SUBROUTINE iau_LTECM ( EPJ, RM ) *+ * - - - - - - - - - - * i a u _ L T E C M * - - - - - - - - - - * * ICRS equatorial to ecliptic rotation matrix, long-term. * * 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) * * Returned: * RM d(3,3) ICRS to ecliptic rotation matrix * * Notes: * * 1) The matrix is in the sense * * E_ep = RM x P_ICRS, * * where P_ICRS is a vector with respect to ICRS right ascension * and declination axes and E_ep is the same vector with respect to * the (inertial) ecliptic and equinox of epoch EPJ. * * 2) P_ICRS is a free vector, merely a direction, typically of unit * magnitude, and not bound to any particular spatial origin, such as * the Earth, Sun or SSB. No assumptions are made about whether it * represents starlight and embodies astrometric effects such as * parallax or aberration. The transformation is approximately that * between mean J2000.0 right ascension and declination and ecliptic * longitude and latitude, 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_LTPEQU equator pole, long term * iau_LTPECL ecliptic pole, long term * iau_PXP vector product * iau_PN normalize vector * * 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: 2015 December 6 * * SOFA release 2023-10-11 * * Copyright (C) 2023 IAU SOFA Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION EPJ, RM(3,3) * Arcseconds to radians DOUBLE PRECISION AS2R PARAMETER ( AS2R = 4.848136811095359935899141D-6 ) * Frame bias (IERS Conventions 2010, Eqs. 5.21 and 5.33) DOUBLE PRECISION DX, DE, DR PARAMETER ( DX = -0.016617D0 * AS2R, : DE = -0.0068192D0 * AS2R, : DR = -0.0146D0 * AS2R ) DOUBLE PRECISION P(3), Z(3), W(3), S, X(3), Y(3) * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Equator pole. CALL iau_LTPEQU ( EPJ, P ) * Ecliptic pole (bottom row of equatorial to ecliptic matrix). CALL iau_LTPECL ( EPJ, Z ) * Equinox (top row of matrix). CALL iau_PXP ( P, Z, W ) CALL iau_PN ( W, S, X ) * Middle row of matrix. CALL iau_PXP ( Z, X, Y ) * Combine with frame bias. RM(1,1) = X(1) - X(2)*DR + X(3)*DX RM(1,2) = X(1)*DR + X(2) + X(3)*DE RM(1,3) = - X(1)*DX - X(2)*DE + X(3) RM(2,1) = Y(1) - Y(2)*DR + Y(3)*DX RM(2,2) = Y(1)*DR + Y(2) + Y(3)*DE RM(2,3) = - Y(1)*DX - Y(2)*DE + Y(3) RM(3,1) = Z(1) - Z(2)*DR + Z(3)*DX RM(3,2) = Z(1)*DR + Z(2) + Z(3)*DE RM(3,3) = - Z(1)*DX - Z(2)*DE + Z(3) * 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. 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