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cf64530270b308b87bcc52942de8e875a33b7948
lunar-calendar/aa.py
Chen Wei cf64530270 add astronomical algorithms for compute solar terms and moon phases. 
aa_full.py uses full LEA-406 and VSOP87D
aa.py uses a truncted version of LEA-406 and VSOP87D
2014-03-10 19:38:37 +08:00

2792 lines
114 KiB
Python
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#!/usr/bin/env python
# -*- coding: utf-8 -*-
from numpy import *
import numexpr as ne
J2000 = 2451545.0
SYNODIC_MONTH = 29.53
MOON_SPEED = 2 * pi / SYNODIC_MONTH
TROPICAL_YEAR = 365.24
SUN_SPEED = 2 * pi / TROPICAL_YEAR
UNIXEPOCH = 2440587.50046567898243 # JDE for 1970-01-01 00:00
ASEC2RAD = 4.848136811095359935899141e-6
DEG2RAD = 0.017453292519943295
ASEC360 = 1296000.0
PI = pi
TWOPI = 2 * pi
# 77 terms IAU2000B Luni-Solar nutation table from USNO NOVAS c source
#
# Luni-Solar argument multipliers, coefficients, unit 1e-7 arcsec
# L L' F D Om longitude (sin, t*sin, cos), obliquity (cos, t*cos, sin)
IAU2000BNutationTable = array([
[ 0, 0, 0, 0, 1, -172064161, -174666, 33386, 92052331, 9086, 15377 ],
[ 0, 0, 2, -2, 2, -13170906, -1675, -13696, 5730336, -3015, -4587 ],
[ 0, 0, 2, 0, 2, -2276413, -234, 2796, 978459, -485, 1374 ],
[ 0, 0, 0, 0, 2, 2074554, 207, -698, -897492, 470, -291 ],
[ 0, 1, 0, 0, 0, 1475877, -3633, 11817, 73871, -184, -1924 ],
[ 0, 1, 2, -2, 2, -516821, 1226, -524, 224386, -677, -174 ],
[ 1, 0, 0, 0, 0, 711159, 73, -872, -6750, 0, 358 ],
[ 0, 0, 2, 0, 1, -387298, -367, 380, 200728, 18, 318 ],
[ 1, 0, 2, 0, 2, -301461, -36, 816, 129025, -63, 367 ],
[ 0, -1, 2, -2, 2, 215829, -494, 111, -95929, 299, 132 ],
[ 0, 0, 2, -2, 1, 128227, 137, 181, -68982, -9, 39 ],
[ -1, 0, 2, 0, 2, 123457, 11, 19, -53311, 32, -4 ],
[ -1, 0, 0, 2, 0, 156994, 10, -168, -1235, 0, 82 ],
[ 1, 0, 0, 0, 1, 63110, 63, 27, -33228, 0, -9 ],
[ -1, 0, 0, 0, 1, -57976, -63, -189, 31429, 0, -75 ],
[ -1, 0, 2, 2, 2, -59641, -11, 149, 25543, -11, 66 ],
[ 1, 0, 2, 0, 1, -51613, -42, 129, 26366, 0, 78 ],
[ -2, 0, 2, 0, 1, 45893, 50, 31, -24236, -10, 20 ],
[ 0, 0, 0, 2, 0, 63384, 11, -150, -1220, 0, 29 ],
[ 0, 0, 2, 2, 2, -38571, -1, 158, 16452, -11, 68 ],
[ 0, -2, 2, -2, 2, 32481, 0, 0, -13870, 0, 0 ],
[ -2, 0, 0, 2, 0, -47722, 0, -18, 477, 0, -25 ],
[ 2, 0, 2, 0, 2, -31046, -1, 131, 13238, -11, 59 ],
[ 1, 0, 2, -2, 2, 28593, 0, -1, -12338, 10, -3 ],
[ -1, 0, 2, 0, 1, 20441, 21, 10, -10758, 0, -3 ],
[ 2, 0, 0, 0, 0, 29243, 0, -74, -609, 0, 13 ],
[ 0, 0, 2, 0, 0, 25887, 0, -66, -550, 0, 11 ],
[ 0, 1, 0, 0, 1, -14053, -25, 79, 8551, -2, -45 ],
[ -1, 0, 0, 2, 1, 15164, 10, 11, -8001, 0, -1 ],
[ 0, 2, 2, -2, 2, -15794, 72, -16, 6850, -42, -5 ],
[ 0, 0, -2, 2, 0, 21783, 0, 13, -167, 0, 13 ],
[ 1, 0, 0, -2, 1, -12873, -10, -37, 6953, 0, -14 ],
[ 0, -1, 0, 0, 1, -12654, 11, 63, 6415, 0, 26 ],
[ -1, 0, 2, 2, 1, -10204, 0, 25, 5222, 0, 15 ],
[ 0, 2, 0, 0, 0, 16707, -85, -10, 168, -1, 10 ],
[ 1, 0, 2, 2, 2, -7691, 0, 44, 3268, 0, 19 ],
[ -2, 0, 2, 0, 0, -11024, 0, -14, 104, 0, 2 ],
[ 0, 1, 2, 0, 2, 7566, -21, -11, -3250, 0, -5 ],
[ 0, 0, 2, 2, 1, -6637, -11, 25, 3353, 0, 14 ],
[ 0, -1, 2, 0, 2, -7141, 21, 8, 3070, 0, 4 ],
[ 0, 0, 0, 2, 1, -6302, -11, 2, 3272, 0, 4 ],
[ 1, 0, 2, -2, 1, 5800, 10, 2, -3045, 0, -1 ],
[ 2, 0, 2, -2, 2, 6443, 0, -7, -2768, 0, -4 ],
[ -2, 0, 0, 2, 1, -5774, -11, -15, 3041, 0, -5 ],
[ 2, 0, 2, 0, 1, -5350, 0, 21, 2695, 0, 12 ],
[ 0, -1, 2, -2, 1, -4752, -11, -3, 2719, 0, -3 ],
[ 0, 0, 0, -2, 1, -4940, -11, -21, 2720, 0, -9 ],
[ -1, -1, 0, 2, 0, 7350, 0, -8, -51, 0, 4 ],
[ 2, 0, 0, -2, 1, 4065, 0, 6, -2206, 0, 1 ],
[ 1, 0, 0, 2, 0, 6579, 0, -24, -199, 0, 2 ],
[ 0, 1, 2, -2, 1, 3579, 0, 5, -1900, 0, 1 ],
[ 1, -1, 0, 0, 0, 4725, 0, -6, -41, 0, 3 ],
[ -2, 0, 2, 0, 2, -3075, 0, -2, 1313, 0, -1 ],
[ 3, 0, 2, 0, 2, -2904, 0, 15, 1233, 0, 7 ],
[ 0, -1, 0, 2, 0, 4348, 0, -10, -81, 0, 2 ],
[ 1, -1, 2, 0, 2, -2878, 0, 8, 1232, 0, 4 ],
[ 0, 0, 0, 1, 0, -4230, 0, 5, -20, 0, -2 ],
[ -1, -1, 2, 2, 2, -2819, 0, 7, 1207, 0, 3 ],
[ -1, 0, 2, 0, 0, -4056, 0, 5, 40, 0, -2 ],
[ 0, -1, 2, 2, 2, -2647, 0, 11, 1129, 0, 5 ],
[ -2, 0, 0, 0, 1, -2294, 0, -10, 1266, 0, -4 ],
[ 1, 1, 2, 0, 2, 2481, 0, -7, -1062, 0, -3 ],
[ 2, 0, 0, 0, 1, 2179, 0, -2, -1129, 0, -2 ],
[ -1, 1, 0, 1, 0, 3276, 0, 1, -9, 0, 0 ],
[ 1, 1, 0, 0, 0, -3389, 0, 5, 35, 0, -2 ],
[ 1, 0, 2, 0, 0, 3339, 0, -13, -107, 0, 1 ],
[ -1, 0, 2, -2, 1, -1987, 0, -6, 1073, 0, -2 ],
[ 1, 0, 0, 0, 2, -1981, 0, 0, 854, 0, 0 ],
[ -1, 0, 0, 1, 0, 4026, 0, -353, -553, 0, -139 ],
[ 0, 0, 2, 1, 2, 1660, 0, -5, -710, 0, -2 ],
[ -1, 0, 2, 4, 2, -1521, 0, 9, 647, 0, 4 ],
[ -1, 1, 0, 1, 1, 1314, 0, 0, -700, 0, 0 ],
[ 0, -2, 2, -2, 1, -1283, 0, 0, 672, 0, 0 ],
[ 1, 0, 2, 2, 1, -1331, 0, 8, 663, 0, 4 ],
[ -2, 0, 2, 2, 2, 1383, 0, -2, -594, 0, -2 ],
[ -1, 0, 0, 0, 2, 1405, 0, 4, -610, 0, 2 ],
[ 1, 1, 2, -2, 2, 1290, 0, 0, -556, 0, 0 ]
])
# The abridged elp-2000 table from A&A p309, TABLE 45.A
moon_tableA = [
[ 0, 0, 1, 0, 6288744, -20905355 ],
[ 2, 0, -1, 0, 1274027, -3699111 ],
[ 2, 0, 0, 0, 658314, -2955968 ],
[ 0, 0, 2, 0, 213618, -569925 ],
[ 0, 1, 0, 0, -185116, 48888 ],
[ 0, 0, 0, 2, -114332, -3149 ],
[ 2, 0, -2, 0, 58793, 246158 ],
[ 2, -1, -1, 0, 57066, -152138 ],
[ 2, 0, 1, 0, 53322, -170733 ],
[ 2, -1, 0, 0, 45758, -204586 ],
[ 0, 1, -1, 0, -40923, -129620 ],
[ 1, 0, 0, 0, -34720, 108743 ],
[ 0, 1, 1, 0, -30383, 104755 ],
[ 2, 0, 0, -2, 15327, 10321 ],
[ 0, 0, 1, 2, -12528, 0 ],
[ 0, 0, 1, -2, 10980, 79661 ],
[ 4, 0, -1, 0, 10675, -34782 ],
[ 0, 0, 3, 0, 10034, -23210 ],
[ 4, 0, -2, 0, 8548, -21636 ],
[ 2, 1, -1, 0, -7888, 24208 ],
[ 2, 1, 0, 0, -6766, 30824 ],
[ 1, 0, -1, 0, -5163, -8379 ],
[ 1, 1, 0, 0, 4987, -16675 ],
[ 2, -1, 1, 0, 4036, -12831 ],
[ 2, 0, 2, 0, 3994, -10445 ],
[ 4, 0, 0, 0, 3861, -11650 ],
[ 2, 0, -3, 0, 3665, 14403 ],
[ 0, 1, -2, 0, -2689, -7003 ],
[ 2, 0, -1, 2, -2602, 0 ],
[ 2, -1, -2, 0, 2390, 10056 ],
[ 1, 0, 1, 0, -2348, 6322 ],
[ 2, -2, 0, 0, 2236, -9884 ],
[ 0, 1, 2, 0, -2120, 5751 ],
[ 0, 2, 0, 0, -2069, 0 ],
[ 2, -2, -1, 0, 2048, -4950 ],
[ 2, 0, 1, -2, -1773, 4130 ],
[ 2, 0, 0, 2, -1595, 0 ],
[ 4, -1, -1, 0, 1215, -3958 ],
[ 0, 0, 2, 2, -1110, 0 ],
[ 3, 0, -1, 0, -892, 3258 ],
[ 2, 1, 1, 0, -810, 2616 ],
[ 4, -1, -2, 0, 759, -1897 ],
[ 0, 2, -1, 0, -713, -2117 ],
[ 2, 2, -1, 0, -700, 2354 ],
[ 2, 1, -2, 0, 691, 0 ],
[ 2, -1, 0, -2, 596, 0 ],
[ 4, 0, 1, 0, 549, -1423 ],
[ 0, 0, 4, 0, 537, -1117 ],
[ 4, -1, 0, 0, 520, -1571 ],
[ 1, 0, -2, 0, -487, -1739 ],
[ 2, 1, 0, -2, -399, 0 ],
[ 0, 0, 2, -2, -381, -4421 ],
[ 1, 1, 1, 0, 351, 0 ],
[ 3, 0, -2, 0, -340, 0 ],
[ 4, 0, -3, 0, 330, 0 ],
[ 2, -1, 2, 0, 327, 0 ],
[ 0, 2, 1, 0, -323, 1165 ],
[ 1, 1, -1, 0, 299, 0 ],
[ 2, 0, 3, 0, 294, 0 ],
[ 2, 0, -1, -2, 0, 8752 ]
]
# VSOP87D tables
earth_L0 = array([
[ 1.75347045673, 0, 0 ],
[ 0.03341656456, 4.66925680417, 6283.0758499914 ],
[ 0.00034894275, 4.62610241759, 12566.1516999828 ],
[ 0.00003417571, 2.82886579606, 3.523118349 ],
[ 0.00003497056, 2.74411800971, 5753.3848848968 ],
[ 0.00003135896, 3.62767041758, 77713.7714681205 ],
[ 0.00002676218, 4.41808351397, 7860.4193924392 ],
[ 0.00002342687, 6.13516237631, 3930.2096962196 ],
[ 0.00001273166, 2.03709655772, 529.6909650946 ],
[ 0.00001324292, 0.74246356352, 11506.7697697936 ],
[ 0.00000901855, 2.04505443513, 26.2983197998 ],
[ 0.00001199167, 1.10962944315, 1577.3435424478 ],
[ 0.00000857223, 3.50849156957, 398.1490034082 ],
[ 0.00000779786, 1.17882652114, 5223.6939198022 ],
[ 0.0000099025, 5.23268129594, 5884.9268465832 ],
[ 0.00000753141, 2.53339053818, 5507.5532386674 ],
[ 0.00000505264, 4.58292563052, 18849.2275499742 ],
[ 0.00000492379, 4.20506639861, 775.522611324 ],
[ 0.00000356655, 2.91954116867, 0.0673103028 ],
[ 0.00000284125, 1.89869034186, 796.2980068164 ],
[ 0.0000024281, 0.34481140906, 5486.777843175 ],
[ 0.00000317087, 5.84901952218, 11790.6290886588 ],
[ 0.00000271039, 0.31488607649, 10977.078804699 ],
[ 0.0000020616, 4.80646606059, 2544.3144198834 ],
[ 0.00000205385, 1.86947813692, 5573.1428014331 ],
[ 0.00000202261, 2.45767795458, 6069.7767545534 ],
[ 0.00000126184, 1.0830263021, 20.7753954924 ],
[ 0.00000155516, 0.83306073807, 213.299095438 ],
[ 0.00000115132, 0.64544911683, 0.9803210682 ],
[ 0.00000102851, 0.63599846727, 4694.0029547076 ],
[ 0.00000101724, 4.26679821365, 7.1135470008 ],
[ 0.00000099206, 6.20992940258, 2146.1654164752 ],
[ 0.00000132212, 3.41118275555, 2942.4634232916 ],
[ 0.00000097607, 0.6810127227, 155.4203994342 ],
[ 0.00000085128, 1.29870743025, 6275.9623029906 ],
[ 0.00000074651, 1.75508916159, 5088.6288397668 ],
[ 0.00000101895, 0.97569221824, 15720.8387848784 ],
[ 0.00000084711, 3.67080093025, 71430.69561812909 ],
[ 0.00000073547, 4.67926565481, 801.8209311238 ],
[ 0.00000073874, 3.50319443167, 3154.6870848956 ],
[ 0.00000078756, 3.03698313141, 12036.4607348882 ],
[ 0.00000079637, 1.807913307, 17260.1546546904 ],
[ 0.00000085803, 5.98322631256, 161000.6857376741 ],
[ 0.00000056963, 2.78430398043, 6286.5989683404 ],
[ 0.00000061148, 1.81839811024, 7084.8967811152 ],
[ 0.00000069627, 0.83297596966, 9437.762934887 ],
[ 0.00000056116, 4.38694880779, 14143.4952424306 ],
[ 0.00000062449, 3.97763880587, 8827.3902698748 ],
[ 0.00000051145, 0.28306864501, 5856.4776591154 ],
[ 0.00000055577, 3.47006009062, 6279.5527316424 ],
[ 0.00000041036, 5.36817351402, 8429.2412664666 ],
[ 0.00000051605, 1.33282746983, 1748.016413067 ],
[ 0.00000051992, 0.18914945834, 12139.5535091068 ],
[ 0.00000049, 0.48735065033, 1194.4470102246 ],
[ 0.000000392, 6.16832995016, 10447.3878396044 ],
[ 0.00000035566, 1.77597314691, 6812.766815086 ],
[ 0.0000003677, 6.04133859347, 10213.285546211 ],
[ 0.00000036596, 2.56955238628, 1059.3819301892 ],
[ 0.00000033291, 0.59309499459, 17789.845619785 ],
[ 0.00000035954, 1.70876111898, 2352.8661537718 ],
[ 0.00000040938, 2.39850881707, 19651.048481098 ],
[ 0.00000030047, 2.73975123935, 1349.8674096588 ],
[ 0.00000030412, 0.44294464135, 83996.84731811189 ],
[ 0.00000023663, 0.48473567763, 8031.0922630584 ],
[ 0.00000023574, 2.06527720049, 3340.6124266998 ],
[ 0.00000021089, 4.14825464101, 951.7184062506 ],
[ 0.00000024738, 0.21484762138, 3.5904286518 ],
[ 0.00000025352, 3.16470953405, 4690.4798363586 ],
[ 0.0000002282, 5.22197888032, 4705.7323075436 ],
[ 0.00000021419, 1.42563735525, 16730.4636895958 ],
[ 0.00000021891, 5.55594302562, 553.5694028424 ],
[ 0.00000017481, 4.56052900359, 135.0650800354 ],
[ 0.00000019925, 5.22208471269, 12168.0026965746 ],
[ 0.0000001986, 5.77470167653, 6309.3741697912 ],
[ 0.000000203, 0.37133792946, 283.8593188652 ],
[ 0.00000014421, 4.19315332546, 242.728603974 ],
[ 0.00000016225, 5.98837722564, 11769.8536931664 ],
[ 0.00000015077, 4.19567181073, 6256.7775301916 ],
[ 0.00000019124, 3.82219996949, 23581.2581773176 ],
[ 0.00000018888, 5.38626880969, 149854.40013480789 ],
[ 0.00000014346, 3.72355084422, 38.0276726358 ],
[ 0.00000017898, 2.21490735647, 13367.9726311066 ],
[ 0.00000012054, 2.62229588349, 955.5997416086 ],
[ 0.00000011287, 0.17739328092, 4164.311989613 ],
[ 0.00000013971, 4.40138139996, 6681.2248533996 ],
[ 0.00000013621, 1.88934471407, 7632.9432596502 ],
[ 0.00000012503, 1.13052412208, 5.5229243074 ],
[ 0.00000010498, 5.35909518669, 1592.5960136328 ],
[ 0.00000009803, 0.99947478995, 11371.7046897582 ],
[ 0.0000000922, 4.57138609781, 4292.3308329504 ],
[ 0.00000010327, 6.19982566125, 6438.4962494256 ],
[ 0.00000012003, 1.003514567, 632.7837393132 ],
[ 0.00000010827, 0.32734520222, 103.0927742186 ],
[ 0.00000008356, 4.53902685948, 25132.3033999656 ],
[ 0.00000010005, 6.0291496328, 5746.271337896 ],
[ 0.00000008409, 3.29946744189, 7234.794256242 ],
[ 0.00000008006, 5.82145271907, 28.4491874678 ],
[ 0.00000010523, 0.93871805506, 11926.2544136688 ],
[ 0.00000007686, 3.12142363172, 7238.6755916 ],
[ 0.00000009378, 2.62414241032, 5760.4984318976 ],
[ 0.00000008127, 6.11228001785, 4732.0306273434 ],
[ 0.00000009232, 0.48343968736, 522.5774180938 ],
[ 0.00000009802, 5.24413991147, 27511.4678735372 ],
[ 0.00000007871, 0.99590177926, 5643.1785636774 ],
[ 0.00000008123, 6.2705301365, 426.598190876 ],
[ 0.00000009048, 5.33686335897, 6386.16862421 ],
[ 0.0000000862, 4.16538210888, 7058.5984613154 ],
[ 0.00000006297, 4.71724819317, 6836.6452528338 ],
[ 0.00000007575, 3.97382858911, 11499.6562227928 ],
[ 0.00000007756, 2.95729056763, 23013.5395395872 ],
[ 0.00000007314, 0.60652505806, 11513.8833167944 ],
[ 0.00000005955, 2.87641047971, 6283.14316029419 ],
[ 0.00000006534, 5.79072926033, 18073.7049386502 ],
[ 0.00000007188, 3.99831508699, 74.7815985673 ],
[ 0.00000007346, 4.38582365437, 316.3918696566 ],
[ 0.00000005413, 5.39199024641, 419.4846438752 ],
[ 0.00000005127, 2.36062848786, 10973.55568635 ],
[ 0.00000007056, 0.32258441903, 263.0839233728 ],
[ 0.00000006625, 3.66475158672, 17298.1823273262 ],
[ 0.00000006762, 5.91132535899, 90955.5516944961 ],
[ 0.00000004938, 5.73672165674, 9917.6968745098 ],
[ 0.00000005547, 2.45152597661, 12352.8526045448 ],
[ 0.00000005958, 3.32051344676, 6283.0085396886 ],
[ 0.00000004471, 2.06385999536, 7079.3738568078 ],
[ 0.00000006153, 1.45823331144, 233141.31440436149 ],
[ 0.00000004348, 4.4234217548, 5216.5803728014 ],
[ 0.00000006123, 1.07494905258, 19804.8272915828 ],
[ 0.00000004488, 3.6528503715, 206.1855484372 ],
[ 0.0000000402, 0.83995823171, 20.3553193988 ],
[ 0.00000005188, 4.06503864016, 6208.2942514241 ],
[ 0.00000005307, 0.38217636096, 31441.6775697568 ],
[ 0.00000003785, 2.34369213733, 3.881335358 ],
[ 0.00000004497, 3.27230796845, 11015.1064773348 ],
[ 0.00000004132, 0.92128915753, 3738.761430108 ],
[ 0.00000003521, 5.97844807108, 3894.1818295422 ],
[ 0.00000004215, 1.90601120623, 245.8316462294 ],
[ 0.00000003701, 5.03069397926, 536.8045120954 ],
[ 0.00000003865, 1.82634360607, 11856.2186514245 ],
[ 0.00000003652, 1.01838584934, 16200.7727245012 ],
[ 0.0000000339, 0.97785123922, 8635.9420037632 ],
[ 0.00000003737, 2.95380107829, 3128.3887650958 ],
[ 0.00000003507, 3.71291946325, 6290.1893969922 ],
[ 0.00000003086, 3.64646921512, 10.6366653498 ],
[ 0.00000003397, 1.10590684017, 14712.317116458 ],
[ 0.00000003334, 0.83684924911, 6496.3749454294 ],
[ 0.00000002805, 2.58504514144, 14314.1681130498 ],
[ 0.0000000365, 1.08344142571, 88860.05707098669 ],
[ 0.00000003388, 3.20185096055, 5120.6011455836 ],
[ 0.00000003252, 3.47859752062, 6133.5126528568 ],
[ 0.00000002553, 3.94869034189, 1990.745017041 ],
[ 0.0000000352, 2.05559692878, 244287.60000722769 ],
[ 0.00000002565, 1.560717849, 23543.23050468179 ],
[ 0.00000002621, 3.85639359951, 266.6070417218 ],
[ 0.00000002955, 3.39692949667, 9225.539273283 ],
[ 0.00000002876, 6.02635617464, 154717.60988768269 ],
[ 0.00000002395, 1.16131956403, 10984.1923516998 ],
[ 0.00000003161, 1.32798718453, 10873.9860304804 ],
[ 0.00000003163, 5.08946464629, 21228.3920235458 ],
[ 0.00000002361, 4.27212906992, 6040.3472460174 ],
[ 0.0000000303, 1.80209931347, 35371.8872659764 ],
[ 0.00000002343, 3.576898605, 10969.9652576982 ],
[ 0.00000002618, 2.57870156528, 22483.84857449259 ],
[ 0.00000002113, 3.71393780256, 65147.6197681377 ],
[ 0.00000002019, 0.81393923319, 170.6728706192 ],
[ 0.00000002003, 0.38091017375, 6172.869528772 ],
[ 0.00000002506, 3.74379142438, 10575.4066829418 ],
[ 0.00000002381, 0.10581361289, 7.046236698 ],
[ 0.00000001949, 4.86892513469, 36.0278666774 ],
[ 0.00000002074, 4.2279477457, 5650.2921106782 ],
[ 0.00000001924, 5.5946054986, 6282.0955289232 ],
[ 0.00000001949, 1.07002512703, 5230.807466803 ],
[ 0.00000001988, 5.19736046771, 6262.300454499 ],
# 172 terms retained
])
earth_L1 = array([
[ 6283.31966747491, 0, 0 ],
[ 0.00206058863, 2.67823455584, 6283.0758499914 ],
[ 0.0000430343, 2.63512650414, 12566.1516999828 ],
[ 0.00000425264, 1.59046980729, 3.523118349 ],
[ 0.00000108977, 2.96618001993, 1577.3435424478 ],
[ 0.00000093478, 2.59212835365, 18849.2275499742 ],
[ 0.00000119261, 5.79557487799, 26.2983197998 ],
[ 0.00000072122, 1.13846158196, 529.6909650946 ],
[ 0.00000067768, 1.87472304791, 398.1490034082 ],
[ 0.00000067327, 4.40918235168, 5507.5532386674 ],
[ 0.00000059027, 2.8879703846, 5223.6939198022 ],
[ 0.00000055976, 2.17471680261, 155.4203994342 ],
[ 0.00000045407, 0.39803079805, 796.2980068164 ],
[ 0.00000036369, 0.46624739835, 775.522611324 ],
[ 0.00000028958, 2.64707383882, 7.1135470008 ],
[ 0.00000019097, 1.84628332577, 5486.777843175 ],
[ 0.00000020844, 5.34138275149, 0.9803210682 ],
[ 0.00000018508, 4.96855124577, 213.299095438 ],
[ 0.00000016233, 0.03216483047, 2544.3144198834 ],
[ 0.00000017293, 2.99116864949, 6275.9623029906 ],
[ 0.00000015832, 1.43049285325, 2146.1654164752 ],
[ 0.00000014615, 1.20532366323, 10977.078804699 ],
[ 0.00000011877, 3.25804815607, 5088.6288397668 ],
[ 0.00000011514, 2.07502418155, 4694.0029547076 ],
[ 0.00000009721, 4.23925472239, 1349.8674096588 ],
[ 0.00000009969, 1.30262991097, 6286.5989683404 ],
[ 0.00000009452, 2.69957062864, 242.728603974 ],
[ 0.00000012461, 2.83432285512, 1748.016413067 ],
[ 0.00000011808, 5.2737979048, 1194.4470102246 ],
[ 0.00000008577, 5.64475868067, 951.7184062506 ],
[ 0.00000010641, 0.76614199202, 553.5694028424 ],
[ 0.00000007576, 5.30062664886, 2352.8661537718 ],
[ 0.00000005834, 1.76649917904, 1059.3819301892 ],
[ 0.00000006385, 2.65033984967, 9437.762934887 ],
[ 0.00000005223, 5.66135767624, 71430.69561812909 ],
[ 0.00000005305, 0.90857521574, 3154.6870848956 ],
[ 0.00000006101, 4.66632584188, 4690.4798363586 ],
[ 0.0000000433, 0.24102555403, 6812.766815086 ],
[ 0.00000005041, 1.42490103709, 6438.4962494256 ],
[ 0.00000004259, 0.77355900599, 10447.3878396044 ],
[ 0.00000005198, 1.85353197345, 801.8209311238 ],
[ 0.00000003744, 2.00119516488, 8031.0922630584 ],
[ 0.00000003558, 2.42901552681, 14143.4952424306 ],
[ 0.00000003372, 3.86210700128, 1592.5960136328 ],
[ 0.00000003374, 0.88776219727, 12036.4607348882 ],
[ 0.00000003175, 3.18785710594, 4705.7323075436 ],
[ 0.00000003221, 0.61599835472, 8429.2412664666 ],
[ 0.00000004132, 5.23992859705, 7084.8967811152 ],
[ 0.0000000297, 6.07026318493, 4292.3308329504 ],
[ 0.000000029, 2.32464208411, 20.3553193988 ],
[ 0.00000003504, 4.79975694359, 6279.5527316424 ],
[ 0.0000000295, 1.43108874817, 5746.271337896 ],
[ 0.00000002697, 4.80368225199, 7234.794256242 ],
[ 0.00000002531, 6.22290682655, 6836.6452528338 ],
[ 0.00000002745, 0.93466065396, 5760.4984318976 ],
[ 0.0000000325, 3.39954640038, 7632.9432596502 ],
[ 0.00000002277, 5.00277837672, 17789.845619785 ],
[ 0.00000002075, 3.95534978634, 10213.285546211 ],
[ 0.00000002061, 2.22411683077, 5856.4776591154 ],
[ 0.00000002252, 5.67166499885, 11499.6562227928 ],
[ 0.00000002148, 5.20184578235, 11513.8833167944 ],
[ 0.00000001886, 0.53198320577, 3340.6124266998 ],
[ 0.00000001875, 4.73511970207, 83996.84731811189 ],
[ 0.0000000206, 2.54987293999, 25132.3033999656 ],
[ 0.00000001794, 1.47435409831, 4164.311989613 ],
[ 0.00000001778, 3.02473091781, 5.5229243074 ],
[ 0.00000002029, 0.90960209983, 6256.7775301916 ],
[ 0.00000002075, 2.26767270157, 522.5774180938 ],
[ 0.00000001772, 3.02622802353, 5753.3848848968 ],
[ 0.00000001569, 6.12410242782, 5216.5803728014 ],
[ 0.0000000159, 4.63713748247, 3.2863574178 ],
[ 0.00000001542, 4.20004448567, 13367.9726311066 ],
[ 0.00000001427, 1.19088061711, 3894.1818295422 ],
[ 0.00000001375, 3.09301252193, 135.0650800354 ],
[ 0.00000001359, 4.24532506641, 426.598190876 ],
[ 0.0000000134, 5.76511818622, 6040.3472460174 ],
[ 0.00000001284, 3.08524663344, 5643.1785636774 ],
[ 0.0000000125, 3.07748157144, 11926.2544136688 ],
[ 0.00000001551, 3.07665451458, 6681.2248533996 ],
[ 0.00000001268, 2.09196018331, 6290.1893969922 ],
[ 0.00000001144, 3.24444699514, 12168.0026965746 ],
[ 0.00000001248, 3.44504937285, 536.8045120954 ],
[ 0.00000001118, 2.31829670425, 16730.4636895958 ],
[ 0.00000001105, 5.31966001019, 23.8784377478 ],
[ 0.00000001051, 3.75015946014, 7860.4193924392 ],
[ 0.00000001025, 2.44688534235, 1990.745017041 ],
[ 0.00000000962, 0.81771017882, 3.881335358 ],
[ 0.0000000091, 0.41727865299, 7079.3738568078 ],
[ 0.00000000883, 5.16833917651, 11790.6290886588 ],
[ 0.00000000957, 4.07673573735, 6127.6554505572 ],
[ 0.0000000111, 3.90096793825, 11506.7697697936 ],
[ 0.00000000802, 3.88778875582, 10973.55568635 ],
[ 0.0000000078, 2.39934293755, 1589.0728952838 ],
[ 0.00000000758, 1.30034364248, 103.0927742186 ],
[ 0.00000000749, 4.962758033, 6496.3749454294 ],
[ 0.00000000765, 3.36312388424, 36.0278666774 ],
[ 0.00000000915, 5.41543742089, 206.1855484372 ],
[ 0.00000000776, 2.57589093871, 11371.7046897582 ],
[ 0.00000000772, 3.98369209464, 955.5997416086 ],
[ 0.00000000749, 5.17890001805, 10969.9652576982 ],
[ 0.00000000806, 0.34218864254, 9917.6968745098 ],
[ 0.00000000728, 5.20962563787, 38.0276726358 ],
[ 0.00000000685, 2.77592961854, 20.7753954924 ],
[ 0.00000000636, 4.28242193632, 28.4491874678 ],
[ 0.00000000608, 5.63278508906, 10984.1923516998 ],
[ 0.00000000704, 5.60738823665, 3738.761430108 ],
[ 0.00000000685, 0.38876148682, 15.252471185 ],
[ 0.00000000601, 0.73489602442, 419.4846438752 ],
[ 0.00000000716, 2.65279791438, 6309.3741697912 ],
[ 0.00000000584, 5.54502568227, 17298.1823273262 ],
[ 0.0000000065, 1.13379656406, 7058.5984613154 ],
[ 0.00000000688, 2.59683891779, 3496.032826134 ],
[ 0.00000000485, 0.44467180946, 12352.8526045448 ],
[ 0.00000000528, 2.74936967681, 3930.2096962196 ],
[ 0.00000000597, 5.27668281777, 10575.4066829418 ],
[ 0.00000000583, 3.1892906781, 4732.0306273434 ],
[ 0.00000000526, 5.01697321546, 5884.9268465832 ],
[ 0.0000000054, 1.29175137075, 640.8776073822 ],
[ 0.00000000473, 5.4995330697, 5230.807466803 ],
[ 0.00000000406, 5.21248452189, 220.4126424388 ],
[ 0.00000000395, 1.87474483222, 16200.7727245012 ],
[ 0.0000000037, 3.84921354713, 18073.7049386502 ],
[ 0.00000000367, 0.88533542778, 6283.14316029419 ],
[ 0.00000000379, 0.37983009325, 10177.2576795336 ],
[ 0.00000000356, 3.84145204913, 11712.9553182308 ],
[ 0.00000000374, 5.01577520608, 7.046236698 ],
[ 0.00000000381, 4.30250406634, 6062.6632075526 ],
[ 0.00000000471, 0.86381834647, 6069.7767545534 ],
[ 0.00000000367, 1.32943839763, 6283.0085396886 ],
[ 0.0000000046, 5.19667219575, 6284.0561710596 ],
[ 0.00000000333, 5.54256205741, 4686.8894077068 ],
[ 0.00000000341, 4.36522989934, 7238.6755916 ],
[ 0.00000000336, 4.00205876835, 3097.88382272579 ],
[ 0.00000000359, 6.22679790284, 245.8316462294 ],
[ 0.00000000307, 2.35299010924, 170.6728706192 ],
[ 0.00000000343, 3.77164927143, 6076.8903015542 ],
[ 0.00000000296, 5.44152227481, 17260.1546546904 ],
[ 0.00000000328, 0.13837875384, 11015.1064773348 ],
[ 0.00000000268, 1.1390455063, 12569.6748183318 ],
[ 0.00000000263, 0.00538633678, 4136.9104335162 ],
[ 0.00000000282, 5.0439983748, 7477.522860216 ],
[ 0.00000000288, 3.13401177517, 12559.038152982 ],
[ 0.00000000259, 0.93882269387, 5642.1982426092 ],
[ 0.00000000292, 1.98420020514, 12132.439962106 ],
[ 0.00000000247, 3.84244798532, 5429.8794682394 ],
[ 0.00000000245, 5.70467521726, 65147.6197681377 ],
[ 0.00000000241, 0.99480969552, 3634.6210245184 ],
[ 0.00000000246, 3.06168069935, 110.2063212194 ],
[ 0.00000000239, 6.11855909114, 11856.2186514245 ],
[ 0.00000000263, 0.66348415419, 21228.3920235458 ],
[ 0.00000000262, 1.51070507866, 12146.6670561076 ],
[ 0.0000000023, 1.75927314884, 9779.1086761254 ],
[ 0.00000000223, 2.00967043606, 6172.869528772 ],
[ 0.00000000246, 1.10411690865, 6282.0955289232 ],
[ 0.00000000221, 3.03945240854, 8635.9420037632 ],
[ 0.00000000214, 4.03840869663, 14314.1681130498 ],
[ 0.00000000236, 5.4691507058, 13916.0191096416 ],
[ 0.00000000224, 4.68408089456, 24072.9214697764 ],
[ 0.00000000212, 2.13695625494, 5849.3641121146 ],
[ 0.00000000207, 3.07724246401, 11.729352836 ],
[ 0.00000000207, 6.10306282747, 23543.23050468179 ],
[ 0.00000000266, 1.00709566823, 2388.8940204492 ],
[ 0.00000000217, 6.27837036335, 17267.26820169119 ],
[ 0.00000000204, 2.34615348695, 266.6070417218 ],
[ 0.00000000195, 5.55015549753, 6133.5126528568 ],
# 165 terms retained
])
earth_L2 = array([
[ 0.0005291887, 0, 0 ],
[ 0.00008719837, 1.07209665242, 6283.0758499914 ],
[ 0.00000309125, 0.86728818832, 12566.1516999828 ],
[ 0.00000027339, 0.05297871691, 3.523118349 ],
[ 0.00000016334, 5.18826691036, 26.2983197998 ],
[ 0.00000015752, 3.6845788943, 155.4203994342 ],
[ 0.00000009541, 0.75742297675, 18849.2275499742 ],
[ 0.00000008937, 2.05705419118, 77713.7714681205 ],
[ 0.00000006952, 0.8267330541, 775.522611324 ],
[ 0.00000005064, 4.66284525271, 1577.3435424478 ],
[ 0.00000004061, 1.03057162962, 7.1135470008 ],
[ 0.00000003463, 5.14074632811, 796.2980068164 ],
[ 0.00000003169, 6.05291851171, 5507.5532386674 ],
[ 0.0000000302, 1.19246506441, 242.728603974 ],
[ 0.00000002886, 6.11652627155, 529.6909650946 ],
[ 0.0000000381, 3.4405080349, 5573.1428014331 ],
[ 0.00000002714, 0.30637881025, 398.1490034082 ],
[ 0.00000002371, 4.38118838167, 5223.6939198022 ],
[ 0.00000002538, 2.27992810679, 553.5694028424 ],
[ 0.00000002079, 3.75435330484, 0.9803210682 ],
[ 0.00000001675, 0.90216407959, 951.7184062506 ],
[ 0.00000001534, 5.75900462759, 1349.8674096588 ],
[ 0.00000001224, 2.97328088405, 2146.1654164752 ],
[ 0.00000001449, 4.3641591397, 1748.016413067 ],
[ 0.00000001341, 3.72061130861, 1194.4470102246 ],
[ 0.00000001254, 2.94846826628, 6438.4962494256 ],
[ 0.00000000999, 5.98640014468, 6286.5989683404 ],
[ 0.00000000917, 4.79788687522, 5088.6288397668 ],
[ 0.00000000828, 3.31321076572, 213.299095438 ],
[ 0.00000001103, 1.27104454479, 161000.6857376741 ],
[ 0.00000000762, 3.41582762988, 5486.777843175 ],
[ 0.00000001044, 0.60409577691, 3154.6870848956 ],
[ 0.00000000887, 5.23465144638, 7084.8967811152 ],
[ 0.00000000645, 1.60096192515, 2544.3144198834 ],
[ 0.00000000681, 3.43155669169, 4694.0029547076 ],
[ 0.00000000605, 2.47806340546, 10977.078804699 ],
[ 0.00000000706, 6.19393222575, 4690.4798363586 ],
[ 0.00000000643, 1.98042503148, 801.8209311238 ],
[ 0.00000000502, 1.44394375363, 6836.6452528338 ],
[ 0.0000000049, 2.34129524194, 1592.5960136328 ],
[ 0.00000000458, 1.30876448575, 4292.3308329504 ],
[ 0.00000000431, 0.03526421494, 7234.794256242 ],
[ 0.00000000379, 3.17030522615, 6309.3741697912 ],
[ 0.00000000348, 0.99049550009, 6040.3472460174 ],
[ 0.00000000386, 1.57019797263, 71430.69561812909 ],
[ 0.00000000347, 0.67013291338, 1059.3819301892 ],
[ 0.00000000458, 3.81499443681, 149854.40013480789 ],
[ 0.00000000302, 1.91760044838, 10447.3878396044 ],
[ 0.00000000307, 3.55343347416, 8031.0922630584 ],
[ 0.00000000395, 4.93701776616, 7632.9432596502 ],
[ 0.00000000314, 3.18093696547, 2352.8661537718 ],
[ 0.00000000282, 4.41936437052, 9437.762934887 ],
[ 0.00000000276, 2.71314254553, 3894.1818295422 ],
[ 0.00000000298, 2.5203747421, 6127.6554505572 ],
[ 0.0000000023, 1.37790215549, 4705.7323075436 ],
[ 0.00000000252, 0.55330133471, 6279.5527316424 ],
[ 0.00000000255, 5.26570187369, 6812.766815086 ],
[ 0.00000000275, 0.67264264272, 25132.3033999656 ],
[ 0.00000000178, 0.92820785174, 1990.745017041 ],
[ 0.00000000221, 0.63897368842, 6256.7775301916 ],
[ 0.00000000155, 0.77319790838, 14143.4952424306 ],
[ 0.0000000015, 2.40470465561, 426.598190876 ],
[ 0.00000000196, 6.06877865012, 640.8776073822 ],
[ 0.00000000137, 2.21679460145, 8429.2412664666 ],
[ 0.00000000127, 3.26094223174, 17789.845619785 ],
[ 0.00000000128, 5.47237279946, 12036.4607348882 ],
[ 0.00000000122, 2.16291082757, 10213.285546211 ],
[ 0.00000000118, 0.45789822268, 7058.5984613154 ],
[ 0.00000000141, 2.34932647403, 11506.7697697936 ],
[ 0.000000001, 0.85621569847, 6290.1893969922 ],
[ 0.00000000092, 5.10587476002, 7079.3738568078 ],
[ 0.00000000126, 2.65428307012, 88860.05707098669 ],
[ 0.00000000106, 5.85646710022, 7860.4193924392 ],
[ 0.00000000084, 3.57457554262, 16730.4636895958 ],
[ 0.00000000089, 4.21433259618, 83996.84731811189 ],
[ 0.00000000097, 5.57938280855, 13367.9726311066 ],
[ 0.00000000102, 2.05853060226, 87.30820453981 ],
[ 0.0000000008, 4.73792651816, 11926.2544136688 ],
[ 0.0000000008, 5.41418965044, 10973.55568635 ],
[ 0.00000000106, 4.10978997399, 3496.032826134 ],
[ 0.00000000102, 3.62650006043, 244287.60000722769 ],
[ 0.00000000075, 4.89483161769, 5643.1785636774 ],
[ 0.00000000087, 0.42863750683, 11015.1064773348 ],
[ 0.00000000069, 1.8890876072, 10177.2576795336 ],
[ 0.00000000089, 1.35567273119, 6681.2248533996 ],
[ 0.00000000066, 0.99455837265, 6525.8044539654 ],
[ 0.00000000067, 5.5124099707, 3097.88382272579 ],
[ 0.00000000076, 2.72016814799, 4164.311989613 ],
[ 0.00000000063, 1.4434990254, 9917.6968745098 ],
[ 0.00000000078, 3.51469733747, 11856.2186514245 ],
[ 0.00000000085, 0.50956043858, 10575.4066829418 ],
[ 0.00000000067, 3.62043033405, 16496.3613962024 ],
[ 0.00000000055, 5.24637517308, 3340.6124266998 ],
# 93 terms retained
])
earth_L3 = array([
[ 0.00000289226, 5.84384198723, 6283.0758499914 ],
[ 0.00000034955, 0, 0 ],
[ 0.00000016819, 5.48766912348, 12566.1516999828 ],
[ 0.00000002962, 5.19577265202, 155.4203994342 ],
[ 0.00000001288, 4.72200252235, 3.523118349 ],
[ 0.00000000635, 5.96925937141, 242.728603974 ],
[ 0.00000000714, 5.30045809128, 18849.2275499742 ],
[ 0.00000000402, 3.78682982419, 553.5694028424 ],
# 8 terms retained
])
earth_L4 = array([
[ 0.00000114084, 3.14159265359, 0 ],
[ 0.00000007717, 4.13446589358, 6283.0758499914 ],
[ 0.00000000765, 3.83803776214, 12566.1516999828 ],
[ 0.0000000042, 0.41925861858, 155.4203994342 ],
# 4 terms retained
])
earth_L5 = array([
[ 0.00000000878, 3.14159265359, 0 ],
[ 0.00000000172, 2.7657906951, 6283.0758499914 ],
[ 0.0000000005, 2.01353298182, 155.4203994342 ],
[ 0.00000000028, 2.21496423926, 12566.1516999828 ],
# 4 terms retained
])
earth_B0 = array([
[ 0.0000027962, 3.19870156017, 84334.66158130829 ],
[ 0.00000101643, 5.42248619256, 5507.5532386674 ],
[ 0.00000080445, 3.88013204458, 5223.6939198022 ],
[ 0.00000043806, 3.70444689758, 2352.8661537718 ],
[ 0.00000031933, 4.00026369781, 1577.3435424478 ],
[ 0.00000022724, 3.9847383156, 1047.7473117547 ],
[ 0.00000016392, 3.56456119782, 5856.4776591154 ],
[ 0.00000018141, 4.98367470263, 6283.0758499914 ],
[ 0.00000014443, 3.70275614914, 9437.762934887 ],
[ 0.00000014304, 3.41117857525, 10213.285546211 ],
[ 0.00000011246, 4.8282069053, 14143.4952424306 ],
[ 0.000000109, 2.08574562327, 6812.766815086 ],
[ 0.00000009714, 3.47303947752, 4694.0029547076 ],
[ 0.00000010367, 4.05663927946, 71092.88135493269 ],
[ 0.00000008775, 4.44016515669, 5753.3848848968 ],
[ 0.00000008366, 4.9925151218, 7084.8967811152 ],
[ 0.00000006921, 4.32559054073, 6275.9623029906 ],
[ 0.00000009145, 1.14182646613, 6620.8901131878 ],
[ 0.00000007194, 3.60193205752, 529.6909650946 ],
[ 0.00000007698, 5.55425745881, 167621.57585086189 ],
# 20 terms retained
])
earth_B1 = array([
[ 0.0000000903, 3.8972906189, 5507.5532386674 ],
[ 0.00000006177, 1.73038850355, 5223.6939198022 ],
[ 0.000000038, 5.24404145734, 2352.8661537718 ],
[ 0.00000002834, 2.4734503745, 1577.3435424478 ],
[ 0.00000001817, 0.41874743765, 6283.0758499914 ],
[ 0.00000001499, 1.83320979291, 5856.4776591154 ],
[ 0.00000001466, 5.69401926017, 5753.3848848968 ],
[ 0.00000001301, 2.18890066314, 9437.762934887 ],
[ 0.00000001233, 4.95222451476, 10213.285546211 ],
[ 0.00000001021, 0.12866660208, 7860.4193924392 ],
[ 0.00000000982, 0.09005453285, 14143.4952424306 ],
[ 0.00000000865, 1.73949953555, 3930.2096962196 ],
# 12 terms retained
])
earth_B2 = array([
[ 0.00000001662, 1.62703209173, 84334.66158130829 ],
[ 0.00000000492, 2.41382223971, 1047.7473117547 ],
[ 0.00000000344, 2.24353004539, 5507.5532386674 ],
[ 0.00000000258, 6.00906896311, 5223.6939198022 ],
# 4 terms retained
])
earth_B3 = array([
[ 0, 0, 0 ],
# 0 terms retained
])
earth_B4 = array([
[ 0, 0, 0 ],
# 0 terms retained
])
earth_R0 = array([
[ 1.00013988799, 0, 0 ],
[ 0.01670699626, 3.09846350771, 6283.0758499914 ],
[ 0.00013956023, 3.0552460962, 12566.1516999828 ],
[ 0.0000308372, 5.19846674381, 77713.7714681205 ],
[ 0.00001628461, 1.17387749012, 5753.3848848968 ],
[ 0.00001575568, 2.84685245825, 7860.4193924392 ],
[ 0.00000924799, 5.45292234084, 11506.7697697936 ],
[ 0.00000542444, 4.56409149777, 3930.2096962196 ],
[ 0.0000047211, 3.66100022149, 5884.9268465832 ],
[ 0.0000032878, 5.89983646482, 5223.6939198022 ],
[ 0.00000345983, 0.96368617687, 5507.5532386674 ],
[ 0.00000306784, 0.29867139512, 5573.1428014331 ],
[ 0.00000174844, 3.01193636534, 18849.2275499742 ],
[ 0.00000243189, 4.27349536153, 11790.6290886588 ],
[ 0.00000211829, 5.84714540314, 1577.3435424478 ],
[ 0.00000185752, 5.02194447178, 10977.078804699 ],
[ 0.00000109835, 5.05510636285, 5486.777843175 ],
[ 0.00000098316, 0.88681311277, 6069.7767545534 ],
[ 0.00000086499, 5.68959778254, 15720.8387848784 ],
[ 0.00000085825, 1.27083733351, 161000.6857376741 ],
[ 0.00000062916, 0.92177108832, 529.6909650946 ],
[ 0.00000057056, 2.01374292014, 83996.84731811189 ],
[ 0.00000064903, 0.27250613787, 17260.1546546904 ],
[ 0.00000049384, 3.24501240359, 2544.3144198834 ],
[ 0.00000055736, 5.24159798933, 71430.69561812909 ],
[ 0.00000042515, 6.01110242003, 6275.9623029906 ],
[ 0.00000046963, 2.57805070386, 775.522611324 ],
[ 0.00000038968, 5.36071738169, 4694.0029547076 ],
[ 0.00000044661, 5.53715807302, 9437.762934887 ],
[ 0.0000003566, 1.67468058995, 12036.4607348882 ],
[ 0.00000031921, 0.18368229781, 5088.6288397668 ],
[ 0.00000031846, 1.77775642085, 398.1490034082 ],
[ 0.00000033193, 0.24370300098, 7084.8967811152 ],
[ 0.00000038245, 2.39255343974, 8827.3902698748 ],
[ 0.00000028464, 1.21344868176, 6286.5989683404 ],
[ 0.0000003749, 0.82952922332, 19651.048481098 ],
[ 0.00000036957, 4.90107591914, 12139.5535091068 ],
[ 0.00000034537, 1.84270693282, 2942.4634232916 ],
[ 0.00000026275, 4.58896850401, 10447.3878396044 ],
[ 0.00000024596, 3.78660875483, 8429.2412664666 ],
[ 0.00000023587, 0.26866117066, 796.2980068164 ],
[ 0.00000027793, 1.89934330904, 6279.5527316424 ],
[ 0.00000023927, 4.99598548138, 5856.4776591154 ],
[ 0.00000020349, 4.65267995431, 2146.1654164752 ],
[ 0.00000023287, 2.80783650928, 14143.4952424306 ],
[ 0.00000022103, 1.95004702988, 3154.6870848956 ],
[ 0.00000019506, 5.38227371393, 2352.8661537718 ],
[ 0.00000017958, 0.19871379385, 6812.766815086 ],
[ 0.00000017174, 4.43315560735, 10213.285546211 ],
[ 0.0000001619, 5.23160507859, 17789.845619785 ],
[ 0.00000017314, 6.15200787916, 16730.4636895958 ],
[ 0.00000013814, 5.18962074032, 8031.0922630584 ],
[ 0.00000018833, 0.67306674027, 149854.40013480789 ],
[ 0.00000018331, 2.25348733734, 23581.2581773176 ],
[ 0.00000013641, 3.68516118804, 4705.7323075436 ],
[ 0.00000013139, 0.65289581324, 13367.9726311066 ],
[ 0.00000010414, 4.33285688538, 11769.8536931664 ],
[ 0.00000009978, 4.20126336355, 6309.3741697912 ],
[ 0.00000010169, 1.59390681369, 4690.4798363586 ],
[ 0.00000007564, 2.6256059739, 6256.7775301916 ],
[ 0.00000009661, 3.6758679122, 27511.4678735372 ],
[ 0.00000006743, 0.56270332741, 3340.6124266998 ],
[ 0.00000008743, 6.06359123461, 1748.016413067 ],
[ 0.00000007786, 3.67371235637, 12168.0026965746 ],
[ 0.00000006633, 5.66149277792, 11371.7046897582 ],
[ 0.00000007712, 0.31242577789, 7632.9432596502 ],
[ 0.00000006592, 3.13576266188, 801.8209311238 ],
[ 0.0000000746, 5.64757188143, 11926.2544136688 ],
[ 0.00000006933, 2.923845864, 6681.2248533996 ],
[ 0.00000006802, 1.4232980642, 23013.5395395872 ],
[ 0.00000006115, 5.13393615454, 1194.4470102246 ],
[ 0.00000006477, 2.64986648492, 19804.8272915828 ],
# 72 terms retained
])
earth_R1 = array([
[ 0.00103018608, 1.10748969588, 6283.0758499914 ],
[ 0.00001721238, 1.06442301418, 12566.1516999828 ],
[ 0.00000702215, 3.14159265359, 0 ],
[ 0.00000032346, 1.02169059149, 18849.2275499742 ],
[ 0.00000030799, 2.84353804832, 5507.5532386674 ],
[ 0.00000024971, 1.31906709482, 5223.6939198022 ],
[ 0.00000018485, 1.42429748614, 1577.3435424478 ],
[ 0.00000010078, 5.91378194648, 10977.078804699 ],
[ 0.00000008634, 0.27146150602, 5486.777843175 ],
[ 0.00000008654, 1.42046854427, 6275.9623029906 ],
# 10 terms retained
])
earth_R2 = array([
[ 0.00004359385, 5.78455133738, 6283.0758499914 ],
[ 0.00000123633, 5.57934722157, 12566.1516999828 ],
[ 0.00000012341, 3.14159265359, 0 ],
[ 0.00000008792, 3.62777733395, 77713.7714681205 ],
[ 0.00000005689, 1.86958905084, 5573.1428014331 ],
[ 0.00000003301, 5.47027913302, 18849.2275499742 ],
# 6 terms retained
])
earth_R3 = array([
[ 0.00000144595, 4.27319435148, 6283.0758499914 ],
[ 0.00000006729, 3.91697608662, 12566.1516999828 ],
# 2 terms retained
])
earth_R4 = array([
[ 0.00000003858, 2.56384387339, 6283.0758499914 ],
# 1 terms retained
])
earth_R5 = array([
[ 0, 0, 0 ],
# 0 terms retained
])
# table for LEA-406 moon solution. Those terms are linear combination
# of integer multipliers of 14 variables (Arg_j_, j=1,14):
# Delaunay variables l, l', F, D;
# mean longitude of the ascending node of the Moon {Omega};
# mean longitudes of eight major planets {lambda}_pl_;
# and the general precession in longitude p_A_.
# terms of 3rd-degree and 4th-degree are ignored
# in arcsec
# generated with threshold 0.05, average error Moon = 0.73", max 1.5"
M_ARG = array([
# 226 terms
[ 485868.249036, 1717915923.21779990, 31.87920 ],
[ 1658653.158348, 1488007279.20020032, -44.62040 ],
[ 2144521.407384, 3205923202.41800022, -12.74120 ],
[ 971736.498072, 3435831846.43559980, 63.75840 ],
[ 1287104.793048, 129596581.04809999, -0.55320 ],
[ 671559.052464, 3479054525.69560003, -25.50240 ],
[ 1172784.909312, -229908644.01759958, -76.49960 ],
[ 371548.365300, 1358410698.15210032, -44.06720 ],
[ 2630389.656420, 4923839125.63580036, 19.13800 ],
[ 857416.614336, 3076326621.36990023, -12.18800 ],
[ 801236.544012, -1588319342.16969991, -32.43240 ],
[ 1072260.703692, 1602961601.20900011, -6.37060 ],
[ 1772973.042084, 1847512504.26589990, 31.32600 ],
[ 1472962.354920, -273131323.27759981, 12.76120 ],
[ 0.000000, 0.00000000, 0.00000 ],
[ 1157427.301500, 5196970448.91339970, 6.37680 ],
[ -185690.803428, -1761138602.47780013, 57.38160 ],
[ 3803174.565732, 4693930481.61820030, -57.36160 ],
[ 1457604.747108, 5153747769.65339947, 95.63760 ],
[ 3317306.316696, 2976014558.40040064, -89.24080 ],
[ 2945757.951396, 1617603860.24830031, -45.17360 ],
[ 3431626.200432, 3335519783.46610022, -13.29440 ],
[ 586392.454656, -114954322.00879979, -38.24980 ],
[ 2359365.496740, 1732558182.25710011, -6.92380 ],
[ 1343284.863372, 4794242544.58769989, 19.69120 ],
[ 3116257.905456, 6641755048.85359955, 51.01720 ],
[ 2746972.885608, 477658.07790603, -67.34420 ],
[ 4289042.814768, 6411846404.83600044, -25.48240 ],
[ 686916.660276, -1947824567.23539925, -108.37880 ],
[ 315368.294976, -3306235265.38749981, -64.31160 ],
[ 2330212.210812, 4967061804.89580059, -70.12280 ],
[ -114319.883736, -359505225.06569958, -75.94640 ],
[ 1558128.952728, 3320877524.42679977, 25.50860 ],
[ -429688.178712, 2946730040.32180023, -11.63480 ],
[ 2258841.291120, 3565428427.48369980, 63.20520 ],
[ 2574209.586096, 259193162.09619999, -1.10640 ],
[ -915556.427748, 1228814117.10400033, -43.51400 ],
[ 450160.398036, -6962890.54310000, 7.47222 ],
[ 1958830.603956, 1444784599.94020033, 44.64040 ],
[ 2816080.459848, 6684977728.11359978, -38.24360 ],
[ 2516069.772684, 4564333900.57010078, -56.80840 ],
[ 1643295.550536, 6914886372.13119984, 38.25600 ],
[ 2730913.862040, 3090968880.40920067, -50.99100 ],
[ 3917494.449468, 5053435706.68389988, 18.58480 ],
[ 2030201.523648, 2846417977.35230112, -88.68760 ],
[ 2088341.337060, -1458722761.12159991, -32.98560 ],
[ 4232862.744444, 1747200441.29640031, -45.72680 ],
[ 2459889.702360, -100312062.96949959, -77.05280 ],
[ 185857.561872, -402727904.32569981, 13.31440 ],
[ 4774911.063804, 8129762328.05380058, 6.39680 ],
[ 1943472.996144, 6871663692.87119961, 127.51680 ],
[ 3001938.021720, 6282249823.78790092, -24.92920 ],
[ 100524.205620, -1832870245.22659969, -70.12900 ],
[ 2760067.147968, -143534742.22949982, 12.20800 ],
[ 300177.445608, -43222679.26000023, 89.26080 ],
[ 2845233.745776, 3450474105.47490025, 24.95540 ],
[ 2245045.613004, 1373052957.19140100, -82.87020 ],
[ 2831438.067660, 1258098635.18260098, -121.12000 ],
[ 1829153.112408, 6512158467.80550003, 51.57040 ],
[ 3060077.835132, 1977109085.31399989, 30.77280 ],
[ 2134680.712596, 1725351443.01107621, -44.04921 ],
[ 1873497.247704, 14642259.03930020, -38.80300 ],
[ 3602126.154492, 8359670972.07139969, 82.89640 ],
[ 3301948.708884, 8402893651.33139992, -6.36440 ],
[ 201048.411240, -3665740490.45319939, -140.25800 ],
[ 293448.038472, 81066394.15011901, 0.02638 ],
[ 1643162.503716, 1717438685.61177826, -210.42628 ],
[ 56180.070324, 4664645963.53960037, 20.24440 ],
[ 3232841.134644, 1718393581.29570580, -35.46500 ],
[ -170499.954060, -5024151188.60529900, -96.19080 ],
[ 2538997.273764, 1731206461.65055728, -44.54126 ],
[ 238013.777124, 118672081.90543799, 0.28560 ],
[ 5090279.358780, 4823527062.66629982, -57.91480 ],
[ 2043997.201764, 5038793447.64459991, 57.38780 ],
[ 400701.651228, -1876092924.48659992, 19.13180 ],
[ 5461827.724080, 6181937760.81840134, -101.98200 ],
[ 501225.856848, -3708963169.71319962, -50.99720 ],
[ -214844.089356, 1473365020.16090012, -5.81740 ],
[ 2744709.540156, 5283344350.70149994, 95.08440 ],
[ 1844343.961776, 3249145881.67800045, -102.00200 ],
[ 936028.647072, 1710953032.67469978, 39.35142 ],
[ -35707.851000, -1724878813.76090002, -24.40698 ],
[ -600188.132772, -2077421148.28349924, -107.82560 ],
[ 2444698.852992, 3162700523.15799952, 76.51960 ],
[ 3963148.815276, 1714428507.27902675, -198.01200 ],
[ 1043107.417764, 4837465223.84770012, -69.56960 ],
[ 1343118.104928, 6958109051.39120007, -51.00480 ],
[ 1958663.845512, 3608651106.74370003, -26.05560 ],
[ 3216782.111076, 4808884803.62700081, -19.11180 ],
[ 5947695.973116, 7899853684.03620148, -70.10280 ],
[ 1528975.666800, 6555381147.06550026, -37.69040 ],
[ 1121719.450500, 3472091635.15250015, -18.03018 ],
[ 671725.810908, 1315188018.89209986, 45.19360 ],
[ 4604411.109744, 3105611139.44850016, -89.79400 ],
[ -9960733.695600, 135571.46521378, 63.51699 ],
[ 1387628.998668, -1703273664.17849970, -70.68220 ],
[ 26423.255340, -32537000.00799108, 44.93644 ],
[ -1716792.971760, 2817133459.27370024, -11.08160 ],
[ 2129163.799572, 8632802295.34899902, 70.13520 ],
[ 1578859.855344, 8210672.20779327, -214.97146 ],
[ 1228964.979636, 4434737319.52200031, -56.25520 ],
[ 2287389.559392, 162132438.11736214, -200.33773 ],
[ 129677.491548, -5067373867.86530018, -6.93000 ],
[ 3131615.513268, 1214875955.92260027, -31.85920 ],
[ -1401424.676784, -489101806.11379957, -75.39320 ],
[ 4975959.475044, 4464021837.60060215, -133.86120 ],
[ 4403362.698504, 6771351629.90170002, 50.46400 ],
[ 5576147.607816, 6541442985.88409996, -26.03560 ],
[ 3487806.270756, 8000165747.00570107, 6.95000 ],
[ 4018018.655088, 3220565461.45730019, -51.54420 ],
[ 3477280.566240, -3487415.93877248, -229.89120 ],
[ 2444532.094548, 5326567029.96150017, 5.82360 ],
[ 1743819.756156, 5082016126.90460014, -31.87300 ],
[ 2545223.058612, 1329830277.93140078, 6.39060 ],
[ 3746994.495408, 29284518.07860041, -77.60600 ],
[ 1648812.463560, 7435519.79327631, -75.92841 ],
[ -2202661.220796, 1099217536.05590034, -42.96080 ],
[ 6176636.963928, 606718.56467720, 146.34632 ],
[ 1443809.068992, 2961372299.36110115, -50.43780 ],
[ 5260779.312840, 9847678251.27160072, 38.27600 ],
[ 1420639.381224, 1369335197.29476237, -44.90600 ],
[ 4474733.618196, 8172985007.31380081, -82.86400 ],
[ 5299552.000908, 121384894.43375297, 62.45638 ],
[ 1602473.088024, -3176638684.33939981, -64.86480 ],
[ 476027.554248, 237344163.81087598, 0.57119 ],
[ 4718730.993480, 3465116364.51420021, -13.84760 ],
[ 9840.694788, 1480571759.40692401, 31.30801 ],
[ 987094.105884, -1991047246.49539971, -19.11800 ],
[ 1974021.453324, -1818227986.18729925, -108.93200 ],
[ -2128477.768848, 113602752.48178008, 40.50488 ],
[ 3988865.369160, 6455069084.09600067, -114.74320 ],
[ 1906507.630260, 3087251120.51256227, -13.02680 ],
[ -4107087.132120, 107747819.74584675, 210.09281 ],
[ 863813.842884, 1487527316.94823694, -132.65705 ],
[ 628736.401044, -1325874841.08283782, -155.71733 ],
[ 602451.478224, -3205445544.34009504, -54.60300 ],
[ 2939360.722848, 3206403164.66996431, 75.29545 ],
[ 743096.730600, 2716821396.30420065, -88.13440 ],
[ -2587922.762544, -1636850170.74401093, 53.56212 ],
[ 1714833.228672, 6152653242.73980045, -24.37600 ],
[ 2453492.473812, 1488487241.45216417, 43.41625 ],
[ 4503886.904124, 4938481384.67510033, -19.66500 ],
[ 247854.471912, 1599243841.31236196, 31.59360 ],
[ -700712.338392, -244550903.05689979, -37.69660 ],
[ -41775.577452, -1650139296.84567857, -64.69155 ],
[ 142868.152008, -3043790764.30063820, -187.59653 ],
[ 824406.231780, 3722788.71663815, -36.85218 ],
[ 3760707.671856, 1406941526.72641158, -130.06172 ],
[ -385344.043416, -3550786168.44439936, -102.00820 ],
[ -1616186.264472, 1798981675.69158912, 117.32052 ],
[ 6433564.222152, 9617769607.25400162, -38.22360 ],
[ -394475.866380, 1474716740.76744270, 31.80006 ],
[ 3787816.957920, 10120809574.54920006, 25.51480 ],
[ 271024.159680, 3191280943.37870026, 26.06180 ],
[ -3915532.327356, -1718055041.34457111, -247.79376 ],
[ -2943795.829284, 1717776805.09102821, -184.03536 ],
[ 4588422.072480, 1333648.70949970, 213.90556 ],
[ -327467.049516, -1015133.54049925, 95.02473 ],
[ 2429341.245180, 8589579616.08899975, 159.39600 ],
[ 723882.026160, 1836588005.12323785, 32.16480 ],
[ 3861314.379144, 388789743.14429998, -1.65960 ],
[ 1544333.274612, 1128502054.13450146, -120.56680 ],
[ 4246575.920892, 3124857449.94421101, -98.18252 ],
[ 4168107.377892, 3198959150.64730024, -5.80178 ],
[ 1818627.407892, -1491494695.13897252, -185.27080 ],
[ 2315021.361444, 8230074391.02330017, 83.44960 ],
[ 3331101.994812, 5168390028.69269943, 56.83460 ],
[ 15357.607812, -5426879092.93099976, -82.87640 ],
[ 10479231.070128, -16418126.94190380, 74.77548 ],
[ 1828986.353964, 8676024974.60899925, -19.12560 ],
[ 4174722.931032, 6052341179.77030182, -101.42880 ],
[ 2577500.752860, -1199777.09773506, -217.20541 ],
[ 1182625.604100, 1250663115.38932443, -45.19159 ],
[ 123665.467464, 10925660.37799100, -0.30604 ],
[ 4960601.867232, 9890900930.53160095, -50.98480 ],
[ 3245935.397004, 1574381180.98829985, 44.08720 ],
[ 1668493.853136, 2968579038.60712433, -13.31239 ],
[ 957940.819956, 1243456376.14330149, -82.31700 ],
[ 6461919.320184, 15996023.02879967, 179.55064 ],
[ 1101413.989620, -1631542021.42970014, 56.82840 ],
[ -377031.566700, -1812274039.13709879, -19.73467 ],
[ 1472795.596476, 1890735183.52590013, -57.93480 ],
[ -857249.855892, -5240193128.17339993, 82.88400 ],
[ 4087994.403528, 10077586895.28919983, 114.77560 ],
[ 11070.933228, -1715208268.04166102, 26.29335 ],
[ 801403.302456, -3752185848.97319984, 38.26360 ],
[ 615545.740584, -3349457944.64750004, 24.94920 ],
[ 2014843.915836, 8273297070.28330040, -5.81120 ],
[ -2546147.185092, 13289126.10166723, 118.25367 ],
[ 4660591.180068, 7770257102.98810196, -69.54960 ],
[ 2620548.961632, 3443267366.22887611, -12.17001 ],
[ -284819.837796, -5383656413.67099953, -172.13720 ],
[ 3008350.635300, -1716566657.86483884, -189.51513 ],
[ 3617317.003860, 5096658385.94390011, -70.67600 ],
[ 4103352.011340, 4650707802.35820007, 31.89920 ],
[ 120935.436876, 3212887254.18870020, -19.68062 ],
[ 4103185.252896, 6814574309.16170025, -38.79680 ],
[ 3545946.084168, 3695025008.53179979, 62.65200 ],
[ 1929677.318028, 4679288222.57890129, -18.55860 ],
[ 542048.319360, 6382561886.75740051, 52.12360 ],
[ 3682239.128856, 1481043227.42950010, -37.68098 ],
[ 1092991.606308, -1709705251.01000595, -246.85066 ],
[ 2064728.104380, 1726126595.42559338, -183.09226 ],
[ -1101247.231176, -532324485.37379980, 13.86760 ],
[ 1310274.480816, 1721633683.11443806, -6.08500 ],
[ 1685076.413688, 1455470279.19220901, 0.31604 ],
[ -300010.687164, -2120643827.54349971, -18.56480 ],
[ -3664055.126520, 2720871.13874409, -227.53801 ],
[ 512291.504376, 1685378923.20980859, 76.81564 ],
[ 3640898.842560, -1366622384.76644802, 107.07678 ],
[ 417145.879260, -1477083922.99626732, -111.06649 ],
[ 14236864.720236, -3208579.51268373, -163.76979 ],
[ 4389567.020388, 4578976159.60939980, -95.61140 ],
[ 786045.694644, 1674693243.95779943, 121.14000 ],
[ 150612.259788, 1555781180.92637992, 76.83608 ],
[ 459444.993696, 1750452923.22579098, -13.05724 ],
[ 176897.182608, 3435351884.18363619, -24.27825 ],
[ -3529183.602852, -2591705.71692875, -226.73272 ],
[ 169814.944332, -1498930214.93224931, -109.34239 ],
[ -356190.757488, -6785289791.08309937, -38.80920 ],
[ 3375446.130108, -1329126180.07349992, -33.53880 ],
[ 2209276.773936, 1754174550.70710015, -50.44218 ],
[ 55466.634672, -1606681665.27969599, -111.04605 ],
[ 1131009.331860, -1880047940.86327744, -141.19115 ],
[ 6062015.856852, 8259358909.10190010, 5.84360 ],
[ 352362.086784, 226418503.43288499, 0.87723 ],
])
# table for LEA-406 moon solution
# Ak0 arcsec Amplitude of the Fourier term
# Ak1 mas/yr Amplitude of the 1st-order Poisson term
# Ak2 uas/yr2 Amplitude of the 2nd-order Poisson term
# [ Ak0, Ak1, Ak2 ] ...
M_AMP = array([
# 226 terms
[ 22639.5864251, 0.190648, 5.529914 ],
[ 4586.4946082, 0.112352, 1.480719 ],
[ 2369.9292836, 0.105206, 1.315910 ],
[ 769.0251380, 0.013309, 0.373136 ],
[ 666.4389699, 16.764899, 0.509567 ],
[ 411.5952546, 0.002764, 0.176172 ],
[ 211.6566179, 0.006615, 0.018535 ],
[ 205.4430995, 5.163882, 0.191171 ],
[ 191.9569463, 0.011624, 0.153634 ],
[ 164.7319041, 4.138198, 0.167655 ],
[ 147.3267606, 3.710258, 0.121729 ],
[ 124.9935117, 0.001183, 0.034216 ],
[ 109.3839297, 2.755639, 0.083615 ],
[ 55.1780671, 0.002891, 0.006919 ],
[ 0.0362449, 1.349731, 45.692267 ],
[ 45.0995619, 0.000090, 0.030602 ],
[ 39.5287366, 0.001225, 0.006971 ],
[ 38.4307291, 0.004006, 0.032533 ],
[ 36.1241571, 0.000898, 0.025549 ],
[ 30.7733692, 0.002140, 0.019268 ],
[ 28.3979625, 0.711689, 0.023432 ],
[ 24.3591471, 0.612529, 0.022527 ],
[ 18.5852985, 0.000437, 0.001521 ],
[ 17.9562255, 0.451214, 0.014878 ],
[ 14.5306503, 0.364691, 0.018609 ],
[ 14.3797216, 0.001391, 0.015092 ],
[ 14.2136673, 0.506954, 0.388974 ],
[ 13.8992155, 0.002252, 0.015581 ],
[ 13.1942141, 0.000494, 0.002232 ],
[ 9.6793682, 0.243746, 0.009212 ],
[ 9.3659379, 0.000333, 0.007150 ],
[ 8.6056849, 0.216461, 0.006770 ],
[ 8.4533524, 0.000386, 0.004712 ],
[ 8.0506614, 0.404649, 0.009300 ],
[ 7.6304201, 0.192240, 0.006663 ],
[ 7.4493429, 0.375004, 0.006549 ],
[ 7.3717333, 0.370557, 0.007936 ],
[ 7.0921386, 0.076778, 0.005079 ],
[ 6.3823525, 0.000616, 0.002913 ],
[ 5.7416948, 0.000257, 0.005899 ],
[ 4.3741497, 0.109740, 0.005590 ],
[ 3.9976117, 0.000026, 0.003764 ],
[ 3.2097860, 0.000695, 0.001883 ],
[ 2.9146498, 0.073322, 0.003241 ],
[ 2.7319853, 0.068620, 0.003016 ],
[ 2.5682050, 0.129294, 0.002534 ],
[ 2.5220218, 0.127230, 0.002163 ],
[ 2.4889981, 0.063117, 0.001806 ],
[ 2.1461452, 0.053905, 0.001745 ],
[ 1.9777716, 0.000440, 0.002642 ],
[ 1.9336777, 0.000069, 0.001990 ],
[ 1.8708161, 0.046884, 0.002864 ],
[ 1.7530780, 0.000160, 0.000246 ],
[ 1.4372113, 0.036159, 0.001127 ],
[ 1.3713028, 0.000041, 0.000141 ],
[ 1.2619335, 0.031743, 0.001156 ],
[ 1.2241492, 0.000087, 0.000559 ],
[ 1.1868343, 0.000109, 0.000580 ],
[ 1.1770227, 0.029544, 0.001701 ],
[ 1.1619378, 0.058532, 0.001032 ],
[ 1.1431465, 0.001145, 0.004116 ],
[ 1.0779824, 0.027072, 0.000890 ],
[ 1.0595012, 0.000125, 0.001494 ],
[ 0.9902267, 0.000067, 0.001314 ],
[ 0.9482810, 0.000049, 0.000381 ],
[ 0.8216250, 0.000304, 0.000090 ],
[ 0.7791738, 0.055305, 0.066699 ],
[ 0.7517241, 0.037784, 0.001034 ],
[ 0.7322303, 0.044974, 0.051647 ],
[ 0.6694015, 0.016850, 0.000770 ],
[ 0.6436261, 0.000332, 0.000422 ],
[ 0.6388982, 0.000303, 0.000313 ],
[ 0.6352378, 0.016019, 0.000773 ],
[ 0.5840142, 0.000053, 0.000496 ],
[ 0.5833144, 0.000000, 0.000051 ],
[ 0.5715783, 0.000117, 0.000766 ],
[ 0.5606404, 0.000000, 0.000176 ],
[ 0.5568122, 0.014135, 0.000470 ],
[ 0.5459375, 0.013761, 0.000538 ],
[ 0.5356650, 0.000028, 0.000298 ],
[ 0.5025507, 0.011924, 0.000650 ],
[ 0.5005117, 0.011841, 0.000959 ],
[ 0.4784073, 0.012033, 0.000371 ],
[ 0.4537245, 0.000048, 0.000336 ],
[ 0.4381375, 0.054206, 0.022773 ],
[ 0.4262242, 0.010710, 0.000506 ],
[ 0.4203282, 0.000000, 0.000355 ],
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[ 0.4041956, 0.000444, 0.000404 ],
[ 0.3945214, 0.000105, 0.000652 ],
[ 0.3821338, 0.009597, 0.000535 ],
[ 0.3748102, 0.011708, 0.000597 ],
[ 0.3744777, 0.009395, 0.000354 ],
[ 0.3575903, 0.009033, 0.000359 ],
[ 0.3416863, 0.352069, 0.220915 ],
[ 0.3495542, 0.008691, 0.000624 ],
[ 0.3435465, 0.009341, 0.007387 ],
[ 0.3398415, 0.025631, 0.000333 ],
[ 0.3286524, 0.000000, 0.000403 ],
[ 0.3248895, 0.001569, 0.031518 ],
[ 0.3087352, 0.015508, 0.000464 ],
[ 0.3016226, 0.005046, 0.028777 ],
[ 0.3015612, 0.007593, 0.000321 ],
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[ 0.2925609, 0.000043, 0.000351 ],
[ 0.2902265, 0.007303, 0.000385 ],
[ 0.2891080, 0.007270, 0.000414 ],
[ 0.2825095, 0.007069, 0.000521 ],
[ 0.2737910, 0.006879, 0.000263 ],
[ 0.2736062, 0.038332, 0.094167 ],
[ 0.2633701, 0.006632, 0.000249 ],
[ 0.2542937, 0.000000, 0.000192 ],
[ 0.2530370, 0.000035, 0.000148 ],
[ 0.2500111, 0.012673, 0.000241 ],
[ 0.2494213, 0.007693, 0.009143 ],
[ 0.2469758, 0.018629, 0.000176 ],
[ 0.1180438, 0.242859, 0.232513 ],
[ 0.2314117, 0.005794, 0.000255 ],
[ 0.2185403, 0.000055, 0.000408 ],
[ 0.2111003, 0.000156, 0.000174 ],
[ 0.2013358, 0.000026, 0.000300 ],
[ 0.1944693, 0.003998, 0.005565 ],
[ 0.1931190, 0.009721, 0.000207 ],
[ 0.1844919, 0.000278, 0.000754 ],
[ 0.1835925, 0.008827, 0.000266 ],
[ 0.1825829, 0.000095, 0.000340 ],
[ 0.1789891, 0.000029, 0.000060 ],
[ 0.1762440, 0.004467, 0.000147 ],
[ 0.1751178, 0.006068, 0.003488 ],
[ 0.1697756, 0.000016, 0.000207 ],
[ 0.1649126, 0.000149, 0.000035 ],
[ 0.1643790, 0.002513, 0.016571 ],
[ 0.1609152, 0.046251, 0.052193 ],
[ 0.1608887, 0.002702, 0.015539 ],
[ 0.1603243, 0.024905, 0.034943 ],
[ 0.1590996, 0.028613, 0.024866 ],
[ 0.1578112, 0.007932, 0.000203 ],
[ 0.1537976, 0.004754, 0.006421 ],
[ 0.1522670, 0.007645, 0.000263 ],
[ 0.1514863, 0.048990, 0.060578 ],
[ 0.1499154, 0.003761, 0.000172 ],
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[ 0.1363584, 0.003428, 0.000102 ],
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[ 0.0891047, 0.000146, 0.000132 ],
[ 0.0860207, 0.003064, 0.003710 ],
[ 0.0849998, 0.000015, 0.000149 ],
[ 0.0847363, 0.002131, 0.000072 ],
[ 0.0840293, 0.000147, 0.000081 ],
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[ 0.0750004, 0.001874, 0.000066 ],
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[ 0.0714181, 0.001784, 0.000140 ],
[ 0.0686150, 0.000124, 0.000210 ],
[ 0.0684983, 0.000000, 0.000045 ],
[ 0.0676977, 0.013106, 0.022804 ],
[ 0.0674175, 0.001690, 0.000069 ],
[ 0.0659954, 0.000011, 0.000077 ],
[ 0.0657981, 0.003704, 0.000148 ],
[ 0.0654081, 0.001645, 0.000080 ],
[ 0.0651462, 0.003283, 0.000055 ],
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[ 0.0610286, 0.034491, 0.021496 ],
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[ 0.0590447, 0.001206, 0.001683 ],
[ 0.0576070, 0.003983, 0.003844 ],
[ 0.0574169, 0.012520, 0.037732 ],
[ 0.0572562, 0.000022, 0.000070 ],
[ 0.0567906, 0.000000, 0.000000 ],
[ 0.0561596, 0.005382, 0.001305 ],
[ 0.0559131, 0.001479, 0.001084 ],
[ 0.0530823, 0.005285, 0.000393 ],
[ 0.0527616, 0.030032, 0.013528 ],
[ 0.0525526, 0.004791, 0.003973 ],
[ 0.0516483, 0.001301, 0.000065 ],
[ 0.0514262, 0.003899, 0.000000 ],
[ 0.0513864, 0.003162, 0.000101 ],
[ 0.0510076, 0.005738, 0.003400 ],
[ 0.0507210, 0.001707, 0.002544 ],
[ 0.0507028, 0.001274, 0.000084 ],
[ 0.0506960, 0.005853, 0.006825 ],
])
# table for LEA-406 moon solution
# phik0 arcsec Phase of the Fourier term
# phik1 arcsec Phase of the 1st-order Poisson term
# phik2 arcsec Phase of the 2nd-order Poisson term
# [ phik0, phik1, phik2 ] ...
M_PHASE = array([
# 226 terms
[ 0.000383901368, -85.864631587374, -90.051320519700 ],
[ 0.002465002781, 43.853451435402, -89.760808801732 ],
[ 0.002701282720, 9.198419860616, -89.927193714594 ],
[ 0.000733167975, -69.133923809631, -89.854596360650 ],
[ 179.998822844683, 0.033165685600, -4.896329847950 ],
[ 179.999821873246, -92.231132704615, 90.039281835354 ],
[ 0.002182942141, 115.589973490862, -89.724570062688 ],
[ 0.004492444068, 179.946598681046, -152.700235600240 ],
[ 0.003074613545, 3.237177076528, -89.045873461368 ],
[ 0.004755315788, 179.925373896526, -139.458634581667 ],
[ 179.998402135869, 0.029599610744, -21.201860289276 ],
[ -179.998700951455, -21.042848422574, 85.696683781596 ],
[ 179.998830243184, 0.038692795619, 12.231960211961 ],
[ 0.002824379245, -1.618145480441, -93.712463437426 ],
[ 90.000000000000, -90.000000000000, -90.000000000000 ],
[ -179.999730775095, 136.948333197864, 90.252913650594 ],
[ 0.000631501778, -27.748331128161, 91.027469629070 ],
[ 0.004768684748, 15.338642008082, -91.448391559281 ],
[ 0.000827624832, -44.890207530000, -94.464735632788 ],
[ 0.004679600181, 28.129778606743, -91.253712037737 ],
[ 179.997410623704, -0.012385396825, 19.711675596544 ],
[ -179.999633530725, -0.005264403413, 33.706044239720 ],
[ -179.998546923256, -52.237586501500, 94.104800351413 ],
[ -0.001202833150, -179.943767466285, -161.488197277814 ],
[ 0.006060440686, 179.946114884688, -128.325040292843 ],
[ 0.003479681319, -5.088467767454, -88.879853308440 ],
[ 76.222761080242, 131.248177879490, 158.937351156777 ],
[ 0.005491991867, 5.559956085120, -89.285634473759 ],
[ 0.001670679988, 119.052640751395, 95.344742980084 ],
[ 179.997512146320, 0.012469626353, -38.622239081360 ],
[ -179.997591940179, -130.753370044026, 90.132938283259 ],
[ 0.004027243751, 179.894863506410, -167.685307438556 ],
[ -179.997888374255, -164.568228146555, 94.313669562461 ],
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[ 0.004516315551, 179.946856948035, -147.990210285414 ],
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[ -179.997028119590, -170.875555577117, 87.517830497342 ],
[ 0.007586565777, 179.860744031295, -126.955336135073 ],
[ -179.999173757590, 173.529013740000, 89.645385356640 ],
[ -179.996333121479, -173.529824098564, 90.691511437192 ],
[ -179.998440539648, 0.000498095926, 46.506659248843 ],
[ 0.007351480495, 179.846498962627, -134.320841941915 ],
[ 179.998955202477, 0.004715888323, -24.817267057930 ],
[ -179.974500785427, 0.037906703343, 16.516954102688 ],
[ 0.004084722791, 179.949205415543, -177.339668887924 ],
[ 0.005169265951, 179.947259672081, -162.782325495969 ],
[ 0.005470571565, 7.802235215572, -91.188350231592 ],
[ 0.001979936864, -49.093247644398, -89.853610040000 ],
[ 0.008430819626, 179.862846789852, -120.579155305642 ],
[ -179.997429267858, 3.689592432343, -8.984125112071 ],
[ 179.999682180708, 0.034556477923, 0.880098853934 ],
[ -179.998734104791, 23.889956013343, 92.315478473154 ],
[ -0.001089631169, -179.953391970037, -148.465693395845 ],
[ -179.995711702960, -44.744675254758, 91.037547248403 ],
[ 0.005618410521, 141.891652358833, -89.245762243791 ],
[ 0.006176245341, 179.923324075525, -121.671975846595 ],
[ -179.990710441378, -0.006065350786, 4.820672054727 ],
[ -179.850243125450, 10.554417037974, 75.954784760505 ],
[ 0.004538058638, 179.991538999959, -178.668525637314 ],
[ 0.004948942002, -2.305853377327, -89.055962190853 ],
[ -179.996220310084, -162.841071063425, 90.115626432671 ],
[ 0.001362391462, 124.153219100000, 89.375195054863 ],
[ -179.987972335590, -9.455484053495, 98.486655980000 ],
[ 100.520850457896, 58.245822583006, 176.656756595668 ],
[ 0.005558909986, 179.939402800171, -129.032487586412 ],
[ 74.866340599937, 113.143692095032, 157.140609294154 ],
[ 179.996802948398, 0.023597286958, -49.820634167458 ],
[ 179.991295527846, 105.627702205222, 104.722979510000 ],
[ 1.229379639312, 14.658638231892, 174.161916553362 ],
[ -179.997302559910, -0.079892424376, 50.903582526549 ],
[ -179.997054101519, -179.406547096258, 88.325519523174 ],
[ -179.997923631717, -21.306014230000, -111.306014230000 ],
[ 0.008920446563, 16.507710861469, -87.001504751198 ],
[ -179.997496718333, -49.229404680000, -96.386960454652 ],
[ 179.993029626649, 0.063953608450, 32.857661723889 ],
[ 179.999568497340, 0.029889128486, 41.670863171014 ],
[ -179.997678361057, -131.554420507361, 90.182772169547 ],
[ -6.998845124057, -179.836968150987, 95.494728149239 ],
[ -6.946998653071, -179.864579320978, 76.439431277611 ],
[ 0.003950080511, 179.877986481689, 178.009646557383 ],
[ -179.995214967737, -178.270591376070, 92.820667680820 ],
[ -169.915008504888, 163.606608570999, 141.706947652864 ],
[ -179.995168304093, -0.129249467750, 51.249058012792 ],
[ -0.000588147800, 76.911637520000, -89.818659700943 ],
[ -0.001541311372, -179.960228699023, -157.839192649548 ],
[ 0.005446540202, 178.120205971300, -91.077675513499 ],
[ 0.009961559799, 12.474727024070, -91.103784962745 ],
[ -179.994627410236, -0.125960849016, 58.152530864523 ],
[ -10.452602212154, -175.909739396951, 95.972435843391 ],
[ -179.993551894629, -0.075640934119, 40.075819425085 ],
[ -179.999730936646, -0.111110307792, 44.048546642547 ],
[ -77.540885610051, -152.586445555125, 101.407916729860 ],
[ 0.012860009915, 179.181823683989, -38.176426666159 ],
[ -159.862611524727, 8.333796508938, 108.553241211148 ],
[ 0.000894638748, 179.956445219452, -108.623909313499 ],
[ -179.998497415727, -141.434388770000, 89.925582532280 ],
[ 33.792050127818, 148.766561177540, 127.241668563970 ],
[ 0.009118370918, 179.900634928826, -123.775932072104 ],
[ -112.134619005092, -20.559070831297, -20.121839387134 ],
[ -0.002033212332, -179.939721200975, 132.145526586787 ],
[ 0.006967986668, 11.254792408294, -89.887013647003 ],
[ 0.004247032092, -179.958621060283, -154.368735202973 ],
[ 0.009442611117, 35.703533951771, -89.937681650476 ],
[ -179.997723052131, -0.017116494452, 54.758385850839 ],
[ -179.995947079637, -0.068525925581, 57.217045528267 ],
[ 0.009819658662, 179.838703270416, -112.860829392226 ],
[ 0.001459400774, 179.958199617562, -139.757079434325 ],
[ -167.517828096945, 168.948506773399, 132.172642029344 ],
[ -0.001169845673, -179.992214129080, -139.036692930000 ],
[ 0.001621751548, -34.394376710000, -89.706775576900 ],
[ -179.994253678680, -163.461615332369, 90.508788209221 ],
[ 179.954707818255, 0.297463641368, 79.938876374848 ],
[ -0.288803957182, 138.401774201477, -90.194124627437 ],
[ -0.000441652594, 179.983728062620, -113.490522358660 ],
[ 113.159919693549, 21.205321636711, -68.950861756151 ],
[ -179.993471286898, -0.138018683023, 48.941925280000 ],
[ 0.008513287422, 9.383107446051, -89.982476550838 ],
[ 178.266197023425, 167.040019546567, 63.337092639167 ],
[ -179.993411147698, -152.143374643636, 90.067296178865 ],
[ 177.709033274638, -94.278194341766, 86.467689692292 ],
[ 179.998212230083, 0.011725483834, -38.211204526568 ],
[ -179.548460175794, 11.748806769316, 155.794165646379 ],
[ 179.696182246530, 8.388992907636, -155.810091409325 ],
[ -179.966541471463, 123.169858230588, 174.061712674745 ],
[ 0.001277362909, -87.646654344739, 28.795532201940 ],
[ 0.006441557128, 179.856257333904, 171.660707410000 ],
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[ -179.993990076579, -136.968231614654, 90.111372676863 ],
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[ -85.595401423341, 33.309416345973, 52.614419166008 ],
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[ -179.994957071833, -0.078650599201, 64.442567813218 ],
[ -167.705956663408, -121.678544311070, 135.639537931150 ],
])
# post process of LEA-406 tables
# horizontal split the numpy array
F0_V, F1_V, F2_V = hsplit(M_ARG, 3)
CV = M_PHASE * DEG2RAD
C_V, CT_V, CTT_V = hsplit(CV, 3)
A_V, AT_V, ATT_V = hsplit(M_AMP, 3)
# for VSOP2010
# Mean Longituee J2000 (radian)
ci0 = [
4.402608631669e0, # Mercury
3.176134461576e0, # Venus
1.753470369433e0, # Earth-Moon Barycenter
6.203500014141e0, # Mars
4.091362210690e0, # Vesta
1.713743790353e0, # Iris
5.598651923117e0, # Bamberga
2.805135511956e0, # Ceres
2.326992146758e0, # Pallas
0.599546107035e0, # Jupiter
0.874018510107e0, # Saturn
5.548122539566e0, # Uranus
5.311897933164e0, # Neptune
0.e0, #
5.19846640063e0, # Moon (e)
1.62790513602e0, # Moon (F)
2.35555563875e0 # Moon (l)
]
# Mean Motions in longituee (radian/cy)
ci1 = [
0.2608790314068555e5, # Mercury
0.1021328554743445e5, # Venus
0.6283075850353215e4, # Earth-Moon Barycenter
0.3340612434145457e4, # Mars
0.1731170540074402e4, # Vesta
0.1704450784022772e4, # Iris
0.1428949097282629e4, # Bamberga
0.1364756486739947e4, # Ceres
0.1361923496417814e4, # Pallas
0.5296909615623250e3, # Jupiter
0.2132990086108488e3, # Saturn
0.7478165090307780e2, # Uranus
0.3813292073732270e2, # Neptune
0.3595362366859080e0, # Pluto (Mu from TOP2010)
0.777137714481804e5, # Moon (e)
0.843346615717837e5, # Moon (F)
0.832869142477147e5 # Moon (l)
]
# Planetary frequency in longituee
freqpla = [
0.2608790314068555e5, # Mecrcury
0.1021328554743445e5, # Venus
0.6283075850353215e4, # Earth-Moon Barycenter
0.3340612434145457e4, # Mars
0.5296909615623250e3, # Jupiter
0.2132990861084880e3, # Saturn
0.7478165903077800e2, # Uranus
0.3813292737322700e2, # Neptune
0.2533634111740826e2 # Pluto
]
def sunbyvsop2010(vsopobj, jde, ignorenutation=False):
''' calculate the apprent place of the Sun.
TODO: use 2014-03 cunfeng as reference, i am 0°0'2.82" off, need fix
Arg:
jde as jde
Return:
geocentric longitude in radians, 0 - 2pi
'''
heliolong = vsopobj.lon(jde)
geolong = heliolong + PI
#if FK5:
#B = vsopLx(earth_B0, t)
#Lp = L - 13.97 * t - 0.031 * t * t
#deltaL = (-0.09033 + 0.03916 *
# (cos(math.radians(Lp)) + sin(math.radians(Lp))) *
# tan(math.radians(B))) / 3600.0
# appears -0.09033 is good enough
#deltaL = math.radians(-0.09033 / 3600.0)
#geolong += deltaL
# compensate nutation
if not ignorenutation:
geolong += nutation(jde)
# compensate light aberration, A&A p152, constant of aberration
# k = 20.49552"
t = (jde - J2000) / 36525.0
t2 = t * t
t3 = t2 * t
# mean anomaly of the Sun
M = 357.52910 + 35999.0503 * t - 0.0001559 * t2 - 0.00000048 * t3
# the eccentricity of Earth's orbit
e = 0.016708617 - 0.000042037 * t - 0.0000001236 * t2
# Sun's equation of center
C = ((1.9146 - 0.004817 * t - 0.000014 * t2) * sin(math.radians(M))
+ (0.019993 - 0.000101 * t) * sin(math.radians(2 * M))
+ 0.00029 * sin(math.radians(3 * M)))
# true anomaly
v = M + C
# Sun's distance from the Earth, in AU
#R = (1.000001018 * (1 - e * e)) / (1 + e * cos(math.radians(v)))
# finally, the aberration in radians
labbr = (math.radians(20.49552 / 3600.0) * (1 + e * cos(math.radians(v))) /
-1.000001018)
#print 'labbr', fmtdeg(math.degrees(labbr))
geolong += labbr
return normrad(geolong)
class VSOP2010():
''' compute mean longitude of the Earth-Moon Barycenter based on VSOP2010.
The coordinates are referred to the inertial frame defined by the dynamical
equinox and ecliptic J2000
'''
def __init__(self):
fp = open('/home/wei/tmp/astro/vsop2010/VSOP2010p3.dat')
headfmt = '9x,3i3,i7'
datafmt = '6x,4i3,1x,5i3,1x,4i4,1x,i6,1x,3i3,2a24'
term_count = 0
# iphi: 17 numerical coefficients a(i) (i=1,17)) (integer)
# ss: coefficient S
# cc: coefficient C
iphi = []
ss = []
cc = []
self.it_count = []
islon = False
delnext = False
for line in fp:
if term_count == 0:
# ip : planete index
# iv : variable index. 2 = mean longitude (radian)
# it : time power
# nt : number of terms in series
ip, iv, it, nt = fortran_readline(line, headfmt)
if iv == 2:
self.it_count.append(nt)
if it == 1:
# remove 1st term of 1st order time power
delnext = True
islon = True
else:
islon = False
term_count = nt
continue
if islon and not delnext:
tmp = fortran_readline(line, datafmt)
iphi.append(tmp[:17])
sa = tmp[17][:20] + 'e' + tmp[17][21:]
ca = tmp[18][:20] + 'e' + tmp[18][21:]
ss.append(float(sa))
cc.append(float(ca))
elif islon and delnext:
delnext = False
term_count -= 1
continue
term_count -= 1
self.it_count[1] -= 1
iphi = array(iphi)
a_ci0 = array(ci0)
a_ci1 = array(ci1)
self.aa = sum(iphi * a_ci0, axis=1)
self.bb = sum(iphi * a_ci1, axis=1)
self.ss = array(ss)
self.cc = array(cc)
def lon(self, jd, ignorenutation=False):
tn = 1
tc = (jd - J2000) / 365250.0
t = []
for it, count in enumerate(self.it_count):
tmp = [tn] * count
t.extend(tmp)
tn *= tc
t = array(t)
aa = self.aa
bb = self.bb
ss = self.ss
cc = self.cc
arg = aa + bb * tc
v = ne.evaluate('sum(t * (ss * sin(arg) + cc * cos(arg)))')
v += freqpla[2] * tc
#prec = precession(jd)
#v += prec
v = normrad(v)
#print 'debug: %f %f ' % (t[1], v)
return v
def vsopLx(vsopterms, t):
''' helper function for calculate VSOP87 '''
lx = vsopterms[:, 0] * cos(vsopterms[:, 1] + vsopterms[:, 2] * t)
#for vsopterm in vsopterms:
# A = vsopterm[0]
# B = vsopterm[1]
# C = vsopterm[2]
# Lx += A * math.cos(B + C * t)
return sum(lx)
def vsop(jde, FK5=True):
''' Calculate ecliptical longitude of earth in heliocentric coordinates,
use VSOP87D table, heliocentric spherical, coordinates referred to the mean
equinox of the date,
In A&A, Meeus said while the complete VSOP87 yields an accuracy of 0.01",
the abridge VSOP87 has an accuracy of 1" for -2000 - +6000.
The VSOP87D table used here is a truncated version, done by the
vsoptrunc-sph.c from Celestia.
Arg:
jde: in JDTT
Return:
earth longitude in radians, referred to mean dynamical ecliptic and
equinox of the date
'''
t = (jde - J2000) / 365250.0
L0 = vsopLx(earth_L0, t)
L1 = vsopLx(earth_L1, t)
L2 = vsopLx(earth_L2, t)
L3 = vsopLx(earth_L3, t)
L4 = vsopLx(earth_L4, t)
L5 = vsopLx(earth_L5, t)
lon = (L0 + t * (L1 + t * (L2 + t * (L3 + t * (L4 + t * L5)))))
if FK5:
#b0 = vsopLx(earth_B0, t)
#b1 = vsopLx(earth_B1, t)
#b2 = vsopLx(earth_B2, t)
#b3 = vsopLx(earth_B3, t)
#b4 = vsopLx(earth_B4, t)
#lat = b0 + t * (b1 + t * (b2 + t * (b3 + t * b4 )))
#lp = lon - 1.397 * t - 0.00031 * t * t
#deltalon = (-0.09033 + 0.03916 * (cos(lp) + sin(lp))
# * tan(lat)) * ASEC2RAD
#print 'FK5 convertion: %s' % fmtdeg(math.degrees(deltalon))
# appears -0.09033 is good enough
#deltal = math.radians(-0.09033 / 3600.0)
deltalon = -4.379321981462438e-07
lon += deltalon
return lon
def rootbysecand(f, angle, x0, x1, precision=0.000000001):
''' solve the equation when function f(jd, angle) reaches zero by
Secand method
'''
fx0, fx1 = f(x0, angle), f(x1, angle)
while abs(fx1) > precision and abs(x0 - x1) > precision and fx0 != fx1:
x2 = x1 - fx1 * (x1 - x0) / (fx1 - fx0)
fx0 = fx1
fx1 = f(x2, angle)
x0 = x1
x1 = x2
return x1
def normrad(r):
''' covernt radian to 0 - 2pi '''
alpha = fmod(r, TWOPI)
if alpha < 0:
alpha += TWOPI
return alpha
def npitopi(r):
''' convert an angle in radians into (-pi, +pi] '''
r = fmod(r, TWOPI)
if r > PI:
r -= TWOPI
elif r <= -1.0 * PI:
r += TWOPI
return r
def fmtdeg(fdegree):
'''convert decimal degree to d m s format string'''
if abs(fdegree) > 360:
fdegree = math.fmod(fdegree, 360.0)
degree = math.fabs(fdegree)
tmp, deg = math.modf(degree)
minutes = tmp * 60
secs = math.modf(minutes)[0] * 60
sign =''
if fdegree < 0:
sign = '-'
res = '''%s%d%s%d'%.6f"''' % (sign, int(deg), u'\N{DEGREE SIGN}',
math.floor(minutes), secs)
return res
def f_solarangle(jd, r_angle):
''' Calculate the difference between target angle and solar geocentric
longitude at a given JDTT
and normalize the angle between Sun's Longitude on a given
day and the angle we are looking for to (-pi, pi), therefore f(x) is
continuous from -pi to pi, '''
return npitopi(apparentsun(jd) - r_angle)
def f_msangle(jd, angle):
''' Calculate difference between target angle and current sun-moon angle
Arg:
jd: time in JDTT
Return:
angle in radians, convert to -PI to + PI range
'''
return npitopi(apparentmoon(jd, ignorenutation=True)
- apparentsun(jd, ignorenutation=True)
- angle)
def solarterm(year, angle):
''' calculate Solar Term by secand method
The Sun's moving speed on ecliptical longitude is 0.04 argsecond / second,
The accuracy of abridged VSOP is 1", nutation by IAU2000B is 0.001"
Args:
year: the year in integer
angle: degree of the solar term, in integer
Return:
time in JDTT
'''
# mean error when compare apparentsun to NASA(1900-2100) is 0.14"
# 0.000000005 radians = 0.001"
ERROR = 0.000000005
r = normrad(math.radians(angle))
# negative angle means we want search backward from Vernal Equinox,
# initialize x0 to the day which apparent Sun longitude close to the angle
# we searching for
est_vejd = g2jd(year, 3, 20.5)
x0 = est_vejd + angle * 360.0 / 365.24 # estimate
#x0 -= solarangle(x0, r) / SUN_SPEED # further closing
x1 = x0 + 0.5
return rootbysecand(f_solarangle, r, x0, x1, precision=ERROR)
def newmoon(jd):
''' search newmoon near a given date.
Angle between Sun-Moon has been converted to [-pi, pi] range so the
function msangle is continuous in that range. Use Secand method to find
root.
newmoon in 5 iterations, if the start is close enough, as the searching of
next newmoon usualy does, it may use only 3 iterations.
Arg:
jd: in JDTT
Return:
JDTT of newmoon
'''
# 0.0000001 radians is about 0.02 arcsecond, mean error of apparentmoon
# when compared to JPL Horizon is about 4 arcsecond
ERROR = 0.0000001
# initilize x0 to the day close to newmoon
x0 = jd - f_msangle(jd, 0) / MOON_SPEED
x1 = x0 + 0.5
return rootbysecand(f_msangle, 0, x0, x1, precision=ERROR)
def findnewmoons(start, count=15):
''' search new moon from specified start time
Arg:
start: the start time in JD, doesn't matter if it is in TT or UT
count: the number of newmoons to search after start time
Return:
a list of JDTT when newmoon occure
'''
nm = 0
newmoons = []
nmcount = 0
count += 1
while nmcount < count:
b = newmoon(start)
if b != nm:
if nm > 0 and abs(nm - b) > (SYNODIC_MONTH + 1):
print 'last newmoon %s, found %s' % (fmtjde2ut(nm),
fmtjde2ut(b))
newmoons.append(b)
nm = b
nmcount += 1
start = nm + SYNODIC_MONTH
else:
start += 1
return newmoons
def apparentmoon(jde, ignorenutation=False):
''' calculate the apparent position of the Moon, it is an alias to the
lea406 function'''
return lea406(jde, ignorenutation)
def apparentsun(jde, ignorenutation=False):
''' calculate the apprent place of the Sun.
TODO: use 2014-03 cunfeng as reference, i am 0°0'2.82" off, need fix
Arg:
jde as jde
Return:
geocentric longitude in radians, 0 - 2pi
'''
heliolong = vsop(jde)
geolong = heliolong + PI
# compensate nutation
if not ignorenutation:
geolong += nutation(jde)
labbr = lightabbr_high(jde)
#print 'labbr = %s' % fmtdeg(math.degrees(labbr))
geolong += labbr
return normrad(geolong)
def lightabbr_low(jde):
''' compute light abberation use less accurate method
compensate light aberration, A&A p152, constant of aberration
k = 20.49552"
the error can be up to 0.01"
'''
t = (jde - J2000) / 36525.0
t2 = t * t
t3 = t2 * t
# mean anomaly of the Sun
M = 357.52910 + 35999.0503 * t - 0.0001559 * t2 - 0.00000048 * t3
# the eccentricity of Earth's orbit
e = 0.016708617 - 0.000042037 * t - 0.0000001236 * t2
# Sun's equation of center
C = ((1.9146 - 0.004817 * t - 0.000014 * t2) * sin(math.radians(M))
+ (0.019993 - 0.000101 * t) * sin(math.radians(2 * M))
+ 0.00029 * sin(math.radians(3 * M)))
# true anomaly
v = M + C
# Sun's distance from the Earth, in AU
#R = (1.000001018 * (1 - e * e)) / (1 + e * cos(math.radians(v)))
# finally, the aberration in radians
labbr = (math.radians(20.49552 / 3600.0) * (1 + e * cos(math.radians(v))) /
-1.000001018)
return labbr
def lightabbr_high(jd):
'''compute light abberation based on A & A p156
the error will be less than 0.001"
'''
t = (jd - J2000) / 365250.0
t2 = t * t
t3 = t * t2
# variation of the Sun's longitude
#var_lon = (3548.193
var_lon = (3548.330
+ 118.568 * sin(math.radians( 87.5287 + 359993.7286 * t ))
+ 2.476 * sin(math.radians( 85.0561 + 719987.4571 * t ))
+ 1.376 * sin(math.radians( 27.8502 +4452671.1152 * t ))
+ 0.119 * sin(math.radians( 73.1375 + 450368.8564 * t ))
+ 0.114 * sin(math.radians( 337.2264 + 329644.6718 * t ))
+ 0.086 * sin(math.radians( 222.5400 + 659289.3436 * t ))
+ 0.078 * sin(math.radians( 162.8136 +9224659.7915 * t ))
+ 0.054 * sin(math.radians( 82.5823 +1079981.1857 * t ))
+ 0.052 * sin(math.radians( 171.5189 + 225184.4282 * t ))
+ 0.034 * sin(math.radians( 30.3214 +4092677.3866 * t ))
+ 0.033 * sin(math.radians( 119.8105 + 337181.4711 * t ))
+ 0.023 * sin(math.radians( 247.5418 + 299295.6151 * t ))
+ 0.023 * sin(math.radians( 325.1526 + 315559.5560 * t ))
+ 0.021 * sin(math.radians( 155.1241 + 675553.2846 * t ))
+ 7.311 * t * sin(math.radians( 333.4515 + 359993.7286 * t ))
+ 0.305 * t * sin(math.radians( 330.9814 + 719987.4571 * t ))
+ 0.010 * t * sin(math.radians( 328.5170 +1079981.1857 * t ))
+ 0.309 * t2 * sin(math.radians( 241.4518 + 359993.7286 * t ))
+ 0.021 * t2 * sin(math.radians( 205.0482 + 719987.4571 * t ))
+ 0.004 * t2 * sin(math.radians( 297.8610 +4452671.1152 * t ))
+ 0.010 * t3 * sin(math.radians( 154.7066 + 359993.7286 * t ))
)
t = (jd - J2000) / 36525.0
t2 = t * t
t3 = t * t2
# mean anomaly of the Sun
M = 357.52910 + 35999.0503 * t - 0.0001559 * t2 - 0.00000048 * t3
# the eccentricity of Earth's orbit
e = 0.016708617 - 0.000042037 * t - 0.0000001236 * t2
# Sun's equation of center
C = ((1.9146 - 0.004817 * t - 0.000014 * t2) * sin(math.radians(M))
+ (0.019993 - 0.000101 * t) * sin(math.radians(2 * M))
+ 0.00029 * sin(math.radians(3 * M)))
# true anomaly
v = M + C
# Sun's distance from the Earth, in AU
R = (1.000001018 * (1 - e * e)) / (1 + e * cos(math.radians(v)))
res = -0.005775518 * R * var_lon * ASEC2RAD
return res
def g2jd(y, m, d):
''' convert a Gregorian date to JD
from AA, p61
'''
if m <= 2:
y -= 1
m += 12
a = int(y / 100)
julian = False
if y < 1582:
julian = True
elif y == 1582:
if m < 10:
julian = True
if m == 10 and d <= 5:
julian = True
if m == 10 and d > 5 and d < 15:
return 2299160.5
if julian:
b = 0
else:
b = 2 - a + int(a / 4)
# 30.6001 is a hack Meeus suggested
return int(365.25 * (y + 4716)) + int(30.6001 * (m + 1)) + d + b - 1524.5
def td2jde(y, m, d):
''' convert Terrestrial (Dynamic) Time to JDE '''
return g2jd(y, m ,d)
def ut2jde(y, m, d):
''' convert UT to JDE, compensate the delta T '''
jd = g2jd(y, m, d)
deltat = deltaT(y, m) / 86400.0
return jd + deltat
def ut2jdut(y, m, d):
''' convert UT to JD, ignore delta T '''
return g2jd(y, m, d)
def jdut2ut(jd):
return jd2g(jd)
def jde2ut(jde, showtime=False):
g = jd2g(jde, showtime)
deltat = deltaT(g[0], g[1]) / 86400.0 # in day
return jd2g(jde - deltat, showtime)
def jde2td(jde):
return jd2g(jde)
def jd2g(jd):
''' convert JD to Gregorian date '''
jd += 0.5
z = int(jd)
f = fmod(jd, 1.0) # decimal part
if z < 2299161:
a = z
else:
alpha = int((z - 1867216.25) / 36524.25)
a = z + 1 + alpha - int(alpha / 4)
b = a + 1524
c = int((b - 122.1) / 365.25)
d = int(365.25 * c)
e = int((b - d) / 30.6001)
res_d = b - d - int(30.6001 * e) + f
if e < 14:
res_m = e - 1
else:
res_m = e - 13
if res_m > 2:
res_y = c - 4716
else:
res_y = c - 4715
return (res_y, res_m, res_d)
def jdptime(isodt, fmt, tz=0, ut=False):
'''
Args:
isodt: datetime string in ISO format
tz: a integer as timezone, e.g. -8 for UTC-8, 2 for UTC2
fmt: like strftime but currently only support three format
%y-%m-%d %H:%M:%S
%y-%m-%d %H:%M
%y-%m-%d
ut: convert to UTC(adjust delta T)
Return:
Julian Day
'''
if fmt == '%y-%m-%d':
isodate = isodt
isot = '00:00:00'
elif fmt == '%y-%m-%d %H:%M':
isodate, isot = isodt.split()
isot += ':00'
else:
isodate, isot = isodt.split()
y, m, d = [int(x) for x in isodate.split('-')]
#if isot:
H, M, S = [int(x) for x in isot.split(':')]
d += (H * 3600 + M * 60 + S) / 86400.0
return g2jd(y, m, d)
def jdftime(jde, fmt='%y-%m-%d %H:%M:%S', tz=0, ut=False):
''' format a Julian Day to ISO format datetime
Args:
jde: time in JDTT
tz: a integer as timezone, e.g. -8 for UTC-8, 2 for UTC2
fmt: like strftime but currently only support three format
%y-%m-%d %H:%M:%S
%y-%m-%d %H:%M
%y-%m-%d
ut: convert to UTC(adjust delta T)
Return:
time string in ISO format, e.g. 1984-01-01 23:59:59
'''
g = jd2g(jde)
deltat = deltaT(g[0], g[1]) if ut else 0
# convert JDE to seconds, then adjust deltat
utsec = jde * 86400.0 + tz * 3600 - deltat
jdut = utsec / 86400.0
# get time in seconds directly to minimize round error
secs = (utsec + 43200) % 86400
if fmt == '%y-%m-%d %H:%M':
secs = int(round(secs / 60.0) * 60.0)
else:
secs = int(secs)
if 86400 == secs:
jdut = int(jdut) + 0.5
secs = 0
y, m, d = jd2g(jdut)
d = int(d)
# use integer math hereafter
H = secs / 3600
ms = secs % 3600
M = ms / 60
S = ms % 60
# padding zero
d = '0%d' % d if d < 10 else str(d)
m = '0%d' % m if m < 10 else str(m)
H = '0%d' % H if H < 10 else str(H)
M = '0%d' % M if M < 10 else str(M)
S = '0%d' % S if S < 10 else str(S)
if fmt == '%y-%m-%d':
isodt = '%d-%s-%s' % (y, m, d)
elif fmt == '%y-%m-%d %H:%M':
isodt = '%d-%s-%s %s:%s' % (y, m, d, H, M)
else:
isodt = '%d-%s-%s %s:%s:%s' % (y, m, d, H, M, S)
return isodt
def deltaT(year, m ,d=0):
''' Polynomial Expressions for Delta T (ΔT) from nasa. Valid for -1999 to
+3000. http://eclipse.gsfc.nasa.gov/LEcat5/deltatpoly.html
Arg:
year: Gregorian year in integer
m: Gregorian month in integer
d: doesn't matter
Result:
ΔT in seconds
verfify against historical records from NASA
year history computed diff
-500 17190 17195.37 5.4
-400 15530 15523.84 6.2
-300 14080 14071.97 8.0
-200 12790 12786.59 3.4
-100 11640 11632.52 7.5
0 10580 10578.95 1.0
100 9600 9592.45 7.6
200 8640 8636.34 3.7
300 7680 7676.67 3.3
400 6700 6694.67 5.3
500 5710 5705.50 4.5
600 4740 4734.89 5.1
700 3810 3809.04 1.0
800 2960 2951.97 8.0
900 2200 2197.11 2.9
1000 1570 1571.65 1.7
1100 1090 1086.99 3.0
1200 740 735.10 4.9
1300 490 490.98 1.0
1400 320 321.09 1.1
1500 200 197.85 2.2
1600 120 119.55 0.5
1700 9 8.90 0.1
1750 13 13.44 0.4
1800 14 13.57 0.4
1850 7 7.16 0.2
1900 -3 -2.12 0.9
1950 29 29.26 0.3
1955 31 31.23 0.1
1960 33 33.31 0.1
1965 36 36.13 0.4
1970 40 40.66 0.5
1975 46 45.94 0.4
1980 50 50.93 0.4
1985 54 54.60 0.3
1990 57 57.20 0.3
1995 61 61.17 0.4
2000 64 64.00 0.2
2005 65 64.85 0.1
Also, JPL uses "last known leap-second is used over any future interval".
It causes the large error when compare apparent sun/moon position with JPL
Horizon
'''
y = year + (m - 0.5) / 12
if year < -500:
u = (year - 1820) / 100.0
return -20 + 32 * u ** 2
elif year < 500:
u = y / 100.0
return 10583.6 + u * (-1014.41 +
u * (33.78311 +
u * (-5.952053 +
u * (-0.1798452 +
u * (0.022174192 +
u * 0.0090316521)))))
elif year < 1600:
u = (y -1000) / 100.0
return 1574.2 + u * (-556.01 +
u * (71.23472 +
u * (0.319781 +
u * (-0.8503463 +
u * (-0.005050998 +
u * 0.0083572073)))))
elif year < 1700:
u = y -1600
return 120 + u * (-0.9808 +
u * (- 0.01532 +
u / 7129))
elif year < 1800:
u = y - 1700
return 8.83 + u * (0.1603 +
u * (-0.0059285 +
u * (0.00013336 +
u / -1174000)))
elif year < 1860:
u = y - 1800
return 13.72 + u * (-0.332447 +
u * (0.0068612 +
u * (0.0041116 +
u * (-0.00037436 +
u * (0.0000121272 +
u * (-0.0000001699 +
u * 0.000000000875))))))
elif year < 1900:
u = y - 1860
return 7.62 + u * (0.5737 +
u * (-0.251754 +
u * (0.01680668 +
u * (-0.0004473624 +
u / 233174))))
elif year < 1920:
u = y - 1900
return -2.79 + u * (1.494119 +
u * (-0.0598939 +
u * (0.0061966 +
u * -0.000197)))
elif year < 1941:
u = y - 1920
return 21.20 + u * (0.84493 +
u * (-0.076100 +
u * 0.0020936))
elif year < 1961:
u = y - 1950
return 29.07 + u * (0.407 +
u * (-1.0 / 233 +
u / 2547))
elif year < 1986:
u = y - 1975
return 45.45 + u * (1.067 +
u * (-1.0 / 260 +
u / -718))
elif year < 2005:
u = y -2000
return 63.86 + u * (0.3345 +
u * (-0.060374 +
u * (0.0017275 +
u * (0.000651814 +
u * 0.00002373599))))
'''
else:
# JPL uses "last known leap-second is used over any future interval" .
# It causes the large error when compare apparent sun/moon position
# with JPL Horizon
return 67.182963
'''
elif year < 2050:
u = y -2000
return 62.92 + u * (0.32217 + u * 0.005589)
elif year < 2150:
u = (y - 1820.0) / 100.0
return -20 + 32 * u ** 2 - 0.5628 * (2150 - y)
else:
u = (y - 1820.0) / 100.0
return -20 + 32 * u ** 2
def nutation(jde):
'''
Calculate nutation angles using the IAU 2000B model.
The table is from NOVAS(USNO) c source flle.
"...the 77-term, IAU-approved truncated nutation series, IAU 2000B, which
is accurate to about 0.001 arcsecond in the interval 1995-2050"
Arg:
jde as JDE
Return:
nutation of longitude in radians
'''
t = (jde - J2000) / 36525.0
#Mean anomaly of the Moon, in arcsec
L = 485868.249036 + t * 1717915923.2178
#Mean anomaly of the Sun.
Lp = 1287104.79305 + t * 129596581.0481
#Mean argument of the latitude of the Moon.
F = 335779.526232 + t * 1739527262.8478
#Mean elongation of the Moon from the Sun.
D = 1072260.70369 + t * 1602961601.2090
#Mean longitude of the ascending node of the Moon.
Om = 450160.398036 - t * 6962890.5431
m1, m2, m3, m4, m5, AA, BB, CC, EE, DD, FF = hsplit(IAU2000BNutationTable,
11)
args = (m1 * L + m2 * Lp + m3 * F + m4 * D + m5 * Om) * ASEC2RAD
lon = sum((AA + BB * t) * sin(args) + CC * cos(args))
# unit of longitude is 1.0e-7 arcsec, convert it to arcsec
lon *= 1.0e-7
# Constant account for the missing long-period planetary terms in the
# truncated nutation model, in arcsec
deplan = 0.000388
lon += deplan
lon *= ASEC2RAD # Convert from arcsec to radians
lon = fmod(lon, TWOPI)
return lon
#------------------------------------------------------------------------------
# LEA-406 Moon Solution
#
# Reference:
# Long-term harmonic development of lunar ephemeris.
# Kudryavtsev S.M. <Astron. Astrophys. 471, 1069 (2007)>
#
# the tables M_AMP, M_PHASE, M_ARG are imported from aa_full_table
#------------------------------------------------------------------------------
FRM = [785939.924268, 1732564372.3047, -5.279, .006665, -5.522e-5 ]
RADEG = 1.7453292519943296e-2
RASEC = 4.8481368110953599e-6
def fortran_parsefmt(fmt):
import re
fmt = fmt.upper()
RE_FORTRAN_FMT = re.compile(r'(\d*)([A-Z]+)(\d*)\.?\d*')
m = RE_FORTRAN_FMT.findall(fmt)
fw = []
# transform Fortran format into (rep, TYPE, width)
for x in m:
count = int(x[0]) if x[0] else 1
width = int(x[2]) if x[2] else 1
fw.append((count, x[1], width))
return fw
def fortran_readline(line, fmt):
''' read fortran formated file into array '''
fw = fortran_parsefmt(fmt)
line.replace('D', 'E') # replace fortran 77 double precision format
tmp = []
i = 0
for rep, ftype, length in fw:
for cnt in xrange(rep):
field = line[i: i + length]
i += length
if ftype == 'F':
field = float(field)
elif ftype == 'I':
field = int(field)
elif ftype == 'A':
field = field
else:
continue
tmp.append(field)
return tmp
def fortran_read(fp, fmt):
''' read fortran formated file into array '''
fw = fortran_parsefmt(fmt)
res = []
for line in fp:
line.replace('D', 'E') # replace fortran 77 double precision format
tmp = []
i = 0
for rep, ftype, length in fw:
for cnt in xrange(rep):
field = line[i: i + length]
i += length
if ftype == 'F':
field = float(field)
elif ftype == 'I':
field = int(field)
elif ftype == 'A':
field = field
else:
continue
tmp.append(field)
res.append(tmp)
return res
def moon_libration(jd):
''' compute libration of the Moon
Arg:
jd JDE
Return:
longitude in radians
'''
t = (jde - J2000) / 36525.0
t2 = t * t
t3 = t2 * t
t4 = t3 * t
# mean longitude, referred to the mean equinox of the date, and including
# the constant term of the effect of light-time
Lp = (218.3164591 + t * 481267.88134236 +
t2 * -0.0013268 +
t3 / 538841.0 +
t4 / 65194000.0)
# mean elongation of the moon
D = (297.8502042 + t * 445267.1115168 +
t2 * -0.00163 +
t3 / 545868.0 +
t4 / 113065000.0)
# sun's mean anomaly
M = (357.5291092 + t * 35999.0502909 +
t2 * -0.0001536 +
t3 / 24490000.0)
# moon's mean anomaly
Mx = (134.9634114 + t * 477198.8676313 +
t2 * 0.0089970 +
t3 / 69699.0 +
t4 / -14712000.0)
# moon's argument of latitude 45.5
F = (93.2720993 + t * 483202.0175273 +
t2 * -0.0034029 +
t3 / 3526000.0 +
t4 / 863310000.0)
# 45.7
OMEGA = (125.044555 - 1934.1361849 * t + 0.0020762 * t2 - t3 / 80053.0
+ t4 / 18999000.0)
# other args in degree
A1 = 119.75 + 131.849 * t
A2 = 53.09 + 479264.29 * t
#A3 = 313.45 + 481266.484 * t
E = 1 + t * (-0.002516 - 0.0000074 * t)
suml = 0
for row in moon_tableA:
pd, pm, pmx, pf, plong, plat = row
if pm == 1 or pm == -1:
pm *= E
elif pm == 2 or pm == -2:
pm *= E * E
arg = pd * D + pm * M + pmx * Mx + pf * F
suml += plong * math.sin(math.radians(arg))
suml += 3958 * math.sin(math.radians(A1))
suml += 1962 * math.sin(math.radians(Lp - F))
suml += 318 * math.sin(math.radians(A2))
# moon longitude in degrees
res = Lp + suml / 1000000.0
# apparent longitude, add nutation
if not ignorenutation:
return math.radians(res % 360) + nutation(jde)
else:
return math.radians(res % 360)
class LEA406():
''' use the full lea406 table '''
def __init__(self):
fp = open('table7.dat')
fmt = 'I6,2X,5I3,1X,8I3,1X,I3,F16.7,2F11.6,3F19.12'
farray = fortran_read(fp, fmt)
LEN = len(farray)
A_V =[]
AT_V =[]
ATT_V =[]
C_V =[]
CT_V =[]
CTT_V =[]
F0_V = [0] * LEN
F1_V = [0] * LEN
F2_V = [0] * LEN
F3_V = [0] * LEN
F4_V = [0] * LEN
count = 0
for a in farray:
#if a[15] < 3660.01:
# count += 1
# continue
IND = a[6:14]
IND.extend([a[5], a[4], a[2], a[1], a[3], a[14]])
I = a[0] - 1 # convert array index start from 1 to 0
#Ak0 arcsec Amplitude of the Fourier term
#Ak1 mas/yr Amplitude of the 1st-order Poisson term
#Ak2 uas/yr2 Amplitude of the 2nd-order Poisson term
#phik0 deg Phase of the Fourier term
#phik1 deg Phase of the 1st-order Poisson term
#phik2 deg Phase of the 2nd-order Poisson term
A_V.append(a[15])
AT_V.append(a[16])
ATT_V.append(a[17])
C_V.append(a[18])
CT_V.append(a[19])
CTT_V.append(a[20])
# CALCULATING THE ARGUMENTS [RAD]
for K in xrange(14):
F0_V[I] += IND[K] * FR[K][0]
F1_V[I] += IND[K] * FR[K][1]
F2_V[I] += IND[K] * FR[K][2]
F3_V[I] += IND[K] * FR[K][3]
F4_V[I] += IND[K] * FR[K][4]
LEN_KEPT = LEN - count
print '%d skipped, %d kept' % (count, LEN_KEPT)
self.A_V =array(A_V)
self.AT_V =array(AT_V)
self.ATT_V =array(ATT_V)
self.C_V =array(C_V) * RADEG
self.CT_V =array(CT_V) * RADEG
self.CTT_V =array(CTT_V) * RADEG
self.F0_V = array(F0_V) * 3600
self.F1_V = array(F1_V)
self.F2_V = array(F2_V)
self.F3_V = array(F3_V)
self.F4_V = array(F4_V)
self.I_V = I
def lon(self, jd, ignorenutation=False):
# CALCULATION OF THE COORDINATE V (LUNAR ECLIPTIC LONGITUDE) AT THE
# INPUT EPOCH [RAD]
DTC = (jd - J2000) / 36525.0
DTC2 = DTC * DTC
DTC3 = DTC2 * DTC
DTC4 = DTC3 * DTC
DTM = DTC / 10.0
DTM2 = DTM * DTM
V=FRM[0]+(((FRM[4]*DTC+FRM[3])*DTC+FRM[2])*DTC+FRM[1])*DTC
# numpy array operation
self.F0_V = around(self.F0_V, 0)
#F1_V = around(self.F1_V, 3) * DTC
#F2_V = around(self.F2_V, 0) * DTC2
#F3_V = around(self.F3_V, 0) * DTC3
#F4_V = around(self.F4_V, 0) * DTC4
F3_V = 0
F4_V = 0
F1_V = self.F1_V * DTC
F2_V = self.F2_V * DTC2
F3_V = self.F3_V * DTC3
F4_V = self.F4_V * DTC4
ARGS = (self.F0_V + F1_V + F2_V + F3_V + F4_V) * ASEC2RAD
P = ( self.A_V * sin(ARGS + self.C_V)
+ self.AT_V * sin(ARGS + self.CT_V) * DTM
+ self.ATT_V * sin(ARGS + self.CTT_V) * DTM2)
V += sum(P)
#absP = abs(P)
#count = 0
#kept_items = []
#for i in xrange(len(P)):
# if absP[i] > 0.05:
# kept_items.append(i)
# count += 1
#print '%d significant' % count
#pp = []
#for i in kept_items:
# pp.append(P[i])
#pp = array(pp)
#V += sum(pp)
V = V * ASEC2RAD
if not ignorenutation:
V += nutation(jd)
return normrad(V)
def lea406(jd, ignorenutation=False):
''' compute moon ecliptic longitude using lea406
numpy is used
'''
t = (jd - J2000) / 36525.0
t2 = t * t
t3 = t2 * t
t4 = t3 * t
tm = t / 10.0
tm2 = tm * tm
V = FRM[0] + (((FRM[4] * t + FRM[3]) * t + FRM[2]) * t + FRM[1]) * t
# numpy array operation
ARGS = ne.evaluate('''( F0_V
+ F1_V * t
+ F2_V * t2) * ASEC2RAD''')
P = ne.evaluate('''( A_V * sin(ARGS + C_V)
+ AT_V * sin(ARGS + CT_V) * tm
+ ATT_V * sin(ARGS + CTT_V) * tm2)''')
V += sum(P)
V = V * ASEC2RAD
if not ignorenutation:
V += nutation(jd)
return normrad(V)
def main():
e = 0.001
#jd = 2444239.5
jd = g2jd(1900, 1, 1)
#lea406class = LEA406()
for i in xrange(1):
#l = normrad(lea406class.lon(jd))
l = normrad(lea406(jd))
#d = fmtdeg(math.degrees(npitopi(e -l )))
print jd, l, fmtdeg(math.degrees(l))
jd += 2000
#print fmtdeg(math.degrees(e) % 360.0)
#angle = -105
#while angle < 360:
# a = solarterm(2014, angle)
# print 'search %d %s' % (angle,jdftime(a, tz=8, ut=True))
# angle += 15
def test():
jd = 2411545.0
year = 2097
for year in xrange(2060, 2060):
print year, deltaT(year, 9)
if __name__ == "__main__":
main()
#test()
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