| 1 | /*
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| 2 | *+
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| 3 | * Name:
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| 4 | * palFk45z
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| 5 |
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| 6 | * Purpose:
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| 7 | * Convert B1950.0 FK4 star data to J2000.0 FK5 assuming zero
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| 8 | * proper motion in the FK5 frame
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| 9 |
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| 10 | * Language:
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| 11 | * Starlink ANSI C
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| 12 |
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| 13 | * Type of Module:
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| 14 | * Library routine
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| 15 |
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| 16 | * Invocation:
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| 17 | * palFk45z( double r1950, double d1950, double bepoch, double *r2000,
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| 18 | * double *d2000 )
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| 19 |
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| 20 | * Arguments:
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| 21 | * r1950 = double (Given)
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| 22 | * B1950.0 FK4 RA at epoch (radians).
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| 23 | * d1950 = double (Given)
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| 24 | * B1950.0 FK4 Dec at epoch (radians).
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| 25 | * bepoch = double (Given)
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| 26 | * Besselian epoch (e.g. 1979.3)
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| 27 | * r2000 = double (Returned)
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| 28 | * J2000.0 FK5 RA (Radians).
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| 29 | * d2000 = double (Returned)
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| 30 | * J2000.0 FK5 Dec(Radians).
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| 31 |
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| 32 | * Description:
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| 33 | * Convert B1950.0 FK4 star data to J2000.0 FK5 assuming zero
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| 34 | * proper motion in the FK5 frame (double precision)
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| 35 | *
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| 36 | * This function converts stars from the Bessel-Newcomb, FK4
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| 37 | * system to the IAU 1976, FK5, Fricke system, in such a
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| 38 | * way that the FK5 proper motion is zero. Because such a star
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| 39 | * has, in general, a non-zero proper motion in the FK4 system,
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| 40 | * the routine requires the epoch at which the position in the
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| 41 | * FK4 system was determined.
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| 42 | *
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| 43 | * The method is from Appendix 2 of Ref 1, but using the constants
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| 44 | * of Ref 4.
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| 45 |
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| 46 | * Notes:
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| 47 | * - The epoch BEPOCH is strictly speaking Besselian, but if a
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| 48 | * Julian epoch is supplied the result will be affected only to
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| 49 | * a negligible extent.
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| 50 | *
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| 51 | * - Conversion from Besselian epoch 1950.0 to Julian epoch 2000.0
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| 52 | * only is provided for. Conversions involving other epochs will
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| 53 | * require use of the appropriate precession, proper motion, and
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| 54 | * E-terms routines before and/or after palFk45z is called.
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| 55 | *
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| 56 | * - In the FK4 catalogue the proper motions of stars within 10
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| 57 | * degrees of the poles do not embody the differential E-term effect
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| 58 | * and should, strictly speaking, be handled in a different manner
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| 59 | * from stars outside these regions. However, given the general lack
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| 60 | * of homogeneity of the star data available for routine astrometry,
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| 61 | * the difficulties of handling positions that may have been
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| 62 | * determined from astrometric fields spanning the polar and non-polar
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| 63 | * regions, the likelihood that the differential E-terms effect was not
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| 64 | * taken into account when allowing for proper motion in past
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| 65 | * astrometry, and the undesirability of a discontinuity in the
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| 66 | * algorithm, the decision has been made in this routine to include the
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| 67 | * effect of differential E-terms on the proper motions for all stars,
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| 68 | * whether polar or not. At epoch 2000, and measuring on the sky rather
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| 69 | * than in terms of dRA, the errors resulting from this simplification
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| 70 | * are less than 1 milliarcsecond in position and 1 milliarcsecond per
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| 71 | * century in proper motion.
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| 72 | *
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| 73 | * References:
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| 74 | * - Aoki,S., et al, 1983. Astron.Astrophys., 128, 263.
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| 75 | * - Smith, C.A. et al, 1989. "The transformation of astrometric
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| 76 | * catalog systems to the equinox J2000.0". Astron.J. 97, 265.
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| 77 | * - Yallop, B.D. et al, 1989. "Transformation of mean star places
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| 78 | * from FK4 B1950.0 to FK5 J2000.0 using matrices in 6-space".
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| 79 | * Astron.J. 97, 274.
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| 80 | * - Seidelmann, P.K. (ed), 1992. "Explanatory Supplement to
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| 81 | * the Astronomical Almanac", ISBN 0-935702-68-7.
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| 82 |
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| 83 | * Authors:
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| 84 | * PTW: Pat Wallace (STFC)
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| 85 | * DSB: David Berry (JAC, Hawaii)
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| 86 | * {enter_new_authors_here}
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| 87 |
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| 88 | * History:
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| 89 | * 2012-02-10 (DSB):
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| 90 | * Initial version with documentation taken from Fortran SLA
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| 91 | * Adapted with permission from the Fortran SLALIB library.
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| 92 | * {enter_further_changes_here}
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| 93 |
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| 94 | * Copyright:
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| 95 | * Copyright (C) 1998 Rutherford Appleton Laboratory
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| 96 | * Copyright (C) 2012 Science and Technology Facilities Council.
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| 97 | * All Rights Reserved.
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| 98 |
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| 99 | * Licence:
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| 100 | * This program is free software: you can redistribute it and/or
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| 101 | * modify it under the terms of the GNU Lesser General Public
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| 102 | * License as published by the Free Software Foundation, either
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| 103 | * version 3 of the License, or (at your option) any later
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| 104 | * version.
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| 105 | *
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| 106 | * This program is distributed in the hope that it will be useful,
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| 107 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 108 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 109 | * GNU Lesser General Public License for more details.
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| 110 | *
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| 111 | * You should have received a copy of the GNU Lesser General
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| 112 | * License along with this program. If not, see
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| 113 | * <http://www.gnu.org/licenses/>.
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| 114 |
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| 115 | * Bugs:
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| 116 | * {note_any_bugs_here}
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| 117 | *-
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| 118 | */
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| 119 |
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| 120 | #include "pal.h"
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| 121 | #include "palmac.h"
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| 122 | #include "pal1sofa.h"
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| 123 |
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| 124 | void palFk45z( double r1950, double d1950, double bepoch, double *r2000,
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| 125 | double *d2000 ){
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| 126 |
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| 127 | /* Local Variables: */
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| 128 | double w;
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| 129 | int i;
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| 130 | int j;
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| 131 | double r0[3], a1[3], v1[3], v2[6]; /* Position and position+velocity vectors */
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| 132 |
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| 133 |
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| 134 | /* CANONICAL CONSTANTS (see references) */
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| 135 |
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| 136 | /* Vector A. */
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| 137 | double a[3] = { -1.62557E-6, -0.31919E-6, -0.13843E-6 };
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| 138 |
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| 139 | /* Vectors Adot. */
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| 140 | double ad[3] = { 1.245E-3, -1.580E-3, -0.659E-3 };
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| 141 |
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| 142 | /* Matrix M (only half of which is needed here). */
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| 143 | double em[6][3] = { {0.9999256782, -0.0111820611, -0.0048579477},
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| 144 | {0.0111820610, 0.9999374784, -0.0000271765},
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| 145 | {0.0048579479, -0.0000271474, 0.9999881997},
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| 146 | {-0.000551, -0.238565, 0.435739},
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| 147 | {0.238514, -0.002667, -0.008541},
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| 148 | {-0.435623, 0.012254, 0.002117} };
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| 149 |
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| 150 |
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| 151 | /* Spherical to Cartesian. */
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| 152 | eraS2c( r1950, d1950, r0 );
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| 153 |
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| 154 | /* Adjust vector A to give zero proper motion in FK5. */
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| 155 | w = ( bepoch - 1950.0 )/PAL__PMF;
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| 156 | for( i = 0; i < 3; i++ ) {
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| 157 | a1[ i ] = a[ i ] + w*ad[ i ];
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| 158 | }
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| 159 |
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| 160 | /* Remove e-terms. */
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| 161 | w = r0[ 0 ]*a1[ 0 ] + r0[ 1 ]*a1[ 1 ] + r0[ 2 ]*a1[ 2 ];
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| 162 | for( i = 0; i < 3; i++ ) {
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| 163 | v1[ i ] = r0[ i ] - a1[ i ] + w*r0[ i ];
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| 164 | }
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| 165 |
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| 166 | /* Convert position vector to Fricke system. */
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| 167 | for( i = 0; i < 6; i++ ) {
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| 168 | w = 0.0;
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| 169 | for( j = 0; j < 3; j++ ) {
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| 170 | w += em[ i ][ j ]*v1[ j ];
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| 171 | }
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| 172 | v2[ i ] = w;
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| 173 | }
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| 174 |
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| 175 | /* Allow for fictitious proper motion in FK4. */
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| 176 | w = ( palEpj( palEpb2d( bepoch ) ) - 2000.0 )/PAL__PMF;
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| 177 | for( i = 0; i < 3; i++ ) {
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| 178 | v2[ i ] += w*v2[ i + 3 ];
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| 179 | }
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| 180 |
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| 181 | /* Revert to spherical coordinates. */
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| 182 | eraC2s( v2, &w, d2000 );
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| 183 | *r2000 = eraAnp( w );
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| 184 | }
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| 185 |
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| 186 |
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