| 1 | #include "slalib.h"
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| 2 | #include "slamac.h"
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| 3 | void slaHfk5z ( double rh, double dh, double epoch,
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| 4 | double *r5, double *d5, double *dr5, double *dd5 )
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| 5 | /*
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| 6 | ** - - - - - - - - -
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| 7 | ** s l a H f k 5 z
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| 8 | ** - - - - - - - - -
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| 9 | **
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| 10 | ** Transform a Hipparcos star position into FK5 J2000, assuming
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| 11 | ** zero Hipparcos proper motion.
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| 12 | **
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| 13 | ** (double precision)
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| 14 | **
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| 15 | ** Given:
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| 16 | ** rh double Hipparcos RA (radians)
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| 17 | ** dh double Hipparcos Dec (radians)
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| 18 | ** epoch double Julian epoch (TDB)
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| 19 | **
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| 20 | ** Returned (all FK5, equinox J2000, epoch EPOCH):
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| 21 | ** r5 double RA (radians)
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| 22 | ** d5 double Dec (radians)
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| 23 | **
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| 24 | ** Called: slaDcs2c, slaDav2m, slaDmxv, slaDav2m, slaDmxm,
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| 25 | ** slaDimxv, slaDvxv, slaDc62s, slaDranrm
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| 26 | **
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| 27 | ** Notes:
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| 28 | **
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| 29 | ** 1) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
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| 30 | **
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| 31 | ** 2) The FK5 to Hipparcos transformation consists of a pure
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| 32 | ** rotation and spin; zonal errors in the FK5 catalogue are
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| 33 | ** not taken into account.
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| 34 | **
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| 35 | ** 3) The published orientation and spin components are interpreted
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| 36 | ** as "axial vectors". An axial vector points at the pole of the
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| 37 | ** rotation and its length is the amount of rotation in radians.
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| 38 | **
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| 39 | ** 4) It was the intention that Hipparcos should be a close
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| 40 | ** approximation to an inertial frame, so that distant objects
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| 41 | ** have zero proper motion; such objects have (in general)
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| 42 | ** non-zero proper motion in FK5, and this routine returns those
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| 43 | ** fictitious proper motions.
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| 44 | **
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| 45 | ** 5) The position returned by this routine is in the FK5 J2000
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| 46 | ** reference frame but at the specified epoch.
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| 47 | **
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| 48 | ** 6) See also slaFk52h, slaH2fk5, slaFk5zhz.
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| 49 | **
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| 50 | ** Reference:
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| 51 | **
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| 52 | ** M.Feissel & F.Mignard, Astron. Astrophys. 331, L33-L36 (1998).
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| 53 | **
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| 54 | ** Last revision: 30 December 1999
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| 55 | **
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| 56 | ** Copyright P.T.Wallace. All rights reserved.
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| 57 | */
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| 58 |
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| 59 | #define AS2R 0.484813681109535994e-5 /* arcseconds to radians */
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| 60 |
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| 61 | {
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| 62 | /* FK5 to Hipparcos orientation and spin (radians, radians/year) */
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| 63 | static double ortn[3] = { -19.9e-3 * AS2R,
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| 64 | -9.1e-3 * AS2R,
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| 65 | 22.9e-3 * AS2R },
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| 66 | s5[3] = { -0.30e-3 * AS2R,
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| 67 | 0.60e-3 * AS2R,
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| 68 | 0.70e-3 * AS2R };
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| 69 |
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| 70 | double ph[3], r5h[3][3], sh[3], t, vst[3], rst[3][3], r5ht[3][3],
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| 71 | pv5e[6], vv[3], w, r, v;
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| 72 | int i;
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| 73 |
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| 74 |
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| 75 | /* Hipparcos barycentric position vector (normalized). */
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| 76 | slaDcs2c ( rh, dh, ph );
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| 77 |
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| 78 | /* FK5 to Hipparcos orientation matrix. */
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| 79 | slaDav2m ( ortn, r5h );
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| 80 |
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| 81 | /* Rotate the spin vector into the Hipparcos frame. */
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| 82 | slaDmxv ( r5h, s5, sh );
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| 83 |
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| 84 | /* Time interval from J2000 to epoch. */
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| 85 | t = epoch - 2000.0;
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| 86 |
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| 87 | /* Axial vector: accumulated Hipparcos wrt FK5 spin over that interval. */
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| 88 | for ( i = 0; i < 3; i++ ) {
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| 89 | vst [ i ] = s5 [ i ] * t;
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| 90 | }
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| 91 |
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| 92 | /* Express the accumulated spin as a rotation matrix. */
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| 93 | slaDav2m ( vst, rst );
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| 94 |
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| 95 | /* Rotation matrix: accumulated spin, then FK5 to Hipparcos. */
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| 96 | slaDmxm ( r5h, rst, r5ht );
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| 97 |
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| 98 | /* De-orient & de-spin the vector into FK5 J2000 at epoch. */
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| 99 | slaDimxv ( r5ht, ph, pv5e );
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| 100 | slaDvxv ( sh, ph, vv );
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| 101 | slaDimxv ( r5ht, vv, pv5e + 3 );
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| 102 |
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| 103 | /* FK5 position/velocity 6-vector to spherical. */
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| 104 | slaDc62s( pv5e, &w, d5, &r, dr5, dd5, &v );
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| 105 | *r5 = slaDranrm ( w );
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| 106 | }
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