SUBROUTINE iau_LTPEQU ( EPJ, VEQ ) *+ * - - - - - - - - - - - * i a u _ L T P E Q U * - - - - - - - - - - - * * Long-term precession of the equator. * * 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: * VEQ d(3) equator pole unit vector * * Notes: * * 1) The returned vector is with respect to the J2000.0 mean equator * and equinox. * * 2) 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. * * 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, VEQ(3) * Arcseconds to radians DOUBLE PRECISION AS2R PARAMETER ( AS2R = 4.848136811095359935899141D-6 ) * 2Pi DOUBLE PRECISION D2PI PARAMETER ( D2PI = 6.283185307179586476925287D0 ) * Number of polynomial terms INTEGER NPOL PARAMETER ( NPOL = 4 ) * Number of periodic terms INTEGER NPER PARAMETER ( NPER = 14 ) * Miscellaneous INTEGER I, J DOUBLE PRECISION T, X, Y, W, A, S, C * Polynomial and periodic coefficients DOUBLE PRECISION XYPOL(NPOL,2), XYPER(5,NPER) * Polynomials DATA ((XYPOL(I,J),I=1,NPOL),J=1,2) / : : +5453.282155 D0, : +0.4252841 D0, : -0.00037173 D0, : -0.000000152 D0, : : -73750.930350 D0, : -0.7675452 D0, : -0.00018725 D0, : +0.000000231 D0 / * Periodics DATA ((XYPER(I,J),I=1,5),J=1,NPER) / : : 256.75D0, -819.940624D0, 75004.344875D0, : 81491.287984D0, 1558.515853D0, : 708.15D0, -8444.676815D0, 624.033993D0, : 787.163481D0, 7774.939698D0, : 274.20D0, 2600.009459D0, 1251.136893D0, : 1251.296102D0, -2219.534038D0, : 241.45D0, 2755.175630D0, -1102.212834D0, : -1257.950837D0, -2523.969396D0, : 2309.00D0, -167.659835D0, -2660.664980D0, : -2966.799730D0, 247.850422D0, : 492.20D0, 871.855056D0, 699.291817D0, : 639.744522D0, -846.485643D0, : 396.10D0, 44.769698D0, 153.167220D0, : 131.600209D0, -1393.124055D0, : 288.90D0, -512.313065D0, -950.865637D0, : -445.040117D0, 368.526116D0, : 231.10D0, -819.415595D0, 499.754645D0, : 584.522874D0, 749.045012D0, : 1610.00D0, -538.071099D0, -145.188210D0, : -89.756563D0, 444.704518D0, : 620.00D0, -189.793622D0, 558.116553D0, : 524.429630D0, 235.934465D0, : 157.87D0, -402.922932D0, -23.923029D0, : -13.549067D0, 374.049623D0, : 220.30D0, 179.516345D0, -165.405086D0, : -210.157124D0, -171.330180D0, : 1200.00D0, -9.814756D0, 9.344131D0, : -44.919798D0, -22.899655D0 / * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Centuries since J2000. T = (EPJ-2000D0)/100D0 * Initialize X and Y accumulators. X = 0D0 Y = 0D0 * Periodic terms. W = D2PI*T DO 1 I=1,NPER A = W/XYPER(1,I) S = SIN(A) C = COS(A) X = X + C*XYPER(2,I) + S*XYPER(4,I) Y = Y + C*XYPER(3,I) + S*XYPER(5,I) 1 CONTINUE * Polynomial terms. W = 1D0 DO 2 I=1,NPOL X = X + XYPOL(I,1)*W Y = Y + XYPOL(I,2)*W W = W*T 2 CONTINUE * X and Y (direction cosines). X = X*AS2R Y = Y*AS2R * Form the equator pole vector. VEQ(1) = X VEQ(2) = Y VEQ(3) = SQRT(MAX(1D0-X*X-Y*Y,0D0)) * 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. 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