[in] diurab not used * \param[in] eral not used * \param[in] refa not used * \param[in] refb not used * * \param[out] astrom star-independent astrometry parameters: * \param[out] pmt unchanged * \param[out] eb unchanged * \param[out] eh unchanged * \param[out] em unchanged * \param[out] v unchanged * \param[out] bm1 unchanged * \param[out] bpn unchanged * \param[out] along unchanged * \param[out] xpl unchanged * \param[out] ypl unchanged * \param[out] sphi unchanged * \param[out] cphi unchanged * \param[out] diurab unchanged * \param[out] eral "local" Earth rotation angle (radians) * \param[out] refa unchanged * \param[out] refb unchanged * * Notes: * * 1) The UT1 date (n.b. not UTC) ut11+ut12 is a Julian Date, * apportioned in any convenient way between the arguments ut11 and * ut12. For example, JD(UT1)=2450123.7 could be expressed in any * of these ways, among others: * * ut11 ut12 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in cases * where the loss of several decimal digits of resolution is * acceptable. The J2000 and MJD methods are good compromises * between resolution and convenience. The date & time method is * best matched to the algorithm used: maximum precision is * delivered when the ut11 argument is for 0hrs UT1 on the day in * question and the ut12 argument lies in the range 0 to 1, or vice * versa. * * 2) If the caller wishes to provide the Earth rotation angle itself, * the function iauAper can be used instead. One use of this * technique is to substitute Greenwich apparent sidereal time and * thereby to support equinox based transformations directly. * * 3) This is one of several functions that inserts into the astrom * structure star-independent parameters needed for the chain of * astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. * * The various functions support different classes of observer and * portions of the transformation chain: * * functions observer transformation * * iauApcg iauApcg13 geocentric ICRS <-> GCRS * iauApci iauApci13 terrestrial ICRS <-> CIRS * iauApco iauApco13 terrestrial ICRS <-> observed * iauApcs iauApcs13 space ICRS <-> GCRS * iauAper iauAper13 terrestrial update Earth rotation * iauApio iauApio13 terrestrial CIRS <-> observed * * Those with names ending in "13" use contemporary SOFA models to * compute the various ephemerides. The others accept ephemerides * supplied by the caller. * * The transformation from ICRS to GCRS covers space motion, * parallax, light deflection, and aberration. From GCRS to CIRS * comprises frame bias and precession-nutation. From CIRS to * observed takes account of Earth rotation, polar motion, diurnal * aberration and parallax (unless subsumed into the ICRS <-> GCRS * transformation), and atmospheric refraction. */ /*!file apio.c \fn void iauApio(double sp, double theta, double elong, double phi, double hm, double xp, double yp, double refa, double refb, iauASTROM *astrom) \ingroup SF \brief prepare star-independent astrometry parameters * * * For a terrestrial observer, prepare star-independent astrometry * parameters for transformations between CIRS and observed * coordinates. The caller supplies the Earth orientation information * and the refraction constants as well as the site coordinates. * * \param[in] sp the TIO locator s' (radians, Note 1) * \param[in] theta Earth rotation angle (radians) * \param[in] elong longitude (radians, east +ve, Note 2) * \param[in] phi geodetic latitude (radians, Note 2) * \param[in] hm height above ellipsoid (m, geodetic Note 2) * \param[in] xp polar motion coordinates (radians, Note 3) * \param[in] yp polar motion coordinates (radians, Note 3) * \param[in] refa refraction constant A (radians, Note 4) * \param[in] refb refraction constant B (radians, Note 4) * * \param[out] astrom star-independent astrometry parameters: * \param[out] pmt unchanged * \param[out] eb unchanged * \param[out] eh unchanged * \param[out] em unchanged * \param[out] v unchanged * \param[out] bm1 unchanged * \param[out] bpn unchanged * \param[out] along longitude + s' (radians) * \param[out] xpl polar motion xp wrt local meridian (radians) * \param[out] ypl polar motion yp wrt local meridian (radians) * \param[out] sphi sine of geodetic latitude * \param[out] cphi cosine of geodetic latitude * \param[out] diurab magnitude of diurnal aberration vector * \param[out] eral "local" Earth rotation angle (radians) * \param[out] refa refraction constant A (radians) * \param[out] refb refraction constant B (radians) * * Notes: * * 1) sp, the TIO locator s', is a tiny quantity needed only by the * most precise applications. It can either be set to zero or * predicted using the SOFA function iauSp00. * * 2) The geographical coordinates are with respect to the WGS84 * reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the * longitude required by the present function is east-positive * (i.e. right-handed), in accordance with geographical convention. * * 3) The polar motion xp,yp can be obtained from IERS bulletins. The * values are the coordinates (in radians) of the Celestial * Intermediate Pole with respect to the International Terrestrial * Reference System (see IERS Conventions 2003), measured along the * meridians 0 and 90 deg west respectively. For many applications, * xp and yp can be set to zero. * * Internally, the polar motion is stored in a form rotated onto the * local meridian. * * 4) The refraction constants refa and refb are for use in a * dZ = A*tan(Z)+B*tan^3(Z) model, where Z is the observed * (i.e. refracted) zenith distance and dZ is the amount of * refraction. * * 5) It is advisable to take great care with units, as even unlikely * values of the input parameters are accepted and processed in * accordance with the models used. * * 6) In cases where the caller does not wish to provide the Earth * rotation information and refraction constants, the function * iauApio13 can be used instead of the present function. This * starts from UTC and weather readings etc. and computes suitable * values using other SOFA functions. * * 7) This is one of several functions that inserts into the astrom * structure star-independent parameters needed for the chain of * astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. * * The various functions support different classes of observer and * portions of the transformation chain: * * functions observer transformation * * iauApcg iauApcg13 geocentric ICRS <-> GCRS * iauApci iauApci13 terrestrial ICRS <-> CIRS * iauApco iauApco13 terrestrial ICRS <-> observed * iauApcs iauApcs13 space ICRS <-> GCRS * iauAper iauAper13 terrestrial update Earth rotation * iauApio iauApio13 terrestrial CIRS <-> observed * * Those with names ending in "13" use contemporary SOFA models to * compute the various ephemerides. The others accept ephemerides * supplied by the caller. * * The transformation from ICRS to GCRS covers space motion, * parallax, light deflection, and aberration. From GCRS to CIRS * comprises frame bias and precession-nutation. From CIRS to * observed takes account of Earth rotation, polar motion, diurnal * aberration and parallax (unless subsumed into the ICRS <-> GCRS * transformation), and atmospheric refraction. * * 8) The context structure astrom produced by this function is used by * iauAtioq and iauAtoiq. */ /*!file apio13.c \fn int iauApio13(double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, iauASTROM *astrom) \ingroup SF \brief prepare star-independent astrometry parameters * * For a terrestrial observer, prepare star-independent astrometry * parameters for transformations between CIRS and observed * coordinates. The caller supplies UTC, site coordinates, ambient air * conditions and observing wavelength. * * \param[in] utc1 UTC as a 2-part quasi Julian Date * \param[in] utc2 UTC as a 2-part quasi Julian Date (Notes 1,2) * \param[in] dut1 UT1-UTC (seconds) * \param[in] elong longitude (radians, east +ve, Note 3) * \param[in] phi geodetic latitude (radians, Note 3) * \param[in] hm height above ellipsoid (m, geodetic Notes 4,6) * \param[in] xp polar motion coordinates (radians, Note 5) * \param[in] yp polar motion coordinates (radians, Note 5) * \param[in] phpa pressure at the observer (hPa = mB, Note 6) * \param[in] tc ambient temperature at the observer (deg C) * \param[in] rh relative humidity at the observer (range 0-1) * \param[in] wl wavelength (micrometers, Note 7) * * \param[out] astrom star-independent astrometry parameters: * \param[out] pmt unchanged * \param[out] eb unchanged * \param[out] eh unchanged * \param[out] em unchanged * \param[out] v unchanged * \param[out] bm1 unchanged * \param[out] bpn unchanged * \param[out] along longitude + s' (radians) * \param[out] xpl polar motion xp wrt local meridian (radians) * \param[out] ypl polar motion yp wrt local meridian (radians) * \param[out] sphi sine of geodetic latitude * \param[out] cphi cosine of geodetic latitude * \param[out] diurab magnitude of diurnal aberration vector * \param[out] eral "local" Earth rotation angle (radians) * \param[out] refa refraction constant A (radians) * \param[out] refb refraction constant B (radians) * * \return * +1 = dubious year (Note 2) * 0 = OK * -1 = unacceptable date * Notes: * * 1) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any * convenient way between the two arguments, for example where utc1 * is the Julian Day Number and utc2 is the fraction of a day. * * However, JD cannot unambiguously represent UTC during a leap * second unless special measures are taken. The convention in the * present function is that the JD day represents UTC days whether * the length is 86399, 86400 or 86401 SI seconds. * * Applications should use the function iauDtf2d to convert from * calendar date and time of day into 2-part quasi Julian Date, as * it implements the leap-second-ambiguity convention just * described. * * 2) The warning status "dubious year" flags UTCs that predate the * introduction of the time scale or that are too far in the future * to be trusted. See iauDat for further details. * * 3) UT1-UTC is tabulated in IERS bulletins. It increases by exactly * one second at the end of each positive UTC leap second, * introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This * practice is under review, and in the future UT1-UTC may grow * essentially without limit. * * 4) The geographical coordinates are with respect to the WGS84 * reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the * longitude required by the present function is east-positive * (i.e. right-handed), in accordance with geographical convention. * * 5) The polar motion xp,yp can be obtained from IERS bulletins. The * values are the coordinates (in radians) of the Celestial * Intermediate Pole with respect to the International Terrestrial * Reference System (see IERS Conventions 2003), measured along the * meridians 0 and 90 deg west respectively. For many applications, * xp and yp can be set to zero. * * Internally, the polar motion is stored in a form rotated onto * the local meridian. * * 6) If hm, the height above the ellipsoid of the observing station * in meters, is not known but phpa, the pressure in hPa (=mB), is * available, an adequate estimate of hm can be obtained from the * expression * * hm = -29.3 * tsl * log ( phpa / 1013.25 ); * * where tsl is the approximate sea-level air temperature in K * (See Astrophysical Quantities, C.W.Allen, 3rd edition, section * 52). Similarly, if the pressure phpa is not known, it can be * estimated from the height of the observing station, hm, as * follows: * * phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) ); * * Note, however, that the refraction is nearly proportional to the * pressure and that an accurate phpa value is important for * precise work. * * 7) The argument wl specifies the observing wavelength in * micrometers. The transition from optical to radio is assumed to * occur at 100 micrometers (about 3000 GHz). * * 8) It is advisable to take great care with units, as even unlikely * values of the input parameters are accepted and processed in * accordance with the models used. * * 9) In cases where the caller wishes to supply his own Earth * rotation information and refraction constants, the function * iauApc can be used instead of the present function. * * 10) This is one of several functions that inserts into the astrom * structure star-independent parameters needed for the chain of * astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed. * * The various functions support different classes of observer and * portions of the transformation chain: * * functions observer transformation * * iauApcg iauApcg13 geocentric ICRS <-> GCRS * iauApci iauApci13 terrestrial ICRS <-> CIRS * iauApco iauApco13 terrestrial ICRS <-> observed * iauApcs iauApcs13 space ICRS <-> GCRS * iauAper iauAper13 terrestrial update Earth rotation * iauApio iauApio13 terrestrial CIRS <-> observed * * Those with names ending in "13" use contemporary SOFA models to * compute the various ephemerides. The others accept ephemerides * supplied by the caller. * * The transformation from ICRS to GCRS covers space motion, * parallax, light deflection, and aberration. From GCRS to CIRS * comprises frame bias and precession-nutation. From CIRS to * observed takes account of Earth rotation, polar motion, diurnal * aberration and parallax (unless subsumed into the ICRS <-> GCRS * transformation), and atmospheric refraction. * * 11) The context structure astrom produced by this function is used * by iauAtioq and iauAtoiq. */ /*!\file atci13.c \fn void iauAtci13(double rc, double dc, double pr, double pd, double px, double rv, double date1, double date2, double *ri, double *di, double *eo) \ingroup SF \brief Transform ICRS star data, epoch J2000.0, to CIRS. * * * \param[in] rc ICRS right ascension at J2000.0 (radians, Note 1) * \param[in] dc ICRS declination at J2000.0 (radians, Note 1) * \param[in] pr RA proper motion (radians/year; Note 2) * \param[in] pd Dec proper motion (radians/year) * \param[in] px parallax (arcsec) * \param[in] rv radial velocity (km/s, +ve if receding) * \param[in] date1 TDB as a 2-part... * \param[in] date2 ...Julian Date (Note 3) * * \param[out] ri CIRS geocentric RA (radians) * \param[out] di CIRS geocentric Dec (radians) * \param[out] eo equation of the origins (ERA-GST, Note 5) * * Notes: * * 1) Star data for an epoch other than J2000.0 (for example from the * Hipparcos catalog, which has an epoch of J1991.25) will require a * preliminary call to iauPmsafe before use. * * 2) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt. * * 3) The TDB date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TDB)=2450123.7 could be expressed in any of these ways, among * others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in cases * where the loss of several decimal digits of resolution is * acceptable. The J2000 method is best matched to the way the * argument is handled internally and will deliver the optimum * resolution. The MJD method and the date & time methods are both * good compromises between resolution and convenience. For most * applications of this function the choice will not be at all * critical. * * TT can be used instead of TDB without any significant impact on * accuracy. * * 4) The available accuracy is better than 1 milliarcsecond, limited * mainly by the precession-nutation model that is used, namely * IAU 2000A/2006. Very close to solar system bodies, additional * errors of up to several milliarcseconds can occur because of * unmodeled light deflection; however, the Sun's contribution is * taken into account, to first order. The accuracy limitations of * the SOFA function iauEpv00 (used to compute Earth position and * velocity) can contribute aberration errors of up to * 5 microarcseconds. Light deflection at the Sun's limb is * uncertain at the 0.4 mas level. * * 5) Should the transformation to (equinox based) apparent place be * required rather than (CIO based) intermediate place, subtract the * equation of the origins from the returned right ascension: * RA = RI - EO. (The iauAnp function can then be applied, as */ /*!\file atciq.c \fn void iauAtciq(double rc, double dc, double pr, double pd, double px, double rv, iauASTROM *astrom, double *ri, double *di) \ingroup SF \brief Quick ICRS, epoch J2000.0, to CIRS transformation * * Quick ICRS, epoch J2000.0, to CIRS transformation, given precomputed * star-independent astrometry parameters. * * Use of this function is appropriate when efficiency is important and * where many star positions are to be transformed for one date. The * star-independent parameters can be obtained by calling one of the * functions iauApci[13], iauApcg[13], iauApco[13] or iauApcs[13]. * * If the parallax and proper motions are zero the iauAtciqz function * can be used instead. * * \param[in] rc ICRS RA at J2000.0 (radians) * \param[in] dc ICRS Dec at J2000.0 (radians) * \param[in] pr RA proper motion (radians/year; Note 3) * \param[in] pd Dec proper motion (radians/year) * \param[in] px parallax (arcsec) * \param[in] rv radial velocity (km/s, +ve if receding) * \param[in] astrom star-independent astrometry parameters: * \param[in] pmt PM time interval (SSB, Julian years) * \param[in] eb SSB to observer (vector, au) * \param[in] eh Sun to observer (unit vector) * \param[in] em distance from Sun to observer (au) * \param[in] v barycentric observer velocity (vector, c) * \param[in] bm1 sqrt(1-|v|^2): reciprocal of Lorenz factor * \param[in] bpn bias-precession-nutation matrix * \param[in] along longitude + s' (radians) * \param[in] xpl polar motion xp wrt local meridian (radians) * \param[in] ypl polar motion yp wrt local meridian (radians) * \param[in] sphi sine of geodetic latitude * \param[in] cphi cosine of geodetic latitude * \param[in] diurab magnitude of diurnal aberration vector * \param[in] eral "local" Earth rotation angle (radians) * \param[in] refa refraction constant A (radians) * \param[in] refb refraction constant B (radians) * * \param[out] ri CIRS RA (radians) * \param[out] di CIRS Dec (radians) * * Notes: * * 1) All the vectors are with respect to BCRS axes. * * 2) Star data for an epoch other than J2000.0 (for example from the * Hipparcos catalog, which has an epoch of J1991.25) will require a * preliminary call to iauPmsafe before use. * * 3) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt. */ /*!\file atciqn.c \fn void iauAtciqn(double rc, double dc, double pr, double pd, double px, double rv, iauASTROM *astrom, int n, iauLDBODY b[], double *ri, double *di) \ingroup SF \brief Quick ICRS, epoch J2000.0, to CIRS transformation. * * Quick ICRS, epoch J2000.0, to CIRS transformation, given precomputed * star-independent astrometry parameters plus a list of light- * deflecting bodies. * * Use of this function is appropriate when efficiency is important and * where many star positions are to be transformed for one date. The * star-independent parameters can be obtained by calling one of the * functions iauApci[13], iauApcg[13], iauApco[13] or iauApcs[13]. * * If the only light-deflecting body to be taken into account is the * Sun, the iauAtciq function can be used instead. If in addition the * parallax and proper motions are zero, the iauAtciqz function can be * used. * * \param[in] rc ICRS RA at J2000.0 (radians) * \param[in] dc ICRS Dec at J2000.0 (radians) * \param[in] pr RA proper motion (radians/year; Note 3) * \param[in] pd Dec proper motion (radians/year) * \param[in] px parallax (arcsec) * \param[in] rv radial velocity (km/s, +ve if receding) * \param[in] astrom star-independent astrometry parameters: * \param[in] pmt PM time interval (SSB, Julian years) * \param[in] eb SSB to observer (vector, au) * \param[in] eh Sun to observer (unit vector) * \param[in] em distance from Sun to observer (au) * \param[in] v barycentric observer velocity (vector, c) * \param[in] bm1 sqrt(1-|v|^2): reciprocal of Lorenz factor * \param[in] bpn bias-precession-nutation matrix * \param[in] along longitude + s' (radians) * \param[in] xpl polar motion xp wrt local meridian (radians) * \param[in] ypl polar motion yp wrt local meridian (radians) * \param[in] sphi sine of geodetic latitude * \param[in] cphi cosine of geodetic latitude * \param[in] diurab magnitude of diurnal aberration vector * \param[in] eral "local" Earth rotation angle (radians) * \param[in] refa refraction constant A (radians) * \param[in] refb refraction constant B (radians) * \param[in] n number of bodies (Note 3) * \param[in] b data for each of the n bodies (Notes 3,4): * \param[in] bm mass of the body (solar masses, Note 5) * \param[in] dl deflection limiter (Note 6) * \param[in] pv barycentric PV of the body (au, au/day) * * \param[out] ri CIRS RA (radians) * \param[out] di CIRS Dec (radians) * * Notes: * * 1) Star data for an epoch other than J2000.0 (for example from the * Hipparcos catalog, which has an epoch of J1991.25) will require a * preliminary call to iauPmsafe before use. * * 2) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt. * * 3) The struct b contains n entries, one for each body to be * considered. If n = 0, no gravitational light deflection will be * applied, not even for the Sun. * * 4) The struct b should include an entry for the Sun as well as for * any planet or other body to be taken into account. The entries * should be in the order in which the light passes the body. * * 5) In the entry in the b struct for body i, the mass parameter * b[i].bm can, as required, be adjusted in order to allow for such * effects as quadrupole field. * * 6) The deflection limiter parameter b[i].dl is phi^2/2, where phi is * the angular separation (in radians) between star and body at * which limiting is applied. As phi shrinks below the chosen * threshold, the deflection is artificially reduced, reaching zero * for phi = 0. Example values suitable for a terrestrial * observer, together with masses, are as follows: * * body i b[i].bm b[i].dl * * Sun 1.0 6e-6 * Jupiter 0.00095435 3e-9 * Saturn 0.00028574 3e-10 * * 7) For efficiency, validation of the contents of the b array is * omitted. The supplied masses must be greater than zero, the * position and velocity vectors must be right, and the deflection * limiter greater than zero. */ /*!\file atciqz.c \fn void iauAtciqz(double rc, double dc, iauASTROM *astrom, double *ri, double *di) \ingroup SF \brief Quick ICRS to CIRS transformation * * Quick ICRS to CIRS transformation, given precomputed star- * independent astrometry parameters, and assuming zero parallax and * proper motion. * * Use of this function is appropriate when efficiency is important and * where many star positions are to be transformed for one date. The * star-independent parameters can be obtained by calling one of the * functions iauApci[13], iauApcg[13], iauApco[13] or iauApcs[13]. * * The corresponding function for the case of non-zero parallax and * proper motion is iauAtciq. * * \param[in] rcc ICRS astrometric RA (radians) * \param[in] dc ICRS astrometric Dec (radians) * \param[in] astrom star-independent astrometry parameters: * \param[in] pmt PM time interval (SSB, Julian years) * \param[in] eb SSB to observer (vector, au) * \param[in] eh Sun to observer (unit vector) * \param[in] em distance from Sun to observer (au) * \param[in] v barycentric observer velocity (vector, c) * \param[in] bm1 sqrt(1-|v|^2): reciprocal of Lorenz factor * \param[in] bpn bias-precession-nutation matrix * \param[in] along longitude + s' (radians) * \param[in] xpl polar motion xp wrt local meridian (radians) * \param[in] ypl polar motion yp wrt local meridian (radians) * \param[in] sphi sine of geodetic latitude * \param[in] cphi cosine of geodetic latitude * \param[in] diurab magnitude of diurnal aberration vector * \param[in] eral "local" Earth rotation angle (radians) * \param[in] refa refraction constant A (radians) * \param[in] refb refraction constant B (radians) * * \param[out] ri CIRS RA (radians) * \param[out] di CIRS Dec (radians) * * Note: * * All the vectors are with respect to BCRS axes. * * References: * * Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to * the Astronomical Almanac, 3rd ed., University Science Books * (2013). * * Klioner, Sergei A., "A practical relativistic model for micro- * arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003). */ /*!\file atco13.c \fn int iauAtco13(double rc, double dc, double pr, double pd, double px, double rv, double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, double *aob, double *zob, double *hob, double *dob, double *rob, double *eo) \ingroup SF \brief ICRS RA,Dec to observed place * * ICRS RA,Dec to observed place. The caller supplies UTC, site * coordinates, ambient air conditions and observing wavelength. * * SOFA models are used for the Earth ephemeris, bias-precession- * nutation, Earth orientation and refraction. * * \param[in] rc ICRS right ascension at J2000.0 (radians, Note 1) * \param[in] dc ICRS declination at J2000.0 (radians, Note 1) * \param[in] pr RA proper motion (radians/year; Note 2) * \param[in] pd Dec proper motion (radians/year) * \param[in] px parallax (arcsec) * \param[in] rv radial velocity (km/s, +ve if receding) * \param[in] utc1 UTC as a 2-part quasi Julian Date * \param[in] utc2 UTC as a 2-part quasi Julian Date (Notes 3-4) * \param[in] dut1 UT1-UTC (seconds, Note 5) * \param[in] elong longitude (radians, east +ve, Note 6) * \param[in] phi latitude (geodetic, radians, Note 6) * \param[in] hm height above ellipsoid (m, geodetic, Notes 6,8) * \param[in] xp polar motion coordinates (radians, Note 7) * \param[in] yp polar motion coordinates (radians, Note 7) * \param[in] phpa pressure at the observer (hPa = mB, Note 8) * \param[in] tc ambient temperature at the observer (deg C) * \param[in] rh relative humidity at the observer (range 0-1) * \param[in] wl wavelength (micrometers, Note 9) * * \param[out] aob observed azimuth (radians: N=0,E=90) * \param[out] zob observed zenith distance (radians) * \param[out] hob observed hour angle (radians) * \param[out] dob observed declination (radians) * \param[out] rob observed right ascension (CIO-based, radians) * \param[out] eo equation of the origins (ERA-GST) * * \return * +1 = dubious year (Note 4) * 0 = OK * -1 = unacceptable date * Notes: * * 1) Star data for an epoch other than J2000.0 (for example from the * Hipparcos catalog, which has an epoch of J1991.25) will require * a preliminary call to iauPmsafe before use. * * 2) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt. * * 3) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any * convenient way between the two arguments, for example where utc1 * is the Julian Day Number and utc2 is the fraction of a day. * * However, JD cannot unambiguously represent UTC during a leap * second unless special measures are taken. The convention in the * present function is that the JD day represents UTC days whether * the length is 86399, 86400 or 86401 SI seconds. * * Applications should use the function iauDtf2d to convert from * calendar date and time of day into 2-part quasi Julian Date, as * it implements the leap-second-ambiguity convention just * described. * * 4) The warning status "dubious year" flags UTCs that predate the * introduction of the time scale or that are too far in the * future to be trusted. See iauDat for further details. * * 5) UT1-UTC is tabulated in IERS bulletins. It increases by exactly * one second at the end of each positive UTC leap second, * introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This * practice is under review, and in the future UT1-UTC may grow * essentially without limit. * * 6) The geographical coordinates are with respect to the WGS84 * reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the * longitude required by the present function is east-positive * (i.e. right-handed), in accordance with geographical convention. * * 7) The polar motion xp,yp can be obtained from IERS bulletins. The * values are the coordinates (in radians) of the Celestial * Intermediate Pole with respect to the International Terrestrial * Reference System (see IERS Conventions 2003), measured along the * meridians 0 and 90 deg west respectively. For many * applications, xp and yp can be set to zero. * * 8) If hm, the height above the ellipsoid of the observing station * in meters, is not known but phpa, the pressure in hPa (=mB), * is available, an adequate estimate of hm can be obtained from * the expression * * hm = -29.3 * tsl * log ( phpa / 1013.25 ); * * where tsl is the approximate sea-level air temperature in K * (See Astrophysical Quantities, C.W.Allen, 3rd edition, section * 52). Similarly, if the pressure phpa is not known, it can be * estimated from the height of the observing station, hm, as * follows: * * phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) ); * * Note, however, that the refraction is nearly proportional to * the pressure and that an accurate phpa value is important for * precise work. * * 9) The argument wl specifies the observing wavelength in * micrometers. The transition from optical to radio is assumed to * occur at 100 micrometers (about 3000 GHz). * * 10) The accuracy of the result is limited by the corrections for * refraction, which use a simple A*tan(z) + B*tan^3(z) model. * Providing the meteorological parameters are known accurately and * there are no gross local effects, the predicted observed * coordinates should be within 0.05 arcsec (optical) or 1 arcsec * (radio) for a zenith distance of less than 70 degrees, better * than 30 arcsec (optical or radio) at 85 degrees and better * than 20 arcmin (optical) or 30 arcmin (radio) at the horizon. * * Without refraction, the complementary functions iauAtco13 and * iauAtoc13 are self-consistent to better than 1 microarcsecond * all over the celestial sphere. With refraction included, * consistency falls off at high zenith distances, but is still * better than 0.05 arcsec at 85 degrees. * * 11) "Observed" Az,ZD means the position that would be seen by a * perfect geodetically aligned theodolite. (Zenith distance is * used rather than altitude in order to reflect the fact that no * allowance is made for depression of the horizon.) This is * related to the observed HA,Dec via the standard rotation, using * the geodetic latitude (corrected for polar motion), while the * observed HA and RA are related simply through the Earth rotation * angle and the site longitude. "Observed" RA,Dec or HA,Dec thus * means the position that would be seen by a perfect equatorial * with its polar axis aligned to the Earth's axis of rotation. * * 12) It is advisable to take great care with units, as even unlikely * values of the input parameters are accepted and processed in * accordance with the models used. */ /*!\file atic13.c \fn void iauAtic13(double ri, double di, double date1, double date2, double *rc, double *dc, double *eo) \ingroup SF \brief Transform star RA,Dec from geocentric CIRS to ICRS astrometric. * * * \param[in] rii CIRS geocentric RA (radians) * \param[in] di CIRS geocentric Dec (radians) * \param[in] date1 TDB as a 2-part... * \param[in] date2 ...Julian Date (Note 1) * * \param[out] rc ICRS astrometric RA (radians) * \param[out] dc ICRS astrometric Dec (radians) * \param[out] eo equation of the origins (ERA-GST, Note 4) * * Notes: * * 1) The TDB date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TDB)=2450123.7 could be expressed in any of these ways, among * others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in cases * where the loss of several decimal digits of resolution is * acceptable. The J2000 method is best matched to the way the * argument is handled internally and will deliver the optimum * resolution. The MJD method and the date & time methods are both * good compromises between resolution and convenience. For most * applications of this function the choice will not be at all * critical. * * TT can be used instead of TDB without any significant impact on * accuracy. * * 2) Iterative techniques are used for the aberration and light * deflection corrections so that the functions iauAtic13 (or * iauAticq) and iauAtci13 (or iauAtciq) are accurate inverses; * even at the edge of the Sun's disk the discrepancy is only about * 1 nanoarcsecond. * * 3) The available accuracy is better than 1 milliarcsecond, limited * mainly by the precession-nutation model that is used, namely * IAU 2000A/2006. Very close to solar system bodies, additional * errors of up to several milliarcseconds can occur because of * unmodeled light deflection; however, the Sun's contribution is * taken into account, to first order. The accuracy limitations of * the SOFA function iauEpv00 (used to compute Earth position and * velocity) can contribute aberration errors of up to * 5 microarcseconds. Light deflection at the Sun's limb is * uncertain at the 0.4 mas level. * * 4) Should the transformation to (equinox based) J2000.0 mean place * be required rather than (CIO based) ICRS coordinates, subtract the * equation of the origins from the returned right ascension: * RA = RI - EO. (The iauAnp function can then be applied, as * required, to keep the result in the conventional 0-2pi range.) */ /*!\file aticq.c \fn void iauAticq(double ri, double di, iauASTROM *astrom, double *rc, double *dc) \ingroup SF \brief Quick CIRS RA,Dec to ICRS astrometric place * * Quick CIRS RA,Dec to ICRS astrometric place, given the star- * independent astrometry parameters. * * Use of this function is appropriate when efficiency is important and * where many star positions are all to be transformed for one date. * The star-independent astrometry parameters can be obtained by * calling one of the functions iauApci[13], iauApcg[13], iauApco[13] * or iauApcs[13]. * * \param[in] ri CIRS RA (radians) * \param[in] di CIRS Dec (radians) * \param[in] astrom star-independent astrometry parameters: * \param[in] pmt PM time interval (SSB, Julian years) * \param[in] eb SSB to observer (vector, au) * \param[in] eh Sun to observer (unit vector) * \param[in] em distance from Sun to observer (au) * \param[in] v barycentric observer velocity (vector, c) * \param[in] bm1 sqrt(1-|v|^2): reciprocal of Lorenz factor * \param[in] bpn bias-precession-nutation matrix * \param[in] along longitude + s' (radians) * \param[in] xpl polar motion xp wrt local meridian (radians) * \param[in] ypl polar motion yp wrt local meridian (radians) * \param[in] sphi sine of geodetic latitude * \param[in] cphi cosine of geodetic latitude * \param[in] diurab magnitude of diurnal aberration vector * \param[in] eral "local" Earth rotation angle (radians) * \param[in] refa refraction constant A (radians) * \param[in] refb refraction constant B (radians) * * \param[out] rc ICRS astrometric RA (radians) * \param[out] dc ICRS astrometric Dec (radians) * * Notes: * * 1) Only the Sun is taken into account in the light deflection * correction. * * 2) Iterative techniques are used for the aberration and light * deflection corrections so that the functions iauAtic13 (or * iauAticq) and iauAtci13 (or iauAtciq) are accurate inverses; * even at the edge of the Sun's disk the discrepancy is only about * 1 nanoarcsecond. */ /*!\file aticqn.c \fn void iauAticqn(double ri, double di, iauASTROM *astrom, int n, iauLDBODY b[], double *rc, double *dc) \ingroup SF \brief Quick CIRS to ICRS astrometric place transformation * * Quick CIRS to ICRS astrometric place transformation, given the star- * independent astrometry parameters plus a list of light-deflecting * bodies. * * Use of this function is appropriate when efficiency is important and * where many star positions are all to be transformed for one date. * The star-independent astrometry parameters can be obtained by * calling one of the functions iauApci[13], iauApcg[13], iauApco[13] * or iauApcs[13]. * If the only light-deflecting body to be taken into account is the * Sun, the iauAticq function can be used instead. * * \param[in] rii CIRS RA (radians) * \param[in] di CIRS Dec (radians) * \param[in] astrom star-independent astrometry parameters: * \param[in] pmt PM time interval (SSB, Julian years) * \param[in] eb SSB to observer (vector, au) * \param[in] eh Sun to observer (unit vector) * \param[in] em distance from Sun to observer (au) * \param[in] v barycentric observer velocity (vector, c) * \param[in] bm1 sqrt(1-|v|^2): reciprocal of Lorenz factor * \param[in] bpn bias-precession-nutation matrix * \param[in] along longitude + s' (radians) * \param[in] xpl polar motion xp wrt local meridian (radians) * \param[in] ypl polar motion yp wrt local meridian (radians) * \param[in] sphi sine of geodetic latitude * \param[in] cphi cosine of geodetic latitude * \param[in] diurab magnitude of diurnal aberration vector * \param[in] eral "local" Earth rotation angle (radians) * \param[in] refa refraction constant A (radians) * \param[in] refb refraction constant B (radians) * \param[in] n number of bodies (Note 3) * \param[in] b data for each of the n bodies (Notes 3,4): * \param[in] bm mass of the body (solar masses, Note 5) * \param[in] dl deflection limiter (Note 6) * \param[in] pv barycentric PV of the body (au, au/day) * * \param[out] rc ICRS astrometric RA (radians) * \param[out] dc ICRS astrometric Dec (radians) * * Notes: * * 1) Iterative techniques are used for the aberration and light * deflection corrections so that the functions iauAticqn and * iauAtciqn are accurate inverses; even at the edge of the Sun's * disk the discrepancy is only about 1 nanoarcsecond. * * 2) If the only light-deflecting body to be taken into account is the * Sun, the iauAticq function can be used instead. * * 3) The struct b contains n entries, one for each body to be * considered. If n = 0, no gravitational light deflection will be * applied, not even for the Sun. * * 4) The struct b should include an entry for the Sun as well as for * any planet or other body to be taken into account. The entries * should be in the order in which the light passes the body. * * 5) In the entry in the b struct for body i, the mass parameter * b[i].bm can, as required, be adjusted in order to allow for such * effects as quadrupole field. * * 6) The deflection limiter parameter b[i].dl is phi^2/2, where phi is * the angular separation (in radians) between star and body at * which limiting is applied. As phi shrinks below the chosen * threshold, the deflection is artificially reduced, reaching zero * for phi = 0. Example values suitable for a terrestrial * observer, together with masses, are as follows: * * body i b[i].bm b[i].dl * * Sun 1.0 6e-6 * Jupiter 0.00095435 3e-9 * Saturn 0.00028574 3e-10 * * 7) For efficiency, validation of the contents of the b array is * omitted. The supplied masses must be greater than zero, the * position and velocity vectors must be right, and the deflection * limiter greater than zero. */ /*!\file atio13.c \fn int iauAtio13(double ri, double di, double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, double *aob, double *zob, double *hob, double *dob, double *rob) \ingroup SF \brief CIRS RA,Dec to observed place * * CIRS RA,Dec to observed place. The caller supplies UTC, site * coordinates, ambient air conditions and observing wavelength. * * \param[in] ri CIRS right ascension (CIO-based, radians) * \param[in] di CIRS declination (radians) * \param[in] utc1 UTC as a 2-part... * \param[in] utc2 ...quasi Julian Date (Notes 1,2) * \param[in] dut1 UT1-UTC (seconds, Note 3) * \param[in] elong longitude (radians, east +ve, Note 4) * \param[in] phi geodetic latitude (radians, Note 4) * \param[in] hm height above ellipsoid (m, geodetic Notes 4,6) * \param[in] xp polar motion coordinates (radians, Note 5) * \param[in] yp polar motion coordinates (radians, Note 5) * \param[in] phpa pressure at the observer (hPa = mB, Note 6) * \param[in] tc ambient temperature at the observer (deg C) * \param[in] rh relative humidity at the observer (range 0-1) * \param[in] wl wavelength (micrometers, Note 7) * * \param[out] aob observed azimuth (radians: N=0,E=90) * \param[out] zob observed zenith distance (radians) * \param[out] hob observed hour angle (radians) * \param[out] dob observed declination (radians) * \param[out] rob observed right ascension (CIO-based, radians) * * \return * +1 = dubious year (Note 2) * 0 = OK * -1 = unacceptable date * * Notes: * * 1) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any * convenient way between the two arguments, for example where utc1 * is the Julian Day Number and utc2 is the fraction of a day. * * However, JD cannot unambiguously represent UTC during a leap * second unless special measures are taken. The convention in the * present function is that the JD day represents UTC days whether * the length is 86399, 86400 or 86401 SI seconds. * * Applications should use the function iauDtf2d to convert from * calendar date and time of day into 2-part quasi Julian Date, as * it implements the leap-second-ambiguity convention just * described. * * 2) The warning status "dubious year" flags UTCs that predate the * introduction of the time scale or that are too far in the * future to be trusted. See iauDat for further details. * * 3) UT1-UTC is tabulated in IERS bulletins. It increases by exactly * one second at the end of each positive UTC leap second, * introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This * practice is under review, and in the future UT1-UTC may grow * essentially without limit. * * 4) The geographical coordinates are with respect to the WGS84 * reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the * longitude required by the present function is east-positive * (i.e. right-handed), in accordance with geographical convention. * * 5) The polar motion xp,yp can be obtained from IERS bulletins. The * values are the coordinates (in radians) of the Celestial * Intermediate Pole with respect to the International Terrestrial * Reference System (see IERS Conventions 2003), measured along the * meridians 0 and 90 deg west respectively. For many * applications, xp and yp can be set to zero. * * 6) If hm, the height above the ellipsoid of the observing station * in meters, is not known but phpa, the pressure in hPa (=mB), is * available, an adequate estimate of hm can be obtained from the * expression * * hm = -29.3 * tsl * log ( phpa / 1013.25 ); * * where tsl is the approximate sea-level air temperature in K * (See Astrophysical Quantities, C.W.Allen, 3rd edition, section * 52). Similarly, if the pressure phpa is not known, it can be * estimated from the height of the observing station, hm, as * follows: * * phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) ); * * Note, however, that the refraction is nearly proportional to * the pressure and that an accurate phpa value is important for * precise work. * * 7) The argument wl specifies the observing wavelength in * micrometers. The transition from optical to radio is assumed to * occur at 100 micrometers (about 3000 GHz). * * 8) "Observed" Az,ZD means the position that would be seen by a * perfect geodetically aligned theodolite. (Zenith distance is * used rather than altitude in order to reflect the fact that no * allowance is made for depression of the horizon.) This is * related to the observed HA,Dec via the standard rotation, using * the geodetic latitude (corrected for polar motion), while the * observed HA and RA are related simply through the Earth rotation * angle and the site longitude. "Observed" RA,Dec or HA,Dec thus * means the position that would be seen by a perfect equatorial * with its polar axis aligned to the Earth's axis of rotation. * * 9) The accuracy of the result is limited by the corrections for * refraction, which use a simple A*tan(z) + B*tan^3(z) model. * Providing the meteorological parameters are known accurately and * there are no gross local effects, the predicted astrometric * coordinates should be within 0.05 arcsec (optical) or 1 arcsec * (radio) for a zenith distance of less than 70 degrees, better * than 30 arcsec (optical or radio) at 85 degrees and better * than 20 arcmin (optical) or 30 arcmin (radio) at the horizon. * * 10) The complementary functions iauAtio13 and iauAtoi13 are self- * consistent to better than 1 microarcsecond all over the * celestial sphere. * * 11) It is advisable to take great care with units, as even unlikely * values of the input parameters are accepted and processed in * accordance with the models used. * * */ /*!\file atioq.c \fn void iauAtioq(double ri, double di, iauASTROM *astrom, double *aob, double *zob, double *hob, double *dob, double *rob) \ingroup SF \brief Quick CIRS to observed place transformation * * Quick CIRS to observed place transformation. * * Use of this function is appropriate when efficiency is important and * where many star positions are all to be transformed for one date. * The star-independent astrometry parameters can be obtained by * calling iauApio[13] or iauApco[13]. * * * * \param[in] ri CIRS right ascension * \param[in] di CIRS declination * \param[in] astrom star-independent astrometry parameters: * \param[in] pmt PM time interval (SSB, Julian years) * \param[in] eb SSB to observer (vector, au) * \param[in] eh Sun to observer (unit vector) * \param[in] em distance from Sun to observer (au) * \param[in] v barycentric observer velocity (vector, c) * \param[in] bm1 sqrt(1-|v|^2): reciprocal of Lorenz factor * \param[in] bpn bias-precession-nutation matrix * \param[in] along longitude + s' (radians) * \param[in] xpl polar motion xp wrt local meridian (radians) * \param[in] ypl polar motion yp wrt local meridian (radians) * \param[in] sphi sine of geodetic latitude * \param[in] cphi cosine of geodetic latitude * \param[in] diurab magnitude of diurnal aberration vector * \param[in] eral "local" Earth rotation angle (radians) * \param[in] refa refraction constant A (radians) * \param[in] refb refraction constant B (radians) * * \param[out] aob observed azimuth (radians: N=0,E=90) * \param[out] zob observed zenith distance (radians) * \param[out] hob observed hour angle (radians) * \param[out] dob observed declination (radians) * \param[out] rob observed right ascension (CIO-based, radians) * * Notes: * * 1) This function returns zenith distance rather than altitude in * order to reflect the fact that no allowance is made for * depression of the horizon. * * 2) The accuracy of the result is limited by the corrections for * refraction, which use a simple A*tan(z) + B*tan^3(z) model. * Providing the meteorological parameters are known accurately and * there are no gross local effects, the predicted observed * coordinates should be within 0.05 arcsec (optical) or 1 arcsec * (radio) for a zenith distance of less than 70 degrees, better * than 30 arcsec (optical or radio) at 85 degrees and better * than 20 arcmin (optical) or 30 arcmin (radio) at the horizon. * * Without refraction, the complementary functions iauAtioq and * iauAtoiq are self-consistent to better than 1 microarcsecond all * over the celestial sphere. With refraction included, consistency * falls off at high zenith distances, but is still better than * 0.05 arcsec at 85 degrees. * * 3) It is advisable to take great care with units, as even unlikely * values of the input parameters are accepted and processed in * accordance with the models used. * * 4) The CIRS RA,Dec is obtained from a star catalog mean place by * allowing for space motion, parallax, the Sun's gravitational lens * effect, annual aberration and precession-nutation. For star * positions in the ICRS, these effects can be applied by means of * the iauAtci13 (etc.) functions. Starting from classical "mean * place" systems, additional transformations will be needed first. * * 5) "Observed" Az,El means the position that would be seen by a * perfect geodetically aligned theodolite. This is obtained from * the CIRS RA,Dec by allowing for Earth orientation and diurnal * aberration, rotating from equator to horizon coordinates, and * then adjusting for refraction. The HA,Dec is obtained by * rotating back into equatorial coordinates, and is the position * that would be seen by a perfect equatorial with its polar axis * aligned to the Earth's axis of rotation. Finally, the RA is * obtained by subtracting the HA from the local ERA. * * 6) The star-independent CIRS-to-observed-place parameters in ASTROM * may be computed with iauApio[13] or iauApco[13]. If nothing has * changed significantly except the time, iauAper[13] may be used to * perform the requisite adjustment to the astrom structure. * * */ /*!\file atoc13.c \fn int iauAtoc13(const char *type, double ob1, double ob2, double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, double *rc, double *dc) \ingroup SF \brief Observed place at a groundbased site to to ICRS astrometric RA,Dec. * * Observed place at a groundbased site to to ICRS astrometric RA,Dec. * The caller supplies UTC, site coordinates, ambient air conditions * and observing wavelength. * * * * \param[in] type type of coordinates - "R", "H" or "A" (Notes 1,2) * \param[in] ob1 observed Az, HA or RA (radians; Az is N=0,E=90) * \param[in] ob2 observed ZD or Dec (radians) * \param[in] utc1 UTC as a 2-part... * \param[in] utc2 ...quasi Julian Date (Notes 3,4) * \param[in] dut1 UT1-UTC (seconds, Note 5) * \param[in] elong longitude (radians, east +ve, Note 6) * \param[in] phi geodetic latitude (radians, Note 6) * \param[in] hm height above ellipsoid (m, geodetic Notes 6,8) * \param[in] xp polar motion coordinates (radians, Note 7) * \param[in] yp polar motion coordinates (radians, Note 7) * \param[in] phpa pressure at the observer (hPa = mB, Note 8) * \param[in] tc ambient temperature at the observer (deg C) * \param[in] rh relative humidity at the observer (range 0-1) * \param[in] wl wavelength (micrometers, Note 9) * * \param[out] rc ICRS astrometric RA,Dec (radians) * \param[out] dc ICRS astrometric RA,Dec (radians) * * \return * +1 = dubious year (Note 4) * 0 = OK * -1 = unacceptable date * * Notes: * * 1) "Observed" Az,ZD means the position that would be seen by a * perfect geodetically aligned theodolite. (Zenith distance is * used rather than altitude in order to reflect the fact that no * allowance is made for depression of the horizon.) This is * related to the observed HA,Dec via the standard rotation, using * the geodetic latitude (corrected for polar motion), while the * observed HA and RA are related simply through the Earth rotation * angle and the site longitude. "Observed" RA,Dec or HA,Dec thus * means the position that would be seen by a perfect equatorial * with its polar axis aligned to the Earth's axis of rotation. * * 2) Only the first character of the type argument is significant. * "R" or "r" indicates that ob1 and ob2 are the observed right * ascension and declination; "H" or "h" indicates that they are * hour angle (west +ve) and declination; anything else ("A" or * "a" is recommended) indicates that ob1 and ob2 are azimuth * (north zero, east 90 deg) and zenith distance. * * 3) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any * convenient way between the two arguments, for example where utc1 * is the Julian Day Number and utc2 is the fraction of a day. * * However, JD cannot unambiguously represent UTC during a leap * second unless special measures are taken. The convention in the * present function is that the JD day represents UTC days whether * the length is 86399, 86400 or 86401 SI seconds. * * Applications should use the function iauDtf2d to convert from * calendar date and time of day into 2-part quasi Julian Date, as * it implements the leap-second-ambiguity convention just * described. * * 4) The warning status "dubious year" flags UTCs that predate the * introduction of the time scale or that are too far in the * future to be trusted. See iauDat for further details. * * 5) UT1-UTC is tabulated in IERS bulletins. It increases by exactly * one second at the end of each positive UTC leap second, * introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This * practice is under review, and in the future UT1-UTC may grow * essentially without limit. * * 6) The geographical coordinates are with respect to the WGS84 * reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the * longitude required by the present function is east-positive * (i.e. right-handed), in accordance with geographical convention. * * 7) The polar motion xp,yp can be obtained from IERS bulletins. The * values are the coordinates (in radians) of the Celestial * Intermediate Pole with respect to the International Terrestrial * Reference System (see IERS Conventions 2003), measured along the * meridians 0 and 90 deg west respectively. For many * applications, xp and yp can be set to zero. * * 8) If hm, the height above the ellipsoid of the observing station * in meters, is not known but phpa, the pressure in hPa (=mB), is * available, an adequate estimate of hm can be obtained from the * expression * * hm = -29.3 * tsl * log ( phpa / 1013.25 ); * * where tsl is the approximate sea-level air temperature in K * (See Astrophysical Quantities, C.W.Allen, 3rd edition, section * 52). Similarly, if the pressure phpa is not known, it can be * estimated from the height of the observing station, hm, as * follows: * * phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) ); * * Note, however, that the refraction is nearly proportional to * the pressure and that an accurate phpa value is important for * precise work. * * 9) The argument wl specifies the observing wavelength in * micrometers. The transition from optical to radio is assumed to * occur at 100 micrometers (about 3000 GHz). * * 10) The accuracy of the result is limited by the corrections for * refraction, which use a simple A*tan(z) + B*tan^3(z) model. * Providing the meteorological parameters are known accurately and * there are no gross local effects, the predicted astrometric * coordinates should be within 0.05 arcsec (optical) or 1 arcsec * (radio) for a zenith distance of less than 70 degrees, better * than 30 arcsec (optical or radio) at 85 degrees and better * than 20 arcmin (optical) or 30 arcmin (radio) at the horizon. * * Without refraction, the complementary functions iauAtco13 and * iauAtoc13 are self-consistent to better than 1 microarcsecond * all over the celestial sphere. With refraction included, * consistency falls off at high zenith distances, but is still * better than 0.05 arcsec at 85 degrees. * * 11) It is advisable to take great care with units, as even unlikely * values of the input parameters are accepted and processed in * accordance with the models used. * * */ /*!\file atoi13.c \fn int iauAtoi13(const char *type, double ob1, double ob2, double utc1, double utc2, double dut1, double elong, double phi, double hm, double xp, double yp, double phpa, double tc, double rh, double wl, double *ri, double *di) \ingroup SF \brief Observed place to CIRS. * * Observed place to CIRS. The caller supplies UTC, site coordinates, * ambient air conditions and observing wavelength. * * * * \param[in] type type of coordinates - "R", "H" or "A" (Notes 1,2) * \param[in] ob1 observed Az, HA or RA (radians; Az is N=0,E=90) * \param[in] ob2 observed ZD or Dec (radians) * \param[in] utc1 UTC as a 2-part... * \param[in] utc2 ...quasi Julian Date (Notes 3,4) * \param[in] dut1 UT1-UTC (seconds, Note 5) * \param[in] elong longitude (radians, east +ve, Note 6) * \param[in] phi geodetic latitude (radians, Note 6) * \param[in] hm height above the ellipsoid (meters, Notes 6,8) * \param[in] xp polar motion coordinates (radians, Note 7) * \param[in] yp polar motion coordinates (radians, Note 7) * \param[in] phpa pressure at the observer (hPa = mB, Note 8) * \param[in] tc ambient temperature at the observer (deg C) * \param[in] rh relative humidity at the observer (range 0-1) * \param[in] wl wavelength (micrometers, Note 9) * * \param[out] ri CIRS right ascension (CIO-based, radians) * \param[out] di CIRS declination (radians) * * \return * +1 = dubious year (Note 2) * 0 = OK * -1 = unacceptable date * * Notes: * * 1) "Observed" Az,ZD means the position that would be seen by a * perfect geodetically aligned theodolite. (Zenith distance is * used rather than altitude in order to reflect the fact that no * allowance is made for depression of the horizon.) This is * related to the observed HA,Dec via the standard rotation, using * the geodetic latitude (corrected for polar motion), while the * observed HA and RA are related simply through the Earth rotation * angle and the site longitude. "Observed" RA,Dec or HA,Dec thus * means the position that would be seen by a perfect equatorial * with its polar axis aligned to the Earth's axis of rotation. * * 2) Only the first character of the type argument is significant. * "R" or "r" indicates that ob1 and ob2 are the observed right * ascension and declination; "H" or "h" indicates that they are * hour angle (west +ve) and declination; anything else ("A" or * "a" is recommended) indicates that ob1 and ob2 are azimuth * (north zero, east 90 deg) and zenith distance. * * 3) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any * convenient way between the two arguments, for example where utc1 * is the Julian Day Number and utc2 is the fraction of a day. * * However, JD cannot unambiguously represent UTC during a leap * second unless special measures are taken. The convention in the * present function is that the JD day represents UTC days whether * the length is 86399, 86400 or 86401 SI seconds. * * Applications should use the function iauDtf2d to convert from * calendar date and time of day into 2-part quasi Julian Date, as * it implements the leap-second-ambiguity convention just * described. * * 4) The warning status "dubious year" flags UTCs that predate the * introduction of the time scale or that are too far in the * future to be trusted. See iauDat for further details. * * 5) UT1-UTC is tabulated in IERS bulletins. It increases by exactly * one second at the end of each positive UTC leap second, * introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This * practice is under review, and in the future UT1-UTC may grow * essentially without limit. * * 6) The geographical coordinates are with respect to the WGS84 * reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the * longitude required by the present function is east-positive * (i.e. right-handed), in accordance with geographical convention. * * 7) The polar motion xp,yp can be obtained from IERS bulletins. The * values are the coordinates (in radians) of the Celestial * Intermediate Pole with respect to the International Terrestrial * Reference System (see IERS Conventions 2003), measured along the * meridians 0 and 90 deg west respectively. For many * applications, xp and yp can be set to zero. * * 8) If hm, the height above the ellipsoid of the observing station * in meters, is not known but phpa, the pressure in hPa (=mB), is * available, an adequate estimate of hm can be obtained from the * expression * * hm = -29.3 * tsl * log ( phpa / 1013.25 ); * * where tsl is the approximate sea-level air temperature in K * (See Astrophysical Quantities, C.W.Allen, 3rd edition, section * 52). Similarly, if the pressure phpa is not known, it can be * estimated from the height of the observing station, hm, as * follows: * * phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) ); * * Note, however, that the refraction is nearly proportional to * the pressure and that an accurate phpa value is important for * precise work. * * 9) The argument wl specifies the observing wavelength in * micrometers. The transition from optical to radio is assumed to * occur at 100 micrometers (about 3000 GHz). * * 10) The accuracy of the result is limited by the corrections for * refraction, which use a simple A*tan(z) + B*tan^3(z) model. * Providing the meteorological parameters are known accurately and * there are no gross local effects, the predicted astrometric * coordinates should be within 0.05 arcsec (optical) or 1 arcsec * (radio) for a zenith distance of less than 70 degrees, better * than 30 arcsec (optical or radio) at 85 degrees and better * than 20 arcmin (optical) or 30 arcmin (radio) at the horizon. * * Without refraction, the complementary functions iauAtio13 and * iauAtoi13 are self-consistent to better than 1 microarcsecond * all over the celestial sphere. With refraction included, * consistency falls off at high zenith distances, but is still * better than 0.05 arcsec at 85 degrees. * * 12) It is advisable to take great care with units, as even unlikely * values of the input parameters are accepted and processed in * accordance with the models used. * * */ /*!\file atoiq.c \fn void iauAtoiq(const char *type, double ob1, double ob2, iauASTROM *astrom, double *ri, double *di) \ingroup SF \brief Quick observed place to CIRS. * * Quick observed place to CIRS, given the star-independent astrometry * parameters. * * Use of this function is appropriate when efficiency is important and * where many star positions are all to be transformed for one date. * The star-independent astrometry parameters can be obtained by * calling iauApio[13] or iauApco[13]. * * * \param[in] type type of coordinates: "R", "H" or "A" (Note 1) * \param[in] ob1 observed Az, HA or RA (radians; Az is N=0,E=90) * \param[in] ob2 observed ZD or Dec (radians) * \param[in] astrom star-independent astrometry parameters: * \param[in] pmt PM time interval (SSB, Julian years) * \param[in] eb SSB to observer (vector, au) * \param[in] eh Sun to observer (unit vector) * \param[in] em distance from Sun to observer (au) * \param[in] v barycentric observer velocity (vector, c) * \param[in] bm1 sqrt(1-|v|^2): reciprocal of Lorenz factor * \param[in] bpn bias-precession-nutation matrix * \param[in] along longitude + s' (radians) * \param[in] xpl polar motion xp wrt local meridian (radians) * \param[in] ypl polar motion yp wrt local meridian (radians) * \param[in] sphi sine of geodetic latitude * \param[in] cphi cosine of geodetic latitude * \param[in] diurab magnitude of diurnal aberration vector * \param[in] eral "local" Earth rotation angle (radians) * \param[in] refa refraction constant A (radians) * \param[in] refb refraction constant B (radians) * * \param[out] ri CIRS right ascension (CIO-based, radians) * \param[out] di CIRS declination (radians) * * Notes: * * 1) "Observed" Az,El means the position that would be seen by a * perfect geodetically aligned theodolite. This is related to * the observed HA,Dec via the standard rotation, using the geodetic * latitude (corrected for polar motion), while the observed HA and * RA are related simply through the Earth rotation angle and the * site longitude. "Observed" RA,Dec or HA,Dec thus means the * position that would be seen by a perfect equatorial with its * polar axis aligned to the Earth's axis of rotation. By removing * from the observed place the effects of atmospheric refraction and * diurnal aberration, the CIRS RA,Dec is obtained. * * 2) Only the first character of the type argument is significant. * "R" or "r" indicates that ob1 and ob2 are the observed right * ascension and declination; "H" or "h" indicates that they are * hour angle (west +ve) and declination; anything else ("A" or * "a" is recommended) indicates that ob1 and ob2 are azimuth (north * zero, east 90 deg) and zenith distance. (Zenith distance is used * rather than altitude in order to reflect the fact that no * allowance is made for depression of the horizon.) * * 3) The accuracy of the result is limited by the corrections for * refraction, which use a simple A*tan(z) + B*tan^3(z) model. * Providing the meteorological parameters are known accurately and * there are no gross local effects, the predicted observed * coordinates should be within 0.05 arcsec (optical) or 1 arcsec * (radio) for a zenith distance of less than 70 degrees, better * than 30 arcsec (optical or radio) at 85 degrees and better than * 20 arcmin (optical) or 30 arcmin (radio) at the horizon. * * Without refraction, the complementary functions iauAtioq and * iauAtoiq are self-consistent to better than 1 microarcsecond all * over the celestial sphere. With refraction included, consistency * falls off at high zenith distances, but is still better than * 0.05 arcsec at 85 degrees. * * 4) It is advisable to take great care with units, as even unlikely * values of the input parameters are accepted and processed in * accordance with the models used. * * */ /*!\file bi00.c \fn void iauBi00(double *dpsibi, double *depsbi, double *dra) \ingroup CM \brief Frame bias components of IAU 2000 precession-nutation models * * Frame bias components of IAU 2000 precession-nutation models (part * of MHB2000 with additions). * * * * Returned: * \param[out] dpsibi longitude and obliquity corrections * \param[out] depsbi longitude and obliquity corrections * \param[out] dra the ICRS RA of the J2000.0 mean equinox * * Notes: * * 1) The frame bias corrections in longitude and obliquity (radians) * are required in order to correct for the offset between the GCRS * pole and the mean J2000.0 pole. They define, with respect to the * GCRS frame, a J2000.0 mean pole that is consistent with the rest * of the IAU 2000A precession-nutation model. * * 2) In addition to the displacement of the pole, the complete * description of the frame bias requires also an offset in right * ascension. This is not part of the IAU 2000A model, and is from * Chapront et al. (2002). It is returned in radians. * * 3) This is a supplemented implementation of one aspect of the IAU * 2000A nutation model, formally adopted by the IAU General * Assembly in 2000, namely MHB2000 (Mathews et al. 2002). * * References: * * Chapront, J., Chapront-Touze, M. & Francou, G., Astron. * Astrophys., 387, 700, 2002. * * Mathews, P.M., Herring, T.A., Buffet, B.A., "Modeling of nutation * and precession New nutation series for nonrigid Earth and * insights into the Earth's interior", J.Geophys.Res., 107, B4, * 2002. The MHB2000 code itself was obtained on 9th September 2002 * from ftp://maia.usno.navy.mil/conv2000/chapter5/IAU2000A. * */ /*!\file bp00.c \fn void iauBp00(double date1, double date2, double rb[3][3], double rp[3][3], double rbp[3][3]) \ingroup CM \brief Frame bias and precession, IAU 2000 * * Frame bias and precession, IAU 2000. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] rb frame bias matrix (Note 2) * \param[out] rp precession matrix (Note 3) * \param[out] rbp bias-precession matrix (Note 4) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The matrix rb transforms vectors from GCRS to mean J2000.0 by * applying frame bias. * * 3) The matrix rp transforms vectors from J2000.0 mean equator and * equinox to mean equator and equinox of date by applying * precession. * * 4) The matrix rbp transforms vectors from GCRS to mean equator and * equinox of date by applying frame bias then precession. It is * the product rp x rb. * * 5) It is permissible to re-use the same array in the returned * arguments. The arrays are filled in the order given. * * Reference: * "Expressions for the Celestial Intermediate Pole and Celestial * Ephemeris Origin consistent with the IAU 2000A precession- * nutation model", Astron.Astrophys. 400, 1145-1154 (2003) * * n.b. The celestial ephemeris origin (CEO) was renamed "celestial * intermediate origin" (CIO) by IAU 2006 Resolution 2. * */ /*!\file bp06.c \fn void iauBp06(double date1, double date2, double rb[3][3], double rp[3][3], double rbp[3][3]) \ingroup SF \brief Frame bias and precession, IAU 2006. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] rb frame bias matrix (Note 2) * \param[out] rp precession matrix (Note 3) * \param[out] rbp bias-precession matrix (Note 4) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The matrix rb transforms vectors from GCRS to mean J2000.0 by * applying frame bias. * * 3) The matrix rp transforms vectors from mean J2000.0 to mean of * date by applying precession. * * 4) The matrix rbp transforms vectors from GCRS to mean of date by * applying frame bias then precession. It is the product rp x rb. * * 5) It is permissible to re-use the same array in the returned * arguments. The arrays are filled in the order given. * * References: * * Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 * * Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 * */ /*!\file bpn2xy.c \fn void iauBpn2xy(double rbpn[3][3], double *x, double *y) \ingroup SF \brief Extract the X,Y coordinates of the Celestial Intermediate Pole * * Extract from the bias-precession-nutation matrix the X,Y coordinates * of the Celestial Intermediate Pole. * * * * \param[in] rbpn celestial-to-true matrix (Note 1) * * \param[out] x Celestial Intermediate Pole (Note 2) * \param[out] y Celestial Intermediate Pole (Note 2) * * Notes: * * 1) The matrix rbpn transforms vectors from GCRS to true equator (and * CIO or equinox) of date, and therefore the Celestial Intermediate * Pole unit vector is the bottom row of the matrix. * * 2) The arguments x,y are components of the Celestial Intermediate * Pole unit vector in the Geocentric Celestial Reference System. * * Reference: * * "Expressions for the Celestial Intermediate Pole and Celestial * Ephemeris Origin consistent with the IAU 2000A precession- * nutation model", Astron.Astrophys. 400, 1145-1154 * (2003) * * n.b. The celestial ephemeris origin (CEO) was renamed "celestial * intermediate origin" (CIO) by IAU 2006 Resolution 2. * */ /*!\file c2i00a.c \fn void iauC2i00a(double date1, double date2, double rc2i[3][3]) \ingroup SF \brief Form the celestial-to-intermediate matrix for a given date. * * Form the celestial-to-intermediate matrix for a given date using the * IAU 2000A precession-nutation model. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] rc2i celestial-to-intermediate matrix (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The matrix rc2i is the first stage in the transformation from * celestial to terrestrial coordinates: * * [TRS] = RPOM * R_3(ERA) * rc2i * [CRS] * * = rc2t * [CRS] * * where [CRS] is a vector in the Geocentric Celestial Reference * System and [TRS] is a vector in the International Terrestrial * Reference System (see IERS Conventions 2003), ERA is the Earth * Rotation Angle and RPOM is the polar motion matrix. * * 3) A faster, but slightly less accurate result (about 1 mas), can be * obtained by using instead the iauC2i00b function. * * * References: * * "Expressions for the Celestial Intermediate Pole and Celestial * Ephemeris Origin consistent with the IAU 2000A precession- * nutation model", Astron.Astrophys. 400, 1145-1154 * (2003) * * n.b. The celestial ephemeris origin (CEO) was renamed "celestial * intermediate origin" (CIO) by IAU 2006 Resolution 2. * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\file c2i00b.c \fn void iauC2i00b(double date1, double date2, double rc2i[3][3]) \ingroup SF \brief Form the celestial-to-intermediate matrix for a given date . * * Form the celestial-to-intermediate matrix for a given date using the * IAU 2000B precession-nutation model. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] rc2i celestial-to-intermediate matrix (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The matrix rc2i is the first stage in the transformation from * celestial to terrestrial coordinates: * * [TRS] = RPOM * R_3(ERA) * rc2i * [CRS] * * = rc2t * [CRS] * * where [CRS] is a vector in the Geocentric Celestial Reference * System and [TRS] is a vector in the International Terrestrial * Reference System (see IERS Conventions 2003), ERA is the Earth * Rotation Angle and RPOM is the polar motion matrix. * * 3) The present function is faster, but slightly less accurate (about * 1 mas), than the iauC2i00a function. * * * References: * * "Expressions for the Celestial Intermediate Pole and Celestial * Ephemeris Origin consistent with the IAU 2000A precession- * nutation model", Astron.Astrophys. 400, 1145-1154 * (2003) * * n.b. The celestial ephemeris origin (CEO) was renamed "celestial * intermediate origin" (CIO) by IAU 2006 Resolution 2. * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\file c2i06a.c \fn void iauC2i06a(double date1, double date2, double rc2i[3][3]) \ingroup SF \brief Form the celestial-to-intermediate matrix for a given date * * Form the celestial-to-intermediate matrix for a given date using the * IAU 2006 precession and IAU 2000A nutation models. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] rc2i celestial-to-intermediate matrix (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The matrix rc2i is the first stage in the transformation from * celestial to terrestrial coordinates: * * [TRS] = RPOM * R_3(ERA) * rc2i * [CRS] * * = RC2T * [CRS] * * where [CRS] is a vector in the Geocentric Celestial Reference * System and [TRS] is a vector in the International Terrestrial * Reference System (see IERS Conventions 2003), ERA is the Earth * Rotation Angle and RPOM is the polar motion matrix. * * * References: * * McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), * IERS Technical Note No. 32, BKG * */ /*!\file c2ibpn.c \fn void iauC2ibpn(double date1, double date2, double rbpn[3][3], double rc2i[3][3]) \ingroup SF \brief Form the celestial-to-intermediate matrix for a given date. * * Form the celestial-to-intermediate matrix for a given date given * the bias-precession-nutation matrix. IAU 2000. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * \param[in] rbpn celestial-to-true matrix (Note 2) * * \param[out] rc2i celestial-to-intermediate matrix (Note 3) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The matrix rbpn transforms vectors from GCRS to true equator (and * CIO or equinox) of date. Only the CIP (bottom row) is used. * * 3) The matrix rc2i is the first stage in the transformation from * celestial to terrestrial coordinates: * * [TRS] = RPOM * R_3(ERA) * rc2i * [CRS] * * = RC2T * [CRS] * * where [CRS] is a vector in the Geocentric Celestial Reference * System and [TRS] is a vector in the International Terrestrial * Reference System (see IERS Conventions 2003), ERA is the Earth * Rotation Angle and RPOM is the polar motion matrix. * * 4) Although its name does not include "00", This function is in fact * specific to the IAU 2000 models. * * References: * "Expressions for the Celestial Intermediate Pole and Celestial * Ephemeris Origin consistent with the IAU 2000A precession- * nutation model", Astron.Astrophys. 400, 1145-1154 (2003) * * n.b. The celestial ephemeris origin (CEO) was renamed "celestial * intermediate origin" (CIO) by IAU 2006 Resolution 2. * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\file c2ixy.c \fn void iauC2ixy(double date1, double date2, double x, double y, double rc2i[3][3]) \ingroup SF \brief Form the celestial to intermediate-frame-of-date matrix. * * Form the celestial to intermediate-frame-of-date matrix for a given * date when the CIP X,Y coordinates are known. IAU 2000. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * \param[in] x Celestial Intermediate Pole (Note 2) * \param[in] y Celestial Intermediate Pole (Note 2) * * \param[out] rc2i celestial-to-intermediate matrix (Note 3) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The Celestial Intermediate Pole coordinates are the x,y components * of the unit vector in the Geocentric Celestial Reference System. * * 3) The matrix rc2i is the first stage in the transformation from * celestial to terrestrial coordinates: * * [TRS] = RPOM * R_3(ERA) * rc2i * [CRS] * * = RC2T * [CRS] * * where [CRS] is a vector in the Geocentric Celestial Reference * System and [TRS] is a vector in the International Terrestrial * Reference System (see IERS Conventions 2003), ERA is the Earth * Rotation Angle and RPOM is the polar motion matrix. * * 4) Although its name does not include "00", This function is in fact * specific to the IAU 2000 models. * * * Reference: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\file c2ixys.c \fn void iauC2ixys(double x, double y, double s, double rc2i[3][3]) \ingroup SF \brief Form the celestial to intermediate-frame-of-date matrix * * Form the celestial to intermediate-frame-of-date matrix given the CIP * X,Y and the CIO locator s. * * * * \param[in] x Celestial Intermediate Pole (Note 1) * \param[in] y Celestial Intermediate Pole (Note 1) * \param[in] s the CIO locator s (Note 2) * * \param[out] rc2i celestial-to-intermediate matrix (Note 3) * * Notes: * * 1) The Celestial Intermediate Pole coordinates are the x,y * components of the unit vector in the Geocentric Celestial * Reference System. * * 2) The CIO locator s (in radians) positions the Celestial * Intermediate Origin on the equator of the CIP. * * 3) The matrix rc2i is the first stage in the transformation from * celestial to terrestrial coordinates: * * [TRS] = RPOM * R_3(ERA) * rc2i * [CRS] * * = RC2T * [CRS] * * where [CRS] is a vector in the Geocentric Celestial Reference * System and [TRS] is a vector in the International Terrestrial * Reference System (see IERS Conventions 2003), ERA is the Earth * Rotation Angle and RPOM is the polar motion matrix. * * * Reference: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\file c2s.c \fn void iauC2s(double p[3], double *theta, double *phi) \ingroup VMSF \brief P-vector to spherical coordinates. * * * * \param[in] p p-vector * * \param[out] theta longitude angle (radians) * \param[out] phi latitude angle (radians) * * Notes: * * 1) The vector p can have any magnitude; only its direction is used. * * 2) If p is null, zero theta and phi are returned. * * 3) At either pole, zero theta is returned. * */ /*!\file c2t00a.c \fn void iauC2t00a(double tta, double ttb, double uta, double utb, double xp, double yp, double rc2t[3][3]) \ingroup SF \brief Form the celestial to terrestrial matrix. * * Form the celestial to terrestrial matrix given the date, the UT1 and * the polar motion, using the IAU 2000A nutation model. * * * * \param[in] tta TT as a 2-part Julian Date (Note 1) * \param[in] ttb TT as a 2-part Julian Date (Note 1) * \param[in] uta UT1 as a 2-part Julian Date (Note 1) * \param[in] utb UT1 as a 2-part Julian Date (Note 1) * \param[in] xp coordinates of the pole (radians, Note 2) * \param[in] yp coordinates of the pole (radians, Note 2) * * \param[out] rc2t celestial-to-terrestrial matrix (Note 3) * * Notes: * * 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, * apportioned in any convenient way between the arguments uta and * utb. For example, JD(UT1)=2450123.7 could be expressed in any of * these ways, among others: * * uta utb * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution is * acceptable. The J2000 and MJD methods are good compromises * between resolution and convenience. In the case of uta,utb, the * date & time method is best matched to the Earth rotation angle * algorithm used: maximum precision is delivered when the uta * argument is for 0hrs UT1 on the day in question and the utb * argument lies in the range 0 to 1, or vice versa. * * 2) The arguments xp and yp are the coordinates (in radians) of the * Celestial Intermediate Pole with respect to the International * Terrestrial Reference System (see IERS Conventions 2003), * measured along the meridians to 0 and 90 deg west respectively. * * 3) The matrix rc2t transforms from celestial to terrestrial * coordinates: * * [TRS] = RPOM * R_3(ERA) * RC2I * [CRS] * * = rc2t * [CRS] * * where [CRS] is a vector in the Geocentric Celestial Reference * System and [TRS] is a vector in the International Terrestrial * Reference System (see IERS Conventions 2003), RC2I is the * celestial-to-intermediate matrix, ERA is the Earth rotation * angle and RPOM is the polar motion matrix. * * 4) A faster, but slightly less accurate result (about 1 mas), can * be obtained by using instead the iauC2t00b function. * * * Reference: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\file c2t00b.c \fn void iauC2t00b(double tta, double ttb, double uta, double utb, double xp, double yp, double rc2t[3][3]) \ingroup SF \brief Form the celestial to terrestrial matrix * * Form the celestial to terrestrial matrix given the date, the UT1 and * the polar motion, using the IAU 2000B nutation model. * * * * \param[in] tta TT as a 2-part Julian Date (Note 1) * \param[in] ttb TT as a 2-part Julian Date (Note 1) * \param[in] uta UT1 as a 2-part Julian Date (Note 1) * \param[in] utb UT1 as a 2-part Julian Date (Note 1) * \param[in] xp coordinates of the pole (radians, Note 2) * \param[in] yp coordinates of the pole (radians, Note 2) * * \param[out] rc2t celestial-to-terrestrial matrix (Note 3) * * Notes: * * 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, * apportioned in any convenient way between the arguments uta and * utb. For example, JD(UT1)=2450123.7 could be expressed in any of * these ways, among others: * * uta utb * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution is * acceptable. The J2000 and MJD methods are good compromises * between resolution and convenience. In the case of uta,utb, the * date & time method is best matched to the Earth rotation angle * algorithm used: maximum precision is delivered when the uta * argument is for 0hrs UT1 on the day in question and the utb * argument lies in the range 0 to 1, or vice versa. * * 2) The arguments xp and yp are the coordinates (in radians) of the * Celestial Intermediate Pole with respect to the International * Terrestrial Reference System (see IERS Conventions 2003), * measured along the meridians to 0 and 90 deg west respectively. * * 3) The matrix rc2t transforms from celestial to terrestrial * coordinates: * * [TRS] = RPOM * R_3(ERA) * RC2I * [CRS] * * = rc2t * [CRS] * * where [CRS] is a vector in the Geocentric Celestial Reference * System and [TRS] is a vector in the International Terrestrial * Reference System (see IERS Conventions 2003), RC2I is the * celestial-to-intermediate matrix, ERA is the Earth rotation * angle and RPOM is the polar motion matrix. * * 4) The present function is faster, but slightly less accurate (about * 1 mas), than the iauC2t00a function. * * * Reference: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\file c2t06a.c \fn void iauC2t06a(double tta, double ttb, double uta, double utb, double xp, double yp, double rc2t[3][3]) \ingroup SF \brief Form the celestial to terrestrial matrix * * Form the celestial to terrestrial matrix given the date, the UT1 and * the polar motion, using the IAU 2006 precession and IAU 2000A * nutation models. * * * * \param[in] tta TT as a 2-part Julian Date (Note 1) * \param[in] ttb TT as a 2-part Julian Date (Note 1) * \param[in] uta UT1 as a 2-part Julian Date (Note 1) * \param[in] utb UT1 as a 2-part Julian Date (Note 1) * \param[in] xp coordinates of the pole (radians, Note 2) * \param[in] yp coordinates of the pole (radians, Note 2) * * \param[out] rc2t celestial-to-terrestrial matrix (Note 3) * * Notes: * * 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, * apportioned in any convenient way between the arguments uta and * utb. For example, JD(UT1)=2450123.7 could be expressed in any of * these ways, among others: * * uta utb * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution is * acceptable. The J2000 and MJD methods are good compromises * between resolution and convenience. In the case of uta,utb, the * date & time method is best matched to the Earth rotation angle * algorithm used: maximum precision is delivered when the uta * argument is for 0hrs UT1 on the day in question and the utb * argument lies in the range 0 to 1, or vice versa. * * 2) The arguments xp and yp are the coordinates (in radians) of the * Celestial Intermediate Pole with respect to the International * Terrestrial Reference System (see IERS Conventions 2003), * measured along the meridians to 0 and 90 deg west respectively. * * 3) The matrix rc2t transforms from celestial to terrestrial * coordinates: * * [TRS] = RPOM * R_3(ERA) * RC2I * [CRS] * * = rc2t * [CRS] * * where [CRS] is a vector in the Geocentric Celestial Reference * System and [TRS] is a vector in the International Terrestrial * Reference System (see IERS Conventions 2003), RC2I is the * celestial-to-intermediate matrix, ERA is the Earth rotation * angle and RPOM is the polar motion matrix. * * * Reference: * * McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), * IERS Technical Note No. 32, BKG * */ /*!\file c2tcio.c \fn void iauC2tcio(double rc2i[3][3], double era, double rpom[3][3], double rc2t[3][3]) \ingroup SF \brief Assemble the celestial to terrestrial matrix * * Assemble the celestial to terrestrial matrix from CIO-based * components (the celestial-to-intermediate matrix, the Earth Rotation * Angle and the polar motion matrix). * * * * \param[in] rc2i celestial-to-intermediate matrix * \param[in] era Earth rotation angle (radians) * \param[in] rpom polar-motion matrix * * \param[out] rc2t celestial-to-terrestrial matrix * * Notes: * * 1) This function constructs the rotation matrix that transforms * vectors in the celestial system into vectors in the terrestrial * system. It does so starting from precomputed components, namely * the matrix which rotates from celestial coordinates to the * intermediate frame, the Earth rotation angle and the polar motion * matrix. One use of the present function is when generating a * series of celestial-to-terrestrial matrices where only the Earth * Rotation Angle changes, avoiding the considerable overhead of * recomputing the precession-nutation more often than necessary to * achieve given accuracy objectives. * * 2) The relationship between the arguments is as follows: * * [TRS] = RPOM * R_3(ERA) * rc2i * [CRS] * * = rc2t * [CRS] * * where [CRS] is a vector in the Geocentric Celestial Reference * System and [TRS] is a vector in the International Terrestrial * Reference System (see IERS Conventions 2003). * * * Reference: * * McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), * IERS Technical Note No. 32, BKG * */ /*!\file c2teqx.c \fn void iauC2teqx(double rbpn[3][3], double gst, double rpom[3][3], double rc2t[3][3]) \ingroup SF \brief Assemble the celestial to terrestrial matrix * * Assemble the celestial to terrestrial matrix from equinox-based * components (the celestial-to-true matrix, the Greenwich Apparent * Sidereal Time and the polar motion matrix). * * * * \param[in] rbpn celestial-to-true matrix * \param[in] gst Greenwich (apparent) Sidereal Time (radians) * \param[in] rpom polar-motion matrix * * \param[out] rc2t celestial-to-terrestrial matrix (Note 2) * * Notes: * * 1) This function constructs the rotation matrix that transforms * vectors in the celestial system into vectors in the terrestrial * system. It does so starting from precomputed components, namely * the matrix which rotates from celestial coordinates to the * true equator and equinox of date, the Greenwich Apparent Sidereal * Time and the polar motion matrix. One use of the present function * is when generating a series of celestial-to-terrestrial matrices * where only the Sidereal Time changes, avoiding the considerable * overhead of recomputing the precession-nutation more often than * necessary to achieve given accuracy objectives. * * 2) The relationship between the arguments is as follows: * * [TRS] = rpom * R_3(gst) * rbpn * [CRS] * * = rc2t * [CRS] * * where [CRS] is a vector in the Geocentric Celestial Reference * System and [TRS] is a vector in the International Terrestrial * Reference System (see IERS Conventions 2003). * * * Reference: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\file c2tpe.c \fn void iauC2tpe(double tta, double ttb, double uta, double utb, double dpsi, double deps, double xp, double yp, double rc2t[3][3]) \ingroup SF \brief Form the celestial to terrestrial matrix * * Form the celestial to terrestrial matrix given the date, the UT1, * the nutation and the polar motion. IAU 2000. * * * * \param[in] tta TT as a 2-part Julian Date (Note 1) * \param[in] ttb TT as a 2-part Julian Date (Note 1) * \param[in] uta UT1 as a 2-part Julian Date (Note 1) * \param[in] utb UT1 as a 2-part Julian Date (Note 1) * \param[in] dpsi nutation (Note 2) * \param[in] deps nutation (Note 2) * \param[in] xp coordinates of the pole (radians, Note 3) * \param[in] yp coordinates of the pole (radians, Note 3) * * \param[out] rc2t celestial-to-terrestrial matrix (Note 4) * * Notes: * * 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, * apportioned in any convenient way between the arguments uta and * utb. For example, JD(UT1)=2450123.7 could be expressed in any of * these ways, among others: * * uta utb * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution is * acceptable. The J2000 and MJD methods are good compromises * between resolution and convenience. In the case of uta,utb, the * date & time method is best matched to the Earth rotation angle * algorithm used: maximum precision is delivered when the uta * argument is for 0hrs UT1 on the day in question and the utb * argument lies in the range 0 to 1, or vice versa. * * 2) The caller is responsible for providing the nutation components; * they are in longitude and obliquity, in radians and are with * respect to the equinox and ecliptic of date. For high-accuracy * applications, free core nutation should be included as well as * any other relevant corrections to the position of the CIP. * * 3) The arguments xp and yp are the coordinates (in radians) of the * Celestial Intermediate Pole with respect to the International * Terrestrial Reference System (see IERS Conventions 2003), * measured along the meridians to 0 and 90 deg west respectively. * * 4) The matrix rc2t transforms from celestial to terrestrial * coordinates: * * [TRS] = RPOM * R_3(GST) * RBPN * [CRS] * * = rc2t * [CRS] * * where [CRS] is a vector in the Geocentric Celestial Reference * System and [TRS] is a vector in the International Terrestrial * Reference System (see IERS Conventions 2003), RBPN is the * bias-precession-nutation matrix, GST is the Greenwich (apparent) * Sidereal Time and RPOM is the polar motion matrix. * * 5) Although its name does not include "00", This function is in fact * specific to the IAU 2000 models. * * * Reference: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\file c2txy.c \fn void iauC2txy(double tta, double ttb, double uta, double utb, double x, double y, double xp, double yp, double rc2t[3][3]) \ingroup SF \brief Form the celestial to terrestrial matrix * * Form the celestial to terrestrial matrix given the date, the UT1, * the CIP coordinates and the polar motion. IAU 2000. * * * * \param[in] tta TT as a 2-part Julian Date (Note 1) * \param[in] ttb TT as a 2-part Julian Date (Note 1) * \param[in] uta UT1 as a 2-part Julian Date (Note 1) * \param[in] utb UT1 as a 2-part Julian Date (Note 1) * \param[in] x Celestial Intermediate Pole (Note 2) * \param[in] y Celestial Intermediate Pole (Note 2) * \param[in] xp coordinates of the pole (radians, Note 3) * \param[in] yp coordinates of the pole (radians, Note 3) * * \param[out] rc2t celestial-to-terrestrial matrix (Note 4) * * Notes: * * 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, * apportioned in any convenient way between the arguments uta and * utb. For example, JD(UT1)=2450123.7 could be expressed in any o * these ways, among others: * * uta utb * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution is * acceptable. The J2000 and MJD methods are good compromises * between resolution and convenience. In the case of uta,utb, the * date & time method is best matched to the Earth rotation angle * algorithm used: maximum precision is delivered when the uta * argument is for 0hrs UT1 on the day in question and the utb * argument lies in the range 0 to 1, or vice versa. * * 2) The Celestial Intermediate Pole coordinates are the x,y * components of the unit vector in the Geocentric Celestial * Reference System. * * 3) The arguments xp and yp are the coordinates (in radians) of the * Celestial Intermediate Pole with respect to the International * Terrestrial Reference System (see IERS Conventions 2003), * measured along the meridians to 0 and 90 deg west respectively. * * 4) The matrix rc2t transforms from celestial to terrestrial * coordinates: * * [TRS] = RPOM * R_3(ERA) * RC2I * [CRS] * * = rc2t * [CRS] * * where [CRS] is a vector in the Geocentric Celestial Reference * System and [TRS] is a vector in the International Terrestrial * Reference System (see IERS Conventions 2003), ERA is the Earth * Rotation Angle and RPOM is the polar motion matrix. * * 5) Although its name does not include "00", This function is in fact * specific to the IAU 2000 models. * * * Reference: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) */ /*!\file cal2jd.c \fn int iauCal2jd(int iy, int im, int id, double *djm0, double *djm) \ingroup SF \brief Gregorian Calendar to Julian Date. * * * * \param[in] iy year in Gregorian calendar (Note 1) * \param[in] im month in Gregorian calendar (Note 1) * \param[in] id day in Gregorian calendar (Note 1) * * \param[out] djm0 MJD zero-point: always 2400000.5 * \param[out] djm Modified Julian Date for 0 hrs * * \return * 0 = OK * -1 = bad year (Note 3: JD not computed) * -2 = bad month (JD not computed) * -3 = bad day (JD computed) * * Notes: * * 1) The algorithm used is valid from -4800 March 1, but this * implementation rejects dates before -4799 January 1. * * 2) The Julian Date is returned in two pieces, in the usual SOFA * manner, which is designed to preserve time resolution. The * Julian Date is available as a single number by adding djm0 and * djm. * * 3) In early eras the conversion is from the "Proleptic Gregorian * Calendar"; no account is taken of the date(s) of adoption of * the Gregorian Calendar, nor is the AD/BC numbering convention * observed. * * Reference: * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992), * Section 12.92 (p604). * */ /*!\file cp.c \fn void iauCp(double p[3], double c[3]) \ingroup VMSF \brief Copy a p-vector. * * * * \param[in] p p-vector to be copied * * \param[out] c copy * */ /*!\file cpv.c \fn void iauCpv(double pv[2][3], double c[2][3]) \ingroup VMSF \brief Copy a position/velocity vector. * * * * \param[in] pv position/velocity vector to be copied * * \param[out] c copy * * */ /*!\file cr.c \fn void iauCr(double r[3][3], double c[3][3]) \ingroup VMSF \brief Copy an r-matrix. * * * * \param[in] r r-matrix to be copied * * \param[out] char[] copy * */ /*!\file d2dtf.c \fn int iauD2dtf(const char *scale, int ndp, double d1, double d2, int *iy, int *im, int *id, int ihmsf[4]) \ingroup SF \brief Format for output a 2-part Julian Date * * Format for output a 2-part Julian Date (or in the case of UTC a * quasi-JD form that includes special provision for leap seconds). * * * * \param[in] scale time scale ID (Note 1) * \param[in] ndp resolution (Note 2) * \param[in] d1 time as a 2-part Julian Date (Notes 3,4) * \param[in] d2 time as a 2-part Julian Date (Notes 3,4) * * \param[out] iy year in Gregorian calendar (Note 5) * \param[out] im month in Gregorian calendar (Note 5) * \param[out] id day in Gregorian calendar (Note 5) * \param[out] ihmsf hours, minutes, seconds, fraction (Note 1) * * \return * +1 = dubious year (Note 5) * 0 = OK * -1 = unacceptable date (Note 6) * * Notes: * * 1) scale identifies the time scale. Only the value "UTC" (in upper * case) is significant, and enables handling of leap seconds (see * Note 4). * * 2) ndp is the number of decimal places in the seconds field, and can * have negative as well as positive values, such as: *\verbatim * ndp resolution * -4 1 00 00 * -3 0 10 00 * -2 0 01 00 * -1 0 00 10 * 0 0 00 01 * 1 0 00 00.1 * 2 0 00 00.01 * 3 0 00 00.001 *\endverbatim * The limits are platform dependent, but a safe range is -5 to +9. * * 3) d1+d2 is Julian Date, apportioned in any convenient way between * the two arguments, for example where d1 is the Julian Day Number * and d2 is the fraction of a day. In the case of UTC, where the * use of JD is problematical, special conventions apply: see the * next note. * * 4) JD cannot unambiguously represent UTC during a leap second unless * special measures are taken. The SOFA internal convention is that * the quasi-JD day represents UTC days whether the length is 86399, * 86400 or 86401 SI seconds. In the 1960-1972 era there were * smaller jumps (in either direction) each time the linear UTC(TAI) * expression was changed, and these "mini-leaps" are also included * in the SOFA convention. * * 5) The warning status "dubious year" flags UTCs that predate the * introduction of the time scale or that are too far in the future * to be trusted. See iauDat for further details. * * 6) For calendar conventions and limitations, see iauCal2jd. * * */ /*! \file d2tf.c \fn void iauD2tf(int ndp, double days, char *sign, int ihmsf[4]) \ingroup VMSF \brief Decompose days to hours, minutes, seconds, fraction. * * * \param[in] ndp resolution (Note 1) * \param[in] days interval in days * * \param[out] sign '+' or '-' * \param[out] ihmsf hours, minutes, seconds, fraction * * Notes: * * 1) The argument ndp is interpreted as follows: *\verbatim * ndp resolution * : ...0000 00 00 * -7 1000 00 00 * -6 100 00 00 * -5 10 00 00 * -4 1 00 00 * -3 0 10 00 * -2 0 01 00 * -1 0 00 10 * 0 0 00 01 * 1 0 00 00.1 * 2 0 00 00.01 * 3 0 00 00.001 * : 0 00 00.000... *\endverbatim * 2) The largest positive useful value for ndp is determined by the * size of days, the format of double on the target platform, and * the risk of overflowing ihmsf[3]. On a typical platform, for * days up to 1.0, the available floating-point precision might * correspond to ndp=12. However, the practical limit is typically * ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is * only 16 bits. * * 3) The absolute value of days may exceed 1.0. In cases where it * does not, it is up to the caller to test for and handle the * case where days is very nearly 1.0 and rounds up to 24 hours, * by testing for ihmsf[0]=24 and setting ihmsf[0-3] to zero. * */ /*!\file dat.c \fn int iauDat(int iy, int im, int id, double fd, double *deltat ) \ingroup SF \brief For a given UTC date, calculate delta(AT) = TAI-UTC. * * :------------------------------------------: * : : * : IMPORTANT : * : : * : A new version of this function must be : * : produced whenever a new leap second is : * : announced. There are four items to : * : change on each such occasion: : * : : * : 1) A new line must be added to the set : * : of statements that initialize the : * : array "changes". : * : : * : 2) The constant IYV must be set to the : * : current year. : * : : * : 3) The "Latest leap second" comment : * : below must be set to the new leap : * : second date. : * : : * : 4) The "This revision" comment, later, : * : must be set to the current date. : * : : * : Change (2) must also be carried out : * : whenever the function is re-issued, : * : even if no leap seconds have been : * : added. : * : : * : Latest leap second: 2015 June 30 : * : : * :__________________________________________: * * * * \param[in] iy UTC: year (Notes 1 and 2) * \param[in] im month (Note 2) * \param[in] id day (Notes 2 and 3) * \param[in] fd fraction of day (Note 4) * * \param[out] deltat TAI minus UTC, seconds * * \return * (Note 5): * 1 = dubious year (Note 1) * 0 = OK * -1 = bad year * -2 = bad month * -3 = bad day (Note 3) * -4 = bad fraction (Note 4) * -5 = internal error (Note 5) * * Notes: * * 1) UTC began at 1960 January 1.0 (JD 2436934.5) and it is improper * to call the function with an earlier date. If this is attempted, * zero is returned together with a warning status. * * Because leap seconds cannot, in principle, be predicted in * advance, a reliable check for dates beyond the valid range is * impossible. To guard against gross errors, a year five or more * after the release year of the present function (see the constant * IYV) is considered dubious. In this case a warning status is * returned but the result is computed in the normal way. * * For both too-early and too-late years, the warning status is +1. * This is distinct from the error status -1, which signifies a year * so early that JD could not be computed. * * 2) If the specified date is for a day which ends with a leap second, * the UTC-TAI value returned is for the period leading up to the * leap second. If the date is for a day which begins as a leap * second ends, the UTC-TAI returned is for the period following the * leap second. * * 3) The day number must be in the normal calendar range, for example * 1 through 30 for April. The "almanac" convention of allowing * such dates as January 0 and December 32 is not supported in this * function, in order to avoid confusion near leap seconds. * * 4) The fraction of day is used only for dates before the * introduction of leap seconds, the first of which occurred at the * end of 1971. It is tested for validity (0 to 1 is the valid * range) even if not used; if invalid, zero is used and status -4 * is returned. For many applications, setting fd to zero is * acceptable; the resulting error is always less than 3 ms (and * occurs only pre-1972). * * 5) The status value returned in the case where there are multiple * errors refers to the first error detected. For example, if the * month and day are 13 and 32 respectively, status -2 (bad month) * will be returned. The "internal error" status refers to a * case that is impossible but causes some compilers to issue a * warning. * * 6) In cases where a valid result is not available, zero is returned. * * References: * * 1) For dates from 1961 January 1 onwards, the expressions from the * file ftp://maia.usno.navy.mil/ser7/tai-utc.dat are used. * * 2) The 5ms timestep at 1961 January 1 is taken from 2.58.1 (p87) of * the 1992 Explanatory Supplement. * */ /*!\file dtdb.c \fn double iauDtdb(double date1, double date2, double ut, double elong, double u, double v) \ingroup SR \brief An approximation to TDB-TT * * An approximation to TDB-TT, the difference between barycentric * dynamical time and terrestrial time, for an observer on the Earth. * * The different time scales - proper, coordinate and realized - are * related to each other: * * TAI <- physically realized * : * offset <- observed (nominally +32.184s) * : * TT <- terrestrial time * : * rate adjustment (L_G) <- definition of TT * : * TCG <- time scale for GCRS * : * "periodic" terms <- iauDtdb is an implementation * : * rate adjustment (L_C) <- function of solar-system ephemeris * : * TCB <- time scale for BCRS * : * rate adjustment (-L_B) <- definition of TDB * : * TDB <- TCB scaled to track TT * : * "periodic" terms <- -iauDtdb is an approximation * : * TT <- terrestrial time * * Adopted values for the various constants can be found in the IERS * Conventions (McCarthy & Petit 2003). * * * * \param[in] date1 date, TDB (Notes 1-3) * \param[in] date2 date, TDB (Notes 1-3) * \param[in] ut universal time (UT1, fraction of one day) * \param[in] elong longitude (east positive, radians) * \param[in] u distance from Earth spin axis (km) * \param[in] v distance north of equatorial plane (km) * * \return * TDB-TT (seconds) * * Notes: * * 1) The date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * Although the date is, formally, barycentric dynamical time (TDB), * the terrestrial dynamical time (TT) can be used with no practical * effect on the accuracy of the prediction. * * 2) TT can be regarded as a coordinate time that is realized as an * offset of 32.184s from International Atomic Time, TAI. TT is a * specific linear transformation of geocentric coordinate time TCG, * which is the time scale for the Geocentric Celestial Reference * System, GCRS. * * 3) TDB is a coordinate time, and is a specific linear transformation * of barycentric coordinate time TCB, which is the time scale for * the Barycentric Celestial Reference System, BCRS. * * 4) The difference TCG-TCB depends on the masses and positions of the * bodies of the solar system and the velocity of the Earth. It is * dominated by a rate difference, the residual being of a periodic * character. The latter, which is modeled by the present function, * comprises a main (annual) sinusoidal term of amplitude * approximately 0.00166 seconds, plus planetary terms up to about * 20 microseconds, and lunar and diurnal terms up to 2 microseconds. * These effects come from the changing transverse Doppler effect * and gravitational red-shift as the observer (on the Earth's * surface) experiences variations in speed (with respect to the * BCRS) and gravitational potential. * * 5) TDB can be regarded as the same as TCB but with a rate adjustment * to keep it close to TT, which is convenient for many applications. * The history of successive attempts to define TDB is set out in * Resolution 3 adopted by the IAU General Assembly in 2006, which * defines a fixed TDB(TCB) transformation that is consistent with * contemporary solar-system ephemerides. Future ephemerides will * imply slightly changed transformations between TCG and TCB, which * could introduce a linear drift between TDB and TT; however, any * such drift is unlikely to exceed 1 nanosecond per century. * * 6) The geocentric TDB-TT model used in the present function is that of * Fairhead & Bretagnon (1990), in its full form. It was originally * supplied by Fairhead (private communications with P.T.Wallace, * 1990) as a Fortran subroutine. The present C function contains an * adaptation of the Fairhead code. The numerical results are * essentially unaffected by the changes, the differences with * respect to the Fairhead & Bretagnon original being at the 1e-20 s * level. * * The topocentric part of the model is from Moyer (1981) and * Murray (1983), with fundamental arguments adapted from * Simon et al. 1994. It is an approximation to the expression * ( v / c ) . ( r / c ), where v is the barycentric velocity of * the Earth, r is the geocentric position of the observer and * c is the speed of light. * * By supplying zeroes for u and v, the topocentric part of the * model can be nullified, and the function will return the Fairhead * & Bretagnon result alone. * * 7) During the interval 1950-2050, the absolute accuracy is better * than +/- 3 nanoseconds relative to time ephemerides obtained by * direct numerical integrations based on the JPL DE405 solar system * ephemeris. * * 8) It must be stressed that the present function is merely a model, * and that numerical integration of solar-system ephemerides is the * definitive method for predicting the relationship between TCG and * TCB and hence between TT and TDB. * * References: * * Fairhead, L., & Bretagnon, P., Astron.Astrophys., 229, 240-247 * (1990). * * IAU 2006 Resolution 3. * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * Moyer, T.D., Cel.Mech., 23, 33 (1981). * * Murray, C.A., Vectorial Astrometry, Adam Hilger (1983). * * Seidelmann, P.K. et al., Explanatory Supplement to the * Astronomical Almanac, Chapter 2, University Science Books (1992). * * Simon, J.L., Bretagnon, P., Chapront, J., Chapront-Touze, M., * Francou, G. & Laskar, J., Astron.Astrophys., 282, 663-683 (1994). * */ /*!\file dtf2d.c \fn int iauDtf2d(const char *scale, int iy, int im, int id, int ihr, int imn, double sec, double *d1, double *d2) \ingroup SF \brief Encode date and time fields into 2-part Julian Date * * Encode date and time fields into 2-part Julian Date (or in the case * of UTC a quasi-JD form that includes special provision for leap * seconds). * * * * \param[in] scale time scale ID (Note 1) * \param[in] iy year in Gregorian calendar (Note 2) * \param[in] im month in Gregorian calendar (Note 2) * \param[in] id day in Gregorian calendar (Note 2) * \param[in] ihr hour * \param[in] imn minute * \param[in] sec seconds * * \param[out] d1 2-part Julian Date (Notes 3,4) * \param[out] d2 2-part Julian Date (Notes 3,4) * * \return * +3 = both of next two * +2 = time is after end of day (Note 5) * +1 = dubious year (Note 6) * 0 = OK * -1 = bad year * -2 = bad month * -3 = bad day * -4 = bad hour * -5 = bad minute * -6 = bad second (<0) * * Notes: * * 1) scale identifies the time scale. Only the value "UTC" (in upper * case) is significant, and enables handling of leap seconds (see * Note 4). * * 2) For calendar conventions and limitations, see iauCal2jd. * * 3) The sum of the results, d1+d2, is Julian Date, where normally d1 * is the Julian Day Number and d2 is the fraction of a day. In the * case of UTC, where the use of JD is problematical, special * conventions apply: see the next note. * * 4) JD cannot unambiguously represent UTC during a leap second unless * special measures are taken. The SOFA internal convention is that * the quasi-JD day represents UTC days whether the length is 86399, * 86400 or 86401 SI seconds. In the 1960-1972 era there were * smaller jumps (in either direction) each time the linear UTC(TAI) * expression was changed, and these "mini-leaps" are also included * in the SOFA convention. * * 5) The warning status "time is after end of day" usually means that * the sec argument is greater than 60.0. However, in a day ending * in a leap second the limit changes to 61.0 (or 59.0 in the case * of a negative leap second). * * 6) The warning status "dubious year" flags UTCs that predate the * introduction of the time scale or that are too far in the future * to be trusted. See iauDat for further details. * * 7) Only in the case of continuous and regular time scales (TAI, TT, * TCG, TCB and TDB) is the result d1+d2 a Julian Date, strictly * speaking. In the other cases (UT1 and UTC) the result must be * used with circumspection; in particular the difference between * two such results cannot be interpreted as a precise time * interval. * * */ /*!\file eceq06 \fn int iauEceq06(double date1, double date2, double dl, double db, double *dr, double *dd) \ingroup SF \brief Transformation from ecliptic coordinates (mean equinox and ecliptic of date) to ICRS RA,Dec, using the IAU 2006 precession model. * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * \verbatim date1 date2 2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method) * \endverbatim * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) No assumptions are made about whether the coordinates represent * starlight and embody astrometric effects such as parallax or * aberration. * * 3) The transformation is approximately that from ecliptic longitude * and latitude (mean equinox and ecliptic of date) to mean J2000.0 * right ascension and declination, with only frame bias (always * less than 25 mas) to disturb this classical picture. * * @param[in] date1 TT as a 2-part Julian date * @param[in] date2 TT as a 2-part Julian date * @param[in] dl ecliptic longitute (radians) * @param[in] db ecliptic latitude (radians) * @return dr ICRS right ascension (radians) * @return dd ICRS right declination (radians) */ /*!\file ecm06.c \fn int iauEcm06(double date1, double date2, double rm[3][3]) \ingroup SF \brief ICRS equatorial to ecliptic rotation matrix, IAU 2006. * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * \verbatim date1 date2 2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method) *\endverbatim * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 1) The matrix is in the sense * * E_ep = rm x P_ICRS, * * where P_ICRS is a vector with respect to ICRS right ascension * and declination axes and E_ep is the same vector with respect to * the (inertial) ecliptic and equinox of date. * * 2) P_ICRS is a free vector, merely a direction, typically of unit * magnitude, and not bound to any particular spatial origin, such * as the Earth, Sun or SSB. No assumptions are made about whether * it represents starlight and embodies astrometric effects such as * parallax or aberration. The transformation is approximately that * between mean J2000.0 right ascension and declination and ecliptic * longitude and latitude, with only frame bias (always less than * 25 mas) to disturb this classical picture. * * @param[in] date1 TT as a 2-part Julian date * @param[in] date2 TT as a 2-part Julian date * @param[out] rm ICRS to ecliptic rotation matrix */ /*!\file ee00.c \fn double iauEe00(double date1, double date2, double epsa, double dpsi) \ingroup CM \brief The equation of the equinoxes * * The equation of the equinoxes, compatible with IAU 2000 resolutions, * given the nutation in longitude and the mean obliquity. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * \param[in] epsa mean obliquity (Note 2) * \param[in] dpsi nutation in longitude (Note 3) * * \return * equation of the equinoxes (Note 4) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The obliquity, in radians, is mean of date. * * 3) The result, which is in radians, operates in the following sense: * * Greenwich apparent ST = GMST + equation of the equinoxes * * 4) The result is compatible with the IAU 2000 resolutions. For * further details, see IERS Conventions 2003 and Capitaine et al. * (2002). * * * References: * * Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to * implement the IAU 2000 definition of UT1", Astronomy & * Astrophysics, 406, 1135-1149 (2003) * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\file ee00a.c \fn double iauEe00a(double date1, double date2) \ingroup SF \brief Equation of the equinoxes * * Equation of the equinoxes, compatible with IAU 2000 resolutions. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \return * equation of the equinoxes (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The result, which is in radians, operates in the following sense: * * Greenwich apparent ST = GMST + equation of the equinoxes * * 3) The result is compatible with the IAU 2000 resolutions. For * further details, see IERS Conventions 2003 and Capitaine et al. * (2002). * * References: * * Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to * implement the IAU 2000 definition of UT1", Astronomy & * Astrophysics, 406, 1135-1149 (2003). * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004). * */ /*!\file ee00b.c \fn double iauEe00b(double date1, double date2) \ingroup SF \brief Equation of the equinoxes * * Equation of the equinoxes, compatible with IAU 2000 resolutions but * using the truncated nutation model IAU 2000B. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \return * equation of the equinoxes (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The result, which is in radians, operates in the following sense: * * Greenwich apparent ST = GMST + equation of the equinoxes * * 3) The result is compatible with the IAU 2000 resolutions except * that accuracy has been compromised for the sake of speed. For * further details, see McCarthy & Luzum (2001), IERS Conventions * 2003 and Capitaine et al. (2003). * * * References: * * Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to * implement the IAU 2000 definition of UT1", Astronomy & * Astrophysics, 406, 1135-1149 (2003) * * McCarthy, D.D. & Luzum, B.J., "An abridged model of the * precession-nutation of the celestial pole", Celestial Mechanics & * Dynamical Astronomy, 85, 37-49 (2003) * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\file ee06a.c \fn double iauEe06a(double date1, double date2) \ingroup SF \brief Equation of the equinoxes * * Equation of the equinoxes, compatible with IAU 2000 resolutions and * IAU 2006/2000A precession-nutation. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \return * equation of the equinoxes (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The result, which is in radians, operates in the following sense: * * Greenwich apparent ST = GMST + equation of the equinoxes * * * Reference: * * McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), * IERS Technical Note No. 32, BKG * */ /*!\file eect00.c \fn double iauEect00(double date1, double date2) \ingroup CM \brief Equation of the equinoxes * * Equation of the equinoxes complementary terms, consistent with * IAU 2000 resolutions. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \return * complementary terms (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The "complementary terms" are part of the equation of the * equinoxes (EE), classically the difference between apparent and * mean Sidereal Time: * * GAST = GMST + EE * * with: * * EE = dpsi * cos(eps) * * where dpsi is the nutation in longitude and eps is the obliquity * of date. However, if the rotation of the Earth were constant in * an inertial frame the classical formulation would lead to * apparent irregularities in the UT1 timescale traceable to side- * effects of precession-nutation. In order to eliminate these * effects from UT1, "complementary terms" were introduced in 1994 * (IAU, 1994) and took effect from 1997 (Capitaine and Gontier, * 1993): * * GAST = GMST + CT + EE * * By convention, the complementary terms are included as part of * the equation of the equinoxes rather than as part of the mean * Sidereal Time. This slightly compromises the "geometrical" * interpretation of mean sidereal time but is otherwise * inconsequential. * * The present function computes CT in the above expression, * compatible with IAU 2000 resolutions (Capitaine et al., 2002, and * IERS Conventions 2003). * * * References: * * Capitaine, N. & Gontier, A.-M., Astron. Astrophys., 275, * 645-650 (1993) * * Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to * implement the IAU 2000 definition of UT1", Astronomy & * Astrophysics, 406, 1135-1149 (2003) * * IAU Resolution C7, Recommendation 3 (1994) * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\file eform.c \fn int iauEform ( int n, double *a, double *f ) \ingroup C \brief Earth reference ellipsoids. * * * * \param[in] n ellipsoid identifier (Note 1) * * \param[out] a equatorial radius (meters, Note 2) * \param[out] f flattening (Note 2) * * \return * 0 = OK * -1 = illegal identifier (Note 3) * * Notes: * * 1) The identifier n is a number that specifies the choice of * reference ellipsoid. The following are supported: * * n ellipsoid * * 1 WGS84 * 2 GRS80 * 3 WGS72 * * The n value has no significance outside the SOFA software. For * convenience, symbols WGS84 etc. are defined in sofam.h. * * 2) The ellipsoid parameters are returned in the form of equatorial * radius in meters (a) and flattening (f). The latter is a number * around 0.00335, i.e. around 1/298. * * 3) For the case where an unsupported n value is supplied, zero a and * f are returned, as well as error status. * * References: * * Department of Defense World Geodetic System 1984, National * Imagery and Mapping Agency Technical Report 8350.2, Third * Edition, p3-2. * * Moritz, H., Bull. Geodesique 66-2, 187 (1992). * * The Department of Defense World Geodetic System 1972, World * Geodetic System Committee, May 1974. * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992), * p220. * */ /*!\file eo06a.c \fn double iauEo06a(double date1, double date2) \ingroup SF \brief Equation of the origins * * Equation of the origins, IAU 2006 precession and IAU 2000A nutation. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \return * equation of the origins in radians * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The equation of the origins is the distance between the true * equinox and the celestial intermediate origin and, equivalently, * the difference between Earth rotation angle and Greenwich * apparent sidereal time (ERA-GST). It comprises the precession * (since J2000.0) in right ascension plus the equation of the * equinoxes (including the small correction terms). * * References: * * Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 * * Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 * */ /*!\file eors.c \fn double iauEors(double rnpb[3][3], double s) \ingroup SF \brief Equation of the origins * * Equation of the origins, given the classical NPB matrix and the * quantity s. * * * * \param[in] rnpb classical nutation x precession x bias matrix * \param[in] s the quantity s (the CIO locator) * * \return * the equation of the origins in radians. * * Notes: * * 1) The equation of the origins is the distance between the true * equinox and the celestial intermediate origin and, equivalently, * the difference between Earth rotation angle and Greenwich * apparent sidereal time (ERA-GST). It comprises the precession * (since J2000.0) in right ascension plus the equation of the * equinoxes (including the small correction terms). * * 2) The algorithm is from Wallace & Capitaine (2006). * * References: * * Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 * * Wallace, P. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 * */ /*!\file epb.c \fn double iauEpb(double dj1, double dj2) \ingroup SF \brief Julian Date to Besselian Epoch. * * * * \param[in] dj1 Julian Date (see note) * \param[in] dj2 Julian Date (see note) * * \return * Besselian Epoch. * * Note: * * The Julian Date is supplied in two pieces, in the usual SOFA * manner, which is designed to preserve time resolution. The * Julian Date is available as a single number by adding dj1 and * dj2. The maximum resolution is achieved if dj1 is 2451545.0 * (J2000.0). * * Reference: * * Lieske, J.H., 1979. Astron.Astrophys., 73, 282. * */ /*!\file epb2jd.c \fn void iauEpb2jd(double epb, double *djm0, double *djm) \ingroup SF \brief Besselian Epoch to Julian Date. * * * * \param[in] epb Besselian Epoch (e.g. 1957.3) * * \param[out] djm0 MJD zero-point: always 2400000.5 * \param[out] djm Modified Julian Date * * Note: * * The Julian Date is returned in two pieces, in the usual SOFA * manner, which is designed to preserve time resolution. The * Julian Date is available as a single number by adding djm0 and * djm. * * Reference: * * Lieske, J.H., 1979, Astron.Astrophys. 73, 282. * */ /*!\file epj.c \fn double iauEpj(double dj1, double dj2) \ingroup SF \brief Julian Date to Julian Epoch. * * * * \param[in] dj1 Julian Date (see note) * \param[in] dj2 Julian Date (see note) * * \return * Julian Epoch * * Note: * * The Julian Date is supplied in two pieces, in the usual SOFA * manner, which is designed to preserve time resolution. The * Julian Date is available as a single number by adding dj1 and * dj2. The maximum resolution is achieved if dj1 is 2451545.0 * (J2000.0). * * Reference: * * Lieske, J.H., 1979, Astron.Astrophys. 73, 282. * */ /*!\file epj2jd.c \fn void iauEpj2jd(double epj, double *djm0, double *djm) \ingroup SF \brief Julian Epoch to Julian Date. * * * * \param[in] epj Julian Epoch (e.g. 1996.8) * * \param[out] djm0 MJD zero-point: always 2400000.5 * \param[out] djm Modified Julian Date * * Note: * * The Julian Date is returned in two pieces, in the usual SOFA * manner, which is designed to preserve time resolution. The * Julian Date is available as a single number by adding djm0 and * djm. * * Reference: * * Lieske, J.H., 1979, Astron.Astrophys. 73, 282. * */ /*!\file epv00.c \fn int iauEpv00(double date1, double date2, double pvh[2][3], double pvb[2][3]) \ingroup SF \brief Earth position and velocity * * Earth position and velocity, heliocentric and barycentric, with * respect to the Barycentric Celestial Reference System. * * * * \param[in] date1 TDB date (Note 1) * \param[in] date2 TDB date (Note 1) * * \param[out] pvh heliocentric Earth position/velocity * \param[out] pvb barycentric Earth position/velocity * * \return * 0 = OK * +1 = warning: date outside * the range 1900-2100 AD * * Notes: * * 1) The TDB date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TDB)=2450123.7 could be expressed in any of these ways, among * others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in cases * where the loss of several decimal digits of resolution is * acceptable. The J2000 method is best matched to the way the * argument is handled internally and will deliver the optimum * resolution. The MJD method and the date & time methods are both * good compromises between resolution and convenience. However, * the accuracy of the result is more likely to be limited by the * algorithm itself than the way the date has been expressed. * * n.b. TT can be used instead of TDB in most applications. * * 2) On return, the arrays pvh and pvb contain the following: * * pvh[0][0] x } * pvh[0][1] y } heliocentric position, AU * pvh[0][2] z } * * pvh[1][0] xdot } * pvh[1][1] ydot } heliocentric velocity, AU/d * pvh[1][2] zdot } * * pvb[0][0] x } * pvb[0][1] y } barycentric position, AU * pvb[0][2] z } * * pvb[1][0] xdot } * pvb[1][1] ydot } barycentric velocity, AU/d * pvb[1][2] zdot } * * The vectors are with respect to the Barycentric Celestial * Reference System. The time unit is one day in TDB. * * 3) The function is a SIMPLIFIED SOLUTION from the planetary theory * VSOP2000 (X. Moisson, P. Bretagnon, 2001, Celes. Mechanics & * Dyn. Astron., 80, 3/4, 205-213) and is an adaptation of original * Fortran code supplied by P. Bretagnon (private comm., 2000). * * 4) Comparisons over the time span 1900-2100 with this simplified * solution and the JPL DE405 ephemeris give the following results: * * RMS max * Heliocentric: * position error 3.7 11.2 km * velocity error 1.4 5.0 mm/s * * Barycentric: * position error 4.6 13.4 km * velocity error 1.4 4.9 mm/s * * Comparisons with the JPL DE406 ephemeris show that by 1800 and * 2200 the position errors are approximately double their 1900-2100 * size. By 1500 and 2500 the deterioration is a factor of 10 and * by 1000 and 3000 a factor of 60. The velocity accuracy falls off * at about half that rate. * * 5) It is permissible to use the same array for pvh and pvb, which * will receive the barycentric values. * */ /*!\file eqec06.c \fn void iauEqec06(double date1, double date2, double dr, double dd, double *dl, double *db) \ingroup SF \brief Transformation from ICRS equatorial coordinates to ecliptic coordinates * Transformation from ICRS equatorial coordinates to ecliptic * coordinates (mean equinox and ecliptic of date) using IAU 2006 * precession model. * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) No assumptions are made about whether the coordinates represent * starlight and embody astrometric effects such as parallax or * aberration. * * 3) The transformation is approximately that from mean J2000.0 right * ascension and declination to ecliptic longitude and latitude * (mean equinox and ecliptic of date), with only frame bias (always * less than 25 mas) to disturb this classical picture. * @param[in] data1 TT as a 2-part Julian date * @param[in] data2 TT as a 2-part Julian date * @param[in] dr ICRS right ascension (radians) * @param[in] dd ICRS right declination (radians) * @param[out] dl ecliptic longitute (radians) * @param[out] db ecliptic latitude (radians) */ /*!\file eqeq94.c \fn double iauEqeq94(double date1, double date2) \ingroup CM \brief Equation of the equinoxes * * Equation of the equinoxes, IAU 1994 model. * * * * \param[in] date1 TDB date (Note 1) * \param[in] date2 TDB date (Note 1) * * \return * equation of the equinoxes (Note 2) * * Notes: * * 1) The date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The result, which is in radians, operates in the following sense: * * Greenwich apparent ST = GMST + equation of the equinoxes * * References: * * IAU Resolution C7, Recommendation 3 (1994). * * Capitaine, N. & Gontier, A.-M., 1993, Astron. Astrophys., 275, * 645-650. * */ /*!\file era00.c \fn double iauEra00(double dj1, double dj2) \ingroup CM \brief Earth rotation angle * * Earth rotation angle (IAU 2000 model). * * * * \param[in] dj1 UT1 as a 2-part Julian Date (see note) * \param[in] dj2 UT1 as a 2-part Julian Date (see note) * * \return * Earth rotation angle (radians), range 0-2pi * * Notes: * * 1) The UT1 date dj1+dj2 is a Julian Date, apportioned in any * convenient way between the arguments dj1 and dj2. For example, * JD(UT1)=2450123.7 could be expressed in any of these ways, * among others: * * dj1 dj2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 and MJD methods are good compromises * between resolution and convenience. The date & time method is * best matched to the algorithm used: maximum precision is * delivered when the dj1 argument is for 0hrs UT1 on the day in * question and the dj2 argument lies in the range 0 to 1, or vice * versa. * * 2) The algorithm is adapted from Expression 22 of Capitaine et al. * 2000. The time argument has been expressed in days directly, * and, to retain precision, integer contributions have been * eliminated. The same formulation is given in IERS Conventions * (2003), Chap. 5, Eq. 14. * * * References: * * Capitaine N., Guinot B. and McCarthy D.D, 2000, Astron. * Astrophys., 355, 398-405. * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\file fad03.c \fn double iauFad03(double t) \ingroup CM \brief mean elongation of the Moon from the Sun * * Fundamental argument, IERS Conventions (2003): * mean elongation of the Moon from the Sun. * * * * \param[in] t TDB, Julian centuries since J2000.0 (Note 1) * * \return * D, radians (Note 2) * * Notes: * * 1) Though t is strictly TDB, it is usually more convenient to use * TT, which makes no significant difference. * * 2) The expression used is as adopted in IERS Conventions (2003) and * is from Simon et al. (1994). * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 * */ /*!\file fae03.c \fn double iauFae03(double t) \ingroup CM \brief mean longitude of Earth. * * Fundamental argument, IERS Conventions (2003): * mean longitude of Earth. * * * * \param[in] t TDB, Julian centuries since J2000.0 (Note 1) * * \return * mean longitude of Earth, radians (Note 2) * * Notes: * * 1) Though t is strictly TDB, it is usually more convenient to use * TT, which makes no significant difference. * * 2) The expression used is as adopted in IERS Conventions (2003) and * comes from Souchay et al. (1999) after Simon et al. (1994). * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 * * Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, * Astron.Astrophys.Supp.Ser. 135, 111 * */ /*!\file faf03.c \fn double iauFaf03(double t) \ingroup CM \brief mean longitude of the Moon minus... * * Fundamental argument, IERS Conventions (2003): * mean longitude of the Moon minus mean longitude of the ascending * node. * * * * \param[in] t TDB, Julian centuries since J2000.0 (Note 1) * * \return * F, radians (Note 2) * * Notes: * * 1) Though t is strictly TDB, it is usually more convenient to use * TT, which makes no significant difference. * * 2) The expression used is as adopted in IERS Conventions (2003) and * is from Simon et al. (1994). * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 * */ /*!\file faju03.c \fn double iauFaju03(double t) \ingroup CM \brief mean longitude of Jupiter * * Fundamental argument, IERS Conventions (2003): * mean longitude of Jupiter. * * * * \param[in] t TDB, Julian centuries since J2000.0 (Note 1) * * \return * mean longitude of Jupiter, radians (Note 2) * * Notes: * * 1) Though t is strictly TDB, it is usually more convenient to use * TT, which makes no significant difference. * * 2) The expression used is as adopted in IERS Conventions (2003) and * comes from Souchay et al. (1999) after Simon et al. (1994). * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 * * Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, * Astron.Astrophys.Supp.Ser. 135, 111 * */ /*!\file fal03.c \fn double iauFal03(double t) \ingroup CM \brief mean anomaly of the Moon * * Fundamental argument, IERS Conventions (2003): * mean anomaly of the Moon. * * * * \param[in] t TDB, Julian centuries since J2000.0 (Note 1) * * \return * l, radians (Note 2) * * Notes: * * 1) Though t is strictly TDB, it is usually more convenient to use * TT, which makes no significant difference. * * 2) The expression used is as adopted in IERS Conventions (2003) and * is from Simon et al. (1994). * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 * */ /*!\file falp03 \fn double iauFalp03(double t) \ingroup CM \brief mean anomaly of the Sun * * Fundamental argument, IERS Conventions (2003): * mean anomaly of the Sun. * * * * \param[in] t TDB, Julian centuries since J2000.0 (Note 1) * * \return * l', radians (Note 2) * * Notes: * * 1) Though t is strictly TDB, it is usually more convenient to use * TT, which makes no significant difference. * * 2) The expression used is as adopted in IERS Conventions (2003) and * is from Simon et al. (1994). * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 * */ /*!\file fama03.c \fn double iauFama03(double t) \ingroup CM \brief mean longitude of Mars. * * Fundamental argument, IERS Conventions (2003): * mean longitude of Mars. * * * * \param[in] t TDB, Julian centuries since J2000.0 (Note 1) * * \return * mean longitude of Mars, radians (Note 2) * * Notes: * * 1) Though t is strictly TDB, it is usually more convenient to use * TT, which makes no significant difference. * * 2) The expression used is as adopted in IERS Conventions (2003) and * comes from Souchay et al. (1999) after Simon et al. (1994). * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 * * Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, * Astron.Astrophys.Supp.Ser. 135, 111 * */ /*!\file fame03.c \fn double iauFame03(double t) \ingroup CM \brief mean longitude of Mercury. * * Fundamental argument, IERS Conventions (2003): * mean longitude of Mercury. * * * * \param[in] t TDB, Julian centuries since J2000.0 (Note 1) * * \return * mean longitude of Mercury, radians (Note 2) * * Notes: * * 1) Though t is strictly TDB, it is usually more convenient to use * TT, which makes no significant difference. * * 2) The expression used is as adopted in IERS Conventions (2003) and * comes from Souchay et al. (1999) after Simon et al. (1994). * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 * * Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, * Astron.Astrophys.Supp.Ser. 135, 111 * */ /*!\file fane03.c \fn double iauFane03(double t) \ingroup CM \brief mean longitude of Neptune. * * Fundamental argument, IERS Conventions (2003): * mean longitude of Neptune. * * * * \param[in] t TDB, Julian centuries since J2000.0 (Note 1) * * \return * mean longitude of Neptune, radians (Note 2) * * Notes: * * 1) Though t is strictly TDB, it is usually more convenient to use * TT, which makes no significant difference. * * 2) The expression used is as adopted in IERS Conventions (2003) and * is adapted from Simon et al. (1994). * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 * */ /*!\file faom03.c \fn double iauFaom03(double t) \ingroup CM \brief mean longitude Moon's ascending node * * Fundamental argument, IERS Conventions (2003): * mean longitude of the Moon's ascending node. * * * * \param[in] t TDB, Julian centuries since J2000.0 (Note 1) * * \return * Omega, radians (Note 2) * * Notes: * * 1) Though t is strictly TDB, it is usually more convenient to use * TT, which makes no significant difference. * * 2) The expression used is as adopted in IERS Conventions (2003) and * is from Simon et al. (1994). * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 * */ /*!\file fapa03.c \fn double iauFapa03(double t) \ingroup CM \brief general accumulated precession in longitude * * Fundamental argument, IERS Conventions (2003): * general accumulated precession in longitude. * * * * \param[in] t TDB, Julian centuries since J2000.0 (Note 1) * * \return * general precession in longitude, radians (Note 2) * * Notes: * * 1) Though t is strictly TDB, it is usually more convenient to use * TT, which makes no significant difference. * * 2) The expression used is as adopted in IERS Conventions (2003). It * is taken from Kinoshita & Souchay (1990) and comes originally * from Lieske et al. (1977). * * References: * * Kinoshita, H. and Souchay J. 1990, Celest.Mech. and Dyn.Astron. * 48, 187 * * Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977, * Astron.Astrophys. 58, 1-16 * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\file fasa03.c \fn double iauFasa03(double t) \ingroup CM \brief mean longitude of Saturn. * * Fundamental argument, IERS Conventions (2003): * mean longitude of Saturn. * * * * \param[in] t TDB, Julian centuries since J2000.0 (Note 1) * * \return * mean longitude of Saturn, radians (Note 2) * * Notes: * * 1) Though t is strictly TDB, it is usually more convenient to use * TT, which makes no significant difference. * * 2) The expression used is as adopted in IERS Conventions (2003) and * comes from Souchay et al. (1999) after Simon et al. (1994). * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 * * Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, * Astron.Astrophys.Supp.Ser. 135, 111 * */ /*!\file faur03.c \fn double iauFaur03(double t) \ingroup CM \brief mean longitude of Uranus * * Fundamental argument, IERS Conventions (2003): * mean longitude of Uranus. * * * * \param[in] t TDB, Julian centuries since J2000.0 (Note 1) * * Returned (function value): * double mean longitude of Uranus, radians (Note 2) * * Notes: * * 1) Though t is strictly TDB, it is usually more convenient to use * TT, which makes no significant difference. * * 2) The expression used is as adopted in IERS Conventions (2003) and * is adapted from Simon et al. (1994). * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 * */ /*!\file fave03.c \fn double iauFave03(double t) \ingroup CM \brief mean longitude of Venus * * Fundamental argument, IERS Conventions (2003): * mean longitude of Venus. * * * * \param[in] t TDB, Julian centuries since J2000.0 (Note 1) * * \return * mean longitude of Venus, radians (Note 2) * * Notes: * * 1) Though t is strictly TDB, it is usually more convenient to use * TT, which makes no significant difference. * * 2) The expression used is as adopted in IERS Conventions (2003) and * comes from Souchay et al. (1999) after Simon et al. (1994). * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 * * Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, * Astron.Astrophys.Supp.Ser. 135, 111 * */ /*!\file fk425.c \fn void iauFk425(double r1950, double d1950, double dr1950, double dd1950, double p1950, double v1950, double *r2000, double *d2000, double *dr2000, double *dd2000, double *p2000, double *v2000) \brief Convert B1950.0 FK4 star catalog data to J2000.0 FK5. \ingroup SF * Notes: * * 1) The proper motions in RA are dRA/dt rather than cos(Dec)*dRA/dt, * and are per year rather than per century. * * 2) The conversion is somewhat complicated, for several reasons: * * . Change of standard epoch from B1950.0 to J2000.0. * * . An intermediate transition date of 1984 January 1.0 TT. * * . A change of precession model. * * . Change of time unit for proper motion (tropical to Julian). * * . FK4 positions include the E-terms of aberration, to simplify * the hand computation of annual aberration. FK5 positions * assume a rigorous aberration computation based on the Earth's * barycentric velocity. * * . The E-terms also affect proper motions, and in particular cause * objects at large distances to exhibit fictitious proper * motions. * * The algorithm is based on Smith et al. (1989) and Yallop et al. * (1989), which presented a matrix method due to Standish (1982) as * developed by Aoki et al. (1983), using Kinoshita's development of * Andoyer's post-Newcomb precession. The numerical constants from * Seidelmann (1992) are used canonically. * * 3) Conversion from B1950.0 FK4 to J2000.0 FK5 only is provided for. * Conversions for different epochs and equinoxes would require * additional treatment for precession, proper motion and E-terms. * * 4) In the FK4 catalog the proper motions of stars within 10 degrees * of the poles do not embody differential E-terms effects and * should, strictly speaking, be handled in a different manner from * stars outside these regions. However, given the general lack of * homogeneity of the star data available for routine astrometry, * the difficulties of handling positions that may have been * determined from astrometric fields spanning the polar and non- * polar regions, the likelihood that the differential E-terms * effect was not taken into account when allowing for proper motion * in past astrometry, and the undesirability of a discontinuity in * the algorithm, the decision has been made in this SOFA algorithm * to include the effects of differential E-terms on the proper * motions for all stars, whether polar or not. At epoch J2000.0, * and measuring "on the sky" rather than in terms of RA change, the * errors resulting from this simplification are less than * 1 milliarcsecond in position and 1 milliarcsecond per century in * proper motion. * @param[in] r1950 B1950.0 RA (rad) * @param[in] d1950 B1950.0 Dec (rad) * @param[in] dr1950 B1950.0 proper motion (rad/trop.yr) * @param[in] dd1950 B1950.0 proper motion (rad/trop.yr) * @param[in] p1950 parallax (arcsec) * @param[in] v1950 radial velocity (km/s, +ve = moving away) * @param[out] r2000 J2000.0 RA (rad) * @param[out] d2000 J2000.0 Dec (rad) * @param[out] dr2000 J2000.0 proper motion (rad/Jul.yr) * @param[out] dd2000 J2000.0 proper motion (rad/Jul.yr) * @param[out] p2000 J2000.0 parallax (arcsec) * @param[out] v2000 J2000.0 radial velocity (km/s, +ve = moving away) */ /*!\file fk45z.c \fn iauFk45z(double r1950, double d1950, double bepoch, double *r2000, double *d2000) \brief Convert a B1950.0 FK4 star position to J2000.0 FK5. \ingroup SF * Convert a B1950.0 FK4 star position to J2000.0 FK5, assuming zero * proper motion in the FK5 system. * This function converts a star's catalog data from the old FK4 * (Bessel-Newcomb) system to the later IAU 1976 FK5 (Fricke) system, * in such a way that the FK5 proper motion is zero. Because such a * star has, in general, a non-zero proper motion in the FK4 system, * the routine requires the epoch at which the position in the FK4 * system was determined. * Notes: * * 1) The epoch bepoch is strictly speaking Besselian, but if a * Julian epoch is supplied the result will be affected only to a * negligible extent. * * 2) The method is from Appendix 2 of Aoki et al. (1983), but using * the constants of Seidelmann (1992). See the routine iauFk425 * for a general introduction to the FK4 to FK5 conversion. * * 3) Conversion from equinox B1950.0 FK4 to equinox J2000.0 FK5 only * is provided for. Conversions for different starting and/or * ending epochs would require additional treatment for precession, * proper motion and E-terms. * * 4) In the FK4 catalog the proper motions of stars within 10 degrees * of the poles do not embody differential E-terms effects and * should, strictly speaking, be handled in a different manner from * stars outside these regions. However, given the general lack of * homogeneity of the star data available for routine astrometry, * the difficulties of handling positions that may have been * determined from astrometric fields spanning the polar and non- * polar regions, the likelihood that the differential E-terms * effect was not taken into account when allowing for proper motion * in past astrometry, and the undesirability of a discontinuity in * the algorithm, the decision has been made in this SOFA algorithm * to include the effects of differential E-terms on the proper * motions for all stars, whether polar or not. At epoch 2000.0, * and measuring "on the sky" rather than in terms of RA change, the * errors resulting from this simplification are less than * 1 milliarcsecond in position and 1 milliarcsecond per century in * proper motion. * @param[in] r1950 B1950.0 FK4 RA at epoch (rad) * @param[in] d1950 B1950.0 FK4 Dec at epoch (rad) * @param[in] bepoch Besselian epoch (eg. 1979.3D0) * @param[out] r2000 J2000.0 FK5 RA (rad) * @param[out] d2000 J2000.0 FK5 Dec (rad) */ /*!\file fk524. \fn void iauFk524(double r2000, double d2000, double dr2000, double dd2000, double p2000, double v2000, double *r1950, double *d1950, double *dr1950, double *dd1950, double *p1950, double *v1950) \brief Convert J2000.0 FK5 star catalog data to B1950.0 FK4. \ingroup SF * Notes: * * 1) The proper motions in RA are dRA/dt rather than cos(Dec)*dRA/dt, * and are per year rather than per century. * * 2) The conversion is somewhat complicated, for several reasons: * * . Change of standard epoch from J2000.0 to B1950.0. * * . An intermediate transition date of 1984 January 1.0 TT. * * . A change of precession model. * * . Change of time unit for proper motion (Julian to tropical). * * . FK4 positions include the E-terms of aberration, to simplify * the hand computation of annual aberration. FK5 positions * assume a rigorous aberration computation based on the Earth's * barycentric velocity. * * . The E-terms also affect proper motions, and in particular cause * objects at large distances to exhibit fictitious proper * motions. * * The algorithm is based on Smith et al. (1989) and Yallop et al. * (1989), which presented a matrix method due to Standish (1982) as * developed by Aoki et al. (1983), using Kinoshita's development of * Andoyer's post-Newcomb precession. The numerical constants from * Seidelmann (1992) are used canonically. * * 4) In the FK4 catalog the proper motions of stars within 10 degrees * of the poles do not embody differential E-terms effects and * should, strictly speaking, be handled in a different manner from * stars outside these regions. However, given the general lack of * homogeneity of the star data available for routine astrometry, * the difficulties of handling positions that may have been * determined from astrometric fields spanning the polar and non- * polar regions, the likelihood that the differential E-terms * effect was not taken into account when allowing for proper motion * in past astrometry, and the undesirability of a discontinuity in * the algorithm, the decision has been made in this SOFA algorithm * to include the effects of differential E-terms on the proper * motions for all stars, whether polar or not. At epoch J2000.0, * and measuring "on the sky" rather than in terms of RA change, the * errors resulting from this simplification are less than * 1 milliarcsecond in position and 1 milliarcsecond per century in * proper motion. * @param[in] r2000 J2000.0 RA (rad) * @param[in] d2000 J2000.0 Dec (rad) * @param[in] dr2000 J2000.0 proper motion (rad/Jul.yr) * @param[in] dd2000 J2000.0 proper motion (rad/Jul.yr) * @param[in] p2000 J2000.0 parallax (arcsec) * @param[in] v2000 J2000.0 radial velocity (km/s, +ve = moving away) * @param[out] r1950 B1950.0 RA (rad) * @param[out] d1950 B1950.0 Dec (rad) * @param[out] dr1950 B1950.0 proper motion (rad/trop.yr) * @param[out] dd1950 B1950.0 proper motion (rad/trop.yr) * @param[out] p1950 parallax (arcsec) * @param[out] v1950 radial velocity (km/s, +ve = moving away) * References: * * Aoki, S. et al., 1983, "Conversion matrix of epoch B1950.0 * FK4-based positions of stars to epoch J2000.0 positions in * accordance with the new IAU resolutions". Astron.Astrophys. * 128, 263-267. * * Seidelmann, P.K. (ed), 1992, "Explanatory Supplement to the * Astronomical Almanac", ISBN 0-935702-68-7. * * Smith, C.A. et al., 1989, "The transformation of astrometric * catalog systems to the equinox J2000.0". Astron.J. 97, 265. * * Standish, E.M., 1982, "Conversion of positions and proper motions * from B1950.0 to the IAU system at J2000.0". Astron.Astrophys., * 115, 1, 20-22. * * Yallop, B.D. et al., 1989, "Transformation of mean star places * from FK4 B1950.0 to FK5 J2000.0 using matrices in 6-space". * Astron.J. 97, 274. */ /*!\file fk52h.c \fn void iauFk52h(double r5, double d5, double dr5, double dd5, double px5, double rv5, double *rh, double *dh, double *drh, double *ddh, double *pxh, double *rvh) \ingroup SF \brief Transform FK5 star data into the Hipparcos system. * * Transform FK5 (J2000.0) star data into the Hipparcos system. * * * * All input parameters are FK5, equinox J2000.0, epoch J2000.0. * \param[in] r5 RA (radians) * \param[in] d5 Dec (radians) * \param[in] dr5 proper motion in RA (dRA/dt, rad/Jyear) * \param[in] dd5 proper motion in Dec (dDec/dt, rad/Jyear) * \param[in] px5 parallax (arcsec) * \param[in] rv5 radial velocity (km/s, positive = receding) * * All output parameters are Hipparcos, epoch J2000.0. * \param[out] rh RA (radians) * \param[out] dh Dec (radians) * \param[out] drh proper motion in RA (dRA/dt, rad/Jyear) * \param[out] ddh proper motion in Dec (dDec/dt, rad/Jyear) * \param[out] pxh parallax (arcsec) * \param[out] rvh radial velocity (km/s, positive = receding) * * Notes: * * 1) This function transforms FK5 star positions and proper motions * into the system of the Hipparcos catalog. * * 2) The proper motions in RA are dRA/dt rather than * cos(Dec)*dRA/dt, and are per year rather than per century. * * 3) The FK5 to Hipparcos transformation is modeled as a pure * rotation and spin; zonal errors in the FK5 catalog are not * taken into account. * * 4) See also iauH2fk5, iauFk5hz, iauHfk5z. * * Reference: * * F.Mignard & M.Froeschle, Astron. Astrophys. 354, 732-739 (2000). * */ /*!\file fk54z.c \fn void iauFk54z(double r2000, double d2000, double bepoch, double *r1950, double *d1950, double *dr1950, double *dd1950) \brief Convert a J2000.0 FK5 star position to B1950.0 FK4 \ingroup SF * Convert a J2000.0 FK5 star position to B1950.0 FK4, assuming zero * proper motion in FK5 and parallax. * Notes: * * 1) In contrast to the iauFk524 routine, here the FK5 proper * motions, the parallax and the radial velocity are presumed zero. * * 2) This function converts a star position from the IAU 1976 FK5 * (Fricke) system to the former FK4 (Bessel-Newcomb) system, for * cases such as distant radio sources where it is presumed there is * zero parallax and no proper motion. Because of the E-terms of * aberration, such objects have (in general) non-zero proper motion * in FK4, and the present routine returns those fictitious proper * motions. * * 3) Conversion from B1950.0 FK4 to J2000.0 FK5 only is provided for. * Conversions involving other equinoxes would require additional * treatment for precession. * * 4) The position returned by this routine is in the B1950.0 FK4 * reference system but at Besselian epoch BEPOCH. For comparison * with catalogs the BEPOCH argument will frequently be 1950.0. (In * this context the distinction between Besselian and Julian epoch * is insignificant.) * * 5) The RA component of the returned (fictitious) proper motion is * dRA/dt rather than cos(Dec)*dRA/dt. * @param[in] r2000 J2000.0 FK5 RA (rad) * @param[in] d2000 J2000.0 FK5 Dec (rad) * @param[in] bepoch Besselian epoch (eg. 1979.3D0) * @param[out] r1950 B1950.0 FK4 RA at epoch (rad) * @param[out] d1950 B1950.0 FK4 Dec at epoch (rad) */ /*!\file fk5hip.c \fn void iauFk5hip(double r5h[3][3], double s5h[3]) \ingroup SF \brief FK5 to Hipparcos rotation and spin. * * * * \param[out] r5h r-matrix: FK5 rotation wrt Hipparcos (Note 2) * \param[out] s5h r-vector: FK5 spin wrt Hipparcos (Note 3) * * Notes: * * 1) This function models the FK5 to Hipparcos transformation as a * pure rotation and spin; zonal errors in the FK5 catalogue are * not taken into account. * * 2) The r-matrix r5h operates in the sense: * * P_Hipparcos = r5h x P_FK5 * * where P_FK5 is a p-vector in the FK5 frame, and P_Hipparcos is * the equivalent Hipparcos p-vector. * * 3) The r-vector s5h represents the time derivative of the FK5 to * Hipparcos rotation. The units are radians per year (Julian, * TDB). * * Reference: * * F.Mignard & M.Froeschle, Astron. Astrophys. 354, 732-739 (2000). * */ /*!\file fk5hz.c \fn void iauFk5hz(double r5, double d5, double date1, double date2, double *rh, double *dh) \ingroup SF \brief Transform an FK5 star position into the Hipparcos system. * * Transform an FK5 (J2000.0) star position into the system of the * Hipparcos catalogue, assuming zero Hipparcos proper motion. * * * * \param[in] r5 FK5 RA (radians), equinox J2000.0, at date * \param[in] d5 FK5 Dec (radians), equinox J2000.0, at date * \param[in] date1 TDB date (Notes 1,2) * \param[in] date2 TDB date (Notes 1,2) * * \param[out] rh Hipparcos RA (radians) * \param[out] dh Hipparcos Dec (radians) * * Notes: * * 1) This function converts a star position from the FK5 system to * the Hipparcos system, in such a way that the Hipparcos proper * motion is zero. Because such a star has, in general, a non-zero * proper motion in the FK5 system, the function requires the date * at which the position in the FK5 system was determined. * * 2) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 3) The FK5 to Hipparcos transformation is modeled as a pure * rotation and spin; zonal errors in the FK5 catalogue are not * taken into account. * * 4) The position returned by this function is in the Hipparcos * reference system but at date date1+date2. * * 5) See also iauFk52h, iauH2fk5, iauHfk5z. * * Reference: * * F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739. * */ /*!\file fw2m.c \fn void iauFw2m(double gamb, double phib, double psi, double eps, double r[3][3]) \ingroup SF \brief Form rotation matrix given the Fukushima-Williams angles. * * * * \param[in] gamb F-W angle gamma_bar (radians) * \param[in] phib F-W angle phi_bar (radians) * \param[in] psi F-W angle psi (radians) * \param[in] eps F-W angle epsilon (radians) * * \param[out] r rotation matrix * * Notes: * * 1) Naming the following points: * * e = J2000.0 ecliptic pole, * p = GCRS pole, * E = ecliptic pole of date, * and P = CIP, * * the four Fukushima-Williams angles are as follows: * * gamb = gamma = epE * phib = phi = pE * psi = psi = pEP * eps = epsilon = EP * * 2) The matrix representing the combined effects of frame bias, * precession and nutation is: * * NxPxB = R_1(-eps).R_3(-psi).R_1(phib).R_3(gamb) * * 3) The present function can construct three different matrices, * depending on which angles are supplied as the arguments gamb, * phib, psi and eps: * * o To obtain the nutation x precession x frame bias matrix, * first generate the four precession angles known conventionally * as gamma_bar, phi_bar, psi_bar and epsilon_A, then generate * the nutation components Dpsi and Depsilon and add them to * psi_bar and epsilon_A, and finally call the present function * using those four angles as arguments. * * o To obtain the precession x frame bias matrix, generate the * four precession angles and call the present function. * * o To obtain the frame bias matrix, generate the four precession * angles for date J2000.0 and call the present function. * * The nutation-only and precession-only matrices can if necessary * be obtained by combining these three appropriately. * * References: * * Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 * Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351 */ /*!\file fw2xy.c \fn void iauFw2xy(double gamb, double phib, double psi, double eps, double *x, double *y) \ingroup SF \brief CIP X,Y given Fukushima-Williams bias-precession-nutation angles. * * * * \param[in] gamb F-W angle gamma_bar (radians) * \param[in] phib F-W angle phi_bar (radians) * \param[in] psi F-W angle psi (radians) * \param[in] eps F-W angle epsilon (radians) * * \param[out] x CIP unit vector X,Y * \param[out] y CIP unit vector X,Y * * Notes: * * 1) Naming the following points: * * e = J2000.0 ecliptic pole, * p = GCRS pole * E = ecliptic pole of date, * and P = CIP, * * the four Fukushima-Williams angles are as follows: * * gamb = gamma = epE * phib = phi = pE * psi = psi = pEP * eps = epsilon = EP * * 2) The matrix representing the combined effects of frame bias, * precession and nutation is: * * NxPxB = R_1(-epsA).R_3(-psi).R_1(phib).R_3(gamb) * * The returned values x,y are elements [2][0] and [2][1] of the * matrix. Near J2000.0, they are essentially angles in radians. * * * Reference: * * Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351 * */ /*!\file g2icrs.c \fn void iauG2icrs ( double dl, double db, double *dr, double *dd ) \ingroup SR \brief Transformation from Galactic Coordinates to ICRS. * * * * \param[in] dl galactic longitude (radians) * \param[in] db galactic latitude (radians) * * \param[out] dr ICRS right ascension (radians) * \param[out] dd ICRS declination (radians) * * Notes: * * 1) The IAU 1958 system of Galactic coordinates was defined with * respect to the now obsolete reference system FK4 B1950.0. When * interpreting the system in a modern context, several factors have * to be taken into account: * * . The inclusion in FK4 positions of the E-terms of aberration. * * . The distortion of the FK4 proper motion system by differential * Galactic rotation. * * . The use of the B1950.0 equinox rather than the now-standard * J2000.0. * * . The frame bias between ICRS and the J2000.0 mean place system. * * The Hipparcos Catalogue (Perryman & ESA 1997) provides a rotation * matrix that transforms directly between ICRS and Galactic * coordinates with the above factors taken into account. The * matrix is derived from three angles, namely the ICRS coordinates * of the Galactic pole and the longitude of the ascending node of * the galactic equator on the ICRS equator. They are given in * degrees to five decimal places and for canonical purposes are * regarded as exact. In the Hipparcos Catalogue the matrix * elements are given to 10 decimal places (about 20 microarcsec). * In the present SOFA function the matrix elements have been * recomputed from the canonical three angles and are given to 30 * decimal places. * * 2) The inverse transformation is performed by the function iauIcrs2g. * * * Reference: * Perryman M.A.C. & ESA, 1997, ESA SP-1200, The Hipparcos and Tycho * catalogues. Astrometric and photometric star catalogues * derived from the ESA Hipparcos Space Astrometry Mission. ESA * Publications Division, Noordwijk, Netherlands. * */ /*!\file gc2gd.c \fn int iauGc2gd ( int n, double xyz[3], double *elong, double *phi, double *height ) \ingroup CT \brief Transform geocentric coordinates to geodetic * * Transform geocentric coordinates to geodetic using the specified * reference ellipsoid. * * * * \param[in] n ellipsoid identifier (Note 1) * \param[in] xyz geocentric vector (Note 2) * * \param[out] elong longitude (radians, east +ve, Note 3) * \param[out] phi latitude (geodetic, radians, Note 3) * \param[out] height height above ellipsoid (geodetic, Notes 2,3) * * \return * 0 = OK * -1 = illegal identifier (Note 3) * -2 = internal error (Note 3) * * Notes: * * 1) The identifier n is a number that specifies the choice of * reference ellipsoid. The following are supported: * * n ellipsoid * * 1 WGS84 * 2 GRS80 * 3 WGS72 * * The n value has no significance outside the SOFA software. For * convenience, symbols WGS84 etc. are defined in sofam.h. * * 2) The geocentric vector (xyz, given) and height (height, returned) * are in meters. * * 3) An error status -1 means that the identifier n is illegal. An * error status -2 is theoretically impossible. In all error cases, * all three results are set to -1e9. * * 4) The inverse transformation is performed in the function iauGd2gc. * * */ /*!\file gc2gde.c \fn int iauGc2gde ( double a, double f, double xyz[3], double *elong, double *phi, double *height ) \ingroup SF \brief Transform geocentric coordinates to geodetic * * Transform geocentric coordinates to geodetic for a reference * ellipsoid of specified form. * * * * \param[in] a equatorial radius (Notes 2,4) * \param[in] f flattening (Note 3) * \param[in] xyz geocentric vector (Note 4) * * \param[out] elong longitude (radians, east +ve) * \param[out] phi latitude (geodetic, radians) * \param[out] height height above ellipsoid (geodetic, Note 4) * * \return * 0 = OK * -1 = illegal f * -2 = illegal a * * Notes: * * 1) This function is based on the GCONV2H Fortran subroutine by * Toshio Fukushima (see reference). * * 2) The equatorial radius, a, can be in any units, but meters is * the conventional choice. * * 3) The flattening, f, is (for the Earth) a value around 0.00335, * i.e. around 1/298. * * 4) The equatorial radius, a, and the geocentric vector, xyz, * must be given in the same units, and determine the units of * the returned height, height. * * 5) If an error occurs (status < 0), elong, phi and height are * unchanged. * * 6) The inverse transformation is performed in the function * iauGd2gce. * * 7) The transformation for a standard ellipsoid (such as WGS84) can * more conveniently be performed by calling iauGc2gd, which uses a * numerical code to identify the required A and F values. * * Reference: * * Fukushima, T., "Transformation from Cartesian to geodetic * coordinates accelerated by Halley's method", J.Geodesy (2006) * 79: 689-693 * */ /*!\file gd2gc.c \fn int iauGd2gc ( int n, double elong, double phi, double height, double xyz[3] ) \ingroup CT \brief Transform geodetic coordinates to geocentric * * Transform geodetic coordinates to geocentric using the specified * reference ellipsoid. * * * * \param[in] n ellipsoid identifier (Note 1) * \param[in] elong longitude (radians, east +ve) * \param[in] phi latitude (geodetic, radians, Note 3) * \param[in] height height above ellipsoid (geodetic, Notes 2,3) * * \param[out] xyz geocentric vector (Note 2) * * \return * 0 = OK * -1 = illegal identifier (Note 3) * -2 = illegal case (Note 3) * * Notes: * * 1) The identifier n is a number that specifies the choice of * reference ellipsoid. The following are supported: * * n ellipsoid * * 1 WGS84 * 2 GRS80 * 3 WGS72 * * The n value has no significance outside the SOFA software. For * convenience, symbols WGS84 etc. are defined in sofam.h. * * 2) The height (height, given) and the geocentric vector (xyz, * returned) are in meters. * * 3) No validation is performed on the arguments elong, phi and * height. An error status -1 means that the identifier n is * illegal. An error status -2 protects against cases that would * lead to arithmetic exceptions. In all error cases, xyz is set * to zeros. * * 4) The inverse transformation is performed in the function iauGc2gd. * * */ /*!\file gd2gce.c \fn int iauGd2gce ( double a, double f, double elong, double phi, double height, double xyz[3] ) \ingroup SF \brief Transform geodetic coordinates to geocentric * * Transform geodetic coordinates to geocentric for a reference * ellipsoid of specified form. * * * * \param[in] a equatorial radius (Notes 1,4) * \param[in] f flattening (Notes 2,4) * \param[in] elong longitude (radians, east +ve) * \param[in] phi latitude (geodetic, radians, Note 4) * \param[in] height height above ellipsoid (geodetic, Notes 3,4) * * \param[out] xyz geocentric vector (Note 3) * * \return * 0 = OK * -1 = illegal case (Note 4) * Notes: * * 1) The equatorial radius, a, can be in any units, but meters is * the conventional choice. * * 2) The flattening, f, is (for the Earth) a value around 0.00335, * i.e. around 1/298. * * 3) The equatorial radius, a, and the height, height, must be * given in the same units, and determine the units of the * returned geocentric vector, xyz. * * 4) No validation is performed on individual arguments. The error * status -1 protects against (unrealistic) cases that would lead * to arithmetic exceptions. If an error occurs, xyz is unchanged. * * 5) The inverse transformation is performed in the function * iauGc2gde. * * 6) The transformation for a standard ellipsoid (such as WGS84) can * more conveniently be performed by calling iauGd2gc, which uses a * numerical code to identify the required a and f values. * * References: * * Green, R.M., Spherical Astronomy, Cambridge University Press, * (1985) Section 4.5, p96. * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992), * Section 4.22, p202. * */ /*!\file gmst00.c \fn double iauGmst00(double uta, double utb, double tta, double ttb) \ingroup CM \brief Greenwich mean sidereal time * * Greenwich mean sidereal time (model consistent with IAU 2000 * resolutions). * * * * \param[in] uta UT1 as a 2-part Julian Date (Notes 1,2) * \param[in] utb UT1 as a 2-part Julian Date (Notes 1,2) * \param[in] tta TT as a 2-part Julian Date (Notes 1,2) * \param[in] ttb TT as a 2-part Julian Date (Notes 1,2) * * \return * Greenwich mean sidereal time (radians) * * Notes: * * 1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both * Julian Dates, apportioned in any convenient way between the * argument pairs. For example, JD=2450123.7 could be expressed in * any of these ways, among others: * * Part A Part B * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable (in the case of UT; the TT is not at all critical * in this respect). The J2000 and MJD methods are good compromises * between resolution and convenience. For UT, the date & time * method is best matched to the algorithm that is used by the Earth * Rotation Angle function, called internally: maximum precision is * delivered when the uta argument is for 0hrs UT1 on the day in * question and the utb argument lies in the range 0 to 1, or vice * versa. * * 2) Both UT1 and TT are required, UT1 to predict the Earth rotation * and TT to predict the effects of precession. If UT1 is used for * both purposes, errors of order 100 microarcseconds result. * * 3) This GMST is compatible with the IAU 2000 resolutions and must be * used only in conjunction with other IAU 2000 compatible * components such as precession-nutation and equation of the * equinoxes. * * 4) The result is returned in the range 0 to 2pi. * * 5) The algorithm is from Capitaine et al. (2003) and IERS * Conventions 2003. * * * References: * * Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to * implement the IAU 2000 definition of UT1", Astronomy & * Astrophysics, 406, 1135-1149 (2003) * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\file gmst06.c \fn double iauGmst06(double uta, double utb, double tta, double ttb) \ingroup CM \brief Greenwich mean sidereal time * * Greenwich mean sidereal time (consistent with IAU 2006 precession). * * * * \param[in] uta UT1 as a 2-part Julian Date (Notes 1,2) * \param[in] utb UT1 as a 2-part Julian Date (Notes 1,2) * \param[in] tta TT as a 2-part Julian Date (Notes 1,2) * \param[in] ttb TT as a 2-part Julian Date (Notes 1,2) * * \return * Greenwich mean sidereal time (radians) * * Notes: * * 1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both * Julian Dates, apportioned in any convenient way between the * argument pairs. For example, JD=2450123.7 could be expressed in * any of these ways, among others: * * Part A Part B * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable (in the case of UT; the TT is not at all critical * in this respect). The J2000 and MJD methods are good compromises * between resolution and convenience. For UT, the date & time * method is best matched to the algorithm that is used by the Earth * rotation angle function, called internally: maximum precision is * delivered when the uta argument is for 0hrs UT1 on the day in * question and the utb argument lies in the range 0 to 1, or vice * versa. * * 2) Both UT1 and TT are required, UT1 to predict the Earth rotation * and TT to predict the effects of precession. If UT1 is used for * both purposes, errors of order 100 microarcseconds result. * * 3) This GMST is compatible with the IAU 2006 precession and must not * be used with other precession models. * * 4) The result is returned in the range 0 to 2pi. * * * Reference: * * Capitaine, N., Wallace, P.T. & Chapront, J., 2005, * Astron.Astrophys. 432, 355 * */ /*!\file gmst82.c \fn double iauGmst82(double dj1, double dj2) \ingroup CM \brief Universal Time to Greenwich mean sidereal time * * Universal Time to Greenwich mean sidereal time (IAU 1982 model). * * * * \param[in] dj1 UT1 Julian Date (see note) * \param[in] dj2 UT1 Julian Date (see note) * * \return Greenwich mean sidereal time (radians) * * Notes: * * 1) The UT1 date dj1+dj2 is a Julian Date, apportioned in any * convenient way between the arguments dj1 and dj2. For example, * JD(UT1)=2450123.7 could be expressed in any of these ways, * among others: * * dj1 dj2 * * 2450123.7 0 (JD method) * 2451545 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 and MJD methods are good compromises * between resolution and convenience. The date & time method is * best matched to the algorithm used: maximum accuracy (or, at * least, minimum noise) is delivered when the dj1 argument is for * 0hrs UT1 on the day in question and the dj2 argument lies in the * range 0 to 1, or vice versa. * * 2) The algorithm is based on the IAU 1982 expression. This is * always described as giving the GMST at 0 hours UT1. In fact, it * gives the difference between the GMST and the UT, the steady * 4-minutes-per-day drawing-ahead of ST with respect to UT. When * whole days are ignored, the expression happens to equal the GMST * at 0 hours UT1 each day. * * 3) In this function, the entire UT1 (the sum of the two arguments * dj1 and dj2) is used directly as the argument for the standard * formula, the constant term of which is adjusted by 12 hours to * take account of the noon phasing of Julian Date. The UT1 is then * added, but omitting whole days to conserve accuracy. * * References: * * Transactions of the International Astronomical Union, * XVIII B, 67 (1983). * * Aoki et al., Astron.Astrophys., 105, 359-361 (1982). */ /*!\file gst00a.c \fn double iauGst00a(double uta, double utb, double tta, double ttb) \ingroup CM \brief Greenwich apparent sidereal time * * Greenwich apparent sidereal time (consistent with IAU 2000 * resolutions). * * * * \param[in] uta UT1 as a 2-part Julian Date (Notes 1,2) * \param[in] utb UT1 as a 2-part Julian Date (Notes 1,2) * \param[in] tta TT as a 2-part Julian Date (Notes 1,2) * \param[in] ttb TT as a 2-part Julian Date (Notes 1,2) * * \return * Greenwich apparent sidereal time (radians) * * Notes: * * 1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both * Julian Dates, apportioned in any convenient way between the * argument pairs. For example, JD=2450123.7 could be expressed in * any of these ways, among others: * * Part A Part B * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable (in the case of UT; the TT is not at all critical * in this respect). The J2000 and MJD methods are good compromises * between resolution and convenience. For UT, the date & time * method is best matched to the algorithm that is used by the Earth * Rotation Angle function, called internally: maximum precision is * delivered when the uta argument is for 0hrs UT1 on the day in * question and the utb argument lies in the range 0 to 1, or vice * versa. * * 2) Both UT1 and TT are required, UT1 to predict the Earth rotation * and TT to predict the effects of precession-nutation. If UT1 is * used for both purposes, errors of order 100 microarcseconds * result. * * 3) This GAST is compatible with the IAU 2000 resolutions and must be * used only in conjunction with other IAU 2000 compatible * components such as precession-nutation. * * 4) The result is returned in the range 0 to 2pi. * * 5) The algorithm is from Capitaine et al. (2003) and IERS * Conventions 2003. * * * References: * * Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to * implement the IAU 2000 definition of UT1", Astronomy & * Astrophysics, 406, 1135-1149 (2003) * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\file gst00b.c \fn double iauGst00b(double uta, double utb) \ingroup SF \brief Greenwich apparent sidereal time * * Greenwich apparent sidereal time (consistent with IAU 2000 * resolutions but using the truncated nutation model IAU 2000B). * * * * \param[in] uta UT1 as a 2-part Julian Date (Notes 1,2) * \param[in] utb UT1 as a 2-part Julian Date (Notes 1,2) * * \return * Greenwich apparent sidereal time (radians) * * Notes: * * 1) The UT1 date uta+utb is a Julian Date, apportioned in any * convenient way between the argument pair. For example, * JD=2450123.7 could be expressed in any of these ways, among * others: * * uta utb * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in cases * where the loss of several decimal digits of resolution is * acceptable. The J2000 and MJD methods are good compromises * between resolution and convenience. For UT, the date & time * method is best matched to the algorithm that is used by the Earth * Rotation Angle function, called internally: maximum precision is * delivered when the uta argument is for 0hrs UT1 on the day in * question and the utb argument lies in the range 0 to 1, or vice * versa. * * 2) The result is compatible with the IAU 2000 resolutions, except * that accuracy has been compromised for the sake of speed and * convenience in two respects: * * . UT is used instead of TDB (or TT) to compute the precession * component of GMST and the equation of the equinoxes. This * results in errors of order 0.1 mas at present. * * . The IAU 2000B abridged nutation model (McCarthy & Luzum, 2001) * is used, introducing errors of up to 1 mas. * * 3) This GAST is compatible with the IAU 2000 resolutions and must be * used only in conjunction with other IAU 2000 compatible * components such as precession-nutation. * * 4) The result is returned in the range 0 to 2pi. * * 5) The algorithm is from Capitaine et al. (2003) and IERS * Conventions 2003. * * * References: * * Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to * implement the IAU 2000 definition of UT1", Astronomy & * Astrophysics, 406, 1135-1149 (2003) * * McCarthy, D.D. & Luzum, B.J., "An abridged model of the * precession-nutation of the celestial pole", Celestial Mechanics & * Dynamical Astronomy, 85, 37-49 (2003) * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\filte gst06.c \fn double iauGst06(double uta, double utb, double tta, double ttb, double rnpb[3][3]) \ingroup SF \brief Greenwich apparent sidereal time * * Greenwich apparent sidereal time, IAU 2006, given the NPB matrix. * * * * \param[in] uta UT1 as a 2-part Julian Date (Notes 1,2) * \param[in] utb UT1 as a 2-part Julian Date (Notes 1,2) * \param[in] tta TT as a 2-part Julian Date (Notes 1,2) * \param[in] ttb TT as a 2-part Julian Date (Notes 1,2) * \param[in] rnpb nutation x precession x bias matrix * * \return * Greenwich apparent sidereal time (radians) * * Notes: * * 1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both * Julian Dates, apportioned in any convenient way between the * argument pairs. For example, JD=2450123.7 could be expressed in * any of these ways, among others: * * Part A Part B * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable (in the case of UT; the TT is not at all critical * in this respect). The J2000 and MJD methods are good compromises * between resolution and convenience. For UT, the date & time * method is best matched to the algorithm that is used by the Earth * rotation angle function, called internally: maximum precision is * delivered when the uta argument is for 0hrs UT1 on the day in * question and the utb argument lies in the range 0 to 1, or vice * versa. * * 2) Both UT1 and TT are required, UT1 to predict the Earth rotation * and TT to predict the effects of precession-nutation. If UT1 is * used for both purposes, errors of order 100 microarcseconds * result. * * 3) Although the function uses the IAU 2006 series for s+XY/2, it is * otherwise independent of the precession-nutation model and can in * practice be used with any equinox-based NPB matrix. * * 4) The result is returned in the range 0 to 2pi. * * * Reference: * * Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 * */ /*!\file gst06a.c \fn double iauGst06a(double uta, double utb, double tta, double ttb) \ingroup CM \brief Greenwich apparent sidereal time * * Greenwich apparent sidereal time (consistent with IAU 2000 and 2006 * resolutions). * * * * \param[in] uta UT1 as a 2-part Julian Date (Notes 1,2) * \param[in] utb UT1 as a 2-part Julian Date (Notes 1,2) * \param[in] tta TT as a 2-part Julian Date (Notes 1,2) * \param[in] ttb TT as a 2-part Julian Date (Notes 1,2) * * \return * Greenwich apparent sidereal time (radians) * * Notes: * * 1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both * Julian Dates, apportioned in any convenient way between the * argument pairs. For example, JD=2450123.7 could be expressed in * any of these ways, among others: * * Part A Part B * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable (in the case of UT; the TT is not at all critical * in this respect). The J2000 and MJD methods are good compromises * between resolution and convenience. For UT, the date & time * method is best matched to the algorithm that is used by the Earth * rotation angle function, called internally: maximum precision is * delivered when the uta argument is for 0hrs UT1 on the day in * question and the utb argument lies in the range 0 to 1, or vice * versa. * * 2) Both UT1 and TT are required, UT1 to predict the Earth rotation * and TT to predict the effects of precession-nutation. If UT1 is * used for both purposes, errors of order 100 microarcseconds * result. * * 3) This GAST is compatible with the IAU 2000/2006 resolutions and * must be used only in conjunction with IAU 2006 precession and * IAU 2000A nutation. * * 4) The result is returned in the range 0 to 2pi. * * * Reference: * * Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 * */ /*!\file gst94.c \fn double iauGst94(double uta, double utb) \ingroup SF \brief Greenwich apparent sidereal time * * Greenwich apparent sidereal time (consistent with IAU 1982/94 * resolutions). * * * * \param[in] uta UT1 as a 2-part Julian Date (Notes 1,2) * \param[in] utb UT1 as a 2-part Julian Date (Notes 1,2) * * \return * Greenwich apparent sidereal time (radians) * * Notes: * * 1) The UT1 date uta+utb is a Julian Date, apportioned in any * convenient way between the argument pair. For example, * JD=2450123.7 could be expressed in any of these ways, among * others: * * uta utb * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in cases * where the loss of several decimal digits of resolution is * acceptable. The J2000 and MJD methods are good compromises * between resolution and convenience. For UT, the date & time * method is best matched to the algorithm that is used by the Earth * Rotation Angle function, called internally: maximum precision is * delivered when the uta argument is for 0hrs UT1 on the day in * question and the utb argument lies in the range 0 to 1, or vice * versa. * * 2) The result is compatible with the IAU 1982 and 1994 resolutions, * except that accuracy has been compromised for the sake of * convenience in that UT is used instead of TDB (or TT) to compute * the equation of the equinoxes. * * 3) This GAST must be used only in conjunction with contemporaneous * IAU standards such as 1976 precession, 1980 obliquity and 1982 * nutation. It is not compatible with the IAU 2000 resolutions. * * 4) The result is returned in the range 0 to 2pi. * * * References: * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992) * * IAU Resolution C7, Recommendation 3 (1994) * */ /*!\file h2fk5.c \fn void iauH2fk5(double rh, double dh, double drh, double ddh, double pxh, double rvh, double *r5, double *d5, double *dr5, double *dd5, double *px5, double *rv5) \ingroup SF \brief Transform Hipparcos star data into the FK5 (J2000.0) system. * * * * All input parameters are Hipparcos, epoch J2000.0. * \param[in] rh RA (radians) * \param[in] dh Dec (radians) * \param[in] drh proper motion in RA (dRA/dt, rad/Jyear) * \param[in] ddh proper motion in Dec (dDec/dt, rad/Jyear) * \param[in] pxh parallax (arcsec) * \param[in] rvh radial velocity (km/s, positive = receding) * * All output parameters are FK5, equinox J2000.0, epoch J2000.0. * \param[out] r5 RA (radians) * \param[out] d5 Dec (radians) * \param[out] dr5 proper motion in RA (dRA/dt, rad/Jyear) * \param[out] dd5 proper motion in Dec (dDec/dt, rad/Jyear) * \param[out] px5 parallax (arcsec) * \param[out] rv5 radial velocity (km/s, positive = receding) * * Notes: * * 1) This function transforms Hipparcos star positions and proper * motions into FK5 J2000.0. * * 2) The proper motions in RA are dRA/dt rather than * cos(Dec)*dRA/dt, and are per year rather than per century. * * 3) The FK5 to Hipparcos transformation is modeled as a pure * rotation and spin; zonal errors in the FK5 catalog are not * taken into account. * * 4) See also iauFk52h, iauFk5hz, iauHfk5z. * * * Reference: * * F.Mignard & M.Froeschle, Astron. Astrophys. 354, 732-739 (2000). * */ /*!\file hd2ae.c \fn void iauHd2ae (double ha, double dec, double phi, double *az, double *el) \ingroup SF \brief Equatorial to horizon coordinates. * Equatorial to horizon coordinates: transform hour angle and * declination to azimuth and altitude. * Notes: * * 1) All the arguments are angles in radians. * * 2) Azimuth is returned in the range 0-2pi; north is zero, and east * is +pi/2. Altitude is returned in the range +/- pi/2. * * 3) The latitude phi is pi/2 minus the angle between the Earth's * rotation axis and the adopted zenith. In many applications it * will be sufficient to use the published geodetic latitude of the * site. In very precise (sub-arcsecond) applications, phi can be * corrected for polar motion. * * 4) The returned azimuth az is with respect to the rotational north * pole, as opposed to the ITRS pole, and for sub-arcsecond * accuracy will need to be adjusted for polar motion if it is to * be with respect to north on a map of the Earth's surface. * * 5) Should the user wish to work with respect to the astronomical * zenith rather than the geodetic zenith, phi will need to be * adjusted for deflection of the vertical (often tens of * arcseconds), and the zero point of the hour angle ha will also * be affected. * * 6) The transformation is the same as Vh = Rz(pi)*Ry(pi/2-phi)*Ve, * where Vh and Ve are lefthanded unit vectors in the (az,el) and * (ha,dec) systems respectively and Ry and Rz are rotations about * first the y-axis and then the z-axis. (n.b. Rz(pi) simply * reverses the signs of the x and y components.) For efficiency, * the algorithm is written out rather than calling other utility * functions. For applications that require even greater * efficiency, additional savings are possible if constant terms * such as functions of latitude are computed once and for all. * * 7) Again for efficiency, no range checking of arguments is carried * out. @param[in] ha hour angle (local) @param[in] dec declination @param[in] phi site latitude @param[out] az azimuth @param[out] el altitude (informally, elevation) */ /*!\file hd2pa.c \fn double iauHd2pa (double ha, double dec, double phi) \brief Parallactic angle for a given hour angle and declination. \ingroup SF * Notes: * * 1) All the arguments are angles in radians. * * 2) The parallactic angle at a point in the sky is the position * angle of the vertical, i.e. the angle between the directions to * the north celestial pole and to the zenith respectively. * * 3) The result is returned in the range -pi to +pi. * * 4) At the pole itself a zero result is returned. * * 5) The latitude phi is pi/2 minus the angle between the Earth's * rotation axis and the adopted zenith. In many applications it * will be sufficient to use the published geodetic latitude of the * site. In very precise (sub-arcsecond) applications, phi can be * corrected for polar motion. * * 6) Should the user wish to work with respect to the astronomical * zenith rather than the geodetic zenith, phi will need to be * adjusted for deflection of the vertical (often tens of * arcseconds), and the zero point of the hour angle ha will also * be affected. * * Reference: * Smart, W.M., "Spherical Astronomy", Cambridge University Press, * 6th edition (Green, 1977), p49. @param[in] ha hour angle @param[in] dec declination @param[in] phi site latitudedeclination @return prallactic angle */ /*!\file hfk5z.c \fn void iauHfk5z(double rh, double dh, double date1, double date2, double *r5, double *d5, double *dr5, double *dd5) \ingroup SF \brief Transform a Hipparcos star position into FK5 J2000.0 * * Transform a Hipparcos star position into FK5 J2000.0, assuming * zero Hipparcos proper motion. * * * * \param[in] rh Hipparcos RA (radians) * \param[in] dh Hipparcos Dec (radians) * \param[in] date1 TDB date (Note 1) * \param[in] date2 TDB date (Note 1) * * All output parameters are FK5, equinox J2000.0, date date1+date2. * \param[out] r5 RA (radians) * \param[out] d5 Dec (radians) * \param[out] dr5 FK5 RA proper motion (rad/year, Note 4) * \param[out] dd5 Dec proper motion (rad/year, Note 4) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt. * * 3) The FK5 to Hipparcos transformation is modeled as a pure rotation * and spin; zonal errors in the FK5 catalogue are not taken into * account. * * 4) It was the intention that Hipparcos should be a close * approximation to an inertial frame, so that distant objects have * zero proper motion; such objects have (in general) non-zero * proper motion in FK5, and this function returns those fictitious * proper motions. * * 5) The position returned by this function is in the FK5 J2000.0 * reference system but at date date1+date2. * * 6) See also iauFk52h, iauH2fk5, iauFk5zhz. * * Reference: * * F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739. * */ /*!\file icrs2g.c \fn void iauIcrs2g ( double dr, double dd, double *dl, double *db ) \ingroup SR \brief Transformation from ICRS to Galactic Coordinates. * * * * \param[in] dr ICRS right ascension (radians) * \param[in] dd ICRS declination (radians) * * \param[in] dl galactic longitude (radians) * \param[in] db galactic latitude (radians) * * Notes: * * 1) The IAU 1958 system of Galactic coordinates was defined with * respect to the now obsolete reference system FK4 B1950.0. When * interpreting the system in a modern context, several factors have * to be taken into account: * * . The inclusion in FK4 positions of the E-terms of aberration. * * . The distortion of the FK4 proper motion system by differential * Galactic rotation. * * . The use of the B1950.0 equinox rather than the now-standard * J2000.0. * * . The frame bias between ICRS and the J2000.0 mean place system. * * The Hipparcos Catalogue (Perryman & ESA 1997) provides a rotation * matrix that transforms directly between ICRS and Galactic * coordinates with the above factors taken into account. The * matrix is derived from three angles, namely the ICRS coordinates * of the Galactic pole and the longitude of the ascending node of * the galactic equator on the ICRS equator. They are given in * degrees to five decimal places and for canonical purposes are * regarded as exact. In the Hipparcos Catalogue the matrix * elements are given to 10 decimal places (about 20 microarcsec). * In the present SOFA function the matrix elements have been * recomputed from the canonical three angles and are given to 30 * decimal places. * * 2) The inverse transformation is performed by the function iauG2icrs. * * * Reference: * Perryman M.A.C. & ESA, 1997, ESA SP-1200, The Hipparcos and Tycho * catalogues. Astrometric and photometric star catalogues * derived from the ESA Hipparcos Space Astrometry Mission. ESA * Publications Division, Noordwijk, Netherlands. * */ /*!\file ir.c \fn void iauIr(double r[3][3]) \ingroup VMSF \brief Initialize an r-matrix to the identity matrix. * * * * Returned: * \param[out] r r-matrix * */ /*!\file jd2cal.c \fn int iauJd2cal(double dj1, double dj2, int *iy, int *im, int *id, double *fd) \ingroup SF \brief Julian Date to Gregorian year, month, day, and fraction of a day. * * * * \param[in] dj1 Julian Date (Notes 1, 2) * \param[in] dj2 Julian Date (Notes 1, 2) * * \param[out] iy year * \param[out] im month * \param[out] id day * \param[out] fd fraction of day * * \return * status: * 0 = OK * -1 = unacceptable date (Note 3) * * Notes: * * 1) The earliest valid date is -68569.5 (-4900 March 1). The * largest value accepted is 1e9. * * 2) The Julian Date is apportioned in any convenient way between * the arguments dj1 and dj2. For example, JD=2450123.7 could * be expressed in any of these ways, among others: * * dj1 dj2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * 3) In early eras the conversion is from the "proleptic Gregorian * calendar"; no account is taken of the date(s) of adoption of * the Gregorian calendar, nor is the AD/BC numbering convention * observed. * * Reference: * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992), * Section 12.92 (p604). * */ /*!\file jdcalf.c \fn int iauJdcalf(int ndp, double dj1, double dj2, int iymdf[4]) \ingroup SF \brief Julian Date to Gregorian Calendar * * Julian Date to Gregorian Calendar, expressed in a form convenient * for formatting messages: rounded to a specified precision. * * * * \param[in] ndp number of decimal places of days in fraction * \param[in] dj1 dj1+dj2 = Julian Date (Note 1) * \param[in] dj2 dj1+dj2 = Julian Date (Note 1) * * \param[out] iymdf year, month, day, fraction in Gregorian * calendar * * \return * status: * -1 = date out of range * 0 = OK * +1 = NDP not 0-9 (interpreted as 0) * * Notes: * * 1) The Julian Date is apportioned in any convenient way between * the arguments dj1 and dj2. For example, JD=2450123.7 could * be expressed in any of these ways, among others: * * dj1 dj2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * 2) In early eras the conversion is from the "Proleptic Gregorian * Calendar"; no account is taken of the date(s) of adoption of * the Gregorian Calendar, nor is the AD/BC numbering convention * observed. * * 3) Refer to the function iauJd2cal. * * 4) NDP should be 4 or less if internal overflows are to be * avoided on machines which use 16-bit integers. * * * Reference: * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992), * Section 12.92 (p604). * */ /*!\file ld.c \fn void iauLd(double bm, double p[3], double q[3], double e[3], double em, double dlim, double p1[3]) \ingroup SF \brief Apply light deflection by a solar-system body * * Apply light deflection by a solar-system body, as part of * transforming coordinate direction into natural direction. * * * * \param[in] bm mass of the gravitating body (solar masses) * \param[in] p direction from observer to source (unit vector) * \param[in] q direction from body to source (unit vector) * \param[in] e direction from body to observer (unit vector) * \param[in] em distance from body to observer (au) * \param[in] dlim deflection limiter (Note 4) * * \param[out] p1 observer to deflected source (unit vector) * * Notes: * * 1) The algorithm is based on Expr. (70) in Klioner (2003) and * Expr. (7.63) in the Explanatory Supplement (Urban & Seidelmann * 2013), with some rearrangement to minimize the effects of machine * precision. * * 2) The mass parameter bm can, as required, be adjusted in order to * allow for such effects as quadrupole field. * * 3) The barycentric position of the deflecting body should ideally * correspond to the time of closest approach of the light ray to * the body. * * 4) The deflection limiter parameter dlim is phi^2/2, where phi is * the angular separation (in radians) between source and body at * which limiting is applied. As phi shrinks below the chosen * threshold, the deflection is artificially reduced, reaching zero * for phi = 0. * * 5) The returned vector p1 is not normalized, but the consequential * departure from unit magnitude is always negligible. * * 6) The arguments p and p1 can be the same array. * * 7) To accumulate total light deflection taking into account the * contributions from several bodies, call the present function for * each body in succession, in decreasing order of distance from the * observer. * * 8) For efficiency, validation is omitted. The supplied vectors must * be of unit magnitude, and the deflection limiter non-zero and * positive. * * References: * * Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to * the Astronomical Almanac, 3rd ed., University Science Books * (2013). * * Klioner, Sergei A., "A practical relativistic model for micro- * arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003). * * */ /*!\file ldn.c \fn void iauLdn(int n, iauLDBODY b[], double ob[3], double sc[3], double sn[3]) \ingroup SF \brief apply light deflection by multiple solar-system bodies * * For a star, apply light deflection by multiple solar-system bodies, * as part of transforming coordinate direction into natural direction. * * * * \param[in] n number of bodies (note 1) * \param[in] b data for each of the n bodies (Notes 1,2): * \param[in] bm mass of the body (solar masses, Note 3) * \param[in] dl deflection limiter (Note 4) * \param[in] pv barycentric PV of the body (au, au/day) * \param[in] ob barycentric position of the observer (au) * \param[in] sc observer to star coord direction (unit vector) * * \param[out] sn observer to deflected star (unit vector) * * 1) The array b contains n entries, one for each body to be * considered. If n = 0, no gravitational light deflection will be * applied, not even for the Sun. * * 2) The array b should include an entry for the Sun as well as for * any planet or other body to be taken into account. The entries * should be in the order in which the light passes the body. * * 3) In the entry in the b array for body i, the mass parameter * b[i].bm can, as required, be adjusted in order to allow for such * effects as quadrupole field. * * 4) The deflection limiter parameter b[i].dl is phi^2/2, where phi is * the angular separation (in radians) between star and body at * which limiting is applied. As phi shrinks below the chosen * threshold, the deflection is artificially reduced, reaching zero * for phi = 0. Example values suitable for a terrestrial * observer, together with masses, are as follows: * * body i b[i].bm b[i].dl * * Sun 1.0 6e-6 * Jupiter 0.00095435 3e-9 * Saturn 0.00028574 3e-10 * * 5) For cases where the starlight passes the body before reaching the * observer, the body is placed back along its barycentric track by * the light time from that point to the observer. For cases where * the body is "behind" the observer no such shift is applied. If * a different treatment is preferred, the user has the option of * instead using the iauLd function. Similarly, iauLd can be used * for cases where the source is nearby, not a star. * * 6) The returned vector sn is not normalized, but the consequential * departure from unit magnitude is always negligible. * * 7) The arguments sc and sn can be the same array. * * 8) For efficiency, validation is omitted. The supplied masses must * be greater than zero, the position and velocity vectors must be * right, and the deflection limiter greater than zero. * * Reference: * * Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to * the Astronomical Almanac, 3rd ed., University Science Books * (2013), Section 7.2.4. * * */ /*!\file ldsun.c \fn void iauLdsun(double p[3], double e[3], double em, double p1[3]) \ingroup SF \brief Deflection of starlight by the Sun. * * * * \param[in] p direction from observer to star (unit vector) * \param[in] e direction from Sun to observer (unit vector) * \param[in] em distance from Sun to observer (au) * * \param[out] p1 observer to deflected star (unit vector) * * Notes: * * 1) The source is presumed to be sufficiently distant that its * directions seen from the Sun and the observer are essentially * the same. * * 2) The deflection is restrained when the angle between the star and * the center of the Sun is less than about 9 arcsec, falling to * zero for zero separation. (The chosen threshold is within the * solar limb for all solar-system applications.) * * 3) The arguments p and p1 can be the same array. * * */ /*!\file lteceq.c \fn void iauLteceq(double epj, double dl, double db, double *dr, double *dd) \brief Transformation from ecliptic coordinates (mean equinox and ecliptic of date) to ICRS RA,Dec. \ingroup SF * * Transformation from ecliptic coordinates (mean equinox and ecliptic * of date) to ICRS RA,Dec, using a long-term precession model. * 1) No assumptions are made about whether the coordinates represent * starlight and embody astrometric effects such as parallax or * aberration. * * 2) The transformation is approximately that from ecliptic longitude * and latitude (mean equinox and ecliptic of date) to mean J2000.0 * right ascension and declination, with only frame bias (always * less than 25 mas) to disturb this classical picture. * * 3) The Vondrak et al. (2011, 2012) 400 millennia precession model * agrees with the IAU 2006 precession at J2000.0 and stays within * 100 microarcseconds during the 20th and 21st centuries. It is * accurate to a few arcseconds throughout the historical period, * worsening to a few tenths of a degree at the end of the * +/- 200,000 year time span. * * References: * * Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession * expressions, valid for long time intervals, Astron.Astrophys. 534, * A22 * * Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession * expressions, valid for long time intervals (Corrigendum), * Astron.Astrophys. 541, C1 @param[in] epj Julian epoch (TT) @param[in] dl ecliptic longitude (radians) @param[in] db ecliptic latitude (radians) @param[out] dr ICRS right ascension (radians) @param[out] dd ICRS declination (radians) */ /*!\file ltecm.c \fn void iauLtecm(double epj, double rm[3][3]) \ingroup SF \brief ICRS equatorial to ecliptic rotation matrix, long-term. * Notes: * * 1) The matrix is in the sense * * E_ep = rm x P_ICRS, * * where P_ICRS is a vector with respect to ICRS right ascension * and declination axes and E_ep is the same vector with respect to * the (inertial) ecliptic and equinox of epoch epj. * * 2) P_ICRS is a free vector, merely a direction, typically of unit * magnitude, and not bound to any particular spatial origin, such * as the Earth, Sun or SSB. No assumptions are made about whether * it represents starlight and embodies astrometric effects such as * parallax or aberration. The transformation is approximately that * between mean J2000.0 right ascension and declination and ecliptic * longitude and latitude, with only frame bias (always less than * 25 mas) to disturb this classical picture. * * 3) The Vondrak et al. (2011, 2012) 400 millennia precession model * agrees with the IAU 2006 precession at J2000.0 and stays within * 100 microarcseconds during the 20th and 21st centuries. It is * accurate to a few arcseconds throughout the historical period, * worsening to a few tenths of a degree at the end of the * +/- 200,000 year time span. @param[in] epj Julian epoch (TT) @param[out] rm IRCS to eclicptic rotation matrix */ /*!\file lteqec.c \fn void iauLteqec(double epj, double dr, double dd, double *dl, double *db) \ingroup SF \brief Transformation from ICRS equatorial coordinates to ecliptic coordinates * Transformation from ICRS equatorial coordinates to ecliptic * coordinates (mean equinox and ecliptic of date) using a long-term * 1) No assumptions are made about whether the coordinates represent * starlight and embody astrometric effects such as parallax or * aberration. * * 2) The transformation is approximately that from mean J2000.0 right * ascension and declination to ecliptic longitude and latitude * (mean equinox and ecliptic of date), with only frame bias (always * less than 25 mas) to disturb this classical picture. * * 3) The Vondrak et al. (2011, 2012) 400 millennia precession model * agrees with the IAU 2006 precession at J2000.0 and stays within * 100 microarcseconds during the 20th and 21st centuries. It is * accurate to a few arcseconds throughout the historical period, * worsening to a few tenths of a degree at the end of the * +/- 200,000 year time span. @param[in] epj Julian epoch (TT) @param[in] dr ICRS right ascension (radians) @param[in] dd ICRS declination (radians) @param[out] dl ecliptic longitude (radians) @param[out] db ecliptic latitude (radians) */ /*!\file ltp.c \fn void iauLtp(double epj, double rp[3][3]) \brief Long-term precession matrix. \ingroup SF * Notes: * * 1) The matrix is in the sense * * P_date = rp x P_J2000, * * where P_J2000 is a vector with respect to the J2000.0 mean * equator and equinox and P_date is the same vector with respect to * the equator and equinox of epoch epj. * * 2) The Vondrak et al. (2011, 2012) 400 millennia precession model * agrees with the IAU 2006 precession at J2000.0 and stays within * 100 microarcseconds during the 20th and 21st centuries. It is * accurate to a few arcseconds throughout the historical period, * worsening to a few tenths of a degree at the end of the * +/- 200,000 year time span. @param[in] epj Julian epoch (TT) @param[out] rp precession matrix, J2000.0 to date */ /*!\file ltpb.c \fn void iauLtpb(double epj, double rpb[3][3]) \brief Long-term precession matrix, including ICRS frame bias. \ingroup SF * Notes: * * 1) The matrix is in the sense * * P_date = rpb x P_ICRS, * * where P_ICRS is a vector in the Geocentric Celestial Reference * System, and P_date is the vector with respect to the Celestial * Intermediate Reference System at that date but with nutation * neglected. * * 2) A first order frame bias formulation is used, of sub- * microarcsecond accuracy compared with a full 3D rotation. * * 3) The Vondrak et al. (2011, 2012) 400 millennia precession model * agrees with the IAU 2006 precession at J2000.0 and stays within * 100 microarcseconds during the 20th and 21st centuries. It is * accurate to a few arcseconds throughout the historical period, * worsening to a few tenths of a degree at the end of the * +/- 200,000 year time span. @param[in] epj Julian epoch (TT) @param[out] rp precession-bias matrix, J2000.0 to date */ /*!\file ltpecl.c \fn void iauLtpecl(double epj, double vec[3]) \brief Long-term precession of the ecliptic. \ingroup SF * Notes: * * 1) The returned vector is with respect to the J2000.0 mean equator * and equinox. * * 2) The Vondrak et al. (2011, 2012) 400 millennia precession model * agrees with the IAU 2006 precession at J2000.0 and stays within * 100 microarcseconds during the 20th and 21st centuries. It is * accurate to a few arcseconds throughout the historical period, * worsening to a few tenths of a degree at the end of the * +/- 200,000 year time span. @param[in] epj Julian epoch (TT) @param[out] vec ecliptic pole unit vector */ /*!\file ltpequ.c \fn void iauLtpequ(double epj, double veq[3]) \brief Long-term precession of the equator. * Notes: * * 1) The returned vector is with respect to the J2000.0 mean equator * and equinox. * * 2) The Vondrak et al. (2011, 2012) 400 millennia precession model * agrees with the IAU 2006 precession at J2000.0 and stays within * 100 microarcseconds during the 20th and 21st centuries. It is * accurate to a few arcseconds throughout the historical period, * worsening to a few tenths of a degree at the end of the * +/- 200,000 year time span. @param[in] epj Julian epoch (TT) @param[out] veq equator pole unit vector */ /*!\file num00a.c \fn void iauNum00a(double date1, double date2, double rmatn[3][3]) \ingroup SF \brief Form the matrix of nutation for a given date * * Form the matrix of nutation for a given date, IAU 2000A model. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] rmatn nutation matrix * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The matrix operates in the sense V(true) = rmatn * V(mean), where * the p-vector V(true) is with respect to the true equatorial triad * of date and the p-vector V(mean) is with respect to the mean * equatorial triad of date. * * 3) A faster, but slightly less accurate result (about 1 mas), can be * obtained by using instead the iauNum00b function. * * Reference: * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992), * Section 3.222-3 (p114). * */ /*!\file num00b.c \fn void iauNum00b(double date1, double date2, double rmatn[3][3]) \ingroup SF \brief Form the matrix of nutation for a given date * * Form the matrix of nutation for a given date, IAU 2000B model. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] rmatn nutation matrix * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The matrix operates in the sense V(true) = rmatn * V(mean), where * the p-vector V(true) is with respect to the true equatorial triad * of date and the p-vector V(mean) is with respect to the mean * equatorial triad of date. * * 3) The present function is faster, but slightly less accurate (about * 1 mas), than the iauNum00a function. * * * Reference: * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992), * Section 3.222-3 (p114). * */ /*!\file num06a.c \fn void iauNum06a(double date1, double date2, double rmatn[3][3]) \ingroup SF \brief Form the matrix of nutation for a given date * * Form the matrix of nutation for a given date, IAU 2006/2000A model. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] rmatn nutation matrix * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The matrix operates in the sense V(true) = rmatn * V(mean), where * the p-vector V(true) is with respect to the true equatorial triad * of date and the p-vector V(mean) is with respect to the mean * equatorial triad of date. * * Reference: * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992), * Section 3.222-3 (p114). * */ /*!\file numat.c \fn void iauNumat(double epsa, double dpsi, double deps, double rmatn[3][3]) \ingroup SF \brief Form the matrix of nutation. * * * * \param[in] epsa mean obliquity of date (Note 1) * \param[in] dpsi nutation (Note 2) * \param[in] deps nutation (Note 2) * * \param[out] rmatn nutation matrix (Note 3) * * Notes: * * 1) The supplied mean obliquity epsa, must be consistent with the * precession-nutation models from which dpsi and deps were obtained. * * 2) The caller is responsible for providing the nutation components; * they are in longitude and obliquity, in radians and are with * respect to the equinox and ecliptic of date. * * 3) The matrix operates in the sense V(true) = rmatn * V(mean), * where the p-vector V(true) is with respect to the true * equatorial triad of date and the p-vector V(mean) is with * respect to the mean equatorial triad of date. * * * Reference: * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992), * Section 3.222-3 (p114). * */ /*!\file nut00a.c \fn void iauNut00a(double date1, double date2, double *dpsi, double *deps) \ingroup CM \brief Nutation, IAU 2000A model * * Nutation, IAU 2000A model (MHB2000 luni-solar and planetary nutation * with free core nutation omitted). * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] dpsi nutation, luni-solar + planetary (Note 2) * \param[out] deps nutation, luni-solar + planetary (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The nutation components in longitude and obliquity are in radians * and with respect to the equinox and ecliptic of date. The * obliquity at J2000.0 is assumed to be the Lieske et al. (1977) * value of 84381.448 arcsec. * * Both the luni-solar and planetary nutations are included. The * latter are due to direct planetary nutations and the * perturbations of the lunar and terrestrial orbits. * * 3) The function computes the MHB2000 nutation series with the * associated corrections for planetary nutations. It is an * implementation of the nutation part of the IAU 2000A precession- * nutation model, formally adopted by the IAU General Assembly in * 2000, namely MHB2000 (Mathews et al. 2002), but with the free * core nutation (FCN - see Note 4) omitted. * * 4) The full MHB2000 model also contains contributions to the * nutations in longitude and obliquity due to the free-excitation * of the free-core-nutation during the period 1979-2000. These FCN * terms, which are time-dependent and unpredictable, are NOT * included in the present function and, if required, must be * independently computed. With the FCN corrections included, the * present function delivers a pole which is at current epochs * accurate to a few hundred microarcseconds. The omission of FCN * introduces further errors of about that size. * * 5) The present function provides classical nutation. The MHB2000 * algorithm, from which it is adapted, deals also with (i) the * offsets between the GCRS and mean poles and (ii) the adjustments * in longitude and obliquity due to the changed precession rates. * These additional functions, namely frame bias and precession * adjustments, are supported by the SOFA functions iauBi00 and * iauPr00. * * 6) The MHB2000 algorithm also provides "total" nutations, comprising * the arithmetic sum of the frame bias, precession adjustments, * luni-solar nutation and planetary nutation. These total * nutations can be used in combination with an existing IAU 1976 * precession implementation, such as iauPmat76, to deliver GCRS- * to-true predictions of sub-mas accuracy at current dates. * However, there are three shortcomings in the MHB2000 model that * must be taken into account if more accurate or definitive results * are required (see Wallace 2002): * * (i) The MHB2000 total nutations are simply arithmetic sums, * yet in reality the various components are successive Euler * rotations. This slight lack of rigor leads to cross terms * that exceed 1 mas after a century. The rigorous procedure * is to form the GCRS-to-true rotation matrix by applying the * bias, precession and nutation in that order. * * (ii) Although the precession adjustments are stated to be with * respect to Lieske et al. (1977), the MHB2000 model does * not specify which set of Euler angles are to be used and * how the adjustments are to be applied. The most literal * and straightforward procedure is to adopt the 4-rotation * epsilon_0, psi_A, omega_A, xi_A option, and to add DPSIPR * to psi_A and DEPSPR to both omega_A and eps_A. * * (iii) The MHB2000 model predates the determination by Chapront * et al. (2002) of a 14.6 mas displacement between the * J2000.0 mean equinox and the origin of the ICRS frame. It * should, however, be noted that neglecting this displacement * when calculating star coordinates does not lead to a * 14.6 mas change in right ascension, only a small second- * order distortion in the pattern of the precession-nutation * effect. * * For these reasons, the SOFA functions do not generate the "total * nutations" directly, though they can of course easily be * generated by calling iauBi00, iauPr00 and the present function * and adding the results. * * 7) The MHB2000 model contains 41 instances where the same frequency * appears multiple times, of which 38 are duplicates and three are * triplicates. To keep the present code close to the original MHB * algorithm, this small inefficiency has not been corrected. * * * References: * * Chapront, J., Chapront-Touze, M. & Francou, G. 2002, * Astron.Astrophys. 387, 700 * * Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977, * Astron.Astrophys. 58, 1-16 * * Mathews, P.M., Herring, T.A., Buffet, B.A. 2002, J.Geophys.Res. * 107, B4. The MHB_2000 code itself was obtained on 9th September * 2002 from ftp//maia.usno.navy.mil/conv2000/chapter5/IAU2000A. * * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 * * Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, * Astron.Astrophys.Supp.Ser. 135, 111 * * Wallace, P.T., "Software for Implementing the IAU 2000 * Resolutions", in IERS Workshop 5.1 (2002) * */ /*!\file nut00b.c \fn void iauNut00b(double date1, double date2, double *dpsi, double *deps) \ingroup CM \brief Nutation, IAU 2000B model. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] dpsi nutation, luni-solar + planetary (Note 2) * \param[out] deps nutation, luni-solar + planetary (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The nutation components in longitude and obliquity are in radians * and with respect to the equinox and ecliptic of date. The * obliquity at J2000.0 is assumed to be the Lieske et al. (1977) * value of 84381.448 arcsec. (The errors that result from using * this function with the IAU 2006 value of 84381.406 arcsec can be * neglected.) * * The nutation model consists only of luni-solar terms, but * includes also a fixed offset which compensates for certain long- * period planetary terms (Note 7). * * 3) This function is an implementation of the IAU 2000B abridged * nutation model formally adopted by the IAU General Assembly in * 2000. The function computes the MHB_2000_SHORT luni-solar * nutation series (Luzum 2001), but without the associated * corrections for the precession rate adjustments and the offset * between the GCRS and J2000.0 mean poles. * * 4) The full IAU 2000A (MHB2000) nutation model contains nearly 1400 * terms. The IAU 2000B model (McCarthy & Luzum 2003) contains only * 77 terms, plus additional simplifications, yet still delivers * results of 1 mas accuracy at present epochs. This combination of * accuracy and size makes the IAU 2000B abridged nutation model * suitable for most practical applications. * * The function delivers a pole accurate to 1 mas from 1900 to 2100 * (usually better than 1 mas, very occasionally just outside * 1 mas). The full IAU 2000A model, which is implemented in the * function iauNut00a (q.v.), delivers considerably greater accuracy * at current dates; however, to realize this improved accuracy, * corrections for the essentially unpredictable free-core-nutation * (FCN) must also be included. * * 5) The present function provides classical nutation. The * MHB_2000_SHORT algorithm, from which it is adapted, deals also * with (i) the offsets between the GCRS and mean poles and (ii) the * adjustments in longitude and obliquity due to the changed * precession rates. These additional functions, namely frame bias * and precession adjustments, are supported by the SOFA functions * iauBi00 and iauPr00. * * 6) The MHB_2000_SHORT algorithm also provides "total" nutations, * comprising the arithmetic sum of the frame bias, precession * adjustments, and nutation (luni-solar + planetary). These total * nutations can be used in combination with an existing IAU 1976 * precession implementation, such as iauPmat76, to deliver GCRS- * to-true predictions of mas accuracy at current epochs. However, * for symmetry with the iauNut00a function (q.v. for the reasons), * the SOFA functions do not generate the "total nutations" * directly. Should they be required, they could of course easily * be generated by calling iauBi00, iauPr00 and the present function * and adding the results. * * 7) The IAU 2000B model includes "planetary bias" terms that are * fixed in size but compensate for long-period nutations. The * amplitudes quoted in McCarthy & Luzum (2003), namely * Dpsi = -1.5835 mas and Depsilon = +1.6339 mas, are optimized for * the "total nutations" method described in Note 6. The Luzum * (2001) values used in this SOFA implementation, namely -0.135 mas * and +0.388 mas, are optimized for the "rigorous" method, where * frame bias, precession and nutation are applied separately and in * that order. During the interval 1995-2050, the SOFA * implementation delivers a maximum error of 1.001 mas (not * including FCN). * * References: * * Lieske, J.H., Lederle, T., Fricke, W., Morando, B., "Expressions * for the precession quantities based upon the IAU /1976/ system of * astronomical constants", Astron.Astrophys. 58, 1-2, 1-16. (1977) * * Luzum, B., private communication, 2001 (Fortran code * MHB_2000_SHORT) * * McCarthy, D.D. & Luzum, B.J., "An abridged model of the * precession-nutation of the celestial pole", Cel.Mech.Dyn.Astron. * 85, 37-49 (2003) * * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., * Francou, G., Laskar, J., Astron.Astrophys. 282, 663-683 (1994) * */ /*!\file nut06a.c \fn void iauNut06a(double date1, double date2, double *dpsi, double *deps) \ingroup CM \brief IAU 2000A nutation with adjustments * * IAU 2000A nutation with adjustments to match the IAU 2006 * precession. * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] dpsi nutation, luni-solar + planetary (Note 2) * \param[out] deps nutation, luni-solar + planetary (Note 2) * * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The nutation components in longitude and obliquity are in radians * and with respect to the mean equinox and ecliptic of date, * IAU 2006 precession model (Hilton et al. 2006, Capitaine et al. * 2005). * * 3) The function first computes the IAU 2000A nutation, then applies * adjustments for (i) the consequences of the change in obliquity * from the IAU 1980 ecliptic to the IAU 2006 ecliptic and (ii) the * secular variation in the Earth's dynamical form factor J2. * * 4) The present function provides classical nutation, complementing * the IAU 2000 frame bias and IAU 2006 precession. It delivers a * pole which is at current epochs accurate to a few tens of * microarcseconds, apart from the free core nutation. * * References: * * Chapront, J., Chapront-Touze, M. & Francou, G. 2002, * Astron.Astrophys. 387, 700 * * Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977, * Astron.Astrophys. 58, 1-16 * * Mathews, P.M., Herring, T.A., Buffet, B.A. 2002, J.Geophys.Res. * 107, B4. The MHB_2000 code itself was obtained on 9th September * 2002 from ftp//maia.usno.navy.mil/conv2000/chapter5/IAU2000A. * * Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., * Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683 * * Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, * Astron.Astrophys.Supp.Ser. 135, 111 * * Wallace, P.T., "Software for Implementing the IAU 2000 * Resolutions", in IERS Workshop 5.1 (2002) * */ /*!\file nut80.c \fn void iauNut80(double date1, double date2, double *dpsi, double *deps) \ingroup CM \brief Nutation, IAU 1980 model. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] dpsi nutation in longitude (radians) * \param[out] deps nutation in obliquity (radians) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The nutation components are with respect to the ecliptic of * date. * * * Reference: * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992), * Section 3.222 (p111). * */ /*!\file nutm80.c \fn void iauNutm80(double date1, double date2, double rmatn[3][3]) \ingroup SF \brief Form the matrix of nutation for a given date, * * Form the matrix of nutation for a given date, IAU 1980 model. * * * * \param[in] date1 TDB date (Note 1) * \param[in] date2 TDB date (Note 1) * * \param[out] rmatn nutation matrix * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The matrix operates in the sense V(true) = rmatn * V(mean), * where the p-vector V(true) is with respect to the true * equatorial triad of date and the p-vector V(mean) is with * respect to the mean equatorial triad of date. * * */ /*!\file obl06.c \fn double iauObl06(double date1, double date2) \ingroup CM \brief Mean obliquity of the ecliptic * * Mean obliquity of the ecliptic, IAU 2006 precession model. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \return * obliquity of the ecliptic (radians, Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The result is the angle between the ecliptic and mean equator of * date date1+date2. * * Reference: * * Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351 * */ /*!\file obl80.c \fn double iauObl80(double date1, double date2) \ingroup CM \brief Mean obliquity of the ecliptic * * Mean obliquity of the ecliptic, IAU 1980 model. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \return * obliquity of the ecliptic (radians, Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The result is the angle between the ecliptic and mean equator of * date date1+date2. * * Reference: * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992), * Expression 3.222-1 (p114). * */ /*!\file p06e.c \fn void iauP06e(double date1, double date2, double *eps0, double *psia, double *oma, double *bpa, double *bqa, double *pia, double *bpia, double *epsa, double *chia, double *za, double *zetaa, double *thetaa, double *pa, double *gam, double *phi, double *psi) \ingroup CM \brief Precession angles * * Precession angles, IAU 2006, equinox based. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * \param[out] eps0 epsilon_0 \param[out] psia psi_A \param[out] oma omega_A \param[out] bpa P_A \param[out] bqa Q_A \param[out] pia pi_A \param[out] bpia Pi_A \param[out] epsa obliquity epsilon_A \param[out] chia chi_A \param[out] za z_A \param[out] zetaa zeta_A \param[out] thetaa theta_A \param[out] pa p_A \param[out] gam F-W angle gamma_J2000 \param[out] phi F-W angle phi_J2000 \param[out] psi F-W angle psi_J2000 * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) This function returns the set of equinox based angles for the * Capitaine et al. "P03" precession theory, adopted by the IAU in * 2006. The angles are set out in Table 1 of Hilton et al. (2006): * * eps0 epsilon_0 obliquity at J2000.0 * psia psi_A luni-solar precession * oma omega_A inclination of equator wrt J2000.0 ecliptic * bpa P_A ecliptic pole x, J2000.0 ecliptic triad * bqa Q_A ecliptic pole -y, J2000.0 ecliptic triad * pia pi_A angle between moving and J2000.0 ecliptics * bpia Pi_A longitude of ascending node of the ecliptic * epsa epsilon_A obliquity of the ecliptic * chia chi_A planetary precession * za z_A equatorial precession: -3rd 323 Euler angle * zetaa zeta_A equatorial precession: -1st 323 Euler angle * thetaa theta_A equatorial precession: 2nd 323 Euler angle * pa p_A general precession * gam gamma_J2000 J2000.0 RA difference of ecliptic poles * phi phi_J2000 J2000.0 codeclination of ecliptic pole * psi psi_J2000 longitude difference of equator poles, J2000.0 * * The returned values are all radians. * * 3) Hilton et al. (2006) Table 1 also contains angles that depend on * models distinct from the P03 precession theory itself, namely the * IAU 2000A frame bias and nutation. The quoted polynomials are * used in other SOFA functions: * * . iauXy06 contains the polynomial parts of the X and Y series. * * . iauS06 contains the polynomial part of the s+XY/2 series. * * . iauPfw06 implements the series for the Fukushima-Williams * angles that are with respect to the GCRS pole (i.e. the variants * that include frame bias). * * 4) The IAU resolution stipulated that the choice of parameterization * was left to the user, and so an IAU compliant precession * implementation can be constructed using various combinations of * the angles returned by the present function. * * 5) The parameterization used by SOFA is the version of the Fukushima- * Williams angles that refers directly to the GCRS pole. These * angles may be calculated by calling the function iauPfw06. SOFA * also supports the direct computation of the CIP GCRS X,Y by * series, available by calling iauXy06. * * 6) The agreement between the different parameterizations is at the * 1 microarcsecond level in the present era. * * 7) When constructing a precession formulation that refers to the GCRS * pole rather than the dynamical pole, it may (depending on the * choice of angles) be necessary to introduce the frame bias * explicitly. * * 8) It is permissible to re-use the same variable in the returned * arguments. The quantities are stored in the stated order. * * Reference: * * Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351 * * */ /*!\file p2pv.c \fn void iauP2pv(double p[3], double pv[2][3]) \ingroup VMSF \brief Extend a p-vector to a pv-vector by appending a zero velocity. * * * * \param[in] p p-vector * * \param[out] pv pv-vector * * */ /*!\file p2s.c \fn void iauP2s(double p[3], double *theta, double *phi, double *r) \ingroup VMSF \brief P-vector to spherical polar coordinates. * * * * \param[in] p p-vector * * \param[out] theta longitude angle (radians) * \param[out] phi latitude angle (radians) * \param[out] r radial distance * * Notes: * * 1) If P is null, zero theta, phi and r are returned. * * 2) At either pole, zero theta is returned. * * */ /*!\file pap.c \fn double iauPap(double a[3], double b[3]) \ingroup VMSF \brief Position-angle from two p-vectors. * * * * \param[in] a direction of reference point * \param[in] b direction of point whose PA is required * * \return * position angle of b with respect to a (radians) * * Notes: * * 1) The result is the position angle, in radians, of direction b with * respect to direction a. It is in the range -pi to +pi. The * sense is such that if b is a small distance "north" of a the * position angle is approximately zero, and if b is a small * distance "east" of a the position angle is approximately +pi/2. * * 2) The vectors a and b need not be of unit length. * * 3) Zero is returned if the two directions are the same or if either * vector is null. * * 4) If vector a is at a pole, the result is ill-defined. * * */ /*!\file pas.c \fn double iauPas(double al, double ap, double bl, double bp) \ingroup VMSF \brief Position-angle from spherical coordinates. * * * * \param[in] al longitude of point A (e.g. RA) in radians * \param[in] ap latitude of point A (e.g. Dec) in radians * \param[in] bl longitude of point B * \param[in] bp latitude of point B * * \return * position angle of B with respect to A * * Notes: * * 1) The result is the bearing (position angle), in radians, of point * B with respect to point A. It is in the range -pi to +pi. The * sense is such that if B is a small distance "east" of point A, * the bearing is approximately +pi/2. * * 2) Zero is returned if the two points are coincident. * */ /*!\file pb06.c \fn void iauPb06(double date1, double date2, double *bzeta, double *bz, double *btheta) \ingroup SF \brief forms three Euler angles which implement general precession from epoch J2000.0, * * This function forms three Euler angles which implement general * precession from epoch J2000.0, using the IAU 2006 model. Frame * bias (the offset between ICRS and mean J2000.0) is included. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] bzeta 1st rotation: radians cw around z * \param[out] bz 3rd rotation: radians cw around z * \param[out] btheta 2nd rotation: radians ccw around y * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The traditional accumulated precession angles zeta_A, z_A, * theta_A cannot be obtained in the usual way, namely through * polynomial expressions, because of the frame bias. The latter * means that two of the angles undergo rapid changes near this * date. They are instead the results of decomposing the * precession-bias matrix obtained by using the Fukushima-Williams * method, which does not suffer from the problem. The * decomposition returns values which can be used in the * conventional formulation and which include frame bias. * * 3) The three angles are returned in the conventional order, which * is not the same as the order of the corresponding Euler * rotations. The precession-bias matrix is * R_3(-z) x R_2(+theta) x R_3(-zeta). * * 4) Should zeta_A, z_A, theta_A angles be required that do not * contain frame bias, they are available by calling the SOFA * function iauP06e. * * */ /*!\file pdp.c \fn double iauPdp(double a[3], double b[3]) \ingroup VMSF \brief p-vector inner (=scalar=dot) product. * * * * \param[in] a first p-vector * \param[in] b second p-vector * * \return * a . b * */ /*!\file pfw06.c \fn void iauPfw06(double date1, double date2, double *gamb, double *phib, double *psib, double *epsa) \ingroup CM \brief Precession angles, IAU 2006 (Fukushima-Williams 4-angle formulation). * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] gamb F-W angle gamma_bar (radians) * \param[out] phib F-W angle phi_bar (radians) * \param[out] psib F-W angle psi_bar (radians) * \param[out] epsa F-W angle epsilon_A (radians) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) Naming the following points: * * e = J2000.0 ecliptic pole, * p = GCRS pole, * E = mean ecliptic pole of date, * and P = mean pole of date, * * the four Fukushima-Williams angles are as follows: * * gamb = gamma_bar = epE * phib = phi_bar = pE * psib = psi_bar = pEP * epsa = epsilon_A = EP * * 3) The matrix representing the combined effects of frame bias and * precession is: * * PxB = R_1(-epsa).R_3(-psib).R_1(phib).R_3(gamb) * * 4) The matrix representing the combined effects of frame bias, * precession and nutation is simply: * * NxPxB = R_1(-epsa-dE).R_3(-psib-dP).R_1(phib).R_3(gamb) * * where dP and dE are the nutation components with respect to the * ecliptic of date. * * Reference: * * Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351 * * */ /*!\file plan94.c \fn int iauPlan94(double date1, double date2, int np, double pv[2][3]) \ingroup SF \brief Approximate heliocentric position and velocity of a planet. * * * * Approximate heliocentric position and velocity of a nominated major * planet: Mercury, Venus, EMB, Mars, Jupiter, Saturn, Uranus or * Neptune (but not the Earth itself). * * \param[in] date1 TDB date part A (Note 1) * \param[in] date2 TDB date part B (Note 1) * \param[in] np planet (1=Mercury, 2=Venus, 3=EMB, 4=Mars, * 5=Jupiter, 6=Saturn, 7=Uranus, 8=Neptune) * * \param[out] pv planet p,v (heliocentric, J2000.0, AU,AU/d) * * \return * status: -1 = illegal NP (outside 1-8) * 0 = OK * +1 = warning: year outside 1000-3000 * +2 = warning: failed to converge * * Notes: * * 1) The date date1+date2 is in the TDB time scale (in practice TT can * be used) and is a Julian Date, apportioned in any convenient way * between the two arguments. For example, JD(TDB)=2450123.7 could * be expressed in any of these ways, among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in cases * where the loss of several decimal digits of resolution is * acceptable. The J2000 method is best matched to the way the * argument is handled internally and will deliver the optimum * resolution. The MJD method and the date & time methods are both * good compromises between resolution and convenience. The limited * accuracy of the present algorithm is such that any of the methods * is satisfactory. * * 2) If an np value outside the range 1-8 is supplied, an error status * (function value -1) is returned and the pv vector set to zeroes. * * 3) For np=3 the result is for the Earth-Moon Barycenter. To obtain * the heliocentric position and velocity of the Earth, use instead * the SOFA function iauEpv00. * * 4) On successful return, the array pv contains the following: * * pv[0][0] x } * pv[0][1] y } heliocentric position, AU * pv[0][2] z } * * pv[1][0] xdot } * pv[1][1] ydot } heliocentric velocity, AU/d * pv[1][2] zdot } * * The reference frame is equatorial and is with respect to the * mean equator and equinox of epoch J2000.0. * * 5) The algorithm is due to J.L. Simon, P. Bretagnon, J. Chapront, * M. Chapront-Touze, G. Francou and J. Laskar (Bureau des * Longitudes, Paris, France). From comparisons with JPL * ephemeris DE102, they quote the following maximum errors * over the interval 1800-2050: * * L (arcsec) B (arcsec) R (km) * * Mercury 4 1 300 * Venus 5 1 800 * EMB 6 1 1000 * Mars 17 1 7700 * Jupiter 71 5 76000 * Saturn 81 13 267000 * Uranus 86 7 712000 * Neptune 11 1 253000 * * Over the interval 1000-3000, they report that the accuracy is no * worse than 1.5 times that over 1800-2050. Outside 1000-3000 the * accuracy declines. * * Comparisons of the present function with the JPL DE200 ephemeris * give the following RMS errors over the interval 1960-2025: * * position (km) velocity (m/s) * * Mercury 334 0.437 * Venus 1060 0.855 * EMB 2010 0.815 * Mars 7690 1.98 * Jupiter 71700 7.70 * Saturn 199000 19.4 * Uranus 564000 16.4 * Neptune 158000 14.4 * * Comparisons against DE200 over the interval 1800-2100 gave the * following maximum absolute differences. (The results using * DE406 were essentially the same.) * * L (arcsec) B (arcsec) R (km) Rdot (m/s) * * Mercury 7 1 500 0.7 * Venus 7 1 1100 0.9 * EMB 9 1 1300 1.0 * Mars 26 1 9000 2.5 * Jupiter 78 6 82000 8.2 * Saturn 87 14 263000 24.6 * Uranus 86 7 661000 27.4 * Neptune 11 2 248000 21.4 * * 6) The present SOFA re-implementation of the original Simon et al. * Fortran code differs from the original in the following respects: * * * C instead of Fortran. * * * The date is supplied in two parts. * * * The result is returned only in equatorial Cartesian form; * the ecliptic longitude, latitude and radius vector are not * returned. * * * The result is in the J2000.0 equatorial frame, not ecliptic. * * * More is done in-line: there are fewer calls to subroutines. * * * Different error/warning status values are used. * * * A different Kepler's-equation-solver is used (avoiding * use of double precision complex). * * * Polynomials in t are nested to minimize rounding errors. * * * Explicit double constants are used to avoid mixed-mode * expressions. * * None of the above changes affects the result significantly. * * 7) The returned status indicates the most serious condition * encountered during execution of the function. Illegal np is * considered the most serious, overriding failure to converge, * which in turn takes precedence over the remote date warning. * * * Reference: Simon, J.L, Bretagnon, P., Chapront, J., * Chapront-Touze, M., Francou, G., and Laskar, J., * Astron. Astrophys. 282, 663 (1994). * */ /*!\file pm.c \fn double iauPm(double p[3]) \ingroup VMSF \brief Modulus of p-vector. * * * * \param[in] p p-vector * * \return * modulus * */ /*!\file pmat00.c \fn void iauPmat00(double date1, double date2, double rbp[3][3]) \ingroup SF \brief Precession matrix from GCRS to specified date. * * Precession matrix (including frame bias) from GCRS to a specified * date, IAU 2000 model. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] rbp double[3][3] bias-precession matrix (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The matrix operates in the sense V(date) = rbp * V(GCRS), where * the p-vector V(GCRS) is with respect to the Geocentric Celestial * Reference System (IAU, 2000) and the p-vector V(date) is with * respect to the mean equatorial triad of the given date. * * * Reference: * * IAU: Trans. International Astronomical Union, Vol. XXIVB; Proc. * 24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6. * (2000) * */ /*!\file pmat06.c \fn void iauPmat06(double date1, double date2, double rbp[3][3]) \ingroup SF \brief Precession matrix from GCRS to a specified date. * * Precession matrix (including frame bias) from GCRS to a specified * date, IAU 2006 model. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] rbp bias-precession matrix (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The matrix operates in the sense V(date) = rbp * V(GCRS), where * the p-vector V(GCRS) is with respect to the Geocentric Celestial * Reference System (IAU, 2000) and the p-vector V(date) is with * respect to the mean equatorial triad of the given date. * * * References: * * Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 * * Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 * */ /*!\file pmat76.c \fn void iauPmat76(double date1, double date2, double rmatp[3][3]) \ingroup SF \brief Precession matrix from J2000.0 to a specified date * * Precession matrix from J2000.0 to a specified date, IAU 1976 model. * * * * \param[in] date1 ending date, TT (Note 1) * \param[in] date2 ending date, TT (Note 1) * * \param[out] rmatp precession matrix, J2000.0 -> date1+date2 * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The matrix operates in the sense V(date) = RMATP * V(J2000), * where the p-vector V(J2000) is with respect to the mean * equatorial triad of epoch J2000.0 and the p-vector V(date) * is with respect to the mean equatorial triad of the given * date. * * 3) Though the matrix method itself is rigorous, the precession * angles are expressed through canonical polynomials which are * valid only for a limited time span. In addition, the IAU 1976 * precession rate is known to be imperfect. The absolute accuracy * of the present formulation is better than 0.1 arcsec from * 1960AD to 2040AD, better than 1 arcsec from 1640AD to 2360AD, * and remains below 3 arcsec for the whole of the period * 500BC to 3000AD. The errors exceed 10 arcsec outside the * range 1200BC to 3900AD, exceed 100 arcsec outside 4200BC to * 5600AD and exceed 1000 arcsec outside 6800BC to 8200AD. * * References: * * Lieske, J.H., 1979, Astron.Astrophys. 73, 282. * equations (6) & (7), p283. * * Kaplan,G.H., 1981. USNO circular no. 163, pA2. * */ /*!\file pmp.c \fn void iauPmp(double a[3], double b[3], double amb[3]) \ingroup VMSF \brief P-vector subtraction. * * * * \param[in] a first p-vector * \param[in] b second p-vector * * \param[out] amb a - b * * Note: * It is permissible to re-use the same array for any of the * arguments. * */ /*!\file pmpx.c \fn void iauPmpx(double rc, double dc, double pr, double pd, double px, double rv, double pmt, double pob[3], double pco[3]) \ingroup SF \brief Proper motion and parallax. * * * * \param[in] rc ICRS RA,Dec at catalog epoch (radians) * \param[in] dc ICRS RA,Dec at catalog epoch (radians) * \param[in] pr RA proper motion (radians/year; Note 1) * \param[in] pd Dec proper motion (radians/year) * \param[in] px parallax (arcsec) * \param[in] rv radial velocity (km/s, +ve if receding) * \param[in] pmt proper motion time interval (SSB, Julian years) * \param[in] pob SSB to observer vector (au) * * \param[out] pco coordinate direction (BCRS unit vector) * * Notes: * * 1) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt. * * 2) The proper motion time interval is for when the starlight * reaches the solar system barycenter. * * 3) To avoid the need for iteration, the Roemer effect (i.e. the * small annual modulation of the proper motion coming from the * changing light time) is applied approximately, using the * direction of the star at the catalog epoch. * * References: * * 1984 Astronomical Almanac, pp B39-B41. * * Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to * the Astronomical Almanac, 3rd ed., University Science Books * (2013), Section 7.2. * * */ /*!\file pmsafe.c \fn int iauPmsafe(double ra1, double dec1, double pmr1, double pmd1, double px1, double rv1, double ep1a, double ep1b, double ep2a, double ep2b, double *ra2, double *dec2, double *pmr2, double *pmd2, double *px2, double *rv2) \ingroup SF \brief Star proper motion. * * Star proper motion: update star catalog data for space motion, with * special handling to handle the zero parallax case. * * * * \param[in] ra1 right ascension (radians), before * \param[in] dec1 declination (radians), before * \param[in] pmr1 RA proper motion (radians/year), before * \param[in] pmd1 Dec proper motion (radians/year), before * \param[in] px1 parallax (arcseconds), before * \param[in] rv1 radial velocity (km/s, +ve = receding), before * \param[in] ep1a "before" epoch, part A (Note 1) * \param[in] ep1b "before" epoch, part B (Note 1) * \param[in] ep2a "after" epoch, part A (Note 1) * \param[in] ep2b "after" epoch, part B (Note 1) * * \param[out] ra2 right ascension (radians), after * \param[out] dec2 declination (radians), after * \param[out] pmr2 RA proper motion (radians/year), after * \param[out] pmd2 Dec proper motion (radians/year), after * \param[out] px2 parallax (arcseconds), after * \param[out] rv2 radial velocity (km/s, +ve = receding), after * * \return * status: * -1 = system error (should not occur) * 0 = no warnings or errors * 1 = distance overridden (Note 6) * 2 = excessive velocity (Note 7) * 4 = solution didn't converge (Note 8) * else = binary logical OR of the above warnings * * Notes: * * 1) The starting and ending TDB epochs ep1a+ep1b and ep2a+ep2b are * Julian Dates, apportioned in any convenient way between the two * parts (A and B). For example, JD(TDB)=2450123.7 could be * expressed in any of these ways, among others: * * epNa epNb * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in cases * where the loss of several decimal digits of resolution is * acceptable. The J2000 method is best matched to the way the * argument is handled internally and will deliver the optimum * resolution. The MJD method and the date & time methods are both * good compromises between resolution and convenience. * * 2) In accordance with normal star-catalog conventions, the object's * right ascension and declination are freed from the effects of * secular aberration. The frame, which is aligned to the catalog * equator and equinox, is Lorentzian and centered on the SSB. * * The proper motions are the rate of change of the right ascension * and declination at the catalog epoch and are in radians per TDB * Julian year. * * The parallax and radial velocity are in the same frame. * * 3) Care is needed with units. The star coordinates are in radians * and the proper motions in radians per Julian year, but the * parallax is in arcseconds. * * 4) The RA proper motion is in terms of coordinate angle, not true * angle. If the catalog uses arcseconds for both RA and Dec proper * motions, the RA proper motion will need to be divided by cos(Dec) * before use. * * 5) Straight-line motion at constant speed, in the inertial frame, is * assumed. * * 6) An extremely small (or zero or negative) parallax is overridden * to ensure that the object is at a finite but very large distance, * but not so large that the proper motion is equivalent to a large * but safe speed (about 0.1c using the chosen constant). A warning * status of 1 is added to the status if this action has been taken. * * 7) If the space velocity is a significant fraction of c (see the * constant VMAX in the function iauStarpv), it is arbitrarily set * to zero. When this action occurs, 2 is added to the status. * * 8) The relativistic adjustment carried out in the iauStarpv function * involves an iterative calculation. If the process fails to * converge within a set number of iterations, 4 is added to the * status. * * */ /*!\file pn.c \fn void iauPn(double p[3], double *r, double u[3]) \ingroup VMSF \brief Convert a p-vector into modulus and unit vector. * * * * \param[in] p p-vector * * \param[out] r modulus * \param[out] u unit vector * * Notes: * * 1) If p is null, the result is null. Otherwise the result is a unit * vector. * * 2) It is permissible to re-use the same array for any of the * arguments. * * */ /*!\file pn00.c \fn void iauPn00(double date1, double date2, double dpsi, double deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]) \ingroup SF \brief Precession-nutation, IAU 2000 model * * Precession-nutation, IAU 2000 model: a multi-purpose function, * supporting classical (equinox-based) use directly and CIO-based * use indirectly. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * \param[in] dpsi nutation (Note 2) * \param[in] deps nutation (Note 2) * * \param[out] epsa mean obliquity (Note 3) * \param[out] rb frame bias matrix (Note 4) * \param[out] rp precession matrix (Note 5) * \param[out] rbp bias-precession matrix (Note 6) * \param[out] rn nutation matrix (Note 7) * \param[out] rbpn GCRS-to-true matrix (Note 8) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The caller is responsible for providing the nutation components; * they are in longitude and obliquity, in radians and are with * respect to the equinox and ecliptic of date. For high-accuracy * applications, free core nutation should be included as well as * any other relevant corrections to the position of the CIP. * * 3) The returned mean obliquity is consistent with the IAU 2000 * precession-nutation models. * * 4) The matrix rb transforms vectors from GCRS to J2000.0 mean * equator and equinox by applying frame bias. * * 5) The matrix rp transforms vectors from J2000.0 mean equator and * equinox to mean equator and equinox of date by applying * precession. * * 6) The matrix rbp transforms vectors from GCRS to mean equator and * equinox of date by applying frame bias then precession. It is * the product rp x rb. * * 7) The matrix rn transforms vectors from mean equator and equinox of * date to true equator and equinox of date by applying the nutation * (luni-solar + planetary). * * 8) The matrix rbpn transforms vectors from GCRS to true equator and * equinox of date. It is the product rn x rbp, applying frame * bias, precession and nutation in that order. * * 9) It is permissible to re-use the same array in the returned * arguments. The arrays are filled in the order given. * * * Reference: * * Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., * "Expressions for the Celestial Intermediate Pole and Celestial * Ephemeris Origin consistent with the IAU 2000A precession- * nutation model", Astron.Astrophys. 400, 1145-1154 (2003) * * n.b. The celestial ephemeris origin (CEO) was renamed "celestial * intermediate origin" (CIO) by IAU 2006 Resolution 2. * */ /*!\file pn00a.c \fn void iauPn00a(double date1, double date2, double *dpsi, double *deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]) \ingroup SF \brief Precession-nutation, IAU 2000A model * * Precession-nutation, IAU 2000A model: a multi-purpose function, * supporting classical (equinox-based) use directly and CIO-based * use indirectly. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] dpsi nutation (Note 2) * \param[out] deps nutation (Note 2) * \param[out] epsa mean obliquity (Note 3) * \param[out] rb frame bias matrix (Note 4) * \param[out] rp precession matrix (Note 5) * \param[out] rbp bias-precession matrix (Note 6) * \param[out] rn nutation matrix (Note 7) * \param[out] rbpn GCRS-to-true matrix (Notes 8,9) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The nutation components (luni-solar + planetary, IAU 2000A) in * longitude and obliquity are in radians and with respect to the * equinox and ecliptic of date. Free core nutation is omitted; * for the utmost accuracy, use the iauPn00 function, where the * nutation components are caller-specified. For faster but * slightly less accurate results, use the iauPn00b function. * * 3) The mean obliquity is consistent with the IAU 2000 precession. * * 4) The matrix rb transforms vectors from GCRS to J2000.0 mean * equator and equinox by applying frame bias. * * 5) The matrix rp transforms vectors from J2000.0 mean equator and * equinox to mean equator and equinox of date by applying * precession. * * 6) The matrix rbp transforms vectors from GCRS to mean equator and * equinox of date by applying frame bias then precession. It is * the product rp x rb. * * 7) The matrix rn transforms vectors from mean equator and equinox * of date to true equator and equinox of date by applying the * nutation (luni-solar + planetary). * * 8) The matrix rbpn transforms vectors from GCRS to true equator and * equinox of date. It is the product rn x rbp, applying frame * bias, precession and nutation in that order. * * 9) The X,Y,Z coordinates of the IAU 2000A Celestial Intermediate * Pole are elements (3,1-3) of the GCRS-to-true matrix, * i.e. rbpn[2][0-2]. * * 10) It is permissible to re-use the same array in the returned * arguments. The arrays are filled in the order given. * * * Reference: * * Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., * "Expressions for the Celestial Intermediate Pole and Celestial * Ephemeris Origin consistent with the IAU 2000A precession- * nutation model", Astron.Astrophys. 400, 1145-1154 (2003) * * n.b. The celestial ephemeris origin (CEO) was renamed "celestial * intermediate origin" (CIO) by IAU 2006 Resolution 2. * */ /*!\file pn00b.c \fn void iauPn00b(double date1, double date2, double *dpsi, double *deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]) \ingroup SF \brief Precession-nutation, IAU 2000B model * * Precession-nutation, IAU 2000B model: a multi-purpose function, * supporting classical (equinox-based) use directly and CIO-based * use indirectly. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] dpsi nutation (Note 2) * \param[out] deps nutation (Note 2) * \param[out] epsa mean obliquity (Note 3) * \param[out] rb frame bias matrix (Note 4) * \param[out] rp precession matrix (Note 5) * \param[out] rbp bias-precession matrix (Note 6) * \param[out] rn nutation matrix (Note 7) * \param[out] rbpn GCRS-to-true matrix (Notes 8,9) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The nutation components (luni-solar + planetary, IAU 2000B) in * longitude and obliquity are in radians and with respect to the * equinox and ecliptic of date. For more accurate results, but * at the cost of increased computation, use the iauPn00a function. * For the utmost accuracy, use the iauPn00 function, where the * nutation components are caller-specified. * * 3) The mean obliquity is consistent with the IAU 2000 precession. * * 4) The matrix rb transforms vectors from GCRS to J2000.0 mean * equator and equinox by applying frame bias. * * 5) The matrix rp transforms vectors from J2000.0 mean equator and * equinox to mean equator and equinox of date by applying * precession. * * 6) The matrix rbp transforms vectors from GCRS to mean equator and * equinox of date by applying frame bias then precession. It is * the product rp x rb. * * 7) The matrix rn transforms vectors from mean equator and equinox * of date to true equator and equinox of date by applying the * nutation (luni-solar + planetary). * * 8) The matrix rbpn transforms vectors from GCRS to true equator and * equinox of date. It is the product rn x rbp, applying frame * bias, precession and nutation in that order. * * 9) The X,Y,Z coordinates of the IAU 2000B Celestial Intermediate * Pole are elements (3,1-3) of the GCRS-to-true matrix, * i.e. rbpn[2][0-2]. * * 10) It is permissible to re-use the same array in the returned * arguments. The arrays are filled in the stated order. * * * Reference: * * Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., * "Expressions for the Celestial Intermediate Pole and Celestial * Ephemeris Origin consistent with the IAU 2000A precession- * nutation model", Astron.Astrophys. 400, 1145-1154 (2003). * * n.b. The celestial ephemeris origin (CEO) was renamed "celestial * intermediate origin" (CIO) by IAU 2006 Resolution 2. * */ /*!\file pn06.c \fn void iauPn06(double date1, double date2, double dpsi, double deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]) \ingroup SF \brief Precession-nutation, IAU 2006 model * * Precession-nutation, IAU 2006 model: a multi-purpose function, * supporting classical (equinox-based) use directly and CIO-based use * indirectly. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * \param[in] dpsi nutation (Note 2) * \param[in] deps nutation (Note 2) * * \param[out] epsa mean obliquity (Note 3) * \param[out] rb frame bias matrix (Note 4) * \param[out] rp precession matrix (Note 5) * \param[out] rbp bias-precession matrix (Note 6) * \param[out] rn nutation matrix (Note 7) * \param[out] rbpn GCRS-to-true matrix (Note 8) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The caller is responsible for providing the nutation components; * they are in longitude and obliquity, in radians and are with * respect to the equinox and ecliptic of date. For high-accuracy * applications, free core nutation should be included as well as * any other relevant corrections to the position of the CIP. * * 3) The returned mean obliquity is consistent with the IAU 2006 * precession. * * 4) The matrix rb transforms vectors from GCRS to J2000.0 mean * equator and equinox by applying frame bias. * * 5) The matrix rp transforms vectors from J2000.0 mean equator and * equinox to mean equator and equinox of date by applying * precession. * * 6) The matrix rbp transforms vectors from GCRS to mean equator and * equinox of date by applying frame bias then precession. It is * the product rp x rb. * * 7) The matrix rn transforms vectors from mean equator and equinox * of date to true equator and equinox of date by applying the * nutation (luni-solar + planetary). * * 8) The matrix rbpn transforms vectors from GCRS to true equator and * equinox of date. It is the product rn x rbp, applying frame * bias, precession and nutation in that order. * * 9) The X,Y,Z coordinates of the Celestial Intermediate Pole are * elements (3,1-3) of the GCRS-to-true matrix, i.e. rbpn[2][0-2]. * * 10) It is permissible to re-use the same array in the returned * arguments. The arrays are filled in the stated order. * * * References: * * Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 * * Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 * */ /*!\file pn06a.c \fn void iauPn06a(double date1, double date2, double *dpsi, double *deps, double *epsa, double rb[3][3], double rp[3][3], double rbp[3][3], double rn[3][3], double rbpn[3][3]) \ingroup SF \brief Precession-nutation, IAU 2006/2000A models * * Precession-nutation, IAU 2006/2000A models: a multi-purpose function, * supporting classical (equinox-based) use directly and CIO-based use * indirectly. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] dpsi nutation (Note 2) * \param[out] deps nutation (Note 2) * \param[out] epsa mean obliquity (Note 3) * \param[out] rb frame bias matrix (Note 4) * \param[out] rp precession matrix (Note 5) * \param[out] rbp bias-precession matrix (Note 6) * \param[out] rn nutation matrix (Note 7) * \param[out] rbpn GCRS-to-true matrix (Notes 8,9) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The nutation components (luni-solar + planetary, IAU 2000A) in * longitude and obliquity are in radians and with respect to the * equinox and ecliptic of date. Free core nutation is omitted; * for the utmost accuracy, use the iauPn06 function, where the * nutation components are caller-specified. * * 3) The mean obliquity is consistent with the IAU 2006 precession. * * 4) The matrix rb transforms vectors from GCRS to mean J2000.0 by * applying frame bias. * * 5) The matrix rp transforms vectors from mean J2000.0 to mean of * date by applying precession. * * 6) The matrix rbp transforms vectors from GCRS to mean of date by * applying frame bias then precession. It is the product rp x rb. * * 7) The matrix rn transforms vectors from mean of date to true of * date by applying the nutation (luni-solar + planetary). * * 8) The matrix rbpn transforms vectors from GCRS to true of date * (CIP/equinox). It is the product rn x rbp, applying frame bias, * precession and nutation in that order. * * 9) The X,Y,Z coordinates of the IAU 2006/2000A Celestial * Intermediate Pole are elements (3,1-3) of the GCRS-to-true * matrix, i.e. rbpn[2][0-2]. * * 10) It is permissible to re-use the same array in the returned * arguments. The arrays are filled in the stated order. * * * Reference: * * Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 * */ /*!\file pnm00a.c \fn void iauPnm00a(double date1, double date2, double rbpn[3][3]) \ingroup SF \brief Form the matrix of precession-nutation * * Form the matrix of precession-nutation for a given date (including * frame bias), equinox-based, IAU 2000A model. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] rbpn classical NPB matrix (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The matrix operates in the sense V(date) = rbpn * V(GCRS), where * the p-vector V(date) is with respect to the true equatorial triad * of date date1+date2 and the p-vector V(GCRS) is with respect to * the Geocentric Celestial Reference System (IAU, 2000). * * 3) A faster, but slightly less accurate result (about 1 mas), can be * obtained by using instead the iauPnm00b function. * * * Reference: * * IAU: Trans. International Astronomical Union, Vol. XXIVB; Proc. * 24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6. * (2000) * */ /*!\file pnm00b.c \fn void iauPnm00b(double date1, double date2, double rbpn[3][3]) \ingroup SF \brief Form the matrix of precession-nutation * * Form the matrix of precession-nutation for a given date (including * frame bias), equinox-based, IAU 2000B model. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] rbpn bias-precession-nutation matrix (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The matrix operates in the sense V(date) = rbpn * V(GCRS), where * the p-vector V(date) is with respect to the true equatorial triad * of date date1+date2 and the p-vector V(GCRS) is with respect to * the Geocentric Celestial Reference System (IAU, 2000). * * 3) The present function is faster, but slightly less accurate (about * 1 mas), than the iauPnm00a function. * * * Reference: * * IAU: Trans. International Astronomical Union, Vol. XXIVB; Proc. * 24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6. * (2000) * */ /*!\file pnm06a.c \fn void iauPnm06a(double date1, double date2, double rnpb[3][3]) \ingroup SF \brief Form the matrix of precession-nutation * * Form the matrix of precession-nutation for a given date (including * frame bias), IAU 2006 precession and IAU 2000A nutation models. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] rnpb bias-precession-nutation matrix (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The matrix operates in the sense V(date) = rnpb * V(GCRS), where * the p-vector V(date) is with respect to the true equatorial triad * of date date1+date2 and the p-vector V(GCRS) is with respect to * the Geocentric Celestial Reference System (IAU, 2000). * * * Reference: * * Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855. * */ /*!\file pnm80.c \fn void iauPnm80(double date1, double date2, double rmatpn[3][3]) \ingroup SF \brief Form the matrix of precession/nutation * * Form the matrix of precession/nutation for a given date, IAU 1976 * precession model, IAU 1980 nutation model. * * * * \param[in] date1 TDB date (Note 1) * \param[in] date2 TDB date (Note 1) * * \param[out] rmatpn combined precession/nutation matrix * * Notes: * * 1) The TDB date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TDB)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The matrix operates in the sense V(date) = rmatpn * V(J2000), * where the p-vector V(date) is with respect to the true equatorial * triad of date date1+date2 and the p-vector V(J2000) is with * respect to the mean equatorial triad of epoch J2000.0. * * * Reference: * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992), * Section 3.3 (p145). * */ /*!\file pom00.c \fn void iauPom00(double xp, double yp, double sp, double rpom[3][3]) \ingroup SF \brief Form the matrix of polar motion * * Form the matrix of polar motion for a given date, IAU 2000. * * * * \param[in] xp coordinates of the pole (radians, Note 1) * \param[in] yp coordinates of the pole (radians, Note 1) * \param[in] sp the TIO locator s' (radians, Note 2) * * \param[out] rpom polar-motion matrix (Note 3) * * Notes: * * 1) The arguments xp and yp are the coordinates (in radians) of the * Celestial Intermediate Pole with respect to the International * Terrestrial Reference System (see IERS Conventions 2003), * measured along the meridians to 0 and 90 deg west respectively. * * 2) The argument sp is the TIO locator s', in radians, which * positions the Terrestrial Intermediate Origin on the equator. It * is obtained from polar motion observations by numerical * integration, and so is in essence unpredictable. However, it is * dominated by a secular drift of about 47 microarcseconds per * century, and so can be taken into account by using s' = -47*t, * where t is centuries since J2000.0. The function iauSp00 * implements this approximation. * * 3) The matrix operates in the sense V(TRS) = rpom * V(CIP), meaning * that it is the final rotation when computing the pointing * direction to a celestial source. * * Reference: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\file ppp.c \fn void iauPpp(double a[3], double b[3], double apb[3]) \ingroup VMSF \brief P-vector addition. * * * * \param[in] a first p-vector * \param[in] b second p-vector * * \param[out] apb a + b * * Note: * It is permissible to re-use the same array for any of the * arguments. * */ /*!\file ppsp.c *\fn void iauPpsp(double a[3], double s, double b[3], double apsb[3]) \ingroup VMSF \brief P-vector scale and addition. * * * \param[in] a first p-vector * \param[in] s scalar (multiplier for b) * \param[in] b second p-vector * * \param[out] apsb a + s*b * * Note: * It is permissible for any of a, b and apsb to be the same array. * * */ /*!\file pr00.c \fn void iauPr00(double date1, double date2, double *dpsipr, double *depspr) \ingroup CM \brief Precession-rate part of the IAU 2000 models * * Precession-rate part of the IAU 2000 precession-nutation models * (part of MHB2000). * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] dpsipr precession corrections (Notes 2,3) * \param[out] depspr precession corrections (Notes 2,3) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The precession adjustments are expressed as "nutation * components", corrections in longitude and obliquity with respect * to the J2000.0 equinox and ecliptic. * * 3) Although the precession adjustments are stated to be with respect * to Lieske et al. (1977), the MHB2000 model does not specify which * set of Euler angles are to be used and how the adjustments are to * be applied. The most literal and straightforward procedure is to * adopt the 4-rotation epsilon_0, psi_A, omega_A, xi_A option, and * to add dpsipr to psi_A and depspr to both omega_A and eps_A. * * 4) This is an implementation of one aspect of the IAU 2000A nutation * model, formally adopted by the IAU General Assembly in 2000, * namely MHB2000 (Mathews et al. 2002). * * References: * * Lieske, J.H., Lederle, T., Fricke, W. & Morando, B., "Expressions * for the precession quantities based upon the IAU (1976) System of * Astronomical Constants", Astron.Astrophys., 58, 1-16 (1977) * * Mathews, P.M., Herring, T.A., Buffet, B.A., "Modeling of nutation * and precession New nutation series for nonrigid Earth and * insights into the Earth's interior", J.Geophys.Res., 107, B4, * 2002. The MHB2000 code itself was obtained on 9th September 2002 * from ftp://maia.usno.navy.mil/conv2000/chapter5/IAU2000A. * * Wallace, P.T., "Software for Implementing the IAU 2000 * Resolutions", in IERS Workshop 5.1 (2002). * */ /*!\file prec76.c \fn void iauPrec76(double date01, double date02, double date11, double date12, double *zeta, double *z, double *theta) \ingroup CM \brief IAU 1976 precession model. * * This function forms the three Euler angles which implement general * precession between two dates, using the IAU 1976 model (as for the * FK5 catalog). * * * * \param[in] date01 TDB starting date (Note 1) * \param[in] date02 TDB starting date (Note 1) * \param[in] date11 TDB ending date (Note 1) * \param[in] date12 TDB ending date (Note 1) * * \param[out] zeta 1st rotation: radians cw around z * \param[out] z 3rd rotation: radians cw around z * \param[out] theta 2nd rotation: radians ccw around y * * Notes: * * 1) The dates date01+date02 and date11+date12 are Julian Dates, * apportioned in any convenient way between the arguments daten1 * and daten2. For example, JD(TDB)=2450123.7 could be expressed in * any of these ways, among others: * * daten1 daten2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in cases * where the loss of several decimal digits of resolution is * acceptable. The J2000 method is best matched to the way the * argument is handled internally and will deliver the optimum * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * The two dates may be expressed using different methods, but at * the risk of losing some resolution. * * 2) The accumulated precession angles zeta, z, theta are expressed * through canonical polynomials which are valid only for a limited * time span. In addition, the IAU 1976 precession rate is known to * be imperfect. The absolute accuracy of the present formulation * is better than 0.1 arcsec from 1960AD to 2040AD, better than * 1 arcsec from 1640AD to 2360AD, and remains below 3 arcsec for * the whole of the period 500BC to 3000AD. The errors exceed * 10 arcsec outside the range 1200BC to 3900AD, exceed 100 arcsec * outside 4200BC to 5600AD and exceed 1000 arcsec outside 6800BC to * 8200AD. * * 3) The three angles are returned in the conventional order, which * is not the same as the order of the corresponding Euler * rotations. The precession matrix is * R_3(-z) x R_2(+theta) x R_3(-zeta). * * Reference: * * Lieske, J.H., 1979, Astron.Astrophys. 73, 282, equations * (6) & (7), p283. * */ /*!\file pv2p.c \fn void iauPv2p(double pv[2][3], double p[3]) \ingroup VMSF \brief Discard velocity component of a pv-vector. * * * * \param[in] pv pv-vector * * \param[out] p p-vector * * */ /*!\file pv2s.c \fn void iauPv2s(double pv[2][3], double *theta, double *phi, double *r, double *td, double *pd, double *rd) \ingroup VMSF \brief Convert position/velocity from Cartesian to spherical coordinates. * * * * \param[in] pv pv-vector * * \param[out] theta longitude angle (radians) * \param[out] phi latitude angle (radians) * \param[out] r radial distance * \param[out] td rate of change of theta * \param[out] pd rate of change of phi * \param[out] rd rate of change of r * * Notes: * * 1) If the position part of pv is null, theta, phi, td and pd * are indeterminate. This is handled by extrapolating the * position through unit time by using the velocity part of * pv. This moves the origin without changing the direction * of the velocity component. If the position and velocity * components of pv are both null, zeroes are returned for all * six results. * * 2) If the position is a pole, theta, td and pd are indeterminate. * In such cases zeroes are returned for all three. * */ /*!\file pvdpv.c \fn void iauPvdpv(double a[2][3], double b[2][3], double adb[2]) \ingroup VMSF \brief Inner (=scalar=dot) product of two pv-vectors. * * * * \param[in] a first pv-vector * \param[in] b second pv-vector * * \param[out] adb a . b (see note) * * Note: * * If the position and velocity components of the two pv-vectors are * ( ap, av ) and ( bp, bv ), the result, a . b, is the pair of * numbers ( ap . bp , ap . bv + av . bp ). The two numbers are the * dot-product of the two p-vectors and its derivative. * * */ /*!\file pvm.c \fn void iauPvm(double pv[2][3], double *r, double *s) \ingroup VMSF \brief Modulus of pv-vector. * * * * \param[in] pv pv-vector * * \param[out] r modulus of position component * \param[out] s modulus of velocity component * * */ /*!\file pvmpv.c \fn void iauPvmpv(double a[2][3], double b[2][3], double amb[2][3]) \ingroup VMSF \brief Subtract one pv-vector from another. * * * * \param[in] a first pv-vector * \param[in] b second pv-vector * * \param[out] amb a - b * * Note: * It is permissible to re-use the same array for any of the * arguments. * * */ /*!\file pvppv.c \fn void iauPvppv(double a[2][3], double b[2][3], double apb[2][3]) \ingroup VMSF \brief Add one pv-vector to another. * * * * \param[in] a first pv-vector * \param[in] b second pv-vector * * \param[out] apb a + b * * Note: * It is permissible to re-use the same array for any of the * arguments. * * */ /*!\file pvstar.c \fn int iauPvstar(double pv[2][3], double *ra, double *dec, double *pmr, double *pmd, double *px, double *rv) \ingroup SF \brief Convert star position+velocity vector to catalog coordinates. * * * * \param[in] pv pv-vector (AU, AU/day) * * \param[out] ra right ascension (radians) * \param[out] dec declination (radians) * \param[out] pmr RA proper motion (radians/year) * \param[out] pmd Dec proper motion (radians/year) * \param[out] px parallax (arcsec) * \param[out] rv radial velocity (km/s, positive = receding) * * \return * status: * 0 = OK * -1 = superluminal speed (Note 5) * -2 = null position vector * * Notes: * * 1) The specified pv-vector is the coordinate direction (and its rate * of change) for the date at which the light leaving the star * reached the solar-system barycenter. * * 2) The star data returned by this function are "observables" for an * imaginary observer at the solar-system barycenter. Proper motion * and radial velocity are, strictly, in terms of barycentric * coordinate time, TCB. For most practical applications, it is * permissible to neglect the distinction between TCB and ordinary * "proper" time on Earth (TT/TAI). The result will, as a rule, be * limited by the intrinsic accuracy of the proper-motion and * radial-velocity data; moreover, the supplied pv-vector is likely * to be merely an intermediate result (for example generated by the * function iauStarpv), so that a change of time unit will cancel * out overall. * * In accordance with normal star-catalog conventions, the object's * right ascension and declination are freed from the effects of * secular aberration. The frame, which is aligned to the catalog * equator and equinox, is Lorentzian and centered on the SSB. * * Summarizing, the specified pv-vector is for most stars almost * identical to the result of applying the standard geometrical * "space motion" transformation to the catalog data. The * differences, which are the subject of the Stumpff paper cited * below, are: * * (i) In stars with significant radial velocity and proper motion, * the constantly changing light-time distorts the apparent proper * motion. Note that this is a classical, not a relativistic, * effect. * * (ii) The transformation complies with special relativity. * * 3) Care is needed with units. The star coordinates are in radians * and the proper motions in radians per Julian year, but the * parallax is in arcseconds; the radial velocity is in km/s, but * the pv-vector result is in AU and AU/day. * * 4) The proper motions are the rate of change of the right ascension * and declination at the catalog epoch and are in radians per Julian * year. The RA proper motion is in terms of coordinate angle, not * true angle, and will thus be numerically larger at high * declinations. * * 5) Straight-line motion at constant speed in the inertial frame is * assumed. If the speed is greater than or equal to the speed of * light, the function aborts with an error status. * * 6) The inverse transformation is performed by the function iauStarpv. * * * Reference: * * Stumpff, P., 1985, Astron.Astrophys. 144, 232-240. * */ /*!\file pvtob.c \fn void iauPvtob(double elong, double phi, double hm, double xp, double yp, double sp, double theta, double pv[2][3]) \ingroup SF \brief Position and velocity of a terrestrial observing station. * * * * \param[in] elong longitude (radians, east +ve, Note 1) * \param[in] phi latitude (geodetic, radians, Note 1) * \param[in] hm height above ref. ellipsoid (geodetic, m) * \param[in] xp coordinates of the pole (radians, Note 2) * \param[in] yp coordinates of the pole (radians, Note 2) * \param[in] sp the TIO locator s' (radians, Note 2) * \param[in] theta Earth rotation angle (radians, Note 3) * * \param[out] pv position/velocity vector (m, m/s, CIRS) * * Notes: * * 1) The terrestrial coordinates are with respect to the WGS84 * reference ellipsoid. * * 2) xp and yp are the coordinates (in radians) of the Celestial * Intermediate Pole with respect to the International Terrestrial * Reference System (see IERS Conventions), measured along the * meridians 0 and 90 deg west respectively. sp is the TIO locator * s', in radians, which positions the Terrestrial Intermediate * Origin on the equator. For many applications, xp, yp and * (especially) sp can be set to zero. * * 3) If theta is Greenwich apparent sidereal time instead of Earth * rotation angle, the result is with respect to the true equator * and equinox of date, i.e. with the x-axis at the equinox rather * than the celestial intermediate origin. * * 4) The velocity units are meters per UT1 second, not per SI second. * This is unlikely to have any practical consequences in the modern * era. * * 5) No validation is performed on the arguments. Error cases that * could lead to arithmetic exceptions are trapped by the iauGd2gc * function, and the result set to zeros. * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to * the Astronomical Almanac, 3rd ed., University Science Books * (2013), Section 7.4.3.3. * * */ /*!\file pvu.c \fn void iauPvu(double dt, double pv[2][3], double upv[2][3]) \ingroup VMSF \brief Update a pv-vector. * * * * \param[in] dt time interval * \param[in] pv pv-vector * * \param[out] upv p updated, v unchanged * * Notes: * * 1) "Update" means "refer the position component of the vector * to a new date dt time units from the existing date". * * 2) The time units of dt must match those of the velocity. * * 3) It is permissible for pv and upv to be the same array. * * */ /*!\file pvup.c \fn void iauPvup(double dt, double pv[2][3], double p[3]) \ingroup VMSF \brief Update a pv-vector, discarding the velocity component. * * * * \param[in] dt time interval * \param[in] pv pv-vector * * \param[out] p p-vector * * Notes: * * 1) "Update" means "refer the position component of the vector to a * new date dt time units from the existing date". * * 2) The time units of dt must match those of the velocity. * */ /*!\file pvxpv.c \fn void iauPvxpv(double a[2][3], double b[2][3], double axb[2][3]) \brief Outer (=vector=cross) product of two pv-vectors. \ingroup VMSF * Notes: * * 1) If the position and velocity components of the two pv-vectors are * ( ap, av ) and ( bp, bv ), the result, a x b, is the pair of * vectors ( ap x bp, ap x bv + av x bp ). The two vectors are the * cross-product of the two p-vectors and its derivative. * * 2) It is permissible to re-use the same array for any of the * arguments. @param[in] a first pv -vector @param[in] b second pv -vector @param[out] axb ax b */ /*!\file pvpv.c \fn void iauPvxpv(double a[2][3], double b[2][3], double axb[2][3]) \ingroup VMSF \brief Outer (=vector=cross) product of two pv-vectors. * * * * \param[in] a first pv-vector * \param[in] b second pv-vector * * \param[out] axb a x b * * Notes: * * 1) If the position and velocity components of the two pv-vectors are * ( ap, av ) and ( bp, bv ), the result, a x b, is the pair of * vectors ( ap x bp, ap x bv + av x bp ). The two vectors are the * cross-product of the two p-vectors and its derivative. * * 2) It is permissible to re-use the same array for any of the * arguments. * * */ /*!\file pxp.c \fn void iauPxp(double a[3], double b[3], double axb[3]) \ingroup VMSF \brief p-vector outer (=vector=cross) product. * * * * \param[in] a first p-vector * \param[in] b second p-vector * * \param[out] axb a x b * * Note: * It is permissible to re-use the same array for any of the * arguments. * */ /*!\file refco.c \fn void iauRefco(double phpa, double tc, double rh, double wl, double *refa, double *refb) \ingroup SF \brief Determine constants in the atmospheric refraction model * * Determine the constants A and B in the atmospheric refraction model * dZ = A tan Z + B tan^3 Z. * * Z is the "observed" zenith distance (i.e. affected by refraction) * and dZ is what to add to Z to give the "topocentric" (i.e. in vacuo) * zenith distance. * * * * \param[in] phpa pressure at the observer (hPa = millibar) * \param[in] tc ambient temperature at the observer (deg C) * \param[in] rh relative humidity at the observer (range 0-1) * \param[in] wl wavelength (micrometers) * * \param[out] refa tan Z coefficient (radians) * \param[out] refb tan^3 Z coefficient (radians) * * Notes: * * 1) The model balances speed and accuracy to give good results in * applications where performance at low altitudes is not paramount. * Performance is maintained across a range of conditions, and * applies to both optical/IR and radio. * * 2) The model omits the effects of (i) height above sea level (apart * from the reduced pressure itself), (ii) latitude (i.e. the * flattening of the Earth), (iii) variations in tropospheric lapse * rate and (iv) dispersive effects in the radio. * * The model was tested using the following range of conditions: * * lapse rates 0.0055, 0.0065, 0.0075 deg/meter * latitudes 0, 25, 50, 75 degrees * heights 0, 2500, 5000 meters ASL * pressures mean for height -10% to +5% in steps of 5% * temperatures -10 deg to +20 deg with respect to 280 deg at SL * relative humidity 0, 0.5, 1 * wavelengths 0.4, 0.6, ... 2 micron, + radio * zenith distances 15, 45, 75 degrees * * The accuracy with respect to raytracing through a model * atmosphere was as follows: * * worst RMS * * optical/IR 62 mas 8 mas * radio 319 mas 49 mas * * For this particular set of conditions: * * lapse rate 0.0065 K/meter * latitude 50 degrees * sea level * pressure 1005 mb * temperature 280.15 K * humidity 80% * wavelength 5740 Angstroms * * the results were as follows: * * ZD raytrace iauRefco Saastamoinen * * 10 10.27 10.27 10.27 * 20 21.19 21.20 21.19 * 30 33.61 33.61 33.60 * 40 48.82 48.83 48.81 * 45 58.16 58.18 58.16 * 50 69.28 69.30 69.27 * 55 82.97 82.99 82.95 * 60 100.51 100.54 100.50 * 65 124.23 124.26 124.20 * 70 158.63 158.68 158.61 * 72 177.32 177.37 177.31 * 74 200.35 200.38 200.32 * 76 229.45 229.43 229.42 * 78 267.44 267.29 267.41 * 80 319.13 318.55 319.10 * * deg arcsec arcsec arcsec * * The values for Saastamoinen's formula (which includes terms * up to tan^5) are taken from Hohenkerk and Sinclair (1985). * * 3) A wl value in the range 0-100 selects the optical/IR case and is * wavelength in micrometers. Any value outside this range selects * the radio case. * * 4) Outlandish input parameters are silently limited to * mathematically safe values. Zero pressure is permissible, and * causes zeroes to be returned. * * 5) The algorithm draws on several sources, as follows: * * a) The formula for the saturation vapour pressure of water as * a function of temperature and temperature is taken from * Equations (A4.5-A4.7) of Gill (1982). * * b) The formula for the water vapour pressure, given the * saturation pressure and the relative humidity, is from * Crane (1976), Equation (2.5.5). * * c) The refractivity of air is a function of temperature, * total pressure, water-vapour pressure and, in the case * of optical/IR, wavelength. The formulae for the two cases are * developed from Hohenkerk & Sinclair (1985) and Rueger (2002). * * d) The formula for beta, the ratio of the scale height of the * atmosphere to the geocentric distance of the observer, is * an adaption of Equation (9) from Stone (1996). The * adaptations, arrived at empirically, consist of (i) a small * adjustment to the coefficient and (ii) a humidity term for the * radio case only. * * e) The formulae for the refraction constants as a function of * n-1 and beta are from Green (1987), Equation (4.31). * * References: * * Crane, R.K., Meeks, M.L. (ed), "Refraction Effects in the Neutral * Atmosphere", Methods of Experimental Physics: Astrophysics 12B, * Academic Press, 1976. * * Gill, Adrian E., "Atmosphere-Ocean Dynamics", Academic Press, * 1982. * * Green, R.M., "Spherical Astronomy", Cambridge University Press, * 1987. * * Hohenkerk, C.Y., & Sinclair, A.T., NAO Technical Note No. 63, * 1985. * * Rueger, J.M., "Refractive Index Formulae for Electronic Distance * Measurement with Radio and Millimetre Waves", in Unisurv Report * S-68, School of Surveying and Spatial Information Systems, * University of New South Wales, Sydney, Australia, 2002. * * Stone, Ronald C., P.A.S.P. 108, 1051-1058, 1996. * */ /*!\file rm2v.c \fn void iauRm2v(double r[3][3], double w[3]) \ingroup VMSF \brief Express an r-matrix as an r-vector. * * * * \param[in] r rotation matrix * * \param[out] w rotation vector (Note 1) * * Notes: * * 1) A rotation matrix describes a rotation through some angle about * some arbitrary axis called the Euler axis. The "rotation vector" * returned by this function has the same direction as the Euler axis, * and its magnitude is the angle in radians. (The magnitude and * direction can be separated by means of the function iauPn.) * * 2) If r is null, so is the result. If r is not a rotation matrix * the result is undefined; r must be proper (i.e. have a positive * determinant) and real orthogonal (inverse = transpose). * * 3) The reference frame rotates clockwise as seen looking along * the rotation vector from the origin. * */ /*!\file rv2m.c \fn void iauRv2m(double w[3], double r[3][3]) \ingroup VMSF \brief Form the r-matrix corresponding to a given r-vector. * * * * \param[in] w rotation vector (Note 1) * * \param[out] r rotation matrix * * Notes: * * 1) A rotation matrix describes a rotation through some angle about * some arbitrary axis called the Euler axis. The "rotation vector" * supplied to This function has the same direction as the Euler * axis, and its magnitude is the angle in radians. * * 2) If w is null, the unit matrix is returned. * * 3) The reference frame rotates clockwise as seen looking along the * rotation vector from the origin. * */ /*!\file rx.c \fn void iauRx(double phi, double r[3][3]) \ingroup VMSF \brief Rotate an r-matrix about the x-axis. * * * * \param[in] phi angle (radians) * * \param[in,out] r r-matrix, rotated * * Notes: * * 1) Calling this function with positive phi incorporates in the * supplied r-matrix r an additional rotation, about the x-axis, * anticlockwise as seen looking towards the origin from positive x. * * 2) The additional rotation can be represented by this matrix: * * ( 1 0 0 ) * ( ) * ( 0 + cos(phi) + sin(phi) ) * ( ) * ( 0 - sin(phi) + cos(phi) ) * */ /*!\file rxp.c \fn void iauRxp(double r[3][3], double p[3], double rp[3]) \ingroup VMSF \brief Multiply a p-vector by an r-matrix. * * * * \param[in] r r-matrix * \param[in] p p-vector * * \param[out] rp r * p * * Note: * It is permissible for p and rp to be the same array. * * */ /*!\file rxpv.c \fn void iauRxpv(double r[3][3], double pv[2][3], double rpv[2][3]) \ingroup VMSF \brief Multiply a pv-vector by an r-matrix. * * * * \param[in] r r-matrix * \param[in] pv pv-vector * * \param[out] rpv r * pv * * Note: * It is permissible for pv and rpv to be the same array. * * */ /*!\file rxr.c \fn void iauRxr(double a[3][3], double b[3][3], double atb[3][3]) \ingroup VMSF \brief Multiply two r-matrices. * * * * \param[in] a first r-matrix * \param[in] b second r-matrix * * \param[out] atb a * b * * Note: * It is permissible to re-use the same array for any of the * arguments. * * */ /*!\file ry.c \fn void iauRy(double theta, double r[3][3]) \ingroup VMSF \brief Rotate an r-matrix about the y-axis. * * * * \param[in] theta angle (radians) * * \param[in,out] r r-matrix, rotated * * Notes: * * 1) Calling this function with positive theta incorporates in the * supplied r-matrix r an additional rotation, about the y-axis, * anticlockwise as seen looking towards the origin from positive y. * * 2) The additional rotation can be represented by this matrix: * * ( + cos(theta) 0 - sin(theta) ) * ( ) * ( 0 1 0 ) * ( ) * ( + sin(theta) 0 + cos(theta) ) * */ /*!\file rz.c \fn void iauRz(double psi, double r[3][3]) \ingroup VMSF \brief Rotate an r-matrix about the z-axis. * * * * \param[in] psi angle (radians) * * \param[in,out] r r-matrix, rotated * * Notes: * * 1) Calling this function with positive psi incorporates in the * supplied r-matrix r an additional rotation, about the z-axis, * anticlockwise as seen looking towards the origin from positive z. * * 2) The additional rotation can be represented by this matrix: * * ( + cos(psi) + sin(psi) 0 ) * ( ) * ( - sin(psi) + cos(psi) 0 ) * ( ) * ( 0 0 1 ) * */ /*!\file s00.c \fn double iauS00(double date1, double date2, double x, double y) \ingroup CM \brief The CIO locators given CIP coordinates. * * The CIO locator s, positioning the Celestial Intermediate Origin on * the equator of the Celestial Intermediate Pole, given the CIP's X,Y * coordinates. Compatible with IAU 2000A precession-nutation. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * \param[in] x CIP coordinates (Note 3) * \param[in] y CIP coordinates (Note 3) * * \return * the CIO locator s in radians (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The CIO locator s is the difference between the right ascensions * of the same point in two systems: the two systems are the GCRS * and the CIP,CIO, and the point is the ascending node of the * CIP equator. The quantity s remains below 0.1 arcsecond * throughout 1900-2100. * * 3) The series used to compute s is in fact for s+XY/2, where X and Y * are the x and y components of the CIP unit vector; this series * is more compact than a direct series for s would be. This * function requires X,Y to be supplied by the caller, who is * responsible for providing values that are consistent with the * supplied date. * * 4) The model is consistent with the IAU 2000A precession-nutation. * * * References: * * Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., * "Expressions for the Celestial Intermediate Pole and Celestial * Ephemeris Origin consistent with the IAU 2000A precession- * nutation model", Astron.Astrophys. 400, 1145-1154 (2003) * * n.b. The celestial ephemeris origin (CEO) was renamed "celestial * intermediate origin" (CIO) by IAU 2006 Resolution 2. * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\file s00a.c \fn double iauS00a(double date1, double date2) \ingroup SF \brief The CIO locator using the IA2000A precission-nutation model * * The CIO locator s, positioning the Celestial Intermediate Origin on * the equator of the Celestial Intermediate Pole, using the IAU 2000A * precession-nutation model. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \return * the CIO locator s in radians (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The CIO locator s is the difference between the right ascensions * of the same point in two systems. The two systems are the GCRS * and the CIP,CIO, and the point is the ascending node of the * CIP equator. The CIO locator s remains a small fraction of * 1 arcsecond throughout 1900-2100. * * 3) The series used to compute s is in fact for s+XY/2, where X and Y * are the x and y components of the CIP unit vector; this series * is more compact than a direct series for s would be. The present * function uses the full IAU 2000A nutation model when predicting * the CIP position. Faster results, with no significant loss of * accuracy, can be obtained via the function iauS00b, which uses * instead the IAU 2000B truncated model. * * * References: * * Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., * "Expressions for the Celestial Intermediate Pole and Celestial * Ephemeris Origin consistent with the IAU 2000A precession- * nutation model", Astron.Astrophys. 400, 1145-1154 (2003) * * n.b. The celestial ephemeris origin (CEO) was renamed "celestial * intermediate origin" (CIO) by IAU 2006 Resolution 2. * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\file s00b.c \fn double iauS00b(double date1, double date2) \ingroup SF \brief The CIO locator using the IAU 2000B precission-nutation model. * * The CIO locator s, positioning the Celestial Intermediate Origin on * the equator of the Celestial Intermediate Pole, using the IAU 2000B * precession-nutation model. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \return * the CIO locator s in radians (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The CIO locator s is the difference between the right ascensions * of the same point in two systems. The two systems are the GCRS * and the CIP,CIO, and the point is the ascending node of the * CIP equator. The CIO locator s remains a small fraction of * 1 arcsecond throughout 1900-2100. * * 3) The series used to compute s is in fact for s+XY/2, where X and Y * are the x and y components of the CIP unit vector; this series * is more compact than a direct series for s would be. The present * function uses the IAU 2000B truncated nutation model when * predicting the CIP position. The function iauS00a uses instead * the full IAU 2000A model, but with no significant increase in * accuracy and at some cost in speed. * * * References: * * Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., * "Expressions for the Celestial Intermediate Pole and Celestial * Ephemeris Origin consistent with the IAU 2000A precession- * nutation model", Astron.Astrophys. 400, 1145-1154 (2003) * * n.b. The celestial ephemeris origin (CEO) was renamed "celestial * intermediate origin" (CIO) by IAU 2006 Resolution 2. * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\file s06.c \fn double iauS06(double date1, double date2, double x, double y) \ingroup CM \brief The CIO locator given CIP coordinates. * * The CIO locator s, positioning the Celestial Intermediate Origin on * the equator of the Celestial Intermediate Pole, given the CIP's X,Y * coordinates. Compatible with IAU 2006/2000A precession-nutation. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * \param[in] x CIP coordinates (Note 3) * \param[in] y CIP coordinates (Note 3) * * \return * the CIO locator s in radians (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The CIO locator s is the difference between the right ascensions * of the same point in two systems: the two systems are the GCRS * and the CIP,CIO, and the point is the ascending node of the * CIP equator. The quantity s remains below 0.1 arcsecond * throughout 1900-2100. * * 3) The series used to compute s is in fact for s+XY/2, where X and Y * are the x and y components of the CIP unit vector; this series * is more compact than a direct series for s would be. This * function requires X,Y to be supplied by the caller, who is * responsible for providing values that are consistent with the * supplied date. * * 4) The model is consistent with the "P03" precession (Capitaine et * al. 2003), adopted by IAU 2006 Resolution 1, 2006, and the * IAU 2000A nutation (with P03 adjustments). * * * References: * * Capitaine, N., Wallace, P.T. & Chapront, J., 2003, Astron. * Astrophys. 432, 355 * * McCarthy, D.D., Petit, G. (eds.) 2004, IERS Conventions (2003), * IERS Technical Note No. 32, BKG * */ /*!\file s06a.c \fn double iauS06a(double date1, double date2) \ingroup SF \brief The CIO locator using IAU2006 precession and IAU 2000A nutation models. * * The CIO locator s, positioning the Celestial Intermediate Origin on * the equator of the Celestial Intermediate Pole, using the IAU 2006 * precession and IAU 2000A nutation models. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \return * the CIO locator s in radians (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The CIO locator s is the difference between the right ascensions * of the same point in two systems. The two systems are the GCRS * and the CIP,CIO, and the point is the ascending node of the * CIP equator. The CIO locator s remains a small fraction of * 1 arcsecond throughout 1900-2100. * * 3) The series used to compute s is in fact for s+XY/2, where X and Y * are the x and y components of the CIP unit vector; this series is * more compact than a direct series for s would be. The present * function uses the full IAU 2000A nutation model when predicting * the CIP position. * * References: * * Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., * "Expressions for the Celestial Intermediate Pole and Celestial * Ephemeris Origin consistent with the IAU 2000A precession- * nutation model", Astron.Astrophys. 400, 1145-1154 (2003) * * n.b. The celestial ephemeris origin (CEO) was renamed "celestial * intermediate origin" (CIO) by IAU 2006 Resolution 2. * * Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 * * McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), * IERS Technical Note No. 32, BKG * * Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 * */ /*!\file s2c.c \fn void iauS2c(double theta, double phi, double c[3]) \ingroup VMSF \brief Convert spherical coordinates to Cartesian. * * * * \param[in] theta longitude angle (radians) * \param[in] phi latitude angle (radians) * * \param[out] c direction cosines * */ /*!\file s2p.c \fn void iauS2p(double theta, double phi, double r, double p[3]) \ingroup VMSF \brief Convert spherical polar coordinates to p-vector. * * * * \param[in] theta longitude angle (radians) * \param[in] phi latitude angle (radians) * \param[in] r radial distance * * \param[out] p Cartesian coordinates * * */ /*!\file s2pv.c \fn void iauS2pv(double theta, double phi, double r, double td, double pd, double rd, \ingroup VMSF \brief Convert position/velocity from spherical to Cartesian coordinates. * * * * \param[in] theta longitude angle (radians) * \param[in] phi latitude angle (radians) * \param[in] r radial distance * \param[in] td rate of change of theta * \param[in] pd rate of change of phi * \param[in] rd rate of change of r * * \param[out] pv pv-vector * */ /*!\file s2xpv.c \fn void iauS2xpv(double s1, double s2, double pv[2][3], double spv[2][3]) \ingroup VMSF \brief Multiply a pv-vector by two scalars. * * * * \param[in] s1 scalar to multiply position component by * \param[in] s2 scalar to multiply velocity component by * \param[in] pv pv-vector * * \param[out] spv pv-vector: p scaled by s1, v scaled by s2 * * Note: * It is permissible for pv and spv to be the same array. * * */ /*!\file sepp.c \fn double iauSepp(double a[3], double b[3]) \ingroup VMSF \brief Angular separation between two p-vectors. * * * * \param[in] a first p-vector (not necessarily unit length) * \param[in] b second p-vector (not necessarily unit length) * * \return * angular separation (radians, always positive) * * Notes: * * 1) If either vector is null, a zero result is returned. * * 2) The angular separation is most simply formulated in terms of * scalar product. However, this gives poor accuracy for angles * near zero and pi. The present algorithm uses both cross product * and dot product, to deliver full accuracy whatever the size of * the angle. * * */ /*!\file seps.c \fn double iauSeps(double al, double ap, double bl, double bp) \ingroup VMSF \brief Angular separation between two sets of spherical coordinates. * * * * \param[in] al first longitude (radians) * \param[in] ap first latitude (radians) * \param[in] bl second longitude (radians) * \param[in] bp second latitude (radians) * * \return * angular separation (radians) * * */ /*!\file sp00.c \fn double iauSp00(double date1, double date2) \ingroup CM \brief The TIO locator. * * The TIO locator s', positioning the Terrestrial Intermediate Origin * on the equator of the Celestial Intermediate Pole. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \return * the TIO locator s' in radians (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The TIO locator s' is obtained from polar motion observations by * numerical integration, and so is in essence unpredictable. * However, it is dominated by a secular drift of about * 47 microarcseconds per century, which is the approximation * evaluated by the present function. * * Reference: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\file starpm.c \fn int iauStarpm(double ra1, double dec1, double pmr1, double pmd1, double px1, double rv1, double ep1a, double ep1b, double ep2a, double ep2b, double *ra2, double *dec2, double *pmr2, double *pmd2, double *px2, double *rv2) \ingroup SF \brief Star proper motion * * Star proper motion: update star catalog data for space motion. * * * * \param[in] ra1 right ascension (radians), before * \param[in] dec1 declination (radians), before * \param[in] pmr1 RA proper motion (radians/year), before * \param[in] pmd1 Dec proper motion (radians/year), before * \param[in] px1 parallax (arcseconds), before * \param[in] rv1 radial velocity (km/s, +ve = receding), before * \param[in] ep1a "before" epoch, part A (Note 1) * \param[in] ep1b "before" epoch, part B (Note 1) * \param[in] ep2a "after" epoch, part A (Note 1) * \param[in] ep2b "after" epoch, part B (Note 1) * * \param[out] ra2 right ascension (radians), after * \param[out] dec2 declination (radians), after * \param[out] pmr2 RA proper motion (radians/year), after * \param[out] pmd2 Dec proper motion (radians/year), after * \param[out] px2 parallax (arcseconds), after * \param[out] rv2 radial velocity (km/s, +ve = receding), after * * \return * status: * -1 = system error (should not occur) * 0 = no warnings or errors * 1 = distance overridden (Note 6) * 2 = excessive velocity (Note 7) * 4 = solution didn't converge (Note 8) * else = binary logical OR of the above warnings * * Notes: * * 1) The starting and ending TDB dates ep1a+ep1b and ep2a+ep2b are * Julian Dates, apportioned in any convenient way between the two * parts (A and B). For example, JD(TDB)=2450123.7 could be * expressed in any of these ways, among others: * * epna epnb * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) In accordance with normal star-catalog conventions, the object's * right ascension and declination are freed from the effects of * secular aberration. The frame, which is aligned to the catalog * equator and equinox, is Lorentzian and centered on the SSB. * * The proper motions are the rate of change of the right ascension * and declination at the catalog epoch and are in radians per TDB * Julian year. * * The parallax and radial velocity are in the same frame. * * 3) Care is needed with units. The star coordinates are in radians * and the proper motions in radians per Julian year, but the * parallax is in arcseconds. * * 4) The RA proper motion is in terms of coordinate angle, not true * angle. If the catalog uses arcseconds for both RA and Dec proper * motions, the RA proper motion will need to be divided by cos(Dec) * before use. * * 5) Straight-line motion at constant speed, in the inertial frame, * is assumed. * * 6) An extremely small (or zero or negative) parallax is interpreted * to mean that the object is on the "celestial sphere", the radius * of which is an arbitrary (large) value (see the iauStarpv * function for the value used). When the distance is overridden in * this way, the status, initially zero, has 1 added to it. * * 7) If the space velocity is a significant fraction of c (see the * constant VMAX in the function iauStarpv), it is arbitrarily set * to zero. When this action occurs, 2 is added to the status. * * 8) The relativistic adjustment carried out in the iauStarpv function * involves an iterative calculation. If the process fails to * converge within a set number of iterations, 4 is added to the * status. * * */ /*!\file starpv.c \fn int iauStarpv(double ra, double dec, double pmr, double pmd, double px, double rv, double pv[2][3]) \ingroup SF \brief Convert star catalog coordinates to position+velocity vector. * * * * \param[in] ra right ascension (radians) * \param[in] dec declination (radians) * \param[in] pmr RA proper motion (radians/year) * \param[in] pmd Dec proper motion (radians/year) * \param[in] px parallax (arcseconds) * \param[in] rv radial velocity (km/s, positive = receding) * * \param[out] pv pv-vector (AU, AU/day) * * \return * status: * 0 = no warnings * 1 = distance overridden (Note 6) * 2 = excessive speed (Note 7) * 4 = solution didn't converge (Note 8) * else = binary logical OR of the above * * Notes: * * 1) The star data accepted by this function are "observables" for an * imaginary observer at the solar-system barycenter. Proper motion * and radial velocity are, strictly, in terms of barycentric * coordinate time, TCB. For most practical applications, it is * permissible to neglect the distinction between TCB and ordinary * "proper" time on Earth (TT/TAI). The result will, as a rule, be * limited by the intrinsic accuracy of the proper-motion and * radial-velocity data; moreover, the pv-vector is likely to be * merely an intermediate result, so that a change of time unit * would cancel out overall. * * In accordance with normal star-catalog conventions, the object's * right ascension and declination are freed from the effects of * secular aberration. The frame, which is aligned to the catalog * equator and equinox, is Lorentzian and centered on the SSB. * * 2) The resulting position and velocity pv-vector is with respect to * the same frame and, like the catalog coordinates, is freed from * the effects of secular aberration. Should the "coordinate * direction", where the object was located at the catalog epoch, be * required, it may be obtained by calculating the magnitude of the * position vector pv[0][0-2] dividing by the speed of light in * AU/day to give the light-time, and then multiplying the space * velocity pv[1][0-2] by this light-time and adding the result to * pv[0][0-2]. * * Summarizing, the pv-vector returned is for most stars almost * identical to the result of applying the standard geometrical * "space motion" transformation. The differences, which are the * subject of the Stumpff paper referenced below, are: * * (i) In stars with significant radial velocity and proper motion, * the constantly changing light-time distorts the apparent proper * motion. Note that this is a classical, not a relativistic, * effect. * * (ii) The transformation complies with special relativity. * * 3) Care is needed with units. The star coordinates are in radians * and the proper motions in radians per Julian year, but the * parallax is in arcseconds; the radial velocity is in km/s, but * the pv-vector result is in AU and AU/day. * * 4) The RA proper motion is in terms of coordinate angle, not true * angle. If the catalog uses arcseconds for both RA and Dec proper * motions, the RA proper motion will need to be divided by cos(Dec) * before use. * * 5) Straight-line motion at constant speed, in the inertial frame, * is assumed. * * 6) An extremely small (or zero or negative) parallax is interpreted * to mean that the object is on the "celestial sphere", the radius * of which is an arbitrary (large) value (see the constant PXMIN). * When the distance is overridden in this way, the status, * initially zero, has 1 added to it. * * 7) If the space velocity is a significant fraction of c (see the * constant VMAX), it is arbitrarily set to zero. When this action * occurs, 2 is added to the status. * * 8) The relativistic adjustment involves an iterative calculation. * If the process fails to converge within a set number (IMAX) of * iterations, 4 is added to the status. * * 9) The inverse transformation is performed by the function * iauPvstar. * * * Reference: * * Stumpff, P., 1985, Astron.Astrophys. 144, 232-240. * */ /*!\file sxp.c \fn void iauSxp(double s, double p[3], double sp[3]) \ingroup VMSF \brief Multiply a p-vector by a scalar. * * * * \param[in] s scalar * \param[in] p p-vector * * \param[out] sp s * p * * Note: * It is permissible for p and sp to be the same array. * */ /*!\file sxpv.c \fn void iauSxpv(double s, double pv[2][3], double spv[2][3]) \ingroup VMSF \brief Multiply a pv-vector by a scalar. * * * * \param[in] s scalar * \param[in] pv pv-vector * * \param[out] spv s * pv * * Note: * It is permissible for pv and spv to be the same array * * */ /*!\file taitt.c \fn int iauTaitt(double tai1, double tai2, double *tt1, double *tt2) \ingroup C \brief TAI to TT. * * Time scale transformation: International Atomic Time, TAI, to * Terrestrial Time, TT. * * * * \param[in] tai1 TAI as a 2-part Julian Date * \param[in] tai2 TAI as a 2-part Julian Date * * \param[out] tt1 TT as a 2-part Julian Date * \param[out] tt2 TT as a 2-part Julian Date * * \return * status: 0 = OK * * Note: * * tai1+tai2 is Julian Date, apportioned in any convenient way * between the two arguments, for example where tai1 is the Julian * Day Number and tai2 is the fraction of a day. The returned * tt1,tt2 follow suit. * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992) * */ /*!\file taiut1.c \fn int iauTaiut1(double tai1, double tai2, double dta, double *ut11, double *ut12) \ingroup C \brief TAI to UT1. * * Time scale transformation: International Atomic Time, TAI, to * Universal Time, UT1. * * * * \param[in] tai1 TAI as a 2-part Julian Date * \param[in] tai2 TAI as a 2-part Julian Date * \param[in] dta UT1-TAI in seconds * * \param[out] ut11 UT1 as a 2-part Julian Date * \param[out] ut12 UT1 as a 2-part Julian Date * * \return * status: 0 = OK * * Notes: * * 1) tai1+tai2 is Julian Date, apportioned in any convenient way * between the two arguments, for example where tai1 is the Julian * Day Number and tai2 is the fraction of a day. The returned * UT11,UT12 follow suit. * * 2) The argument dta, i.e. UT1-TAI, is an observed quantity, and is * available from IERS tabulations. * * Reference: * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992) * */ /*!\file taiutc.c \fn int iauTaiutc(double tai1, double tai2, double *utc1, double *utc2) \ingroup C \brief TAI to UTC. * * Time scale transformation: International Atomic Time, TAI, to * Coordinated Universal Time, UTC. * * * * \param[in] tai1 TAI as a 2-part Julian Date (Note 1) * \param[in] tai2 TAI as a 2-part Julian Date (Note 1) * * \param[out] utc1 UTC as a 2-part quasi Julian Date (Notes 1-3) * \param[out] utc2 UTC as a 2-part quasi Julian Date (Notes 1-3) * * \return * status: +1 = dubious year (Note 4) * 0 = OK * -1 = unacceptable date * * Notes: * * 1) tai1+tai2 is Julian Date, apportioned in any convenient way * between the two arguments, for example where tai1 is the Julian * Day Number and tai2 is the fraction of a day. The returned utc1 * and utc2 form an analogous pair, except that a special convention * is used, to deal with the problem of leap seconds - see the next * note. * * 2) JD cannot unambiguously represent UTC during a leap second unless * special measures are taken. The convention in the present * function is that the JD day represents UTC days whether the * length is 86399, 86400 or 86401 SI seconds. In the 1960-1972 era * there were smaller jumps (in either direction) each time the * linear UTC(TAI) expression was changed, and these "mini-leaps" * are also included in the SOFA convention. * * 3) The function iauD2dtf can be used to transform the UTC quasi-JD * into calendar date and clock time, including UTC leap second * handling. * * 4) The warning status "dubious year" flags UTCs that predate the * introduction of the time scale or that are too far in the future * to be trusted. See iauDat for further details. * * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992) * */ /*!\file tcbtdb.c \fn int iauTcbtdb(double tcb1, double tcb2, double *tdb1, double *tdb2) \ingroup C \brief TCB to TDB * * Time scale transformation: Barycentric Coordinate Time, TCB, to * Barycentric Dynamical Time, TDB. * * * * \param[in] tcb1 TCB as a 2-part Julian Date * \param[in] tcb2 TCB as a 2-part Julian Date * * \param[out] tdb1 TDB as a 2-part Julian Date * \param[out] tdb2 TDB as a 2-part Julian Date * * \return * status: 0 = OK * * Notes: * * 1) tcb1+tcb2 is Julian Date, apportioned in any convenient way * between the two arguments, for example where tcb1 is the Julian * Day Number and tcb2 is the fraction of a day. The returned * tdb1,tdb2 follow suit. * * 2) The 2006 IAU General Assembly introduced a conventional linear * transformation between TDB and TCB. This transformation * compensates for the drift between TCB and terrestrial time TT, * and keeps TDB approximately centered on TT. Because the * relationship between TT and TCB depends on the adopted solar * system ephemeris, the degree of alignment between TDB and TT over * long intervals will vary according to which ephemeris is used. * Former definitions of TDB attempted to avoid this problem by * stipulating that TDB and TT should differ only by periodic * effects. This is a good description of the nature of the * relationship but eluded precise mathematical formulation. The * conventional linear relationship adopted in 2006 sidestepped * these difficulties whilst delivering a TDB that in practice was * consistent with values before that date. * * 3) TDB is essentially the same as Teph, the time argument for the * JPL solar system ephemerides. * * Reference: * * IAU 2006 Resolution B3 * */ /*!\file tcgtt.c \fn int iauTcgtt(double tcg1, double tcg2, double *tt1, double *tt2) \ingroup C \brief TCG to TT * * Time scale transformation: Geocentric Coordinate Time, TCG, to * Terrestrial Time, TT. * * * * \param[in] tcg1 TCG as a 2-part Julian Date * \param[in] tcg2 TCG as a 2-part Julian Date * * \param[out] tt1 TT as a 2-part Julian Date * \param[out] tt2 TT as a 2-part Julian Date * * \return * status: 0 = OK * * Note: * * tcg1+tcg2 is Julian Date, apportioned in any convenient way * between the two arguments, for example where tcg1 is the Julian * Day Number and tcg22 is the fraction of a day. The returned * tt1,tt2 follow suit. * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),. * IERS Technical Note No. 32, BKG (2004) * * IAU 2000 Resolution B1.9 * */ /*!\file tdbtcb.c \fn int iauTdbtcb(double tdb1, double tdb2, double *tcb1, double *tcb2) \ingroup C \brief TDB to TCB * * Time scale transformation: Barycentric Dynamical Time, TDB, to * Barycentric Coordinate Time, TCB. * * * * \param[in] tdb1 TDB as a 2-part Julian Date * \param[in] tdb2 TDB as a 2-part Julian Date * * \param[out] tcb1 TCB as a 2-part Julian Date * \param[out] tcb2 TCB as a 2-part Julian Date * * \return * status: 0 = OK * * Notes: * * 1) tdb1+tdb2 is Julian Date, apportioned in any convenient way * between the two arguments, for example where tdb1 is the Julian * Day Number and tdb2 is the fraction of a day. The returned * tcb1,tcb2 follow suit. * * 2) The 2006 IAU General Assembly introduced a conventional linear * transformation between TDB and TCB. This transformation * compensates for the drift between TCB and terrestrial time TT, * and keeps TDB approximately centered on TT. Because the * relationship between TT and TCB depends on the adopted solar * system ephemeris, the degree of alignment between TDB and TT over * long intervals will vary according to which ephemeris is used. * Former definitions of TDB attempted to avoid this problem by * stipulating that TDB and TT should differ only by periodic * effects. This is a good description of the nature of the * relationship but eluded precise mathematical formulation. The * conventional linear relationship adopted in 2006 sidestepped * these difficulties whilst delivering a TDB that in practice was * consistent with values before that date. * * 3) TDB is essentially the same as Teph, the time argument for the * JPL solar system ephemerides. * * Reference: * * IAU 2006 Resolution B3 * */ /*!\file tdbtt.c \fn int iauTdbtt(double tdb1, double tdb2, double dtr, double *tt1, double *tt2 ) \ingroup C \brief TDB to TT * * Time scale transformation: Barycentric Dynamical Time, TDB, to * Terrestrial Time, TT. * * * * \param[in] tdb1 TDB as a 2-part Julian Date * \param[in] tdb2 TDB as a 2-part Julian Date * \param[in] dtr TDB-TT in seconds * * \param[out] tt1 TT as a 2-part Julian Date * \param[out] tt2 TT as a 2-part Julian Date * * \return * status: 0 = OK * * Notes: * * 1) tdb1+tdb2 is Julian Date, apportioned in any convenient way * between the two arguments, for example where tdb1 is the Julian * Day Number and tdb2 is the fraction of a day. The returned * tt1,tt2 follow suit. * * 2) The argument dtr represents the quasi-periodic component of the * GR transformation between TT and TCB. It is dependent upon the * adopted solar-system ephemeris, and can be obtained by numerical * integration, by interrogating a precomputed time ephemeris or by * evaluating a model such as that implemented in the SOFA function * iauDtdb. The quantity is dominated by an annual term of 1.7 ms * amplitude. * * 3) TDB is essentially the same as Teph, the time argument for the * JPL solar system ephemerides. * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * IAU 2006 Resolution 3 * */ /*!\file tf2a.c \fn int iauTf2a(char s, int ihour, int imin, double sec, double *rad) \ingroup SF \brief Convert hours, minutes, seconds to radians. * * * * \param[in] s sign: '-' = negative, otherwise positive * \param[in] ihour hours * \param[in] imin minutes * \param[in] sec seconds * * \param[out] rad angle in radians * * \return * status: 0 = OK * 1 = ihour outside range 0-23 * 2 = imin outside range 0-59 * 3 = sec outside range 0-59.999... * * Notes: * * 1) The result is computed even if any of the range checks fail. * * 2) Negative ihour, imin and/or sec produce a warning status, but * the absolute value is used in the conversion. * * 3) If there are multiple errors, the status value reflects only the * first, the smallest taking precedence. * */ /*!\file tf2d.c \fn int iauTf2d(char s, int ihour, int imin, double sec, double *days) \ingroup SF \brief Convert hours, minutes, seconds to days. * * * * \param[in] s sign: '-' = negative, otherwise positive * \param[in] ihour hours * \param[in] imin minutes * \param[in] sec seconds * * \param[out] days interval in days * * \return * status: 0 = OK * 1 = ihour outside range 0-23 * 2 = imin outside range 0-59 * 3 = sec outside range 0-59.999... * * Notes: * * 1) The result is computed even if any of the range checks fail. * * 2) Negative ihour, imin and/or sec produce a warning status, but * the absolute value is used in the conversion. * * 3) If there are multiple errors, the status value reflects only the * first, the smallest taking precedence. * */ /*!\file tpors.c \fn int iauTpors(double xi, double eta, double a, double b, double *a01, double *b01, double *a02, double *b02) \brief In the tangent plane projection, determine the spherical coordinates of the tangent point. * In the tangent plane projection, given the rectangular coordinates * of a star and its spherical coordinates, determine the spherical * coordinates of the tangent point. * Notes: * * 1) The tangent plane projection is also called the "gnomonic * projection" and the "central projection". * * 2) The eta axis points due north in the adopted coordinate system. * If the spherical coordinates are observed (RA,Dec), the tangent * plane coordinates (xi,eta) are conventionally called the * "standard coordinates". If the spherical coordinates are with * respect to a right-handed triad, (xi,eta) are also right-handed. * The units of (xi,eta) are, effectively, radians at the tangent * point. * * 3) All angular arguments are in radians. * * 4) The angles a01 and a02 are returned in the range 0-2pi. The * angles b01 and b02 are returned in the range +/-pi, but in the * usual, non-pole-crossing, case, the range is +/-pi/2. * * 5) Cases where there is no solution can arise only near the poles. * For example, it is clearly impossible for a star at the pole * itself to have a non-zero xi value, and hence it is meaningless * to ask where the tangent point would have to be to bring about * this combination of xi and dec. * * 6) Also near the poles, cases can arise where there are two useful * solutions. The return value indicates whether the second of the * two solutions returned is useful; 1 indicates only one useful * solution, the usual case. * * 7) The basis of the algorithm is to solve the spherical triangle PSC, * where P is the north celestial pole, S is the star and C is the * tangent point. The spherical coordinates of the tangent point are * [a0,b0]; writing rho^2 = (xi^2+eta^2) and r^2 = (1+rho^2), side c * is then (pi/2-b), side p is sqrt(xi^2+eta^2) and side s (to be * found) is (pi/2-b0). Angle C is given by sin(C) = xi/rho and * cos(C) = eta/rho. Angle P (to be found) is the longitude * difference between star and tangent point (a-a0). * * 8) This function is a member of the following set: \verbatim spherical vector solve for iauTpxes iauTpxev xi,eta iauTpsts iauTpstv star > iauTpors < iauTporv origin \endverbatim @param[in] xi rectangular coordinates of star image @param[in] eta rectangular coordinates of star image @param[out] a01 tangent point's spherical coordinates soln 1 @param[out] b01 tangent point's spherical coordinates soln 1 @param[out] a02 tangent point's spherical coordinates soln 2 @param[out] b02 tangent point's spherical coordinates soln 2 @return number of solutions: 0= no solutions returnd, 1 = only the first solution is useful, * 2= both solutions are useful. */ /*!\file tporv.c \fn int iauTporv(double xi, double eta, double v[3], double v01[3], double v02[3]) \ingroup SF \brief In the tangent plane projection, determine the direction cosines of the tangent point. * Notes: * * 1) The tangent plane projection is also called the "gnomonic * projection" and the "central projection". * * 2) The eta axis points due north in the adopted coordinate system. * If the direction cosines represent observed (RA,Dec), the tangent * plane coordinates (xi,eta) are conventionally called the * "standard coordinates". If the direction cosines are with * respect to a right-handed triad, (xi,eta) are also right-handed. * The units of (xi,eta) are, effectively, radians at the tangent * point. * * 3) The vector v must be of unit length or the result will be wrong. * * 4) Cases where there is no solution can arise only near the poles. * For example, it is clearly impossible for a star at the pole * itself to have a non-zero xi value, and hence it is meaningless * to ask where the tangent point would have to be. * * 5) Also near the poles, cases can arise where there are two useful * solutions. The return value indicates whether the second of the * two solutions returned is useful; 1 indicates only one useful * solution, the usual case. * * 6) The basis of the algorithm is to solve the spherical triangle * PSC, where P is the north celestial pole, S is the star and C is * the tangent point. Calling the celestial spherical coordinates * of the star and tangent point (a,b) and (a0,b0) respectively, and * writing rho^2 = (xi^2+eta^2) and r^2 = (1+rho^2), and * transforming the vector v into (a,b) in the normal way, side c is * then (pi/2-b), side p is sqrt(xi^2+eta^2) and side s (to be * found) is (pi/2-b0), while angle C is given by sin(C) = xi/rho * and cos(C) = eta/rho; angle P (to be found) is (a-a0). After * solving the spherical triangle, the result (a0,b0) can be * expressed in vector form as v0. * * 7) This function is a member of the following set: \verbatim spherical vector solve for iauTpxes iauTpxev xi,eta iauTpsts iauTpstv star iauTpors > iauTporv < origin \endverbatim @param[in] xi rectangular coordinates of star image @param[in] eta rectangular coordinates of star image @param[in] v star's direction cosines @param[out] v01 tangent point's direction socinse, solution 1. @param[out] v02 tangent point's direction socinse, solution 2. @return number of solutions: 0= no solutions returnd, 1 = only the first solution is useful, 2= both solutions are useful. */ /*!\file tpsts.c \fn void iauTpsts(double xi, double eta, double a0, double b0, double *a, double *b) \ingroup SF \brief In the tangent plane projection, solve for the spherical coordinates of the star. * In the tangent plane projection, given the star's rectangular * coordinates and the spherical coordinates of the tangent point, * solve for the spherical coordinates of the star. * 1) The tangent plane projection is also called the "gnomonic * projection" and the "central projection". * * 2) The eta axis points due north in the adopted coordinate system. * If the spherical coordinates are observed (RA,Dec), the tangent * plane coordinates (xi,eta) are conventionally called the * "standard coordinates". If the spherical coordinates are with * respect to a right-handed triad, (xi,eta) are also right-handed. * The units of (xi,eta) are, effectively, radians at the tangent * point. * * 3) All angular arguments are in radians. * * 4) This function is a member of the following set: \verbatim spherical vector solve for iauTpxes iauTpxev xi,eta > iauTpsts < iauTpstv star iauTpors iauTporv origin \endverbatim @param[in] xi rectangular coordinates of star image @param[in] eta rectangular coordinates of star image @param[in] a0 tange points' spherical cordinate @param[in] b0 tange points' spherical cordinate @param[out] a star's spherical coordinate @param[out] b star's spherical coordinate */ /*!\file tpstv.c \fn void iauTpstv(double xi, double eta, double v0[3], double v[3]) \ingroup SF \brief In the tangent plane projection, solve for the direction cosines of the star. * In the tangent plane projection, given the star's rectangular * coordinates and the direction cosines of the tangent point, solve * for the direction cosines of the star. * 1) The tangent plane projection is also called the "gnomonic * projection" and the "central projection". * * 2) The eta axis points due north in the adopted coordinate system. * If the direction cosines represent observed (RA,Dec), the tangent * plane coordinates (xi,eta) are conventionally called the * "standard coordinates". If the direction cosines are with * respect to a right-handed triad, (xi,eta) are also right-handed. * The units of (xi,eta) are, effectively, radians at the tangent * point. * * 3) The method used is to complete the star vector in the (xi,eta) * based triad and normalize it, then rotate the triad to put the * tangent point at the pole with the x-axis aligned to zero * longitude. Writing (a0,b0) for the celestial spherical * coordinates of the tangent point, the sequence of rotations is * (b-pi/2) around the x-axis followed by (-a-pi/2) around the * z-axis. * * 4) If vector v0 is not of unit length, the returned vector v will * be wrong. * * 5) If vector v0 points at a pole, the returned vector v will be * based on the arbitrary assumption that the longitude coordinate * of the tangent point is zero. * * 6) This function is a member of the following set: \verbatim spherical vector solve for iauTpxes iauTpxev xi,eta iauTpsts > iauTpstv < star iauTpors iauTporv origin \endverbatim @param[in] xi rectangular coordinates of star image @param[in] eta rectangular coordinates of star image @param[in] v0 tangent point's direction cosines @param[out] v star's directino cosines */ /*!\file tpxes.c \fn int iauTpxes(double a, double b, double a0, double b0, double *xi, double *eta) \ingroup SF \brief In the tangent plane projection, solve for the star's rectangular coordinates in the tangent plane. \ingroup SF * Notes: * * 1) The tangent plane projection is also called the "gnomonic * projection" and the "central projection". * * 2) The eta axis points due north in the adopted coordinate system. * If the spherical coordinates are observed (RA,Dec), the tangent * plane coordinates (xi,eta) are conventionally called the * "standard coordinates". For right-handed spherical coordinates, * (xi,eta) are also right-handed. The units of (xi,eta) are, * effectively, radians at the tangent point. * * 3) All angular arguments are in radians. * * 4) This function is a member of the following set: \verbatim spherical vector solve for > iauTpxes < iauTpxev xi,eta iauTpsts iauTpstv star iauTpors iauTporv origin \endverbatim @param[in] a star's spherical coordinate @param[in] b star's spherical coordinate @param[in] a0 tangent point's spherical coordinate @param[in] b0 tangent point's spherical coordinate @return 0=OK, 1=star too far from axis, 2=antistar on tangent plane, 3= antistar too far from axis. */ /*!\file tpxev.c \fn int iauTpxev(double v[3], double v0[3], double *xi, double *eta) \ingroup SF \brief In the tangent plane projection, solve for the star's rectangular coordinates in the tangent plane. \ingroup SF * In the tangent plane projection, given celestial direction cosines * for a star and the tangent point, solve for the star's rectangular * coordinates in the tangent plane. * Notes: * * 1) The tangent plane projection is also called the "gnomonic * projection" and the "central projection". * * 2) The eta axis points due north in the adopted coordinate system. * If the direction cosines represent observed (RA,Dec), the tangent * plane coordinates (xi,eta) are conventionally called the * "standard coordinates". If the direction cosines are with * respect to a right-handed triad, (xi,eta) are also right-handed. * The units of (xi,eta) are, effectively, radians at the tangent * point. * * 3) The method used is to extend the star vector to the tangent * plane and then rotate the triad so that (x,y) becomes (xi,eta). * Writing (a,b) for the celestial spherical coordinates of the * star, the sequence of rotations is (a+pi/2) around the z-axis * followed by (pi/2-b) around the x-axis. * * 4) If vector v0 is not of unit length, or if vector v is of zero * length, the results will be wrong. * * 5) If v0 points at a pole, the returned (xi,eta) will be based on * the arbitrary assumption that the longitude coordinate of the * tangent point is zero. * * 6) This function is a member of the following set: \verbatim spherical vector solve for iauTpxes > iauTpxev < xi,eta iauTpsts iauTpstv star iauTpors iauTporv origin \endverbatim @param[in] v direction cosines of the start @param[in] v0 direction cosines of the tangent point @param[in] xi tanget plane coordinate of star @param[in] eta tanget plane coordinate of star @return 0=OK, 1=star too far from axis, 2=antistar on tangent plane, 3= antistar too far from axis. */ /*!\file tr.c \fn void iauTr(double r[3][3], double rt[3][3]) \ingroup VMSF \brief Transpose an r-matrix. * * * * \param[in] r r-matrix * * \param[out] rt transpose * * Note: * It is permissible for r and rt to be the same array. * * */ /*!\file trxp.c \fn void iauTrxp(double r[3][3], double p[3], double trp[3]) \ingroup VMSF \brief Multiply a p-vector by the transpose of an r-matrix. * * \param[in] r r-matrix * \param[in] p p-vector * * \param[out] trp r^T * p * * Note: * It is permissible for p and trp to be the same array. */ /*!\file trxpv.c \fn void iauTrxpv(double r[3][3], double pv[2][3], double trpv[2][3]) \ingroup VMSF \brief Multiply a pv-vector by the transpose of an r-matrix. * * \param[in] r r-matrix * \param[in] pv pv-vector * * \param[out] trpv r * pv * * Note: * It is permissible for pv and trpv to be the same array. */ /*!\file tttai.c \fn int iauTttai(double tt1, double tt2, double *tai1, double *tai2) \ingroup C \brief TT to TAI * * Time scale transformation: Terrestrial Time, TT, to International * Atomic Time, TAI. * * * * \param[in] tt1 TT as a 2-part Julian Date * \param[in] tt2 TT as a 2-part Julian Date * * \param[out] tai1 TAI as a 2-part Julian Date * \param[out] tai2 TAI as a 2-part Julian Date * * \return * status: 0 = OK * * Note: * * tt1+tt2 is Julian Date, apportioned in any convenient way between * the two arguments, for example where tt1 is the Julian Day Number * and tt2 is the fraction of a day. The returned tai1,tai2 follow * suit. * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992) * */ /*!\file tttcg.c \fn int iauTttcg(double tt1, double tt2, double *tcg1, double *tcg2) \ingroup C \brief TT to TCG * * Time scale transformation: Terrestrial Time, TT, to Geocentric * Coordinate Time, TCG. * * * * \param[in] tt1 TT as a 2-part Julian Date * \param[in] tt2 TT as a 2-part Julian Date * * \param[out] tcg1 TCG as a 2-part Julian Date * \param[out] tcg2 TCG as a 2-part Julian Date * * \return * status: 0 = OK * * Note: * * tt1+tt2 is Julian Date, apportioned in any convenient way between * the two arguments, for example where tt1 is the Julian Day Number * and tt2 is the fraction of a day. The returned tcg1,tcg2 follow * suit. * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * IAU 2000 Resolution B1.9 * */ /*!\file tttdb.c \fn int iauTttdb(double tt1, double tt2, double dtr, double *tdb1, double *tdb2) \ingroup C \brief TT to TDB. * * Time scale transformation: Terrestrial Time, TT, to Barycentric * Dynamical Time, TDB. * * * * \param[in] tt1 TT as a 2-part Julian Date * \param[in] tt2 TT as a 2-part Julian Date * \param[in] dtr TDB-TT in seconds * * \param[out] tdb1 TDB as a 2-part Julian Date * \param[out] tdb2 TDB as a 2-part Julian Date * * \return * status: 0 = OK * * Notes: * * 1) tt1+tt2 is Julian Date, apportioned in any convenient way between * the two arguments, for example where tt1 is the Julian Day Number * and tt2 is the fraction of a day. The returned tdb1,tdb2 follow * suit. * * 2) The argument dtr represents the quasi-periodic component of the * GR transformation between TT and TCB. It is dependent upon the * adopted solar-system ephemeris, and can be obtained by numerical * integration, by interrogating a precomputed time ephemeris or by * evaluating a model such as that implemented in the SOFA function * iauDtdb. The quantity is dominated by an annual term of 1.7 ms * amplitude. * * 3) TDB is essentially the same as Teph, the time argument for the JPL * solar system ephemerides. * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * IAU 2006 Resolution 3 * */ /*!\file ttut1.c \fn int iauTtut1(double tt1, double tt2, double dt, double *ut11, double *ut12) \ingroup C \brief TT to UT1 * * Time scale transformation: Terrestrial Time, TT, to Universal Time, * UT1. * * * * \param[in] tt1 TT as a 2-part Julian Date * \param[in] tt2 TT as a 2-part Julian Date * \param[in] dt TT-UT1 in seconds * * \param[out] ut11 UT1 as a 2-part Julian Date * \param[out] ut12 UT1 as a 2-part Julian Date * * \return * 0 = OK * * Notes: * * 1) tt1+tt2 is Julian Date, apportioned in any convenient way between * the two arguments, for example where tt1 is the Julian Day Number * and tt2 is the fraction of a day. The returned ut11,ut12 follow * suit. * * 2) The argument dt is classical Delta T. * * Reference: * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992) * */ /*!\file ut1tai.c \fn int iauUt1tai(double ut11, double ut12, double dta, double *tai1, double *tai2) \ingroup C \brief UT1 to TAI * * Time scale transformation: Universal Time, UT1, to International * Atomic Time, TAI. * * * * \param[in] ut11 UT1 as a 2-part Julian Date * \param[in] ut12 UT1 as a 2-part Julian Date * \param[in] dta UT1-TAI in seconds * * \param[out] tai1 TAI as a 2-part Julian Date * \param[out] tai2 TAI as a 2-part Julian Date * * \return * 0 = OK * * Notes: * * 1) ut11+ut12 is Julian Date, apportioned in any convenient way * between the two arguments, for example where ut11 is the Julian * Day Number and ut12 is the fraction of a day. The returned * tai1,tai2 follow suit. * * 2) The argument dta, i.e. UT1-TAI, is an observed quantity, and is * available from IERS tabulations. * * Reference: * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992) * */ /*!\file ut1tt.c \fn int iauUt1tt(double ut11, double ut12, double dt, double *tt1, double *tt2) \ingroup C \brief UT1 to TT * * Time scale transformation: Universal Time, UT1, to Terrestrial * Time, TT. * * * * \param[in] ut11 UT1 as a 2-part Julian Date * \param[in] ut12 UT1 as a 2-part Julian Date * \param[in] dt TT-UT1 in seconds * * \param[out] tt1 TT as a 2-part Julian Date * \param[out] tt2 TT as a 2-part Julian Date * * \return * 0 = OK * * Notes: * * 1) ut11+ut12 is Julian Date, apportioned in any convenient way * between the two arguments, for example where ut11 is the Julian * Day Number and ut12 is the fraction of a day. The returned * tt1,tt2 follow suit. * * 2) The argument dt is classical Delta T. * * Reference: * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992) * */ /*!\file ut1utc.c \fn int iauUt1utc(double ut11, double ut12, double dut1, double *utc1, double *utc2) \ingroup C \brief UT1 to UTC * * Time scale transformation: Universal Time, UT1, to Coordinated * Universal Time, UTC. * * * * \param[in] ut11 UT1 as a 2-part Julian Date (Note 1) * \param[in] ut12 UT1 as a 2-part Julian Date (Note 1) * \param[in] dut1 Delta UT1: UT1-UTC in seconds (Note 2) * * \param[out] utc1 UTC as a 2-part quasi Julian Date (Notes 3,4) * \param[out] utc2 UTC as a 2-part quasi Julian Date (Notes 3,4) * * \return * +1 = dubious year (Note 5) * 0 = OK * -1 = unacceptable date * * Notes: * * 1) ut11+ut12 is Julian Date, apportioned in any convenient way * between the two arguments, for example where ut11 is the Julian * Day Number and ut12 is the fraction of a day. The returned utc1 * and utc2 form an analogous pair, except that a special convention * is used, to deal with the problem of leap seconds - see Note 3. * * 2) Delta UT1 can be obtained from tabulations provided by the * International Earth Rotation and Reference Systems Service. The * value changes abruptly by 1s at a leap second; however, close to * a leap second the algorithm used here is tolerant of the "wrong" * choice of value being made. * * 3) JD cannot unambiguously represent UTC during a leap second unless * special measures are taken. The convention in the present * function is that the returned quasi JD day UTC1+UTC2 represents * UTC days whether the length is 86399, 86400 or 86401 SI seconds. * * 4) The function iauD2dtf can be used to transform the UTC quasi-JD * into calendar date and clock time, including UTC leap second * handling. * * 5) The warning status "dubious year" flags UTCs that predate the * introduction of the time scale or that are too far in the future * to be trusted. See iauDat for further details. * * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992) * */ /*!\file utctai.c \fn int iauUtctai(double utc1, double utc2, double *tai1, double *tai2) \ingroup C \brief UTC to TAI. * * Time scale transformation: Coordinated Universal Time, UTC, to * International Atomic Time, TAI. * * * * \param[in] utc1 UTC as a 2-part quasi Julian Date (Notes 1-4) * \param[in] utc2 UTC as a 2-part quasi Julian Date (Notes 1-4) * * \param[out] tai1 TAI as a 2-part Julian Date (Note 5) * \param[out] tai2 TAI as a 2-part Julian Date (Note 5) * * \return * +1 = dubious year (Note 3) * 0 = OK * -1 = unacceptable date * * Notes: * * 1) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any * convenient way between the two arguments, for example where utc1 * is the Julian Day Number and utc2 is the fraction of a day. * * 2) JD cannot unambiguously represent UTC during a leap second unless * special measures are taken. The convention in the present * function is that the JD day represents UTC days whether the * length is 86399, 86400 or 86401 SI seconds. In the 1960-1972 era * there were smaller jumps (in either direction) each time the * linear UTC(TAI) expression was changed, and these "mini-leaps" * are also included in the SOFA convention. * * 3) The warning status "dubious year" flags UTCs that predate the * introduction of the time scale or that are too far in the future * to be trusted. See iauDat for further details. * * 4) The function iauDtf2d converts from calendar date and time of day * into 2-part Julian Date, and in the case of UTC implements the * leap-second-ambiguity convention described above. * * 5) The returned TAI1,TAI2 are such that their sum is the TAI Julian * Date. * * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992) * */ /*!\file utcut1.c \fn int iauUtcut1(double utc1, double utc2, double dut1, double *ut11, double *ut12) \ingroup C \brief UTC to UT1 * * Time scale transformation: Coordinated Universal Time, UTC, to * Universal Time, UT1. * * * * \param[in] utc1 UTC as a 2-part quasi Julian Date (Notes 1-4) * \param[in] utc2 UTC as a 2-part quasi Julian Date (Notes 1-4) * \param[in] dut1 Delta UT1 = UT1-UTC in seconds (Note 5) * * \param[out] ut11 UT1 as a 2-part Julian Date (Note 6) * \param[out] ut12 UT1 as a 2-part Julian Date (Note 6) * * \return * +1 = dubious year (Note 3) * 0 = OK * -1 = unacceptable date * * Notes: * * 1) utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any * convenient way between the two arguments, for example where utc1 * is the Julian Day Number and utc2 is the fraction of a day. * * 2) JD cannot unambiguously represent UTC during a leap second unless * special measures are taken. The convention in the present * function is that the JD day represents UTC days whether the * length is 86399, 86400 or 86401 SI seconds. * * 3) The warning status "dubious year" flags UTCs that predate the * introduction of the time scale or that are too far in the future * to be trusted. See iauDat for further details. * * 4) The function iauDtf2d converts from calendar date and time of * day into 2-part Julian Date, and in the case of UTC implements * the leap-second-ambiguity convention described above. * * 5) Delta UT1 can be obtained from tabulations provided by the * International Earth Rotation and Reference Systems Service. * It is the caller's responsibility to supply a dut1 argument * containing the UT1-UTC value that matches the given UTC. * * 6) The returned ut11,ut12 are such that their sum is the UT1 Julian * Date. * * References: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * * Explanatory Supplement to the Astronomical Almanac, * P. Kenneth Seidelmann (ed), University Science Books (1992) * * */ /*!\file xy06.c \fn void iauXy06(double date1, double date2, double *x, double *y) \ingroup CM \brief X,Y coordinates of celestial intermediate pole * * X,Y coordinates of celestial intermediate pole from series based * on IAU 2006 precession and IAU 2000A nutation. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] x CIP X,Y coordinates (Note 2) * \param[out] y CIP X,Y coordinates (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The X,Y coordinates are those of the unit vector towards the * celestial intermediate pole. They represent the combined effects * of frame bias, precession and nutation. * * 3) The fundamental arguments used are as adopted in IERS Conventions * (2003) and are from Simon et al. (1994) and Souchay et al. * (1999). * * 4) This is an alternative to the angles-based method, via the SOFA * function iauFw2xy and as used in iauXys06a for example. The two * methods agree at the 1 microarcsecond level (at present), a * negligible amount compared with the intrinsic accuracy of the * models. However, it would be unwise to mix the two methods * (angles-based and series-based) in a single application. * * References: * * Capitaine, N., Wallace, P.T. & Chapront, J., 2003, * Astron.Astrophys., 412, 567 * * Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 * * McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), * IERS Technical Note No. 32, BKG * * Simon, J.L., Bretagnon, P., Chapront, J., Chapront-Touze, M., * Francou, G. & Laskar, J., Astron.Astrophys., 1994, 282, 663 * * Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M., 1999, * Astron.Astrophys.Supp.Ser. 135, 111 * * Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 */ /*!\file xys00a.c \fn void iauXys00a(double date1, double date2, double *x, double *y, double *s) \ingroup SF \brief Compute X,Y coordinates of the CIP and CIO locator * * For a given TT date, compute the X,Y coordinates of the Celestial * Intermediate Pole and the CIO locator s, using the IAU 2000A * precession-nutation model. * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] x Celestial Intermediate Pole (Note 2) * \param[out] y Celestial Intermediate Pole (Note 2) * \param[out] s the CIO locator s (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The Celestial Intermediate Pole coordinates are the x,y * components of the unit vector in the Geocentric Celestial * Reference System. * * 3) The CIO locator s (in radians) positions the Celestial * Intermediate Origin on the equator of the CIP. * * 4) A faster, but slightly less accurate result (about 1 mas for * X,Y), can be obtained by using instead the iauXys00b function. * * Reference: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) */ /*!\file xys00b.c \fn void iauXys00b(double date1, double date2, double *x, double *y, double *s) \ingroup SF \brief Compute X,Y coordinates of the CIP and CIO locator * * For a given TT date, compute the X,Y coordinates of the Celestial * Intermediate Pole and the CIO locator s, using the IAU 2000B * precession-nutation model. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] x Celestial Intermediate Pole (Note 2) * \param[out] y Celestial Intermediate Pole (Note 2) * \param[out] s the CIO locator s (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The Celestial Intermediate Pole coordinates are the x,y * components of the unit vector in the Geocentric Celestial * Reference System. * * 3) The CIO locator s (in radians) positions the Celestial * Intermediate Origin on the equator of the CIP. * * 4) The present function is faster, but slightly less accurate (about * 1 mas in X,Y), than the iauXys00a function. * * * Reference: * * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), * IERS Technical Note No. 32, BKG (2004) * */ /*!\file xys06a.c \fn void iauXys06a(double date1, double date2, double *x, double *y, double *s) \ingroup SF \brief Compute X,Y coordinates of the CIP and CIO locator * * For a given TT date, compute the X,Y coordinates of the Celestial * Intermediate Pole and the CIO locator s, using the IAU 2006 * precession and IAU 2000A nutation models. * * * * \param[in] date1 TT as a 2-part Julian Date (Note 1) * \param[in] date2 TT as a 2-part Julian Date (Note 1) * * \param[out] x Celestial Intermediate Pole (Note 2) * \param[out] y Celestial Intermediate Pole (Note 2) * \param[out] s the CIO locator s (Note 2) * * Notes: * * 1) The TT date date1+date2 is a Julian Date, apportioned in any * convenient way between the two arguments. For example, * JD(TT)=2450123.7 could be expressed in any of these ways, * among others: * * date1 date2 * * 2450123.7 0.0 (JD method) * 2451545.0 -1421.3 (J2000 method) * 2400000.5 50123.2 (MJD method) * 2450123.5 0.2 (date & time method) * * The JD method is the most natural and convenient to use in * cases where the loss of several decimal digits of resolution * is acceptable. The J2000 method is best matched to the way * the argument is handled internally and will deliver the * optimum resolution. The MJD method and the date & time methods * are both good compromises between resolution and convenience. * * 2) The Celestial Intermediate Pole coordinates are the x,y components * of the unit vector in the Geocentric Celestial Reference System. * * 3) The CIO locator s (in radians) positions the Celestial * Intermediate Origin on the equator of the CIP. * * 4) Series-based solutions for generating X and Y are also available: * see Capitaine & Wallace (2006) and iauXy06. * * * References: * * Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855 * * Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981 * */ /*!\file zp.c *\fn iauZp(double p[3]) \ingroup VMSF \brief Zero a p-vector. * * * * Returned: * \param[out] p p-vector * */ /*!\file zpv.c \fn void iauZpv(double pv[2][3]) \ingroup VMSF \brief Zero a pv-vector. * * * * Returned: * \param[out] pv pv-vector * * */ /*!\file zr.c \fn void iauZr(double r[3][3]) \ingroup VMSF \brief Initialize an r-matrix to the null matrix. * * * * Returned: * \param[out] r r-matrix * */ /*! \file sofam.h */ /*!\struct iauASTROM * \brief Star-independent astrometry parameters * (Vectors eb, eh, em and v are all with respect to BCRS axes.) * \var iauASTROM::pmt * \brief PM time interval (SSB, Julian years) * * \var iauASTROM::eb * \brief SSB to observer (vector, au) * \var iauASTROM::eh * \brief Sun to observer (unit vector) * \var iauASTROM::em * \brief distance from Sun to observer (au) * \var iauASTROM::v * \brief barycentric observer velocity (vector, c) * \var iauASTROM::bm1 * \brief sqrt(1-|v|^2): reciprocal of Lorenz factor * \var iauASTROM::bpn * \brief bias-precession-nutation matrix * \var iauASTROM::along * \brief longitude + s' + dERA(DUT) (radians) * \var iauASTROM::phi * \brief geodetic latitude (radians) * \var iauASTROM::xpl * \brief polar motion xp wrt local meridian (radians) * \var iauASTROM::ypl * \brief polar motion yp wrt local meridian (radians) * \var iauASTROM::sphi * \brief sine of geodetic latitude * \var iauASTROM::cphi * \brief cosine of geodetic latitude * \var iauASTROM::diurab * \brief magnitude of diurnal aberration vector * \var iauASTROM::eral * \brief "local" Earth rotation angle (radians) * \var iauASTROM::refa * \brief refraction constant A (radians) * \var iauASTROM::refb * \brief refraction constant B (radians) */ /*! \struct iauLDBODY * \brief Body parameters for light deflection * \var iauLDBODY::bm * \brief mass of the body (solar masses) * \var iauLDBODY::dl * \brief deflection limiter (radians^2/2) * \var iauLDBODY::pv * \brief barycentric PV of the body (au, au/day) */ /*! \def DPI * \brief Pi */ /*! \def D2PI * \brief 2 times pi */ /*! \def DR2D * \brief Radians to degrees */ /*! \def DD2R * \brief Degrees to radians */ /*! \def DR2AS * \brief Radians to arcseconds */ /*! \def DAS2R * \brief Arcseconds to radians */ /*! \def DS2R * \brief Seconds of time to radians */ /*! \def TURNAS * \brief Arcseconds in a full circle */ /*! \def DMAS2R * \brief Milliarcseconds to radians */ /*! \def DTY * \brief Length of tropical year B1900 (days) */ /*! \def DAYSEC * \brief Seconds per day. */ /*! \def DJY * \brief Days per Julian year */ /*! \def DJC * \brief Days per Julian century */ /*! \def DJM * \brief Days per Julian millennium */ /*! \def DJ00 * \brief Reference epoch (J2000.0), Julian Date */ */ /*! \def DJM0 * \brief Julian Date of Modified Julian Date zero */ */ /*! \def DJM00 * \brief Reference epoch (J2000.0), Modified Julian Date */ */ /*! \def DJM77 * \brief 1977 Jan 1.0 as MJD */ */ /*! \def TTMTAI * \brief TT minus TAI (s) */ */ /*! \def DAU * \brief Astronomical unit (m, IAU 2012) */ */ /*! \def CMPS * \brief Speed of light (m/s) */ */ /*! \def AULT * \brief Light time for 1 au (s) */ */ /*! \def DC * \brief Speed of light (AU per day) */ */ /*! \def ELG * \brief L_G = 1 - d(TT)/d(TCG) */ */ /*! \def ELB * \brief L_B = 1 - d(TDB)/d(TCB) */ /*! \def TDB0 * \brief TDB (s) at TAI 1977/1/1.0 */ */ /*! \def SRS * \brief Schwarzschild radius of the Sun (au) * = 2 * 1.32712440041e20 / (2.99792458e8)^2 / 1.49597870700e11 */ /*! \def dint * \brief truncate to nearest whole number towards zero (double) */ */ /*! \def dnint * \brief round to nearest whole number (double) */ */ /*! \def dsign * \brief magnitude of A with sign of B (double) */ */ /*! \def gmax * \brief larger (most +ve) of two numbers (generic) */ */ /*! \def gmin * \brief smaller (least +ve) of two numbers (generic) */ */ /*! \def WGS84 \brief Reference ellipsoid */ /*! \def GRS80 \brief Reference ellipsoid */ /*! \def WGS72 \brief Reference ellipsoid */