#include "sofa.h" #include "sofam.h" 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) /* ** - - - - - - - - - ** i a u F k 5 2 4 ** - - - - - - - - - ** ** Convert J2000.0 FK5 star catalog data to B1950.0 FK4. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: (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) ** ** Returned: (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) ** ** 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. ** ** Called: ** iauAnp normalize angle into range 0 to 2pi ** iauPdp scalar product of two p-vectors ** iauPm modulus of p-vector ** iauPmp p-vector minus p-vector ** iauPpp p-vector pluus p-vector ** iauPv2s pv-vector to spherical coordinates ** 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: 2021 February 24 ** ** SOFA release 2021-05-12 ** ** Copyright (C) 2021 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; /* Vectors, p and pv */ double r0[2][3], r1[2][3], p1[3], p2[3], pv[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 3.592-1, matrix M^-1) */ static double em[2][3][2][3] = { { { { +0.9999256795, +0.0111814828, +0.0048590039, }, { -0.00000242389840, -0.00000002710544, -0.00000001177742 } }, { { -0.0111814828, +0.9999374849, -0.0000271771, }, { +0.00000002710544, -0.00000242392702, +0.00000000006585 } }, { { -0.0048590040, -0.0000271557, +0.9999881946, }, { +0.00000001177742, +0.00000000006585, -0.00000242404995 } } }, { { { -0.000551, +0.238509, -0.435614, }, { +0.99990432, +0.01118145, +0.00485852 } }, { { -0.238560, -0.002667, +0.012254, }, { -0.01118145, +0.99991613, -0.00002717 } }, { { +0.435730, -0.008541, +0.002117, }, { -0.00485852, -0.00002716, +0.99996684 } } } }; /*- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ /* The FK5 data (units radians and arcsec per Julian century). */ r = r2000; d = d2000; ur = dr2000*PMF; ud = dd2000*PMF; px = p2000; rv = v2000; /* Express as a pv-vector. */ pxvf = px * VF; w = rv * pxvf; iauS2pv(r, d, 1.0, ur, ud, w, r0); /* Convert pv-vector to Bessel-Newcomb system (cf. Seidelmann 3.592-1). */ 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] * r0[k][l]; } } r1[i][j] = w; } } /* Apply E-terms (equivalent to Seidelmann 3.592-3, one iteration). */ /* Direction. */ w = iauPm(r1[0]); iauSxp(iauPdp(r1[0],a[0]), r1[0], p1); iauSxp(w, a[0], p2); iauPmp(p2, p1, p1); iauPpp(r1[0], p1, p1); /* Recompute length. */ w = iauPm(p1); /* Direction. */ iauSxp(iauPdp(r1[0],a[0]), r1[0], p1); iauSxp(w, a[0], p2); iauPmp(p2, p1, p1); iauPpp(r1[0], p1, pv[0]); /* Derivative. */ iauSxp(iauPdp(r1[0],a[1]), pv[0], p1); iauSxp(w, a[1], p2); iauPmp(p2, p1, p1); iauPpp(r1[1], p1, pv[1]); /* Revert to catalog form. */ iauPv2s(pv, &r, &d, &w, &ur, &ud, &rd); if ( px > TINY ) { rv = rd/pxvf; px = px/w; } /* Return the results. */ *r1950 = iauAnp(r); *d1950 = d; *dr1950 = ur/PMF; *dd1950 = ud/PMF; *p1950 = px; *v1950 = rv; /* Finished. */ /*---------------------------------------------------------------------- ** ** Copyright (C) 2021 ** 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. 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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 ** **--------------------------------------------------------------------*/ }