#include "sofa.h" void iauLteceq(double epj, double dl, double db, double *dr, double *dd) /* ** - - - - - - - - - - ** i a u L t e c e q ** - - - - - - - - - - ** ** Transformation from ecliptic coordinates (mean equinox and ecliptic ** of date) to ICRS RA,Dec, using a long-term precession model. ** ** This function is part of the International Astronomical Union's ** SOFA (Standards of Fundamental Astronomy) software collection. ** ** Status: support function. ** ** Given: ** epj double Julian epoch (TT) ** dl,db double ecliptic longitude and latitude (radians) ** ** Returned: ** dr,dd double ICRS right ascension and declination (radians) ** ** 1) No assumptions are made about whether the coordinates represent ** starlight and embody astrometric effects such as parallax or ** aberration. ** ** 2) The transformation is approximately that from ecliptic longitude ** and latitude (mean equinox and ecliptic of date) to mean J2000.0 ** right ascension and declination, with only frame bias (always ** less than 25 mas) to disturb this classical picture. ** ** 3) The Vondrak et al. (2011, 2012) 400 millennia precession model ** agrees with the IAU 2006 precession at J2000.0 and stays within ** 100 microarcseconds during the 20th and 21st centuries. It is ** accurate to a few arcseconds throughout the historical period, ** worsening to a few tenths of a degree at the end of the ** +/- 200,000 year time span. ** ** Called: ** iauS2c spherical coordinates to unit vector ** iauLtecm J2000.0 to ecliptic rotation matrix, long term ** iauTrxp product of transpose of r-matrix and p-vector ** iauC2s unit vector to spherical coordinates ** iauAnp normalize angle into range 0 to 2pi ** iauAnpm normalize angle into range +/- pi ** ** References: ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession ** expressions, valid for long time intervals, Astron.Astrophys. 534, ** A22 ** ** Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession ** expressions, valid for long time intervals (Corrigendum), ** Astron.Astrophys. 541, C1 ** ** This revision: 2016 February 9 ** ** SOFA release 2018-01-30 ** ** Copyright (C) 2018 IAU SOFA Board. See notes at end. */ { double rm[3][3], v1[3], v2[3], a, b; /* Spherical to Cartesian. */ iauS2c(dl, db, v1); /* Rotation matrix, ICRS equatorial to ecliptic. */ iauLtecm(epj, rm); /* The transformation from ecliptic to ICRS. */ iauTrxp(rm, v1, v2); /* Cartesian to spherical. */ iauC2s(v2, &a, &b); /* Express in conventional ranges. */ *dr = iauAnp(a); *dd = iauAnpm(b); /*---------------------------------------------------------------------- ** ** Copyright (C) 2018 ** Standards Of Fundamental Astronomy Board ** of the International Astronomical Union. ** ** ===================== ** SOFA Software License ** ===================== ** ** NOTICE TO USER: ** ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND ** CONDITIONS WHICH APPLY TO ITS USE. ** ** 1. The Software is owned by the IAU SOFA Board ("SOFA"). ** ** 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 distribute SOFA source code to others, ** and use and adapt its code and algorithms in your own software, ** on a world-wide, royalty-free basis. That portion of your ** distribution that does not consist of intact and unchanged copies ** of SOFA source code files is a "derived work" that must comply ** 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 itself constitute software provided by and/or ** endorsed by SOFA. ** ** b) The source code of your derived work must contain descriptions ** of how the derived work is based upon, contains and/or differs ** from the original SOFA software. ** ** c) The names of all routines in your derived work shall not ** include the prefix "iau" or "sofa" or trivial modifications ** thereof such as changes of case. ** ** d) 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. ** ** e) 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. ** ** Note that, as originally distributed, the SOFA software is ** intended to be a definitive implementation of the IAU standards, ** and consequently third-party modifications are discouraged. All ** variations, no matter how minor, must be explicitly marked as ** such, as explained above. ** ** 4. You shall not cause the SOFA software to be brought into ** disrepute, either by misuse, or use for inappropriate tasks, or ** by inappropriate modification. ** ** 5. The SOFA software is provided "as is" and SOFA makes no warranty ** as to its use or performance. SOFA does not and cannot warrant ** the performance or results which the user may obtain by using the ** SOFA software. SOFA 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 SOFA be ** liable to the user for any consequential, incidental, or special ** damages, including any lost profits or lost savings, even if a ** SOFA representative has been advised of such damages, or for any ** claim by any third party. ** ** 6. 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. * ** In any published work or commercial product which uses the SOFA ** software directly, acknowledgement (see www.iausofa.org) is ** appreciated. ** ** Correspondence concerning SOFA software should be addressed as ** follows: ** ** By email: sofa@ukho.gov.uk ** By post: IAU SOFA Center ** HM Nautical Almanac Office ** UK Hydrographic Office ** Admiralty Way, Taunton ** Somerset, TA1 2DN ** United Kingdom ** **--------------------------------------------------------------------*/ }