/* *+ * Name: * palFk524 * Purpose: * Convert J2000.0 FK5 star data to B1950.0 FK4. * Language: * Starlink ANSI C * Type of Module: * Library routine * Invocation: * palFk524( double r2000, double d2000, double dr2000, double dd2000, * double p2000, double v2000, double *r1950, double *d1950, * double *dr1950, double *dd1950, double *p1950, double *v1950 ) * Arguments: * r2000 = double (Given) * J2000.0 FK5 RA (radians). * d2000 = double (Given) * J2000.0 FK5 Dec (radians). * dr2000 = double (Given) * J2000.0 FK5 RA proper motion (rad/Jul.yr) * dd2000 = double (Given) * J2000.0 FK5 Dec proper motion (rad/Jul.yr) * p2000 = double (Given) * J2000.0 FK5 parallax (arcsec) * v2000 = double (Given) * J2000.0 FK5 radial velocity (km/s, +ve = moving away) * r1950 = double * (Returned) * B1950.0 FK4 RA (radians). * d1950 = double * (Returned) * B1950.0 FK4 Dec (radians). * dr1950 = double * (Returned) * B1950.0 FK4 RA proper motion (rad/Jul.yr) * dd1950 = double * (Returned) * B1950.0 FK4 Dec proper motion (rad/Jul.yr) * p1950 = double * (Returned) * B1950.0 FK4 parallax (arcsec) * v1950 = double * (Returned) * B1950.0 FK4 radial velocity (km/s, +ve = moving away) * Description: * This function converts stars from the IAU 1976, FK5, Fricke * system, to the Bessel-Newcomb, FK4 system. The precepts * of Smith et al (Ref 1) are followed, using the implementation * by Yallop et al (Ref 2) of a matrix method due to Standish. * Kinoshita's development of Andoyer's post-Newcomb precession is * used. The numerical constants from Seidelmann et al (Ref 3) are * used canonically. * Notes: * - The proper motions in RA are dRA/dt rather than * cos(Dec)*dRA/dt, and are per year rather than per century. * - Note that conversion from Julian epoch 2000.0 to Besselian * epoch 1950.0 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 * FK524 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: * - 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: * 2012-02-13 (DSB): * Initial version with documentation taken from Fortran SLA * {enter_further_changes_here} * Copyright: * 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 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 General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 * USA. * Bugs: * {note_any_bugs_here} *- */ #include "pal.h" #include "palmac.h" #include "math.h" void palFk524( double r2000, double d2000, double dr2000, double dd2000, double p2000, double v2000, double *r1950, double *d1950, double *dr1950, double *dd1950, double *p1950, double *v1950 ){ /* Local Variables; */ double r, d, ur, ud, px, rv; double sr, cr, sd, cd, x, y, z, w; double v1[ 6 ], v2[ 6 ]; double xd, yd, zd; double rxyz, wd, rxysq, rxy; int i, j; /* Small number to avoid arithmetic problems. */ static const double tiny = 1.0-30; /* Canonical constants (see references). Constant vector and matrix. */ double a[ 6 ] = { -1.62557E-6, -0.31919E-6, -0.13843E-6, +1.245E-3, -1.580E-3, -0.659E-3 }; double emi[ 6 ][ 6 ] = { { 0.9999256795, 0.0111814828, 0.0048590039, -0.00000242389840, -0.00000002710544, -0.00000001177742}, {-0.0111814828, 0.9999374849, -0.0000271771, 0.00000002710544, -0.00000242392702, 0.00000000006585 }, {-0.0048590040, -0.0000271557, 0.9999881946, 0.00000001177742, 0.00000000006585, -0.00000242404995 }, {-0.000551, 0.238509, -0.435614, 0.99990432, 0.01118145, 0.00485852 }, {-0.238560, -0.002667, 0.012254, -0.01118145, 0.99991613, -0.00002717}, { 0.435730, -0.008541, 0.002117, -0.00485852, -0.00002716, 0.99996684 } }; /* Pick up J2000 data (units radians and arcsec/JC). */ r = r2000; d = d2000; ur = dr2000*PAL__PMF; ud = dd2000*PAL__PMF; px = p2000; rv = v2000; /* Spherical to Cartesian. */ sr = sin( r ); cr = cos( r ); sd = sin( d ); cd = cos( d ); x = cr*cd; y = sr*cd; z = sd; w = PAL__VF*rv*px; v1[ 0 ] = x; v1[ 1 ] = y; v1[ 2 ] = z; v1[ 3 ] = -ur*y - cr*sd*ud + w*x; v1[ 4 ] = ur*x - sr*sd*ud + w*y; v1[ 5 ] = cd*ud + w*z; /* Convert position+velocity vector to BN system. */ for( i = 0; i < 6; i++ ) { w = 0.0; for( j = 0; j < 6; j++ ) { w += emi[ i ][ j ]*v1[ j ]; } v2[ i ] = w; } /* Position vector components and magnitude. */ x = v2[ 0 ]; y = v2[ 1 ]; z = v2[ 2 ]; rxyz = sqrt( x*x + y*y + z*z ); /* Apply E-terms to position. */ w = x*a[ 0 ] + y*a[ 1 ] + z*a[ 2 ]; x += a[ 0 ]*rxyz - w*x; y += a[ 1 ]*rxyz - w*y; z += a[ 2 ]*rxyz - w*z; /* Recompute magnitude. */ rxyz = sqrt( x*x + y*y + z*z ); /* Apply E-terms to both position and velocity. */ x = v2[ 0 ]; y = v2[ 1 ]; z = v2[ 2 ]; w = x*a[ 0 ] + y*a[ 1 ] + z*a[ 2 ]; wd = x*a[ 3 ] + y*a[ 4 ] + z*a[ 5 ]; x += a[ 0 ]*rxyz - w*x; y += a[ 1 ]*rxyz - w*y; z += a[ 2 ]*rxyz - w*z; xd = v2[ 3 ] + a[ 3 ]*rxyz - wd*x; yd = v2[ 4 ] + a[ 4 ]*rxyz - wd*y; zd = v2[ 5 ] + a[ 5 ]*rxyz - wd*z; /* Convert to spherical. */ rxysq = x*x + y*y; rxy = sqrt( rxysq ); if( x == 0.0 && y == 0.0 ) { r = 0.0; } else { r = atan2( y, x ); if( r < 0.0 ) r += PAL__D2PI; } d = atan2( z, rxy ); if( rxy > tiny ) { ur = ( x*yd - y*xd )/rxysq; ud = ( zd*rxysq - z*( x*xd + y*yd ) )/( ( rxysq + z*z )*rxy ); } /* Radial velocity and parallax. */ if( px > tiny ) { rv = ( x*xd + y*yd + z*zd )/( px*PAL__VF*rxyz ); px /= rxyz; } /* Return results. */ *r1950 = r; *d1950 = d; *dr1950 = ur/PAL__PMF; *dd1950 = ud/PAL__PMF; *p1950 = px; *v1950 = rv; }