SUBROUTINE slF45Z (R1950,D1950,BEPOCH,R2000,D2000) *+ * - - - - - - * F 4 5 Z * - - - - - - * * Convert B1950.0 FK4 star data to J2000.0 FK5 assuming zero * proper motion in the FK5 frame (double precision) * * This routine converts stars from the old, Bessel-Newcomb, FK4 * system to the new, 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. * * The method is from Appendix 2 of Ref 1, but using the constants * of Ref 4. * * Given: * R1950,D1950 dp B1950.0 FK4 RA,Dec at epoch (rad) * BEPOCH dp Besselian epoch (e.g. 1979.3D0) * * Returned: * R2000,D2000 dp 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) Conversion from Besselian epoch 1950.0 to Julian epoch * 2000.0 only is provided for. Conversions involving other * epochs will require use of the appropriate precession, * proper motion, and E-terms routines before and/or * after FK45Z is called. * * 3) In the FK4 catalogue the proper motions of stars within * 10 degrees of the poles do not embody the differential * E-term effect 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 routine to * include the effect of differential E-terms on the proper * motions for all stars, whether polar or not. At epoch 2000, * and measuring on the sky rather than in terms of dRA, the * errors resulting from this simplification are less than * 1 milliarcsecond in position and 1 milliarcsecond per * century in proper motion. * * References: * * 1 Aoki,S., et al, 1983. Astron.Astrophys., 128, 263. * * 2 Smith, C.A. et al, 1989. "The transformation of astrometric * catalog systems to the equinox J2000.0". Astron.J. 97, 265. * * 3 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. * * 4 Seidelmann, P.K. (ed), 1992. "Explanatory Supplement to * the Astronomical Almanac", ISBN 0-935702-68-7. * * Called: slDS2C, slEPJ, slEB2D, slDC2S, slDA2P * * P.T.Wallace Starlink 21 September 1998 * * Copyright (C) 1998 Rutherford Appleton Laboratory * * License: * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program (see SLA_CONDITIONS); if not, write to the * Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, * Boston, MA 02110-1301 USA * * Copyright (C) 1995 Association of Universities for Research in Astronomy Inc. *- IMPLICIT NONE DOUBLE PRECISION R1950,D1950,BEPOCH,R2000,D2000 DOUBLE PRECISION D2PI PARAMETER (D2PI=6.283185307179586476925287D0) DOUBLE PRECISION W INTEGER I,J * Position and position+velocity vectors DOUBLE PRECISION R0(3),A1(3),V1(3),V2(6) * Radians per year to arcsec per century DOUBLE PRECISION PMF PARAMETER (PMF=100D0*60D0*60D0*360D0/D2PI) * Functions DOUBLE PRECISION slEPJ,slEB2D,slDA2P * * CANONICAL CONSTANTS (see references) * * Vectors A and Adot, and matrix M (only half of which is needed here) DOUBLE PRECISION A(3),AD(3),EM(6,3) DATA A,AD/ -1.62557D-6, -0.31919D-6, -0.13843D-6, : +1.245D-3, -1.580D-3, -0.659D-3/ DATA (EM(I,1),I=1,6) / +0.9999256782D0, : +0.0111820610D0, : +0.0048579479D0, : -0.000551D0, : +0.238514D0, : -0.435623D0 / DATA (EM(I,2),I=1,6) / -0.0111820611D0, : +0.9999374784D0, : -0.0000271474D0, : -0.238565D0, : -0.002667D0, : +0.012254D0 / DATA (EM(I,3),I=1,6) / -0.0048579477D0, : -0.0000271765D0, : +0.9999881997D0, : +0.435739D0, : -0.008541D0, : +0.002117D0 / * Spherical to Cartesian CALL slDS2C(R1950,D1950,R0) * Adjust vector A to give zero proper motion in FK5 W=(BEPOCH-1950D0)/PMF DO I=1,3 A1(I)=A(I)+W*AD(I) END DO * Remove e-terms W=R0(1)*A1(1)+R0(2)*A1(2)+R0(3)*A1(3) DO I=1,3 V1(I)=R0(I)-A1(I)+W*R0(I) END DO * Convert position vector to Fricke system DO I=1,6 W=0D0 DO J=1,3 W=W+EM(I,J)*V1(J) END DO V2(I)=W END DO * Allow for fictitious proper motion in FK4 W=(slEPJ(slEB2D(BEPOCH))-2000D0)/PMF DO I=1,3 V2(I)=V2(I)+W*V2(I+3) END DO * Revert to spherical coordinates CALL slDC2S(V2,W,D2000) R2000=slDA2P(W) END