SUBROUTINE iau_LTPECL ( EPJ, VEC ) *+ * - - - - - - - - - - - * i a u _ L T P E C L * - - - - - - - - - - - * * Long-term precession of the ecliptic. * * 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: * VEC d(3) ecliptic 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, VEC(3) * Arcseconds to radians DOUBLE PRECISION DAS2R PARAMETER ( DAS2R = 4.848136811095359935899141D-6 ) * 2Pi DOUBLE PRECISION D2PI PARAMETER ( D2PI = 6.283185307179586476925287D0 ) * Obliquity at J2000.0 (radians). DOUBLE PRECISION EPS0 PARAMETER ( EPS0 = 84381.406D0 * DAS2R ) * Number of polynomial terms INTEGER NPOL PARAMETER ( NPOL = 4 ) * Number of periodic terms INTEGER NPER PARAMETER ( NPER = 8 ) * Miscellaneous INTEGER I, J DOUBLE PRECISION T, P, Q, W, A, S, C * Polynomial and periodic coefficients DOUBLE PRECISION PQPOL(NPOL,2), PQPER(5,NPER) * Polynomials DATA ((PQPOL(I,J),I=1,NPOL),J=1,2) / : : +5851.607687 D0, : -0.1189000 D0, : -0.00028913 D0, : +0.000000101 D0, : : -1600.886300 D0, : +1.1689818 D0, : -0.00000020 D0, : -0.000000437 D0 / * Periodics DATA ((PQPER(I,J),I=1,5),J=1,NPER) / : : 708.15D0, -5486.751211D0, -684.661560D0, : 667.666730D0, -5523.863691D0, : 2309.00D0, -17.127623D0, 2446.283880D0, : -2354.886252D0, -549.747450D0, : 1620.00D0, -617.517403D0, 399.671049D0, : -428.152441D0, -310.998056D0, : 492.20D0, 413.442940D0, -356.652376D0, : 376.202861D0, 421.535876D0, : 1183.00D0, 78.614193D0, -186.387003D0, : 184.778874D0, -36.776172D0, : 622.00D0, -180.732815D0, -316.800070D0, : 335.321713D0, -145.278396D0, : 882.00D0, -87.676083D0, 198.296701D0, : -185.138669D0, -34.744450D0, : 547.00D0, 46.140315D0, 101.135679D0, : -120.972830D0, 22.885731D0 / * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Centuries since J2000. T = (EPJ-2000D0)/100D0 * Initialize P_A and Q_A accumulators. P = 0D0 Q = 0D0 * Periodic terms. W = D2PI*T DO 1 I=1,NPER A = W/PQPER(1,I) S = SIN(A) C = COS(A) P = P + C*PQPER(2,I) + S*PQPER(4,I) Q = Q + C*PQPER(3,I) + S*PQPER(5,I) 1 CONTINUE * Polynomial terms. W = 1D0 DO 2 I=1,NPOL P = P + PQPOL(I,1)*W Q = Q + PQPOL(I,2)*W W = W*T 2 CONTINUE * P_A and Q_A (radians). P = P*DAS2R Q = Q*DAS2R * Form the ecliptic pole vector. W = SQRT(MAX(1D0-P*P-Q*Q,0D0)) S = SIN(EPS0) C = COS(EPS0) VEC(1) = P VEC(2) = - Q*C - W*S VEC(3) = - Q*S + W*C * 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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