void iauAticqn(double ri, double di, iauASTROM *astrom, int n, iauLDBODY b[], double *rc, double *dc) /* ** - - - - - - - - - ** i a u A t i c q n ** - - - - - - - - - ** ** 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. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** ri,di double CIRS RA,Dec (radians) ** astrom iauASTROM* star-independent astrometry parameters: ** pmt double PM time interval (SSB, Julian years) ** eb double[3] SSB to observer (vector, au) ** eh double[3] Sun to observer (unit vector) ** em double distance from Sun to observer (au) ** v double[3] barycentric observer velocity (vector, c) ** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor ** bpn double[3][3] bias-precession-nutation matrix ** along double longitude + s' (radians) ** xpl double polar motion xp wrt local meridian (radians) ** ypl double polar motion yp wrt local meridian (radians) ** sphi double sine of geodetic latitude ** cphi double cosine of geodetic latitude ** diurab double magnitude of diurnal aberration vector ** eral double "local" Earth rotation angle (radians) ** refa double refraction constant A (radians) ** refb double refraction constant B (radians) ** n int number of bodies (Note 3) ** b iauLDBODY[n] data for each of the n bodies (Notes 3,4): ** bm double mass of the body (solar masses, Note 5) ** dl double deflection limiter (Note 6) ** pv [2][3] barycentric PV of the body (au, au/day) ** ** Returned: ** rc,dc double ICRS astrometric RA,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. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauTrxp product of transpose of r-matrix and p-vector ** iauZp zero p-vector ** iauAb stellar aberration ** iauLdn light deflection by n bodies ** iauC2s p-vector to spherical ** iauAnp normalize angle into range +/- pi ** ** This revision: 2013 October 9 ** ** SOFA release 2015-02-09 ** ** Copyright (C) 2015 IAU SOFA Board. See notes at end. */ { int j, i; double pi[3], ppr[3], pnat[3], pco[3], w, d[3], before[3], r2, r, after[3]; /* CIRS RA,Dec to Cartesian. */ iauS2c(ri, di, pi); /* Bias-precession-nutation, giving GCRS proper direction. */ iauTrxp(astrom->bpn, pi, ppr); /* Aberration, giving GCRS natural direction. */ iauZp(d); for (j = 0; j < 2; j++) { r2 = 0.0; for (i = 0; i < 3; i++) { w = ppr[i] - d[i]; before[i] = w; r2 += w*w; } r = sqrt(r2); for (i = 0; i < 3; i++) { before[i] /= r; } iauAb(before, astrom->v, astrom->em, astrom->bm1, after); r2 = 0.0; for (i = 0; i < 3; i++) { d[i] = after[i] - before[i]; w = ppr[i] - d[i]; pnat[i] = w; r2 += w*w; } r = sqrt(r2); for (i = 0; i < 3; i++) { pnat[i] /= r; } } /* Light deflection, giving BCRS coordinate direction. */ iauZp(d); for (j = 0; j < 5; j++) { r2 = 0.0; for (i = 0; i < 3; i++) { w = pnat[i] - d[i]; before[i] = w; r2 += w*w; } r = sqrt(r2); for (i = 0; i < 3; i++) { before[i] /= r; } iauLdn(n, b, astrom->eb, before, after); r2 = 0.0; for (i = 0; i < 3; i++) { d[i] = after[i] - before[i]; w = pnat[i] - d[i]; pco[i] = w; r2 += w*w; } r = sqrt(r2); for (i = 0; i < 3; i++) { pco[i] /= r; } } /* ICRS astrometric RA,Dec. */ iauC2s(pco, &w, dc); *rc = iauAnp(w); /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2015 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: [email protected] ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ }
void iauHfk5z(double rh, double dh, double date1, double date2, double *r5, double *d5, double *dr5, double *dd5) /* ** - - - - - - - - - ** i a u H f k 5 z ** - - - - - - - - - ** ** Transform a Hipparcos star position into FK5 J2000.0, assuming ** zero Hipparcos proper motion. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** rh double Hipparcos RA (radians) ** dh double Hipparcos Dec (radians) ** date1,date2 double TDB date (Note 1) ** ** Returned (all FK5, equinox J2000.0, date date1+date2): ** r5 double RA (radians) ** d5 double Dec (radians) ** dr5 double FK5 RA proper motion (rad/year, Note 4) ** dd5 double 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. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauFk5hip FK5 to Hipparcos rotation and spin ** iauRxp product of r-matrix and p-vector ** iauSxp multiply p-vector by scalar ** iauRxr product of two r-matrices ** iauTrxp product of transpose of r-matrix and p-vector ** iauPxp vector product of two p-vectors ** iauPv2s pv-vector to spherical ** iauAnp normalize angle into range 0 to 2pi ** ** Reference: ** ** F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739. ** ** This revision: 2013 June 18 ** ** SOFA release 2013-12-02 ** ** Copyright (C) 2013 IAU SOFA Board. See notes at end. */ { double t, ph[3], r5h[3][3], s5h[3], sh[3], vst[3], rst[3][3], r5ht[3][3], pv5e[2][3], vv[3], w, r, v; /* Time interval from fundamental epoch J2000.0 to given date (JY). */ t = ((date1 - DJ00) + date2) / DJY; /* Hipparcos barycentric position vector (normalized). */ iauS2c(rh, dh, ph); /* FK5 to Hipparcos orientation matrix and spin vector. */ iauFk5hip(r5h, s5h); /* Rotate the spin into the Hipparcos system. */ iauRxp(r5h, s5h, sh); /* Accumulated Hipparcos wrt FK5 spin over that interval. */ iauSxp(t, s5h, vst); /* Express the accumulated spin as a rotation matrix. */ iauRv2m(vst, rst); /* Rotation matrix: accumulated spin, then FK5 to Hipparcos. */ iauRxr(r5h, rst, r5ht); /* De-orient & de-spin the Hipparcos position into FK5 J2000.0. */ iauTrxp(r5ht, ph, pv5e[0]); /* Apply spin to the position giving a space motion. */ iauPxp(sh, ph, vv); /* De-orient & de-spin the Hipparcos space motion into FK5 J2000.0. */ iauTrxp(r5ht, vv, pv5e[1]); /* FK5 position/velocity pv-vector to spherical. */ iauPv2s(pv5e, &w, d5, &r, dr5, dd5, &v); *r5 = iauAnp(w); return; /*---------------------------------------------------------------------- ** ** Copyright (C) 2013 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: [email protected] ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ }
void iauLteceq(double epj, double dl, double db, double *dr, double *dd) /* ** - - - - - - - - - - ** i a u L t e c e q ** - - - - - - - - - - ** ** Transformation from ecliptic coordinates (mean equinox and ecliptic ** of date) to ICRS RA,Dec, using a long-term precession model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** epj double Julian epoch (TT) ** dl,db double ecliptic longitude and latitude (radians) ** ** Returned: ** dr,dd double ICRS right ascension and declination (radians) ** ** 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. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauLtecm J2000.0 to ecliptic rotation matrix, long term ** iauTrxp product of transpose of r-matrix and p-vector ** iauC2s unit vector to spherical coordinates ** iauAnp normalize angle into range 0 to 2pi ** iauAnpm normalize angle into range +/- pi ** ** 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 ** ** This revision: 2016 February 9 ** ** SOFA release 2016-05-03 ** ** Copyright (C) 2016 IAU SOFA Board. See notes at end. */ { double rm[3][3], v1[3], v2[3], a, b; /* Spherical to Cartesian. */ iauS2c(dl, db, v1); /* Rotation matrix, ICRS equatorial to ecliptic. */ iauLtecm(epj, rm); /* The transformation from ecliptic to ICRS. */ iauTrxp(rm, v1, v2); /* Cartesian to spherical. */ iauC2s(v2, &a, &b); /* Express in conventional ranges. */ *dr = iauAnp(a); *dd = iauAnpm(b); /*---------------------------------------------------------------------- ** ** Copyright (C) 2016 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** with the following requirements: ** ** a) Your work shall be marked or carry a statement that it ** (i) uses routines and computations derived by you from ** software provided by SOFA under license to you; and ** (ii) does not itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) The origin of the SOFA components of your derived work must ** not be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** e) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have ** granted a further right to modify the source code of your ** derived work. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA makes no warranties, express or implied, as ** to non-infringement of third party rights, merchantability, or ** fitness for any particular purpose. In no event will SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: [email protected] ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ }