251 lines
11 KiB
C++
251 lines
11 KiB
C++
// nutation.cpp
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//
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// Calculate nutation 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 "nutation.h"
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using namespace std;
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struct NutationTableEntry
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{
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// Multiples of arguments
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int lMult;
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int l_Mult;
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int FMult;
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int DMult;
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int OmMult;
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double l1; // longitude, sin
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double l2; // longitude, t*sin
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double o1; // obliquity, cos
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double o2; // obliquity, t*cos
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double l3; // longitude, cos
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double o3; // obliquity, sin
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};
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// Luni-Solar nutation coefficients, units 0.1 microarcsec:
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// longitude (sin, t*sin, cos), obliquity (cos, t*cos, sin)
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static const NutationTableEntry IAU2000BNutationTable[] =
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{
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{ 0, 0, 0, 0, 1,-172064161, -174666, 92052331, 9086, 33386, 15377 },
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{ 0, 0, 2, -2, 2, -13170906, -1675, 5730336, -3015,-13696, -4587 },
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{ 0, 0, 2, 0, 2, -2276413, -234, 978459, -485, 2796, 1374 },
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{ 0, 0, 0, 0, 2, 2074554, 207, -897492, 470, -698, -291 },
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{ 0, 1, 0, 0, 0, 1475877, -3633, 73871, -184, 11817, -1924 },
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{ 0, 1, 2, -2, 2, -516821, 1226, 224386, -677, -524, -174 },
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{ 1, 0, 0, 0, 0, 711159, 73, -6750, 0, -872, 358 },
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{ 0, 0, 2, 0, 1, -387298, -367, 200728, 18, 380, 318 },
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{ 1, 0, 2, 0, 2, -301461, -36, 129025, -63, 816, 367 },
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{ 0, -1, 2, -2, 2, 215829, -494, -95929, 299, 111, 132 },
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{ 0, 0, 2, -2, 1, 128227, 137, -68982, -9, 181, 39 },
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{-1, 0, 2, 0, 2, 123457, 11, -53311, 32, 19, -4 },
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{-1, 0, 0, 2, 0, 156994, 10, -1235, 0, -168, 82 },
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{ 1, 0, 0, 0, 1, 63110, 63, -33228, 0, 27, -9 },
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{-1, 0, 0, 0, 1, -57976, -63, 31429, 0, -189, -75 },
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{-1, 0, 2, 2, 2, -59641, -11, 25543, -11, 149, 66 },
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{ 1, 0, 2, 0, 1, -51613, -42, 26366, 0, 129, 78 },
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{-2, 0, 2, 0, 1, 45893, 50, -24236, -10, 31, 20 },
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{ 0, 0, 0, 2, 0, 63384, 11, -1220, 0, -150, 29 },
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{ 0, 0, 2, 2, 2, -38571, -1, 16452, -11, 158, 68 },
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{-2, 0, 0, 2, 0, -47722, 0, 477, 0, -18, -25 },
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{ 2, 0, 2, 0, 2, -31046, -1, 13238, -11, 131, 59 },
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{ 1, 0, 2, -2, 2, 28593, 0, -12338, 10, -1, -3 },
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{-1, 0, 2, 0, 1, 20441, 21, -10758, 0, 10, -3 },
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{ 2, 0, 0, 0, 0, 29243, 0, -609, 0, -74, 13 },
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{ 0, 0, 2, 0, 0, 25887, 0, -550, 0, -66, 11 },
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{ 0, 1, 0, 0, 1, -14053, -25, 8551, -2, 79, -45 },
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{-1, 0, 0, 2, 1, 15164, 10, -8001, 0, 11, -1 },
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{ 0, 2, 2, -2, 2, -15794, 72, 6850, -42, -16, -5 },
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{ 0, 0, -2, 2, 0, 21783, 0, -167, 0, 13, 13 },
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{ 1, 0, 0, -2, 1, -12873, -10, 6953, 0, -37, -14 },
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{ 0, -1, 0, 0, 1, -12654, 11, 6415, 0, 63, 26 },
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{-1, 0, 2, 2, 1, -10204, 0, 5222, 0, 25, 15 },
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{ 0, 2, 0, 0, 0, 16707, -85, 168, -1, -10, 10 },
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{ 1, 0, 2, 2, 2, -7691, 0, 3268, 0, 44, 19 },
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{-2, 0, 2, 0, 0, -11024, 0, 104, 0, -14, 2 },
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{ 0, 1, 2, 0, 2, 7566, -21, -3250, 0, -11, -5 },
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{ 0, 0, 2, 2, 1, -6637, -11, 3353, 0, 25, 14 },
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{ 0, -1, 2, 0, 2, -7141, 21, 3070, 0, 8, 4 },
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{ 0, 0, 0, 2, 1, -6302, -11, 3272, 0, 2, 4 },
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{ 1, 0, 2, -2, 1, 5800, 10, -3045, 0, 2, -1 },
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{ 2, 0, 2, -2, 2, 6443, 0, -2768, 0, -7, -4 },
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{-2, 0, 0, 2, 1, -5774, -11, 3041, 0, -15, -5 },
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{ 2, 0, 2, 0, 1, -5350, 0, 2695, 0, 21, 12 },
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{ 0, -1, 2, -2, 1, -4752, -11, 2719, 0, -3, -3 },
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{ 0, 0, 0, -2, 1, -4940, -11, 2720, 0, -21, -9 },
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{-1, -1, 0, 2, 0, 7350, 0, -51, 0, -8, 4 },
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{ 2, 0, 0, -2, 1, 4065, 0, -2206, 0, 6, 1 },
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{ 1, 0, 0, 2, 0, 6579, 0, -199, 0, -24, 2 },
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{ 0, 1, 2, -2, 1, 3579, 0, -1900, 0, 5, 1 },
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{ 1, -1, 0, 0, 0, 4725, 0, -41, 0, -6, 3 },
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{-2, 0, 2, 0, 2, -3075, 0, 1313, 0, -2, -1 },
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{ 3, 0, 2, 0, 2, -2904, 0, 1233, 0, 15, 7 },
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{ 0, -1, 0, 2, 0, 4348, 0, -81, 0, -10, 2 },
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{ 1, -1, 2, 0, 2, -2878, 0, 1232, 0, 8, 4 },
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{ 0, 0, 0, 1, 0, -4230, 0, -20, 0, 5, -2 },
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{-1, -1, 2, 2, 2, -2819, 0, 1207, 0, 7, 3 },
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{-1, 0, 2, 0, 0, -4056, 0, 40, 0, 5, -2 },
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{ 0, -1, 2, 2, 2, -2647, 0, 1129, 0, 11, 5 },
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{-2, 0, 0, 0, 1, -2294, 0, 1266, 0, -10, -4 },
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{ 1, 1, 2, 0, 2, 2481, 0, -1062, 0, -7, -3 },
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{ 2, 0, 0, 0, 1, 2179, 0, -1129, 0, -2, -2 },
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{-1, 1, 0, 1, 0, 3276, 0, -9, 0, 1, 0 },
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{ 1, 1, 0, 0, 0, -3389, 0, 35, 0, 5, -2 },
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{ 1, 0, 2, 0, 0, 3339, 0, -107, 0, -13, 1 },
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{-1, 0, 2, -2, 1, -1987, 0, 1073, 0, -6, -2 },
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{ 1, 0, 0, 0, 2, -1981, 0, 854, 0, 0, 0 },
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{-1, 0, 0, 1, 0, 4026, 0, -553, 0, -353, -139 },
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{ 0, 0, 2, 1, 2, 1660, 0, -710, 0, -5, -2 },
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{-1, 0, 2, 4, 2, -1521, 0, 647, 0, 9, 4 },
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{-1, 1, 0, 1, 1, 1314, 0, -700, 0, 0, 0 },
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{ 0, -2, 2, -2, 1, -1283, 0, 672, 0, 0, 0 },
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{ 1, 0, 2, 2, 1, -1331, 0, 663, 0, 8, 4 },
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{-2, 0, 2, 2, 2, 1383, 0, -594, 0, -2, -2 },
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{-1, 0, 0, 0, 2, 1405, 0, -610, 0, 4, 2 },
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{ 1, 1, 2, -2, 2, 1290, 0, -556, 0, 0, 0 },
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{-2, 0, 2, 4, 2, -1214, 0, 518, 0, 5, 2 },
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{-1, 0, 4, 0, 2, 1146, 0, -490, 0, -3, -1 },
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};
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double arcsecToRad(double as)
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{
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return degToRad(as / 3600.0);
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}
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double milliarcsecToRad(double as)
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{
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return degToRad(as / 3600000.0);
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}
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double microarcsecToRad(double as)
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{
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return degToRad(as / 3600000000.0);
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}
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/*! Calculate nutation angles using the IAU2000B model. This model is a
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* truncated version of the IAU2000A model. It uses 77 terms for lunisolar
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* nutation and just a single constant term for planetary precession.
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*
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* T is a time in Julian centuries (day number / 36525) from J2000 TT. The
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* angles returned are in radians. Note the use of Terrestrial Time instead
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* of TDB: this will not result in any meaningful discrepancy.
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*
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* For further information, see IERS Technical Note 32:
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* http://www.iers.org/documents/publications/tn/tn32/tn32_033.pdf
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*/
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astro::NutationAngles
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astro::Nutation_IAU2000B(double T)
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{
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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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// Mean anomaly of the Moon
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double l = arcsecToRad(134.96340251
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+ 1717915923.2178 * T
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+ 31.8792 * T2
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+ 0.051635 * T3
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- 0.00024470 * T4);
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// Mean anomaly of the Sun.
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double l_ = arcsecToRad(357.52910918
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+ 129596581.0481 * T
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- 0.5532 * T2
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+ 0.000136 * T3
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- 0.00001149 * T4);
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// Mean longitude of the Moon minus the mean longitude of the Moon's
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// node.
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double F = arcsecToRad(93.27209062
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+ 1739527262.8478 * T
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- 12.7512 * T2
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- 0.001037 * T3
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+ 0.00000417 * T4);
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// Mean elongation of the Moon from the Sun
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double D = arcsecToRad(29.785019547
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+ 1602961601.2090 * T
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- 6.3706 * T2
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+ 0.006593 * T3
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- 0.00003169 * T4);
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// Longitude of the ascending node of the Moon's orbit on the ecliptic
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// measured from the mean equinox of date.
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double Om = arcsecToRad(125.04455501
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- 6962890.5431 * T
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+ 7.4722 * T2
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+ 0.007702 * T3
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- 0.00005939 * T4);
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double obliquity = 0.0;
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double longitude = 0.0;
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unsigned int nEntries = sizeof(IAU2000BNutationTable) /
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sizeof(IAU2000BNutationTable[0]);
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for (unsigned int i = 0; i < nEntries; i++)
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{
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const NutationTableEntry& ent = IAU2000BNutationTable[i];
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double arg = (l * ent.lMult +
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l_ * ent.l_Mult +
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F * ent.FMult +
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D * ent.DMult +
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Om * ent.OmMult);
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double S = sin(arg);
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double C = cos(arg);
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longitude += (ent.l1 + ent.l2 * T) * S + ent.l3 * C;
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obliquity += (ent.o1 + ent.o2 * T) * C + ent.o3 * S;
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}
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// These constant terms account for the missing long-period planetary
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// terms in the truncated nutation model.
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double oblPlanetary = milliarcsecToRad(-0.135);
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double longPlanetary = milliarcsecToRad(+0.388);
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NutationAngles nutation;
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// Convert to radians from units of 0.1 microarcsec
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nutation.obliquity = microarcsecToRad(obliquity * 0.1);
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nutation.longitude = microarcsecToRad(longitude * 0.1);
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// Add planetary nutation
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nutation.obliquity += oblPlanetary;
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nutation.longitude += longPlanetary;
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return nutation;
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}
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#if TEST
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using namespace astro;
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int main()
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{
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for (int i = -50; i < 50; i++)
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{
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NutationAngles nutation = Nutation_IAU2000B((double) i / 100.0);
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cout << radToDeg(nutation.longitude) * 3600.0 << ", "
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<< radToDeg(nutation.obliquity) * 3600.0 << endl;
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}
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}
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#endif
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