SUBROUTINE iau_FK425 ( R1950, D1950, : DR1950, DD1950, P1950, V1950, : R2000, D2000, : DR2000, DD2000, P2000, V2000 ) *+ * - - - - - - - - - - * i a u _ F K 4 2 5 * - - - - - - - - - - * * Convert B1950.0 FK4 star catalog data to J2000.0 FK5. * * 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. * * Given: (all B1950.0, FK4) * R1950,D1950 d B1950.0 RA,Dec (rad) * DR1950,DD1950 d B1950.0 proper motions (rad/trop.yr) * P1950 d parallax (arcsec) * V1950 d radial velocity (km/s, +ve = moving away) * * Returned: (all J2000.0, FK5) * R2000,D2000 d J2000.0 RA,Dec (rad) * DR2000,DD2000 d J2000.0 proper motions (rad/Jul.yr) * P2000 d parallax (arcsec) * V2000 d 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: * iau_ANP normalize angle into range 0 to 2pi * iau_PV2S pv-vector to spherical coordinates * iau_PDP scalar product of two p-vectors * iau_PVMPV pv-vector minus pv_vector * iau_PVPPV pv-vector plus pv_vector * iau_S2PV spherical coordinates to pv-vector * iau_SXP 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: 2023 March 20 * * SOFA release 2023-10-11 * * Copyright (C) 2023 IAU SOFA Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION R1950, D1950, DR1950, DD1950, P1950, V1950, : R2000, D2000, DR2000, DD2000, P2000, V2000 * 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 ) * Small number to avoid arithmetic problems DOUBLE PRECISION TINY PARAMETER ( TINY = 1D-30 ) * Miscellaneous DOUBLE PRECISION R, D, UR, UD, PX, RV, PXVF, W, RD INTEGER L, K, J, I * Pv-vectors DOUBLE PRECISION R0(3,2), PV1(3,2), PV2(3,2), PV3(3,2) * Functions DOUBLE PRECISION iau_ANP * * CANONICAL CONSTANTS (Seidelmann 1992) * * Km per sec to au per tropical century * = 86400 * 36524.2198782 / 149597870.7 DOUBLE PRECISION VF PARAMETER ( VF = 21.095D0 ) * Constant pv-vector (cf. Seidelmann 3.591-2, vectors A and Adot) DOUBLE PRECISION A(3,2) DATA A / -1.62557D-6, -0.31919D-6, -0.13843D-6, : +1.245D-3, -1.580D-3, -0.659D-3 / * 3x2 matrix of pv-vectors (cf. Seidelmann 3.591-4, matrix M) DOUBLE PRECISION EM(3,2,3,2) DATA EM / : +0.9999256782D0, -0.0111820611D0, -0.0048579477D0, : +0.00000242395018D0, -0.00000002710663D0, -0.00000001177656D0, : : +0.0111820610D0, +0.9999374784D0, -0.0000271765D0, : +0.00000002710663D0, +0.00000242397878D0, -0.00000000006587D0, : : +0.0048579479D0, -0.0000271474D0, +0.9999881997D0, : +0.00000001177656D0, -0.00000000006582D0, +0.00000242410173D0, : : -0.000551D0, -0.238565D0, +0.435739D0, : +0.99994704D0, -0.01118251D0, -0.00485767D0, : : +0.238514D0, -0.002667D0, -0.008541D0, : +0.01118251D0, +0.99995883D0, -0.00002718D0, : : -0.435623D0, +0.012254D0, +0.002117D0, : +0.00485767D0, -0.00002714D0, +1.00000956D0 : / * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * 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 CALL iau_S2PV ( R, D, 1D0, UR, UD, W, R0 ) * Allow for E-terms (cf. Seidelmann 3.591-2). CALL iau_PVMPV ( R0, A, PV1 ) CALL iau_PDP ( R0, A, W ) CALL iau_SXP ( W, R0, PV2 ) CALL iau_PDP ( R0, A(1,2), W ) CALL iau_SXP ( W, R0, PV2(1,2) ) CALL iau_PVPPV ( PV1, PV2, PV3 ) * Convert pv-vector to Fricke system (cf. Seidelmann 3.591-3). DO 4 L = 1,2 DO 3 K=1,3 W = 0D0 DO 2 J=1,2 DO 1 I=1,3 W = W + EM(I,J,K,L)*PV3(I,J) 1 CONTINUE 2 CONTINUE PV1(K,L) = W 3 CONTINUE 4 CONTINUE * Revert to catalog form. CALL iau_PV2S ( PV1, R, D, W, UR, UD, RD ) IF ( PX.GT.TINY ) THEN RV = RD/PXVF PX = PX/W END IF * Return the results. R2000 = iau_ANP(R) D2000 = D DR2000 = UR/PMF DD2000 = UD/PMF V2000 = RV P2000 = PX * Finished. *+---------------------------------------------------------------------- * * Copyright (C) 2023 * 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 * *----------------------------------------------------------------------- END