SUBROUTINE iau_FK45Z ( R1950, D1950, BEPOCH, R2000, 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 routine is part of the International Astronomical Union's * SOFA (Standards of Fundamental Astronomy) software collection. * * Status: support routine. * * This routine 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 d B1950.0 FK4 RA,Dec at epoch (rad) * BEPOCH d Besselian epoch (e.g. 1979.3D0) * * Returned: * R2000,D2000 d 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 iau_FK425 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: * iau_ANP normalize angle into range 0 to 2pi * iau_C2S p-vector to spherical * iau_EPB2JD Besselian epoch to Julian date * iau_EPJ Julian date to Julian epoch * iau_PDP scalar product of two p-vectors * iau_PMP p-vector minus p-vector * iau_PPSP p-vector plus scaled p-vector * iau_PVU update a pv-vector * iau_S2C spherical to p-vector * * This revision: 2018 January 11 * * SOFA release 2021-05-12 * * Copyright (C) 2021 IAU SOFA Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION R1950, D1950, BEPOCH, R2000, D2000 * 2pi DOUBLE PRECISION D2PI PARAMETER ( D2PI = 6.283185307179586476925287D0 ) * Radians per year to arcsec per century DOUBLE PRECISION PMF PARAMETER ( PMF = 100D0*60D0*60D0*360D0/D2PI ) * Position and position+velocity vectors DOUBLE PRECISION R0(3), A1(3), P1(3), P2(3), PV1(3,2), PV2(3,2) * Miscellaneous DOUBLE PRECISION W, DJM0, DJM INTEGER K, J, I * Functions DOUBLE PRECISION iau_EPJ, iau_ANP * * CANONICAL CONSTANTS * * Vectors A and Adot (Seidelmann 3.591-2) DOUBLE PRECISION A(3), AD(3) DATA A,AD/ -1.62557D-6, -0.31919D-6, -0.13843D-6, : +1.245D-3, -1.580D-3, -0.659D-3 / * 3x2 matrix of p-vectors (cf. Seidelmann 3.591-4, matrix M) DOUBLE PRECISION EM(3,3,2) DATA EM / : +0.9999256782D0, -0.0111820611D0, -0.0048579477D0, : +0.0111820610D0, +0.9999374784D0, -0.0000271765D0, : +0.0048579479D0, -0.0000271474D0, +0.9999881997D0, : -0.000551D0, -0.238565D0, +0.435739D0, : +0.238514D0, -0.002667D0, -0.008541D0, : -0.435623D0, +0.012254D0, +0.002117D0 : / * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Spherical coordinates to p-vector. CALL iau_S2C ( R1950, D1950, R0 ) * Adjust p-vector A to give zero proper motion in FK5. W = ( BEPOCH - 1950D0 ) / PMF CALL iau_PPSP ( A, W, AD, A1 ) * Remove E-terms. CALL iau_PDP ( R0, A1, W ) CALL iau_PPSP ( A1, -W, R0, P1 ) CALL iau_PMP ( R0, P1, P2 ) * Convert to Fricke system pv-vector (cf. Seidelmann 3.591-3). DO 3 K = 1,2 DO 2 J=1,3 W = 0D0 DO 1 I=1,3 W = W + EM(I,J,K)*P2(I) 1 CONTINUE PV1(J,K) = W 2 CONTINUE 3 CONTINUE * Allow for fictitious proper motion. CALL iau_EPB2JD ( BEPOCH, DJM0, DJM ) W = ( iau_EPJ(DJM0,DJM) - 2000D0 ) / PMF CALL iau_PVU ( W, PV1, PV2 ) * Revert to spherical coordinates. CALL iau_C2S ( PV2, W, D2000 ) R2000 = iau_ANP ( W ) * 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. 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 * *----------------------------------------------------------------------- END