#include "sofa.h" 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) /* ** - - - - - - - - - ** i a u F k 4 2 5 ** - - - - - - - - - ** ** Convert B1950.0 FK4 star catalog data to J2000.0 FK5. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** This function converts a star's catalog data from the old FK4 ** (Bessel-Newcomb) system to the later IAU 1976 FK5 (Fricke) system. ** ** Given: (all B1950.0, FK4) ** r1950,d1950 double B1950.0 RA,Dec (rad) ** dr1950,dd1950 double B1950.0 proper motions (rad/trop.yr) ** p1950 double parallax (arcsec) ** v1950 double radial velocity (km/s, +ve = moving away) ** ** Returned: (all J2000.0, FK5) ** r2000,d2000 double J2000.0 RA,Dec (rad) ** dr2000,dd2000 double J2000.0 proper motions (rad/Jul.yr) ** p2000 double parallax (arcsec) ** v2000 double radial velocity (km/s, +ve = moving away) ** ** 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. ** ** Called: ** iauAnp normalize angle into range 0 to 2pi ** iauPv2s pv-vector to spherical coordinates ** iauPdp scalar product of two p-vectors ** iauPvmpv pv-vector minus pv_vector ** iauPvppv pv-vector plus pv_vector ** iauS2pv spherical coordinates to pv-vector ** iauSxp multiply p-vector by scalar ** ** 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. ** ** This revision: 2018 December 5 ** ** SOFA release 2020-07-21 ** ** Copyright (C) 2020 IAU SOFA Board. See notes at end. */ { /* Radians per year to arcsec per century */ const double PMF = 100.0*DR2AS; /* Small number to avoid arithmetic problems */ const double TINY = 1e-30; /* Miscellaneous */ double r, d, ur, ud, px, rv, pxvf, w, rd; int i, j, k, l; /* Pv-vectors */ double r0[2][3], pv1[2][3], pv2[2][3]; /* ** CANONICAL CONSTANTS (Seidelmann 1992) */ /* Km per sec to AU per tropical century */ /* = 86400 * 36524.2198782 / 149597870.7 */ const double VF = 21.095; /* Constant pv-vector (cf. Seidelmann 3.591-2, vectors A and Adot) */ static double a[2][3] = { { -1.62557e-6, -0.31919e-6, -0.13843e-6 }, { +1.245e-3, -1.580e-3, -0.659e-3 } }; /* 3x2 matrix of pv-vectors (cf. Seidelmann 3.591-4, matrix M) */ static double em[2][3][2][3] = { { { { +0.9999256782, -0.0111820611, -0.0048579477 }, { +0.00000242395018, -0.00000002710663, -0.00000001177656 } }, { { +0.0111820610, +0.9999374784, -0.0000271765 }, { +0.00000002710663, +0.00000242397878, -0.00000000006587 } }, { { +0.0048579479, -0.0000271474, +0.9999881997, }, { +0.00000001177656, -0.00000000006582, +0.00000242410173 } } }, { { { -0.000551, -0.238565, +0.435739 }, { +0.99994704, -0.01118251, -0.00485767 } }, { { +0.238514, -0.002667, -0.008541 }, { +0.01118251, +0.99995883, -0.00002718 } }, { { -0.435623, +0.012254, +0.002117 }, { +0.00485767, -0.00002714, +1.00000956 } } } }; /*- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ /* The FK4 data (units radians and arcsec per tropical century). */ r = r1950; d = d1950; ur = dr1950*PMF; ud = dd1950*PMF; px = p1950; rv = v1950; /* Express as a pv-vector. */ pxvf = px*VF; w = rv*pxvf; iauS2pv(r, d, 1.0, ur, ud, w, r0); /* Allow for E-terms (cf. Seidelmann 3.591-2). */ iauPvmpv(r0, a, pv1); iauSxp(iauPdp(r0[0], a[0]), r0[0], pv2[0]); iauSxp(iauPdp(r0[0], a[1]), r0[0], pv2[1]); iauPvppv(pv1, pv2, pv1); /* Convert pv-vector to Fricke system (cf. Seidelmann 3.591-3). */ for ( i = 0; i < 2; i++ ) { for ( j = 0; j < 3; j++ ) { w = 0.0; for ( k = 0; k < 2; k++ ) { for ( l = 0; l < 3; l++ ) { w += em[i][j][k][l] * pv1[k][l]; } } pv2[i][j] = w; } } /* Revert to catalog form. */ iauPv2s(pv2, &r, &d, &w, &ur, &ud, &rd); if ( px > TINY ) { rv = rd/pxvf; px = px/w; } /* Return the results. */ *r2000 = iauAnp(r); *d2000 = d; *dr2000 = ur/PMF; *dd2000 = ud/PMF; *v2000 = rv; *p2000 = px; /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2020 ** 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: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ }