| 1 | #include "slalib.h"
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| 2 | #include "slamac.h"
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| 3 | void slaFk425 ( double r1950, double d1950, double dr1950,
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| 4 | double dd1950, double p1950, double v1950,
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| 5 | double *r2000, double *d2000, double *dr2000,
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| 6 | double *dd2000, double *p2000, double *v2000 )
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| 7 | /*
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| 8 | ** - - - - - - - - -
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| 9 | ** s l a F k 4 2 5
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| 10 | ** - - - - - - - - -
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| 11 | **
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| 12 | ** Convert B1950.0 FK4 star data to J2000.0 FK5.
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| 13 | **
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| 14 | ** (double precision)
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| 15 | **
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| 16 | ** This routine converts stars from the old, Bessel-Newcomb, FK4
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| 17 | ** system to the new, IAU 1976, FK5, Fricke system. The precepts
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| 18 | ** of Smith et al (Ref 1) are followed, using the implementation
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| 19 | ** by Yallop et al (Ref 2) of a matrix method due to Standish.
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| 20 | ** Kinoshita's development of Andoyer's post-Newcomb precession is
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| 21 | ** used. The numerical constants from Seidelmann et al (Ref 3) are
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| 22 | ** used canonically.
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| 23 | **
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| 24 | ** Given: (all B1950.0,FK4)
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| 25 | **
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| 26 | ** r1950,d1950 double B1950.0 RA,dec (rad)
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| 27 | ** dr1950,dd1950 double B1950.0 proper motions (rad/trop.yr)
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| 28 | ** p1950 double parallax (arcsec)
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| 29 | ** v1950 double radial velocity (km/s, +ve = moving away)
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| 30 | **
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| 31 | ** Returned: (all J2000.0,FK5)
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| 32 | **
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| 33 | ** *r2000,*d2000 double J2000.0 RA,dec (rad)
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| 34 | ** *dr2000,*dd2000 double J2000.0 proper motions (rad/jul.yr)
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| 35 | ** *p2000 double parallax (arcsec)
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| 36 | ** *v2000 double radial velocity (km/s, +ve = moving away)
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| 37 | **
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| 38 | ** Notes:
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| 39 | **
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| 40 | ** 1) The proper motions in RA are dRA/dt rather than
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| 41 | ** cos(Dec)*dRA/dt, and are per year rather than per century.
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| 42 | **
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| 43 | ** 2) Conversion from Besselian epoch 1950.0 to Julian epoch
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| 44 | ** 2000.0 only is provided for. Conversions involving other
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| 45 | ** epochs will require use of the appropriate precession,
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| 46 | ** proper motion, and E-terms routines before and/or
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| 47 | ** after FK425 is called.
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| 48 | **
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| 49 | ** 3) In the FK4 catalogue the proper motions of stars within
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| 50 | ** 10 degrees of the poles do not embody the differential
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| 51 | ** E-term effect and should, strictly speaking, be handled
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| 52 | ** in a different manner from stars outside these regions.
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| 53 | ** However, given the general lack of homogeneity of the star
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| 54 | ** data available for routine astrometry, the difficulties of
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| 55 | ** handling positions that may have been determined from
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| 56 | ** astrometric fields spanning the polar and non-polar regions,
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| 57 | ** the likelihood that the differential E-terms effect was not
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| 58 | ** taken into account when allowing for proper motion in past
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| 59 | ** astrometry, and the undesirability of a discontinuity in
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| 60 | ** the algorithm, the decision has been made in this routine to
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| 61 | ** include the effect of differential E-terms on the proper
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| 62 | ** motions for all stars, whether polar or not. At epoch 2000,
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| 63 | ** and measuring on the sky rather than in terms of dRA, the
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| 64 | ** errors resulting from this simplification are less than
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| 65 | ** 1 milliarcsecond in position and 1 milliarcsecond per
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| 66 | ** century in proper motion.
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| 67 | **
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| 68 | ** References:
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| 69 | **
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| 70 | ** 1 Smith, C.A. et al, 1989. "The transformation of astrometric
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| 71 | ** catalog systems to the equinox J2000.0". Astron.J. 97, 265.
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| 72 | **
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| 73 | ** 2 Yallop, B.D. et al, 1989. "Transformation of mean star places
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| 74 | ** from FK4 B1950.0 to FK5 J2000.0 using matrices in 6-space".
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| 75 | ** Astron.J. 97, 274.
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| 76 | **
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| 77 | ** 3 Seidelmann, P.K. (ed), 1992. "Explanatory Supplement to
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| 78 | ** the Astronomical Almanac", ISBN 0-935702-68-7.
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| 79 | **
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| 80 | ** Defined in slamac.h: D2PI
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| 81 | **
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| 82 | ** Last revision: 26 September 1998
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| 83 | **
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| 84 | ** Copyright P.T.Wallace. All rights reserved.
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| 85 | */
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| 86 | {
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| 87 | double r, d, ur, ud, px, rv, sr, cr, sd, cd, w, wd,
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| 88 | x, y, z, xd, yd, zd,
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| 89 | rxysq, rxyzsq, rxy, rxyz, spxy, spxyz;
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| 90 | int i, j;
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| 91 |
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| 92 | /* Star position and velocity vectors */
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| 93 | double r0[3], rd0[3];
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| 94 |
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| 95 | /* Combined position and velocity vectors */
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| 96 | double v1[6], v2[6];
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| 97 |
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| 98 | /* Radians per year to arcsec per century */
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| 99 | static double pmf = 100.0 * 60.0 * 60.0 * 360.0 / D2PI;
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| 100 |
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| 101 | /* Small number to avoid arithmetic problems */
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| 102 | double tiny = 1.0e-30;
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| 103 |
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| 104 | /*
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| 105 | ** Canonical constants (see references)
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| 106 | */
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| 107 |
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| 108 | /*
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| 109 | ** Km per sec to AU per tropical century
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| 110 | ** = 86400 * 36524.2198782 / 1.49597870e8
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| 111 | */
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| 112 | double vf = 21.095;
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| 113 |
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| 114 | /* Constant vector and matrix (by rows) */
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| 115 | static double a[3] = { -1.62557e-6, -0.31919e-6, -0.13843e-6 };
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| 116 | static double ad[3] = { 1.245e-3, -1.580e-3, -0.659e-3 };
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| 117 | static double em[6][6] =
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| 118 | {
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| 119 | { 0.9999256782, /* em[0][0] */
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| 120 | -0.0111820611, /* em[0][1] */
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| 121 | -0.0048579477, /* em[0][2] */
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| 122 | 0.00000242395018, /* em[0][3] */
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| 123 | -0.00000002710663, /* em[0][4] */
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| 124 | -0.00000001177656 }, /* em[0][5] */
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| 125 |
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| 126 | { 0.0111820610, /* em[1][0] */
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| 127 | 0.9999374784, /* em[1][1] */
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| 128 | -0.0000271765, /* em[1][2] */
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| 129 | 0.00000002710663, /* em[1][3] */
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| 130 | 0.00000242397878, /* em[1][4] */
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| 131 | -0.00000000006587 }, /* em[1][5] */
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| 132 |
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| 133 | { 0.0048579479, /* em[2][0] */
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| 134 | -0.0000271474, /* em[2][1] */
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| 135 | 0.9999881997, /* em[2][2] */
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| 136 | 0.00000001177656, /* em[2][3] */
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| 137 | -0.00000000006582, /* em[2][4] */
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| 138 | 0.00000242410173 }, /* em[2][5] */
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| 139 |
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| 140 | { -0.000551, /* em[3][0] */
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| 141 | -0.238565, /* em[3][1] */
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| 142 | 0.435739, /* em[3][2] */
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| 143 | 0.99994704, /* em[3][3] */
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| 144 | -0.01118251, /* em[3][4] */
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| 145 | -0.00485767 }, /* em[3][5] */
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| 146 |
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| 147 | { 0.238514, /* em[4][0] */
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| 148 | -0.002667, /* em[4][1] */
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| 149 | -0.008541, /* em[4][2] */
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| 150 | 0.01118251, /* em[4][3] */
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| 151 | 0.99995883, /* em[4][4] */
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| 152 | -0.00002718 }, /* em[4][5] */
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| 153 |
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| 154 | { -0.435623, /* em[5][0] */
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| 155 | 0.012254, /* em[5][1] */
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| 156 | 0.002117, /* em[5][2] */
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| 157 | 0.00485767, /* em[5][3] */
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| 158 | -0.00002714, /* em[5][4] */
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| 159 | 1.00000956 } /* em[5][5] */
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| 160 | };
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| 161 |
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| 162 | /* Pick up B1950 data (units radians and arcsec/tc) */
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| 163 | r = r1950;
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| 164 | d = d1950;
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| 165 | ur = dr1950 * pmf;
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| 166 | ud = dd1950 * pmf;
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| 167 | px = p1950;
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| 168 | rv = v1950;
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| 169 |
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| 170 | /* Spherical to Cartesian */
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| 171 | sr = sin ( r );
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| 172 | cr = cos ( r );
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| 173 | sd = sin ( d );
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| 174 | cd = cos ( d );
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| 175 |
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| 176 | r0[0] = cr * cd;
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| 177 | r0[1] = sr * cd;
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| 178 | r0[2] = sd;
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| 179 |
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| 180 | w = vf * rv * px;
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| 181 |
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| 182 | rd0[0] = ( -sr * cd * ur ) - ( cr * sd * ud ) + ( w * r0[0] );
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| 183 | rd0[1] = ( cr * cd * ur ) - ( sr * sd * ud ) + ( w * r0[1] );
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| 184 | rd0[2] = ( cd * ud ) + ( w * r0[2] );
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| 185 |
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| 186 | /* Allow for e-terms and express as position+velocity 6-vector */
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| 187 | w = ( r0[0] * a[0] ) + ( r0[1] * a[1] ) + ( r0[2] * a[2] );
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| 188 | wd = ( r0[0] * ad[0] ) + ( r0[1] * ad[1] ) + ( r0[2] * ad[2] );
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| 189 |
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| 190 | for ( i = 0; i < 3; i++ ) {
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| 191 | v1[i] = r0[i] - a[i] + w * r0[i];
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| 192 | v1[i+3] = rd0[i] - ad[i] + wd * r0[i];
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| 193 | }
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| 194 |
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| 195 | /* Convert position+velocity vector to Fricke system */
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| 196 | for ( i = 0; i < 6; i++ ) {
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| 197 | w = 0.0;
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| 198 | for ( j = 0; j < 6; j++ ) {
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| 199 | w += em[i][j] * v1[j];
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| 200 | }
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| 201 | v2[i] = w;
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| 202 | }
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| 203 |
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| 204 | /* Revert to spherical coordinates */
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| 205 | x = v2[0];
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| 206 | y = v2[1];
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| 207 | z = v2[2];
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| 208 | xd = v2[3];
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| 209 | yd = v2[4];
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| 210 | zd = v2[5];
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| 211 |
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| 212 | rxysq = ( x * x ) + ( y * y );
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| 213 | rxyzsq = ( rxysq ) + ( z * z );
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| 214 | rxy = sqrt ( rxysq );
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| 215 | rxyz = sqrt ( rxyzsq );
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| 216 |
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| 217 | spxy = ( x * xd ) + ( y * yd );
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| 218 | spxyz = spxy + ( z * zd );
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| 219 |
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| 220 | if ( (x == 0.0) && (y == 0.0) )
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| 221 | r = 0.0;
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| 222 | else {
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| 223 | r = atan2 ( y, x );
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| 224 | if ( r < 0.0 )
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| 225 | r += D2PI;
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| 226 | }
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| 227 | d = atan2 ( z, rxy );
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| 228 |
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| 229 | if ( rxy > tiny ) {
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| 230 | ur = ( ( x * yd ) - ( y * xd ) ) / rxysq;
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| 231 | ud = ( ( zd * rxysq ) - ( z * spxy ) ) / ( rxyzsq * rxy );
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| 232 | }
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| 233 |
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| 234 | if ( px > tiny ) {
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| 235 | rv = spxyz / ( px * rxyz * vf );
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| 236 | px = px / rxyz;
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| 237 | }
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| 238 |
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| 239 | /* Return results */
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| 240 | *r2000 = r;
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| 241 | *d2000 = d;
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| 242 | *dr2000 = ur / pmf;
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| 243 | *dd2000 = ud / pmf;
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| 244 | *v2000 = rv;
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| 245 | *p2000 = px;
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| 246 | }
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