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 2021-05-12
*
* Copyright (C) 2021 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) 2021
* Standards Of Fundamental Astronomy Board
* of the International Astronomical Union.
*
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*-----------------------------------------------------------------------
END