SUBROUTINE iau_LTECEQ ( EPJ, DL, DB, DR, 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 routine is part of the International Astronomical Union's * SOFA (Standards of Fundamental Astronomy) software collection. * * Status: support routine. * * Given: * EPJ d Julian epoch (TT) * DL,DB d ecliptic longitude and latitude (radians) * * Returned: * DR,DD d 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: * iau_S2C spherical coordinates to unit vector * iau_LTECM J2000.0 to ecliptic rotation matrix, long term * iau_TRXP product of transpose of r-matrix and p-vector * iau_C2S unit vector to spherical coordinates * iau_ANP normalize angle into range 0 to 2pi * iau_ANPM 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 2023-10-11 * * Copyright (C) 2023 IAU SOFA Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION EPJ, DL, DB, DR, DD DOUBLE PRECISION RM(3,3), V1(3), V2(3), A, B DOUBLE PRECISION iau_ANP, iau_ANPM * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Spherical to Cartesian. CALL iau_S2C ( DL, DB, V1 ) * Rotation matrix, ICRS equatorial to ecliptic. CALL iau_LTECM ( EPJ, RM ) * The transformation from ecliptic to ICRS. CALL iau_TRXP ( RM, V1, V2 ) * Cartesian to spherical. CALL iau_C2S ( V2, A, B ) * Express in conventional ranges. DR = iau_ANP ( A ) DD = iau_ANPM ( B ) * Finished. *+---------------------------------------------------------------------- * * Copyright (C) 2023 * 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 * *----------------------------------------------------------------------- END