#include "sofa.h" void iauFk45z(double r1950, double d1950, double bepoch, double *r2000, double *d2000) /* ** - - - - - - - - - ** i a u F k 4 5 z ** - - - - - - - - - ** ** Convert a B1950.0 FK4 star position to J2000.0 FK5, assuming zero ** proper motion in the FK5 system. ** ** 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, ** 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. ** ** Given: ** r1950,d1950 double B1950.0 FK4 RA,Dec at epoch (rad) ** bepoch double Besselian epoch (e.g. 1979.3D0) ** ** Returned: ** r2000,d2000 double J2000.0 FK5 RA,Dec (rad) ** ** 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. ** ** 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. ** ** Called: ** iauAnp normalize angle into range 0 to 2pi ** iauC2s p-vector to spherical ** iauEpb2jd Besselian epoch to Julian date ** iauEpj Julian date to Julian epoch ** iauPdp scalar product of two p-vectors ** iauPmp p-vector minus p-vector ** iauPpsp p-vector plus scaled p-vector ** iauPvu update a pv-vector ** iauS2c spherical to p-vector ** ** 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; /* Position and position+velocity vectors */ double r0[3], p[3], pv[2][3]; /* Miscellaneous */ double w, djm0, djm; int i, j, k; /* ** CANONICAL CONSTANTS (Seidelmann 1992) */ /* Vectors A and Adot (Seidelmann 3.591-2) */ static double a[3] = { -1.62557e-6, -0.31919e-6, -0.13843e-6 }; static double ad[3] = { +1.245e-3, -1.580e-3, -0.659e-3 }; /* 3x2 matrix of p-vectors (cf. Seidelmann 3.591-4, matrix M) */ static double em[2][3][3] = { { { +0.9999256782, -0.0111820611, -0.0048579477 }, { +0.0111820610, +0.9999374784, -0.0000271765 }, { +0.0048579479, -0.0000271474, +0.9999881997 } }, { { -0.000551, -0.238565, +0.435739 }, { +0.238514, -0.002667, -0.008541 }, { -0.435623, +0.012254, +0.002117 } } }; /*- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ /* Spherical coordinates to p-vector. */ iauS2c(r1950, d1950, r0); /* Adjust p-vector A to give zero proper motion in FK5. */ w = (bepoch - 1950) / PMF; iauPpsp(a, w, ad, p); /* Remove E-terms. */ iauPpsp(p, -iauPdp(r0,p), r0, p); iauPmp(r0, p, p); /* Convert to Fricke system pv-vector (cf. Seidelmann 3.591-3). */ for ( i = 0; i < 2; i++ ) { for ( j = 0; j < 3; j++ ) { w = 0.0; for ( k = 0; k < 3; k++ ) { w += em[i][j][k] * p[k]; } pv[i][j] = w; } } /* Allow for fictitious proper motion. */ iauEpb2jd(bepoch, &djm0, &djm); w = (iauEpj(djm0,djm)-2000.0) / PMF; iauPvu(w, pv, pv); /* Revert to spherical coordinates. */ iauC2s(pv[0], &w, d2000); *r2000 = iauAnp(w); /* 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 ** **--------------------------------------------------------------------*/ }