| 1 | #include "slalib.h"
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| 2 | #include "slamac.h"
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| 3 | void slaPrec ( double ep0, double ep1, double rmatp[3][3] )
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| 4 | /*
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| 5 | ** - - - - - - - -
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| 6 | ** s l a P r e c
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| 7 | ** - - - - - - - -
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| 8 | **
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| 9 | ** Form the matrix of precession between two epochs (IAU 1976, FK5).
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| 10 | **
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| 11 | ** (double precision)
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| 12 | **
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| 13 | ** Given:
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| 14 | ** ep0 double beginning epoch
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| 15 | ** ep1 double ending epoch
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| 16 | **
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| 17 | ** Returned:
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| 18 | ** rmatp double[3][3] precession matrix
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| 19 | **
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| 20 | ** Notes:
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| 21 | **
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| 22 | ** 1) The epochs are TDB (loosely ET) Julian epochs.
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| 23 | **
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| 24 | ** 2) The matrix is in the sense v(ep1) = rmatp * v(ep0) .
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| 25 | **
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| 26 | ** 3) Though the matrix method itself is rigorous, the precession
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| 27 | ** angles are expressed through canonical polynomials which are
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| 28 | ** valid only for a limited time span. There are also known
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| 29 | ** errors in the IAU precession rate. The absolute accuracy
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| 30 | ** of the present formulation is better than 0.1 arcsec from
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| 31 | ** 1960AD to 2040AD, better than 1 arcsec from 1640AD to 2360AD,
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| 32 | ** and remains below 3 arcsec for the whole of the period
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| 33 | ** 500BC to 3000AD. The errors exceed 10 arcsec outside the
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| 34 | ** range 1200BC to 3900AD, exceed 100 arcsec outside 4200BC to
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| 35 | ** 5600AD and exceed 1000 arcsec outside 6800BC to 8200AD.
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| 36 | ** The SLALIB routine slaPrecl implements a more elaborate
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| 37 | ** model which is suitable for problems spanning several
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| 38 | ** thousand years.
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| 39 | **
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| 40 | ** References:
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| 41 | ** Lieske,J.H., 1979. Astron. Astrophys.,73,282.
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| 42 | ** equations (6) & (7), p283.
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| 43 | ** Kaplan,G.H., 1981. USNO circular no. 163, pa2.
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| 44 | **
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| 45 | ** Called: slaDeuler
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| 46 | **
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| 47 | ** Defined in slamac.h: DAS2R
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| 48 | **
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| 49 | ** Last revision: 10 July 1994
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| 50 | **
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| 51 | ** Copyright P.T.Wallace. All rights reserved.
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| 52 | */
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| 53 | {
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| 54 | double t0, t, tas2r, w, zeta, z, theta;
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| 55 |
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| 56 | /* Interval between basic epoch J2000.0 and beginning epoch (JC) */
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| 57 | t0 = ( ep0 - 2000.0 ) / 100.0;
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| 58 |
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| 59 | /* Interval over which precession required (JC) */
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| 60 | t = ( ep1 - ep0 ) / 100.0;
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| 61 |
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| 62 | /* Euler angles */
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| 63 | tas2r = t * DAS2R;
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| 64 | w = 2306.2181 + ( ( 1.39656 - ( 0.000139 * t0 ) ) * t0 );
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| 65 | zeta = (w + ( ( 0.30188 - 0.000344 * t0 ) + 0.017998 * t ) * t ) * tas2r;
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| 66 | z = (w + ( ( 1.09468 + 0.000066 * t0 ) + 0.018203 * t ) * t ) * tas2r;
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| 67 | theta = ( ( 2004.3109 + ( - 0.85330 - 0.000217 * t0 ) * t0 )
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| 68 | + ( ( -0.42665 - 0.000217 * t0 ) - 0.041833 * t ) * t ) * tas2r;
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| 69 |
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| 70 | /* Rotation matrix */
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| 71 | slaDeuler ( "ZYZ", -zeta, theta, -z, rmatp );
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| 72 | }
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