/* *+ * Name: * palFk45z * Purpose: * Convert B1950.0 FK4 star data to J2000.0 FK5 assuming zero * proper motion in the FK5 frame * Language: * Starlink ANSI C * Type of Module: * Library routine * Invocation: * palFk45z( double r1950, double d1950, double bepoch, double *r2000, * double *d2000 ) * Arguments: * r1950 = double (Given) * B1950.0 FK4 RA at epoch (radians). * d1950 = double (Given) * B1950.0 FK4 Dec at epoch (radians). * bepoch = double (Given) * Besselian epoch (e.g. 1979.3) * r2000 = double (Returned) * J2000.0 FK5 RA (Radians). * d2000 = double (Returned) * J2000.0 FK5 Dec(Radians). * Description: * Convert B1950.0 FK4 star data to J2000.0 FK5 assuming zero * proper motion in the FK5 frame (double precision) * * This function converts stars from the Bessel-Newcomb, FK4 * system to the 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. * Notes: * - The epoch BEPOCH is strictly speaking Besselian, but if a * Julian epoch is supplied the result will be affected only to * a negligible extent. * * - 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 palFk45z is called. * * - 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: * - Aoki,S., et al, 1983. Astron.Astrophys., 128, 263. * - Smith, C.A. et al, 1989. "The transformation of astrometric * catalog systems to the equinox J2000.0". Astron.J. 97, 265. * - 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. * - Seidelmann, P.K. (ed), 1992. "Explanatory Supplement to * the Astronomical Almanac", ISBN 0-935702-68-7. * Authors: * PTW: Pat Wallace (STFC) * DSB: David Berry (JAC, Hawaii) * {enter_new_authors_here} * History: * 2012-02-10 (DSB): * Initial version with documentation taken from Fortran SLA * Adapted with permission from the Fortran SLALIB library. * {enter_further_changes_here} * Copyright: * Copyright (C) 1998 Rutherford Appleton Laboratory * Copyright (C) 2012 Science and Technology Facilities Council. * All Rights Reserved. * Licence: * This program is free software: you can redistribute it and/or * modify it under the terms of the GNU Lesser General Public * License as published by the Free Software Foundation, either * version 3 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 Lesser General Public License for more details. * * You should have received a copy of the GNU Lesser General * License along with this program. If not, see * . * Bugs: * {note_any_bugs_here} *- */ #include "pal.h" #include "palmac.h" #include "pal1sofa.h" void palFk45z( double r1950, double d1950, double bepoch, double *r2000, double *d2000 ){ /* Local Variables: */ double w; int i; int j; double r0[3], a1[3], v1[3], v2[6]; /* Position and position+velocity vectors */ /* CANONICAL CONSTANTS (see references) */ /* Vector A. */ double a[3] = { -1.62557E-6, -0.31919E-6, -0.13843E-6 }; /* Vectors Adot. */ double ad[3] = { 1.245E-3, -1.580E-3, -0.659E-3 }; /* Matrix M (only half of which is needed here). */ double em[6][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 to Cartesian. */ eraS2c( r1950, d1950, r0 ); /* Adjust vector A to give zero proper motion in FK5. */ w = ( bepoch - 1950.0 )/PAL__PMF; for( i = 0; i < 3; i++ ) { a1[ i ] = a[ i ] + w*ad[ i ]; } /* Remove e-terms. */ w = r0[ 0 ]*a1[ 0 ] + r0[ 1 ]*a1[ 1 ] + r0[ 2 ]*a1[ 2 ]; for( i = 0; i < 3; i++ ) { v1[ i ] = r0[ i ] - a1[ i ] + w*r0[ i ]; } /* Convert position vector to Fricke system. */ for( i = 0; i < 6; i++ ) { w = 0.0; for( j = 0; j < 3; j++ ) { w += em[ i ][ j ]*v1[ j ]; } v2[ i ] = w; } /* Allow for fictitious proper motion in FK4. */ w = ( palEpj( palEpb2d( bepoch ) ) - 2000.0 )/PAL__PMF; for( i = 0; i < 3; i++ ) { v2[ i ] += w*v2[ i + 3 ]; } /* Revert to spherical coordinates. */ eraC2s( v2, &w, d2000 ); *r2000 = eraAnp( w ); }