#include "sofam.h" void iauPrec76(double ep01, double ep02, double ep11, double ep12, double *zeta, double *z, double *theta) /* ** - - - - - - - - - - ** i a u P r e c 7 6 ** - - - - - - - - - - ** ** IAU 1976 precession model. ** ** This function forms the three Euler angles which implement general ** precession between two epochs, using the IAU 1976 model (as for ** the FK5 catalog). ** ** This function is part of the International Astronomical Union's ** SOFA (Standards Of Fundamental Astronomy) software collection. ** ** Status: canonical model. ** ** Given: ** ep01,ep02 double TDB starting epoch (Note 1) ** ep11,ep12 double TDB ending epoch (Note 1) ** ** Returned: ** zeta double 1st rotation: radians cw around z ** z double 3rd rotation: radians cw around z ** theta double 2nd rotation: radians ccw around y ** ** Notes: ** ** 1) The epochs ep01+ep02 and ep11+ep12 are Julian Dates, apportioned ** in any convenient way between the arguments epn1 and epn2. For ** example, JD(TDB)=2450123.7 could be expressed in any of these ** ways, among others: ** ** epn1 epn2 ** ** 2450123.7 0.0 (JD method) ** 2451545.0 -1421.3 (J2000 method) ** 2400000.5 50123.2 (MJD method) ** 2450123.5 0.2 (date & time method) ** ** The JD method is the most natural and convenient to use in cases ** where the loss of several decimal digits of resolution is ** acceptable. The J2000 method is best matched to the way the ** argument is handled internally and will deliver the optimum ** optimum resolution. The MJD method and the date & time methods ** are both good compromises between resolution and convenience. ** The two epochs may be expressed using different methods, but at ** the risk of losing some resolution. ** ** 2) The accumulated precession angles zeta, z, theta are expressed ** through canonical polynomials which are valid only for a limited ** time span. In addition, the IAU 1976 precession rate is known to ** be imperfect. The absolute accuracy of the present formulation ** is better than 0.1 arcsec from 1960AD to 2040AD, better than ** 1 arcsec from 1640AD to 2360AD, and remains below 3 arcsec for ** the whole of the period 500BC to 3000AD. The errors exceed ** 10 arcsec outside the range 1200BC to 3900AD, exceed 100 arcsec ** outside 4200BC to 5600AD and exceed 1000 arcsec outside 6800BC to ** 8200AD. ** ** 3) The three angles are returned in the conventional order, which ** is not the same as the order of the corresponding Euler ** rotations. The precession matrix is ** R_3(-z) x R_2(+theta) x R_3(-zeta). ** ** Reference: ** ** Lieske, J.H., 1979, Astron.Astrophys. 73, 282, equations ** (6) & (7), p283. ** ** This revision: 2008 May 24 ** ** Copyright (C) 2008 IAU SOFA Review Board. See notes at end. */ { double t0, t, tas2r, w; /* Interval between fundamental epoch J2000.0 and beginning epoch (JC). */ t0 = ((ep01 - DJ00) + ep02) / DJC; /* Interval over which precession required (JC). */ t = ((ep11 - ep01) + (ep12 - ep02)) / DJC; /* Euler angles. */ tas2r = t * DAS2R; w = 2306.2181 + (1.39656 - 0.000139 * t0) * t0; *zeta = (w + ((0.30188 - 0.000344 * t0) + 0.017998 * t) * t) * tas2r; *z = (w + ((1.09468 + 0.000066 * t0) + 0.018203 * t) * t) * tas2r; *theta = ((2004.3109 + (-0.85330 - 0.000217 * t0) * t0) + ((-0.42665 - 0.000217 * t0) - 0.041833 * t) * t) * tas2r; return; /*----------------------------------------------------------------------- ** ** Copyright (C) 2008 ** Standards Of Fundamental Astronomy Review Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING TERMS AND CONDITIONS ** WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Review Board ("the Board"). ** ** 2. Permission is granted to anyone to use the SOFA software for any ** purpose, including commercial applications, free of charge and ** without payment of royalties, subject to the conditions and ** restrictions listed below. ** ** 3. You (the user) may copy and adapt the SOFA software and its ** algorithms for your own purposes and you may copy and distribute ** a resulting "derived work" to others on a world-wide, royalty-free ** basis, provided that the derived work complies with the following ** requirements: ** ** a) Your work shall be marked or carry a statement that it (i) uses ** routines and computations derived by you from software provided ** by SOFA under license to you; and (ii) does not contain ** software provided by SOFA or software that has been distributed ** by or endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon and/or differs from the ** original SOFA software. ** ** c) The name(s) of all routine(s) that you distribute shall differ ** from the SOFA names, even when the SOFA content has not been ** otherwise changed. ** ** d) The routine-naming prefix "iau" shall not be used. ** ** e) The origin of the SOFA components of your derived work must not ** be misrepresented; you must not claim that you wrote the ** original software, nor file a patent application for SOFA ** software or algorithms embedded in the SOFA software. ** ** f) These requirements must be reproduced intact in any source ** distribution and shall apply to anyone to whom you have granted ** a further right to modify the source code of your derived work. ** ** 4. In any published work or commercial products which includes ** results achieved by using the SOFA software, you shall acknowledge ** that the SOFA software was used in obtaining those results. ** ** 5. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or by ** inappropriate modification. ** ** 6. The SOFA software is provided "as is" and the Board makes no ** warranty as to its use or performance. The Board does not and ** cannot warrant the performance or results which the user may obtain ** by using the SOFA software. The Board makes no warranties, express ** or implied, as to non-infringement of third party rights, ** merchantability, or fitness for any particular purpose. In no ** event will the Board be liable to the user for any consequential, ** incidental, or special damages, including any lost profits or lost ** savings, even if a Board representative has been advised of such ** damages, or for any claim by any third party. ** ** 7. The provision of any version of the SOFA software under the terms ** and conditions specified herein does not imply that future ** versions will also be made available under the same terms and ** conditions. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** Internet email: sofa@rl.ac.uk ** Postal address: IAU SOFA Center ** Rutherford Appleton Laboratory ** Chilton, Didcot, Oxon OX11 0QX ** United Kingdom ** **---------------------------------------------------------------------*/ }