286 lines
8.2 KiB
C++
286 lines
8.2 KiB
C++
// precession.cpp
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//
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// Calculate precession angles for Earth.
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//
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// Copyright (C) 2008, the Celestia Development Team
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// Initial version by Chris Laurel, claurel@gmail.com
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//
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// This program is free software; you can redistribute it and/or
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// modify it under the terms of the GNU General Public License
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// as published by the Free Software Foundation; either version 2
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// of the License, or (at your option) any later version.
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#include <cmath>
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#include <iostream>
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#include <celmath/mathlib.h>
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#include "precession.h"
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using namespace std;
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// Periodic term for the long-period extension of the P03 precession
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// model.
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struct EclipticPrecessionTerm
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{
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double Pc;
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double Qc;
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double Ps;
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double Qs;
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double period;
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};
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static EclipticPrecessionTerm EclipticPrecessionTerms[] =
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{
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{ 486.230527, 2559.065245, -2578.462809, 485.116645, 2308.98 },
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{ -963.825784, 247.582718, -237.405076, -971.375498, 1831.25 },
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{ -1868.737098, -957.399054, 1007.593090, -1930.464338, 687.52 },
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{ -1589.172175, 493.021354, -423.035168, -1634.905683, 729.97 },
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{ 429.442489, -328.301413, 337.266785, 429.594383, 492.21 },
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{ -2244.742029, -339.969833, 221.240093, -2131.745072, 708.13 },
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};
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// Periodic term for the long-period extension of the P03 precession
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// model.
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struct PrecessionTerm
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{
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double pc;
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double epsc;
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double ps;
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double epss;
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double period;
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};
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static PrecessionTerm PrecessionTerms[] =
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{
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{ -6180.062400, 807.904635, -2434.845716, -2056.455197, 409.90 },
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{ -2721.869299, -177.959383, 538.034071, -912.727303, 396.15 },
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{ 1460.746498, 371.942696, -1245.689351, 447.710000, 536.91 },
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{ -1838.488899, -176.029134, 529.220775, -611.297411, 402.90 },
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{ 949.518077, -89.154030, 277.195375, 315.900626, 417.15 },
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{ 32.701460, -336.048179, 945.979710, 12.390157, 288.92 },
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{ 598.054819, -17.415730, -955.163661, -15.922155, 4042.97 },
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{ -293.145284, -28.084479, 93.894079, -102.870153, 304.90 },
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{ 66.354942, 21.456146, 0.671968, 24.123484, 281.46 },
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{ 18.894136, 30.917011, -184.663935, 2.512708, 204.38 },
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};
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/*! Compute the precession of the ecliptic, based on a long-period
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* extension of the the P03 model, presented in "Long-periodic Precession
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* Parameters", J. Vondrak (2006)
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* http://www.astronomy2006.com/files/vondrak.pdf
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* For an explanation of the angles used in the P03 model, see
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* "Expressions for IAU2000 precession quantities", N. Capitaine et al,
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* Astronomy & Astrophysics, v.412, p.567-586 (2003).
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*
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* Also: "Expressions for the Precession Quantities", J. H. Lieske et al,
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* Astronomy & Astrophysics, v.58, p. 1-16 (1977).
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*
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* 6 long-periodic terms, plus a cubic polynomial for longer terms.
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* The terms are fitted to the P03 model withing 1000 years of J2000.
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*
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* T is the time in centuries since J2000. The angles returned are
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* in arcseconds.
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*/
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astro::EclipticPole
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astro::EclipticPrecession_P03LP(double T)
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{
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EclipticPole pole;
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double T2 = T * T;
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double T3 = T2 * T;
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pole.PA = (5750.804069
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+ 0.1948311 * T
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- 0.00016739 * T2
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- 4.8e-8 * T3);
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pole.QA = (-1673.999018
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+ 0.3474459 * T
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+ 0.00011243 * T2
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- 6.4e-8 * T3);
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unsigned int nTerms = sizeof(EclipticPrecessionTerms) / sizeof(EclipticPrecessionTerms[0]);
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for (unsigned int i = 0; i < nTerms; i++)
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{
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const EclipticPrecessionTerm& p = EclipticPrecessionTerms[i];
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double theta = 2.0 * PI * T / p.period;
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double s = sin(theta);
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double c = cos(theta);
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pole.PA += p.Pc * c + p.Ps * s;
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pole.QA += p.Qc * c + p.Qs * s;
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}
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return pole;
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}
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/*! Compute the general precession and obliquity, based on the model
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* presented in "Long-periodic Precession Parameters", J. Vondrak, 2006
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* http://www.astronomy2006.com/files/vondrak.pdf
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*
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* T is the time in centuries since J2000. The angles returned are
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* in arcseconds.
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*/
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astro::PrecessionAngles
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astro::PrecObliquity_P03LP(double T)
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{
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PrecessionAngles angles;
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double T2 = T * T;
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double T3 = T2 * T;
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angles.pA = ( 7907.295950
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+ 5044.374034 * T
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- 0.00713473 * T2
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+ 6e-9 * T3);
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angles.epsA = ( 83973.876448
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- 0.0425899 * T
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- 0.00000113 * T2);
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unsigned int nTerms = sizeof(PrecessionTerms) / sizeof(PrecessionTerms[0]);
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for (unsigned int i = 0; i < nTerms; i++)
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{
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const PrecessionTerm& p = PrecessionTerms[i];
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double theta = 2.0 * PI * T / p.period;
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double s = sin(theta);
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double c = cos(theta);
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angles.pA += p.pc * c + p.ps * s;
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angles.epsA += p.epsc * c + p.epss * s;
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}
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return angles;
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}
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/*! Compute equatorial precession angles z, zeta, and theta using the P03
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* precession model.
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*/
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astro::EquatorialPrecessionAngles
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astro::EquatorialPrecessionAngles_P03(double T)
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{
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EquatorialPrecessionAngles prec;
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double T2 = T * T;
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double T3 = T2 * T;
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double T4 = T3 * T;
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double T5 = T4 * T;
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prec.zetaA = ( 2.650545
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+ 2306.083227 * T
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+ 0.2988499 * T2
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+ 0.01801828 * T3
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- 0.000005971 * T4
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- 0.0000003173 * T5);
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prec.zA = ( - 2.650545
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+ 2306.077181 * T
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+ 1.0927348 * T2
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+ 0.01826837 * T3
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- 0.000028596 * T4
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- 0.0000002904 * T5);
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prec.thetaA = ( 2004.191903 * T
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- 0.4294934 * T2
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- 0.04182264 * T3
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- 0.000007089 * T4
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- 0.0000001274 * T5);
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return prec;
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}
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/*! Compute the ecliptic pole coordinates PA and QA using the P03 precession
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* model. The quantities PA and QA are coordinates, but they are given in
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* units of arcseconds in P03. They should be divided by 1296000/2pi.
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*/
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astro::EclipticPole
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astro::EclipticPrecession_P03(double T)
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{
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astro::EclipticPole pole;
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double T2 = T * T;
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double T3 = T2 * T;
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double T4 = T3 * T;
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double T5 = T4 * T;
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pole.PA = ( 4.199094 * T
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+ 0.1939873 * T2
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- 0.00022466 * T3
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- 0.000000912 * T4
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+ 0.0000000120 * T5);
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pole.QA = (-46.811015 * T
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+ 0.0510283 * T2
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+ 0.00052413 * T3
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- 0.00000646 * T4
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- 0.0000000172 * T5);
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return pole;
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}
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/*! Calculate the angles of the ecliptic of date with respect to
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* the J2000 ecliptic using the P03 precession model.
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*/
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astro::EclipticAngles
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astro::EclipticPrecessionAngles_P03(double T)
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{
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astro::EclipticAngles ecl;
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double T2 = T * T;
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double T3 = T2 * T;
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double T4 = T3 * T;
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double T5 = T4 * T;
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ecl.piA = ( 46.998973 * T
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- 0.0334926 * T2
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- 0.00012559 * T3
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+ 0.000000113 * T4
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- 0.0000000022 * T5);
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ecl.PiA = (629546.7936
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- 867.95758 * T
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+ 0.157992 * T2
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- 0.0005371 * T3
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- 0.00004797 * T4
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+ 0.000000072 * T5);
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return ecl;
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}
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// DE405 obliquity of the ecliptic
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static const double eps0 = 84381.40889;
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/*! Compute the general precession and obliquity using the P03
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* precession model. See PrecObliquity_P03LP for more details.
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*/
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astro::PrecessionAngles
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astro::PrecObliquity_P03(double T)
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{
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astro::PrecessionAngles prec;
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double T2 = T * T;
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double T3 = T2 * T;
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double T4 = T3 * T;
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double T5 = T4 * T;
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prec.epsA = (eps0
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- 46.836769 * T
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- 0.0001831 * T2
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+ 0.00200340 * T3
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- 0.000000576 * T4
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- 0.0000000434 * T5);
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prec.pA = ( 5028.796195 * T
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+ 1.1054348 * T2
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+ 0.00007964 * T3
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- 0.000023857 * T4
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- 0.0000000383 * T5);
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#if 0
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prec.chiA = ( 10.556403 * T
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- 2.3814292 * T2
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- 0.00121197 * T3
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+ 0.000170663 * T4
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- 0.0000000560 * T5);
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#endif
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return prec;
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}
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