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4b0a8aafd77798b587842482225d11da589176d5
lunar-calendar/c/lea406.c
Wei Chen 4b0a8aafd7 update copyright to 2020
2020-02-21 15:51:43 -06:00

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/*
copyright 2020, Chen Wei <weichen302@gmail.com>
version 0.0.3
Implement astronomical algorithms for finding solar terms and moon phases.
Truncated LEA-406 for calculate Moon's apparent longitude;
Reference:
LEA-406: S. M. Kudryavtsev (2007) "Long-term harmonic development of
lunar ephemeris", Astronomy and Astrophysics 471, 1069-1075
*/
#include <stdio.h>
#include <math.h>
#include "astro.h"
static double FRM[5] = {
785939.924268, 1732564372.3047, -5.279, .006665, -5.522e-5
};
/*
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
average error Moon = 0.73", max 1.5"
*/
static double M_ARG[226][3] = {
{ 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 } ...
*/
static double M_AMP[226][3] = {
{ 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 },
{ 0.4134074, 0.010391, 0.000347 },
{ 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 },
{ 0.3008704, 0.000080, 0.000190 },
{ 0.2942052, 0.014800, 0.000232 },
{ 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 },
{ 0.1432907, 0.000164, 0.002489 },
{ 0.1363584, 0.003428, 0.000102 },
{ 0.1360093, 0.005055, 0.007270 },
{ 0.1342991, 0.002202, 0.012985 },
{ 0.1317702, 0.012996, 0.046203 },
{ 0.1312510, 0.004067, 0.005441 },
{ 0.1281174, 0.000034, 0.000093 },
{ 0.1274662, 0.003938, 0.005376 },
{ 0.1261665, 0.000044, 0.000252 },
{ 0.1251903, 0.000032, 0.000034 },
{ 0.1238568, 0.000012, 0.000201 },
{ 0.1207260, 0.003037, 0.000112 },
{ 0.1177733, 0.104057, 0.092375 },
{ 0.1166401, 0.105848, 0.086210 },
{ 0.1145920, 0.065094, 0.062264 },
{ 0.1127967, 0.017578, 0.045202 },
{ 0.1110004, 0.000000, 0.000148 },
{ 0.1100790, 0.000037, 0.000050 },
{ 0.1014638, 0.007699, 0.000024 },
{ 0.0998164, 0.002513, 0.000094 },
{ 0.0992925, 0.003076, 0.004114 },
{ 0.0971982, 0.005531, 0.000173 },
{ 0.0935175, 0.010642, 0.005973 },
{ 0.0932035, 0.002337, 0.000160 },
{ 0.0920486, 0.002316, 0.000087 },
{ 0.0915362, 0.000000, 0.000057 },
{ 0.0909223, 0.014292, 0.002950 },
{ 0.0909178, 0.000000, 0.000101 },
{ 0.0903302, 0.002261, 0.000156 },
{ 0.0585008, 0.089697, 0.078271 },
{ 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 },
{ 0.0831051, 0.002088, 0.000051 },
{ 0.0829235, 0.005841, 0.006803 },
{ 0.0828709, 0.002083, 0.000063 },
{ 0.0824031, 0.004719, 0.002548 },
{ 0.0805004, 0.002028, 0.000058 },
{ 0.0801760, 0.000019, 0.000000 },
{ 0.0776552, 0.000012, 0.000133 },
{ 0.0755097, 0.005767, 0.017169 },
{ 0.0752280, 0.000083, 0.000049 },
{ 0.0750004, 0.001874, 0.000066 },
{ 0.0737291, 0.001851, 0.000119 },
{ 0.0718922, 0.005260, 0.006839 },
{ 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 },
{ 0.0650640, 0.001653, 0.000084 },
{ 0.0643910, 0.003236, 0.000104 },
{ 0.0643077, 0.003626, 0.000118 },
{ 0.0640864, 0.000767, 0.007024 },
{ 0.0633090, 0.000680, 0.006279 },
{ 0.0631287, 0.003177, 0.000038 },
{ 0.0622945, 0.001764, 0.000987 },
{ 0.0617621, 0.001669, 0.001381 },
{ 0.0610645, 0.001547, 0.000186 },
{ 0.0610286, 0.034491, 0.021496 },
{ 0.0605601, 0.001685, 0.001334 },
{ 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 } ...
*/
static double M_PHASE[226][3] = {
{ 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 },
{ 0.004280309127, 179.942703717388, -140.168177475912 },
{ 179.999403180215, 0.057104471446, 29.127407493447 },
{ -179.986595625958, -0.009533448592, -7.291531705498 },
{ 0.004516315551, 179.946856948035, -147.990210285414 },
{ -2.292723477875, 179.558678822974, 99.917394355623 },
{ -179.995813706528, 174.359278613627, 85.899138385237 },
{ -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 },
{ -73.684186429799, 66.397350353519, -166.301305668267 },
{ -179.993990076579, -136.968231614654, 90.111372676863 },
{ 178.195523468679, 167.215437886350, 100.414547150000 },
{ 33.641453360113, -165.302705060093, -60.601265278652 },
{ -69.150402372136, -59.249946857851, -144.807244596642 },
{ -112.036976032111, -23.538862057265, -19.703539149818 },
{ 71.225252170846, 89.953326699449, 149.522242168418 },
{ -106.906299285279, -128.752837957579, -35.167482742815 },
{ 0.008709768323, 179.926987734485, -128.528021306430 },
{ 125.434998080106, -144.834917590238, 33.658347760855 },
{ 0.009988580138, 179.896870091933, -116.342563520000 },
{ -112.167984339780, -118.315481678004, -31.324502874434 },
{ 0.001914516745, 179.958829517227, -128.259077640388 },
{ 178.919893127688, 111.151535580000, 127.496580553665 },
{ 179.997049090149, 0.013601633772, -2.620698856245 },
{ -72.167265771598, -161.189710332737, 19.930112286947 },
{ -111.985346564208, -23.928553663926, -20.132412817928 },
{ 29.213939211730, 160.784938812168, -84.562976989473 },
{ 54.598102587697, -34.751396609636, 146.388967571845 },
{ 179.997627140643, -20.956099913023, -107.488668694704 },
{ 125.438781294500, -144.945781138477, 33.725620650288 },
{ 0.011052840008, 12.898827180000, -89.856260770306 },
{ 179.874812111593, -138.253779548140, 27.781164827339 },
{ -179.995364958510, -152.171377200000, 90.034521688113 },
{ 179.999571716845, 0.088736680056, 43.415194343448 },
{ 15.485979928550, 79.333070815266, 171.905198795860 },
{ 15.814692146435, 81.813245835498, 173.563281819956 },
{ 131.151069984933, -154.395177439830, -38.414622359212 },
{ -44.655851925818, 117.757239601126, 162.851093530505 },
{ 0.002900038346, 135.182987450000, -89.948686156302 },
{ 1.103187588210, 22.976396007451, -111.078340600000 },
{ -179.887622646628, -0.016270483931, -31.472745223488 },
{ 0.007797056081, 179.864439387698, -138.165985101854 },
{ 54.595537656712, -34.659546623063, 146.299996591100 },
{ -80.604321141847, 23.349211093147, 124.690639100328 },
{ 9.950565354210, -20.646007710451, -20.232712520916 },
{ 0.007228561268, 179.913696450803, -114.674710042095 },
{ 0.000031181430, -179.969483846305, -115.306109670000 },
{ -179.998385048108, 85.733997830000, -94.266002170000 },
{ 126.785821299905, 46.152057795628, 40.582093829691 },
{ 0.000067308052, -58.051764990000, -90.033259843394 },
{ 0.011879132634, 179.748408306343, -114.695467227172 },
{ -170.230856074017, 100.037571146737, -1.882374403492 },
{ -0.844779089926, 176.042515812187, -118.079402338350 },
{ -73.380351208713, 159.697723721737, -39.602387509092 },
{ -179.992838936462, -160.881735064112, 90.089950323242 },
{ 0.008160895360, 179.745911260715, -149.577199957246 },
{ -0.946094322429, 178.710437293623, -77.509104380747 },
{ -179.993591655201, -0.214491674788, 93.905327790000 },
{ 156.746173873619, -64.861968042177, 49.372967047162 },
{ -179.999469648778, -0.016408343945, -35.948330450000 },
{ 37.928299901718, 129.004508305459, 132.215335260474 },
{ 179.998321758011, 0.020516890633, 4.395108701959 },
{ -179.991344977137, 26.519098943619, -31.875040030000 },
{ 0.005727141458, 4.355481318395, -90.149163090774 },
{ -21.479998361998, -146.605834790916, 58.779750145468 },
{ -179.964083052415, -55.875067383234, 47.387971540000 },
{ -0.001625399610, -179.904773285909, 142.248731360116 },
{ -179.993620429096, -0.123104591073, 70.321134490000 },
{ -162.315246851023, -72.633139513377, 112.510164638260 },
{ 0.012390392562, 179.760835926114, -111.438742365499 },
{ -179.872748658637, 50.117769415320, 168.302109917160 },
{ 0.000466648467, 169.116621610000, 79.116621610000 },
{ 68.455744968383, -114.610536287778, -179.414411109053 },
{ -0.002100097173, 179.947053742654, -135.363706761591 },
{ -179.991954083944, -149.820003150000, 89.975569316466 },
{ -102.019559358387, 161.184331716547, 85.320435106082 },
{ 0.000547819855, 179.949477302242, -126.016097727692 },
{ -179.987915461393, -0.051829095371, 5.014976620001 },
{ 0.008347581988, 179.849649173293, -123.589509971061 },
{ 0.006800628510, 179.936140204095, -119.801617824531 },
{ -73.109646466056, 9.949188683703, 119.696875238960 },
{ 38.312689959023, -174.350323749453, 129.275979873543 },
{ 38.530542970871, -178.317385228219, 132.123003310646 },
{ 0.006989175447, -179.665485193957, -124.587860108589 },
{ 177.277845106886, 126.415631259050, -109.793598391998 },
{ -161.442918729888, 2.240961856056, 106.127634621147 },
{ -179.990868095964, -3.697578545908, 7.251882193224 },
{ 61.035930743232, -40.663545438817, -108.996557846408 },
{ -158.629498383529, 16.851256552374, 110.695920982574 },
{ 176.824703041161, -98.747691569943, 85.257139856799 },
{ 177.683627303808, -120.178114678752, -84.678375180739 },
{ 145.813265306575, 165.236834102475, -115.686032935051 },
{ -179.990848592847, -174.767338145272, 87.971105506103 },
{ 179.998967305008, -128.346026290000, -128.346026290000 },
{ 109.706873518703, -161.692320544537, 8.071930386460 },
{ -21.373532585359, -175.453622486338, 97.727650370240 },
{ -76.964196141885, -25.052062779649, -88.184334546093 },
{ 174.044963900841, 69.697068381257, -103.438549174491 },
{ 1.411566523810, -63.763692231235, 96.605146342888 },
{ -0.002484367922, -179.922758430555, 124.122955805312 },
{ -179.975293067009, 0.144068585072, -127.623925030000 },
{ -85.595401423341, 33.309416345973, 52.614419166008 },
{ -2.682922479904, 90.346879348731, 101.825176323036 },
{ -72.194222741362, -164.226260049548, 24.011727797009 },
{ -179.994957071833, -0.078650599201, 64.442567813218 },
{ -167.705956663408, -121.678544311070, 135.639537931150 },
};
/*
* LEA-406 Moon Solution
*
* Reference:
* Long-term harmonic development of lunar ephemeris.
* Kudryavtsev S.M. <Astron. Astrophys. 471, 1069 (2007)>
*
*/
/* compute moon ecliptic longitude using lea406 */
double lea406(double jd, int ignorenutation) {
double t, tm, tm2;
t = (jd - J2000) / 36525.0;
tm = t / 10.0;
tm2 = tm * tm;
double V, arg;
V = FRM[0] + (((FRM[4] * t + FRM[3]) * t + FRM[2]) * t + FRM[1]) * t;
int i;
for (i = 0; i < 226; i++) {
arg = (M_ARG[i][0] + t * (M_ARG[i][1] + M_ARG[i][2] * t)) * ASEC2RAD;
V += M_AMP[i][0] * sin(arg + M_PHASE[i][0] * DEG2RAD)
+ M_AMP[i][1] * sin(arg + M_PHASE[i][1] * DEG2RAD) * tm
+ M_AMP[i][2] * sin(arg + M_PHASE[i][2] * DEG2RAD) * tm2;
}
V *= ASEC2RAD;
if (!ignorenutation) {
V += nutation(jd);
/* printf("debug lea406, nutation been adjusted"); */
}
return V;
}
/* calculate the apparent position of the Moon, it is an alias to the
* lea406 function
*/
double apparentmoon(double jd, int ignorenutation)
{
return lea406(jd, ignorenutation);
}
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