# -*- coding: utf-8 -*-
# PyMeeus: Python module implementing astronomical algorithms.
# Copyright (C) 2018 Dagoberto Salazar
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
from math import sin, cos, tan, acos, atan2, sqrt, radians, log10
from pymeeus.Angle import Angle
from pymeeus.Epoch import Epoch, JDE2000
from pymeeus.Interpolation import Interpolation
from pymeeus.Coordinates import (
geometric_vsop_pos, apparent_vsop_pos, orbital_elements,
nutation_longitude, true_obliquity, ecliptical2equatorial,
passage_nodes_elliptic
)
from pymeeus.Earth import Earth
from pymeeus.Sun import Sun
"""
.. module:: Mars
:synopsis: Class to model Mars planet
:license: GNU Lesser General Public License v3 (LGPLv3)
.. moduleauthor:: Dagoberto Salazar
"""
VSOP87_L = [
# L0
[
[620347711.583, 0.00000000000, 0.00000000000],
[18656368.100, 5.05037100303, 3340.61242669980],
[1108216.792, 5.40099836958, 6681.22485339960],
[91798.394, 5.75478745111, 10021.83728009940],
[27744.987, 5.97049512942, 3.52311834900],
[10610.230, 2.93958524973, 2281.23049651060],
[12315.897, 0.84956081238, 2810.92146160520],
[8926.772, 4.15697845939, 0.01725365220],
[8715.688, 6.11005159792, 13362.44970679920],
[6797.552, 0.36462243626, 398.14900340820],
[7774.867, 3.33968655074, 5621.84292321040],
[3575.079, 1.66186540141, 2544.31441988340],
[4161.101, 0.22814975330, 2942.46342329160],
[3075.250, 0.85696597082, 191.44826611160],
[2628.122, 0.64806143570, 3337.08930835080],
[2937.543, 6.07893711408, 0.06731030280],
[2389.420, 5.03896401349, 796.29800681640],
[2579.842, 0.02996706197, 3344.13554504880],
[1528.140, 1.14979306228, 6151.53388830500],
[1798.808, 0.65634026844, 529.69096509460],
[1264.356, 3.62275092231, 5092.15195811580],
[1286.232, 3.06795924626, 2146.16541647520],
[1546.408, 2.91579633392, 1751.53953141600],
[1024.907, 3.69334293555, 8962.45534991020],
[891.567, 0.18293899090, 16703.06213349900],
[858.760, 2.40093704204, 2914.01423582380],
[832.718, 2.46418591282, 3340.59517304760],
[832.724, 4.49495753458, 3340.62968035200],
[712.899, 3.66336014788, 1059.38193018920],
[748.724, 3.82248399468, 155.42039943420],
[723.863, 0.67497565801, 3738.76143010800],
[635.557, 2.92182704275, 8432.76438481560],
[655.163, 0.48864075176, 3127.31333126180],
[550.472, 3.81001205408, 0.98032106820],
[552.746, 4.47478863016, 1748.01641306700],
[425.972, 0.55365138172, 6283.07584999140],
[415.132, 0.49662314774, 213.29909543800],
[472.164, 3.62547819410, 1194.44701022460],
[306.552, 0.38052862973, 6684.74797174860],
[312.141, 0.99853322843, 6677.70173505060],
[293.199, 4.22131277914, 20.77539549240],
[302.377, 4.48618150321, 3532.06069281140],
[274.028, 0.54222141841, 3340.54511639700],
[281.073, 5.88163372945, 1349.86740965880],
[231.185, 1.28240685294, 3870.30339179440],
[283.600, 5.76885494123, 3149.16416058820],
[236.114, 5.75504515576, 3333.49887969900],
[274.035, 0.13372501211, 3340.67973700260],
[299.396, 2.78323705697, 6254.62666252360],
[204.161, 2.82133266185, 1221.84856632140],
[238.857, 5.37155471672, 4136.91043351620],
[188.639, 1.49103016486, 9492.14631500480],
[221.225, 3.50466672203, 382.89653222320],
[179.196, 1.00561112574, 951.71840625060],
[172.110, 0.43943041719, 5486.77784317500],
[193.126, 3.35715137745, 3.59042865180],
[144.305, 1.41874193418, 135.06508003540],
[160.011, 3.94854735192, 4562.46099302120],
[174.068, 2.41360332576, 553.56940284240],
[130.993, 4.04491720264, 12303.06777661000],
[138.245, 4.30145176915, 7.11354700080],
[128.062, 1.80665643332, 5088.62883976680],
[139.897, 3.32592516164, 2700.71514038580],
[128.102, 2.20806651008, 1592.59601363280],
[116.945, 3.12805282207, 7903.07341972100],
[110.375, 1.05195079687, 242.72860397400],
[113.486, 3.70070798123, 1589.07289528380],
[100.090, 3.24343740861, 11773.37681151540],
[95.592, 0.53954181149, 20043.67456019880],
[98.947, 4.84558294740, 6681.24210705180],
[104.541, 0.78535382076, 8827.39026987480],
[84.187, 3.98970720730, 4399.99435688900],
[86.931, 2.20186740523, 11243.68584642080],
[71.437, 2.80307550016, 3185.19202726560],
[72.091, 5.84672102525, 5884.92684658320],
[73.476, 2.18428012567, 8429.24126646660],
[98.946, 2.81481140371, 6681.20759974740],
[68.414, 2.73834914412, 2288.34404351140],
[86.751, 1.02092221563, 7079.37385680780],
[65.320, 2.68118597578, 28.44918746780],
[83.749, 3.20256130990, 4690.47983635860],
[75.034, 0.76643418252, 6467.92575796160],
[68.984, 3.76399731788, 6041.32756708560],
[66.706, 0.73630620766, 3723.50895892300],
[63.314, 4.52771470470, 426.59819087600],
[61.683, 6.16831509419, 2274.11694950980],
[52.256, 0.89941531307, 9623.68827669120],
[55.488, 4.60625467020, 4292.33083295040],
[51.332, 4.14823636534, 3341.59274776800],
[56.629, 5.06250410206, 15.25247118500],
[63.376, 0.91296240798, 3553.91152213780],
[45.829, 0.78784235062, 1990.74501704100],
[48.542, 3.95670418719, 4535.05943692440],
[41.223, 6.02019329922, 3894.18182954220],
[41.939, 3.58326425115, 8031.09226305840],
[56.396, 1.68727150304, 6872.67311951120],
[55.909, 3.46260833495, 263.08392337280],
[51.678, 2.81307492682, 3339.63210563160],
[40.671, 3.13832621829, 9595.23908922340],
[38.107, 0.73401946320, 10025.36039844840],
[39.495, 5.63225392160, 3097.88382272579],
[44.174, 3.19529736702, 5628.95647021120],
[36.716, 2.63720775102, 692.15760122680],
[45.905, 0.28718981497, 5614.72937620960],
[38.352, 5.82880707426, 3191.04922956520],
[38.206, 2.34835984063, 162.46663613220],
[32.562, 0.48400659333, 6681.29216370240],
[37.135, 0.68508150774, 2818.03500860600],
[31.168, 3.98160912982, 20.35531939880],
[32.561, 0.89250316888, 6681.15754309680],
[37.752, 4.15482955299, 2803.80791460440],
[33.626, 6.11992401052, 6489.77658728800],
[29.007, 2.42707385674, 3319.83703120740],
[38.790, 1.35198498795, 10018.31416175040],
[33.148, 1.14023770004, 5.52292430740],
[27.584, 1.59691203058, 7210.91581849420],
[28.686, 5.72055456734, 7477.52286021600],
[34.031, 2.59544082509, 11769.85369316640],
[25.380, 0.52093116112, 10.63666534980],
[26.357, 1.34532646574, 3496.03282613400],
[24.554, 4.00323183088, 11371.70468975820],
[25.637, 0.24963523420, 522.57741809380],
[27.278, 4.55645328122, 3361.38782219220],
[23.764, 1.84058377256, 12832.75874170460],
[22.816, 3.52628212106, 1648.44675719740],
[22.274, 0.72106133721, 266.60704172180],
[21.202, 3.11824472284, 2957.71589447660],
[20.158, 3.67131504946, 1758.65307841680],
[21.530, 6.15388757177, 3264.34635542420],
[20.093, 1.08247416065, 7064.12138562280],
[21.343, 4.28218757863, 4032.77002792660],
[27.540, 6.08389942337, 6674.11130639880],
[19.849, 2.37668920745, 10713.99488132620],
[25.512, 3.43242352804, 3443.70520091840],
[22.542, 5.64861703438, 2388.89402044920],
[24.378, 0.96994696413, 632.78373931320],
[23.079, 4.74990214223, 3347.72597370060],
[17.709, 3.69742343974, 3344.20285535160],
[22.662, 3.95446324417, 4989.05918389720],
[22.604, 5.24082917494, 3205.54734666440],
[16.811, 5.48619684111, 3.88133535800],
[18.422, 4.22535881468, 2787.04302385740],
[22.737, 4.98520896596, 7632.94325965020],
[16.648, 2.52823633184, 14584.29827312060],
[20.963, 4.27878216453, 5099.26550511660],
[16.042, 1.76786752521, 3475.67750673520],
[15.816, 3.13240869691, 59.37386191360],
[18.113, 3.25756020453, 3337.02199804800],
[19.295, 3.23911854642, 7.04623669800],
[16.772, 4.39731507110, 15643.68020330980],
[17.555, 4.09197396097, 74.78159856730],
[13.704, 2.54117018160, 4933.20844033260],
[16.011, 1.54669633224, 14054.60730802600],
[13.547, 4.04152185347, 4929.68532198360],
[14.566, 3.45210993051, 7373.38245462640],
[13.926, 5.40797129468, 10973.55568635000],
[14.246, 0.59808746067, 23.87843774780],
[14.023, 1.44218648988, 10404.73381232260],
[16.051, 3.79409950488, 2118.76386037840],
[13.714, 3.59050634457, 15113.98923821520],
[18.038, 4.25391532000, 2487.41604494780],
[15.846, 0.56901288692, 103.09277421860],
[13.403, 5.16920432994, 10213.28554621100],
[16.069, 2.36895958451, 3265.83082813250],
[12.773, 0.10483085657, 7234.79425624200],
[12.199, 1.73079687044, 36.02786667740],
[12.283, 5.19940030635, 10021.85453375160],
[11.945, 5.47997890162, 2921.12778282460],
[11.890, 4.76593905835, 5828.02847164760],
[12.283, 3.16862882612, 10021.82002644720],
[13.274, 6.17806905340, 1744.42598441520],
[11.777, 5.72731550900, 0.42007609361],
[12.340, 2.52146766331, 2906.90068882300],
[14.458, 4.38010658432, 316.39186965660],
[10.639, 3.45016942919, 639.89728631400],
[10.925, 0.60397688999, 5085.03841111500],
[10.645, 5.47696728127, 419.48464387520],
[10.797, 1.37191539718, 10419.98628350760],
[10.565, 1.09061610786, 12168.00269657460],
[9.578, 4.89489266197, 3230.40610548040],
[9.808, 5.83632873998, 14314.16811304980],
[9.720, 6.28282606427, 9225.53927328300],
[9.146, 1.10220667397, 9808.53818466140],
[12.733, 1.79883375851, 13745.34623902240],
[9.779, 3.60056884868, 206.18554843720],
[12.156, 4.42295240981, 14712.31711645800],
[8.801, 3.97218590685, 170.67287061920],
[10.685, 4.33894776374, 7740.60678358880],
[10.041, 1.38294666830, 3583.34103067380],
[8.499, 4.29275471153, 0.42988312670],
[9.882, 2.69148019691, 36.60536530420],
[10.585, 0.89641284928, 23384.28698689860],
[8.478, 2.86886131803, 9381.93999378540],
[9.560, 4.33382353581, 131.54196168640],
[8.433, 3.15239733970, 6525.80445396540],
[7.517, 1.24476310635, 6894.52394883760],
[6.753, 1.58869332894, 6836.64525283380],
[6.666, 4.38910103043, 66.48740891440],
[6.697, 5.77315870484, 5202.35827933520],
[6.188, 1.57847967850, 3325.35995551480],
[8.392, 2.90734956761, 43.71891230500],
[6.427, 6.03333185624, 574.34479833480],
[6.296, 0.06976040737, 1964.83862685400],
[6.144, 5.43713363624, 1861.74585263540],
[8.180, 0.43967386003, 2707.82868738660],
[6.532, 1.24907069366, 12964.30070339100],
[7.341, 4.95693808975, 3767.21061757580],
[6.134, 3.16322441707, 6680.24453233140],
[5.937, 4.22752447794, 4459.36821880260],
[5.848, 4.30379700916, 7875.67186362420],
[5.895, 0.77226207039, 2699.73481931760],
[5.962, 3.01318151415, 3369.06161416760],
[6.307, 1.77830983983, 2178.13772229200],
[6.103, 4.49866000852, 6682.20517446780],
[5.770, 0.96127853878, 13916.01910964160],
[5.725, 4.93042706875, 2384.32327072920],
[7.576, 6.16308742022, 6531.66165626500],
[7.285, 0.52756973131, 10575.40668294180],
[5.212, 3.48999909365, 12935.85151592320],
[5.266, 4.51201042373, 6144.42034130420],
[6.632, 3.48100908925, 1118.75579210280],
[5.182, 3.25459432228, 2391.43681773000],
[5.214, 0.01023839897, 533.21408344360],
[5.436, 6.18510045571, 8425.65083781480],
[5.491, 3.42235890731, 3134.42687826260],
[5.773, 3.55190490896, 8969.56889691100],
[5.093, 0.60873962999, 8955.34180290940],
[4.798, 4.63144694279, 4569.57454002200],
[5.773, 5.92316959013, 640.87760738220],
[5.661, 0.75892958537, 3120.19978426100],
[4.912, 1.70762118141, 13358.92658845020],
[5.438, 4.29256867866, 3503.07906283200],
[4.631, 3.34058594066, 3116.26763099790],
[5.823, 2.39009621568, 3302.47939106200],
[5.095, 1.12497131307, 5331.35744374080],
[4.409, 1.38708732950, 17256.63153634140],
[4.193, 0.19116539271, 9830.38901398780],
[4.164, 0.43798301495, 1066.49547719000],
[4.220, 1.69427060019, 13524.91634293140],
[5.192, 3.63500646439, 536.80451209540],
[5.664, 0.50446281443, 5305.45105355380],
[5.264, 5.40031180025, 3355.86489788480],
[5.403, 5.96867227489, 3074.00538497800],
[4.046, 0.83826342101, 10021.90459040220],
[4.153, 3.14497570817, 8439.87793181640],
[4.820, 1.09025983917, 13365.97282514820],
[4.906, 3.73078406569, 1228.96211332220],
[4.576, 0.99344843456, 6158.64743530580],
[4.211, 3.87091723842, 3312.16323923200],
[4.917, 6.25051681717, 17654.78053974960],
[3.597, 6.07298181151, 10818.13528691580],
[3.547, 1.87663674277, 17395.21973472580],
[3.734, 1.37011069213, 3973.39616601300],
[4.422, 2.89974680697, 6247.51311552280],
[3.975, 4.03441621102, 1052.26838318840],
[4.466, 4.59188422424, 5518.75014899180],
[3.445, 4.26610076208, 3178.14579056760],
[3.607, 4.24527056399, 8329.67161059700],
[3.511, 1.95133364438, 10177.25767953360],
[3.300, 0.68865737747, 149.56319713460],
[3.235, 3.90171358031, 27.40155609680],
[3.946, 5.81982010903, 6261.74020952440],
[3.387, 0.14377701728, 10014.72373309860],
[3.374, 0.74722238154, 6048.44111408640],
[3.090, 3.98540766861, 2648.45482547300],
[3.821, 5.23987859516, 5724.93569742900],
[3.026, 0.34314724795, 220.41264243880],
[4.052, 1.24671617482, 10021.76996979660],
[2.937, 0.73100893561, 2.75151061100],
[3.084, 3.79925632319, 169.58018313300],
[4.040, 2.91258200196, 22747.29071487440],
[3.246, 4.90760526525, 6702.00024889200],
[3.223, 0.92640008610, 16865.52876963120],
[2.879, 1.47180601483, 3346.13535100720],
[3.723, 0.49978317761, 1.48447270830],
[2.798, 3.26910698548, 9168.64089834740],
[3.347, 0.68791690253, 3863.18984479360],
[3.440, 2.77706064625, 6660.44945790720],
[2.798, 2.79673379094, 16858.48253293320],
[2.753, 4.41190782119, 3415.39402526710],
[2.703, 0.19222683184, 3237.51965248120],
[2.719, 3.26628341377, 3914.95722503460],
[2.941, 3.76169133143, 6784.31762761820],
[3.078, 5.48104322207, 3335.08950239240],
[2.701, 5.08537226206, 6688.33840040040],
[2.606, 4.83032556909, 4672.66731424060],
[2.883, 2.64068086362, 3320.25710730100],
[3.089, 4.39619824300, 1332.05488754080],
[3.438, 1.93467064449, 10551.52824519400],
[3.433, 0.20933510815, 6604.95878212400],
[2.513, 2.88151502604, 17924.91069982040],
[2.683, 3.68680362407, 3603.69635007260],
[2.696, 2.66931776730, 10184.30391623160],
[2.386, 1.05710815775, 3607.21946842160],
[2.444, 3.46901444423, 6298.32832117640],
[2.566, 5.55941956468, 6546.15977336420],
[2.354, 0.85896789940, 3351.24909204960],
[2.304, 6.07210985790, 1214.73501932060],
[2.387, 4.30419979225, 3360.96774609859],
[3.109, 2.18099805904, 16173.37116840440],
[2.907, 3.43894993113, 2693.60159338500],
[2.550, 4.18354174372, 3546.79797513700],
[2.991, 2.37500894603, 13517.87010623340],
[2.508, 5.99249607455, 5729.50644714900],
[2.202, 5.58486973955, 664.75604513000],
[2.467, 2.81052575497, 15110.46611986620],
[2.154, 3.59696831702, 6677.63442474780],
[2.166, 3.35965682842, 589.06482700820],
[2.112, 4.57048853017, 6127.65545055720],
[2.178, 3.21663279493, 20199.09495963300],
[2.260, 3.62776666288, 7799.98064550240],
[2.703, 5.89441421026, 6438.49624942560],
[2.201, 4.69972051344, 17277.40693183380],
[2.131, 2.51801264340, 1545.35398297880],
[2.093, 4.03688419630, 6684.81528205140],
[2.249, 5.26171743929, 5618.31980486140],
[2.117, 4.80404492675, 3657.00429635640],
[2.265, 3.87401620754, 110.20632121940],
[2.521, 4.21237950687, 2494.52959194860],
[2.492, 6.10452779411, 3329.97576135000],
[2.154, 4.59093274516, 5625.36604155940],
[1.929, 1.21920197307, 21.85082932640],
[2.343, 0.90613584736, 227.47613278900],
[1.871, 2.03707390080, 56.89837493560],
[1.894, 4.12432529517, 3399.98628861340],
[2.271, 3.78951734652, 7910.18696672180],
[1.876, 3.02034887080, 4885.96640967860],
[2.145, 4.74972617629, 18984.29263000960],
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[0.096, 4.29245810274, 7906.59653807000],
[0.096, 3.08847844641, 3468.63127003720],
[0.095, 6.09186084700, 10037.08975128440],
[0.094, 1.79812841802, 20047.19767854780],
[0.110, 4.24859410294, 3337.07205469860],
[0.093, 2.17945548408, 16066.06586147480],
[0.115, 5.44548079869, 11353.89216764020],
[0.098, 1.89605054783, 33406.12426699800],
[0.101, 3.00793005829, 3528.53757446240],
[0.096, 5.40659912420, 5749.86176654780],
[0.113, 3.93443805059, 7167.19690618920],
[0.092, 3.58985964414, 6724.94376570460],
[0.119, 3.90561570260, 11346.77862063940],
[0.097, 2.57280790230, 1747.60737815290],
[0.118, 3.82111723459, 9072.66167112960],
[0.096, 0.72646224606, 3152.68727893721],
[0.092, 6.23928508055, 24491.42579258340],
[0.099, 1.86991802881, 72.05573335480],
[0.094, 1.51091806861, 9801.42463766060],
[0.091, 4.94377681711, 8756.26980147300],
[0.095, 2.58771497236, 11663.17049029600],
[0.093, 0.66092443320, 30.99198474860],
[0.088, 2.47386826588, 17232.75309859360],
[0.100, 0.19616913512, 11883.58313273480],
[0.094, 0.61277732908, 73.63546321960],
[0.091, 6.04139177526, 153.92523352440],
[0.095, 0.30865798871, 29168.59654624120],
[0.110, 6.27936643935, 3337.10656200300],
[0.087, 2.09287965409, 10264.56588407340],
[0.089, 3.27633365389, 3002.36972771680],
[0.091, 1.89622049447, 37895.42629036740],
[0.118, 3.88268323672, 1236.07566032300],
[0.094, 2.27819061990, 4845.90023579280],
[0.085, 3.07438636612, 9983.70424446160],
[0.086, 3.94463425808, 16.76489074700],
[0.099, 4.58890225582, 3774.32416457660],
[0.086, 1.27758598252, 34513.26307268280],
[0.118, 6.10625309129, 454.90936652730],
[0.096, 6.08772700197, 1755.47168467910],
[0.085, 4.73193631802, 4576.68808702280],
[0.116, 0.88573303872, 16511.61386738740],
[0.083, 3.13948373813, 10191.41746323240],
[0.083, 0.36972674664, 9755.23023837760],
[0.112, 2.26524635842, 10006.58480891440],
[0.087, 4.25461508452, 8.16813658240],
[0.087, 5.31716927554, 1868.85939963620],
[0.115, 3.30507830050, 14157.70008224460],
[0.087, 2.90507350729, 36.99559061100],
[0.083, 3.58400049244, 12928.73796892240],
[0.086, 2.46839611271, 113.72943956840],
[0.096, 2.99829695985, 6510.55198278040],
[0.084, 1.34333260788, 4133.38731516720],
[0.093, 2.41895388985, 20040.15144184979],
[0.085, 5.92093268818, 12299.54465826100],
[0.082, 4.71321236549, 7733.49323658800],
[0.081, 5.26971110105, 12199.97500239140],
[0.080, 4.34410099751, 7218.02936549500],
[0.095, 0.02613500045, 2.90101428980],
[0.094, 6.22018441621, 20043.69181385099],
[0.085, 4.66573809999, 8638.94993325280],
[0.079, 2.89839604813, 22854.59602180400],
[0.104, 0.94882888784, 2735.76268599500],
[0.080, 1.68097745917, 12839.87228870540],
[0.085, 1.95515305721, 4686.95671800959],
[0.094, 0.58147434179, 14128.24277124560],
[0.091, 1.16317999954, 3495.96551583120],
[0.084, 4.04104644774, 9815.65173166220],
[0.082, 1.83662951627, 19190.47817844680],
[0.080, 4.04733274699, 3188.71514561460],
[0.084, 2.71620952175, 12089.76868117200],
[0.080, 2.77363158210, 9495.66943335380],
[0.078, 5.77285430206, 10397.60301166960],
[0.084, 0.78188080031, 7214.43893684320],
[0.094, 2.14762315943, 13532.02988993220],
[0.101, 5.76349087526, 1484.93248969420],
[0.082, 3.11421789241, 8446.99147881720],
[0.096, 5.85152670536, 3492.50970778500],
[0.079, 4.69625309523, 5298.33750655300],
[0.097, 3.97960395898, 18208.34994259200],
[0.105, 1.74376904536, 36.64856292950],
[0.094, 4.18941238607, 20043.65730654660],
[0.075, 3.46629875063, 13341.67431130680],
[0.092, 2.67278833288, 6680.79497027290],
[0.075, 4.59723160021, 9993.38809263160],
[0.087, 0.91979096638, 8425.71814811760],
[0.074, 0.42228487063, 48429.28218232440],
[0.074, 0.48470953224, 11456.98494185880],
[0.077, 0.10707484151, 1371.41176345600],
[0.093, 1.38010528069, 3145.64104223920],
[0.075, 5.28061257070, 12306.59089495900],
[0.079, 3.78666386040, 7.57867920960],
[0.073, 4.42902162523, 14.73728232560],
[0.084, 3.41538432898, 6637.50594109460],
[0.093, 3.41302342683, 1596.11913198180],
[0.071, 3.13537213242, 9488.62319665580],
[0.079, 2.33442828498, 12465.53441274220],
[0.078, 2.21525134547, 2810.98877190800],
[0.099, 0.48801369293, 17499.36014031540],
[0.075, 4.10299895268, 5525.86369599260],
[0.071, 4.04186021414, 259.49349472100],
[0.073, 2.20102876718, 30774.50164257480],
[0.074, 4.93439968296, 13517.80279593060],
[0.071, 5.32625652676, 6670.17915313570],
[0.078, 2.17664185326, 13421.82356871280],
[0.088, 5.38469204503, 17762.44406368820],
[0.081, 2.48353174238, 73.60095591520],
[0.092, 1.13088448190, 7747.72033058960],
[0.070, 1.16361323015, 5220.17080145320],
[0.084, 5.83220387910, 22.37827130260],
[0.076, 5.21065604639, 4271.97551355160],
[0.080, 4.01817623627, 3311.18291816379],
[0.068, 2.45937697940, 6279.55273164240],
[0.067, 4.31723563048, 2281.29780681340],
[0.067, 4.88776321797, 4379.63903749020],
[0.069, 3.57006764536, 14955.04572043200],
[0.078, 2.62374773232, 2810.85415130240],
[0.067, 4.76301301456, 6812.76681508600],
[0.070, 5.60319851277, 13383.22510229160],
[0.070, 3.05647570196, 10081.21114201300],
[0.081, 4.91537623765, 3333.92876282570],
[0.082, 5.49204987110, 5483.25472482600],
[0.065, 3.50466797067, 9161.52735134660],
[0.065, 2.79212460026, 13497.51478683460],
[0.070, 0.93640431668, 6106.88005506480],
[0.073, 2.57583496978, 6614.73744448520],
[0.070, 0.84170070580, 16695.94858649819],
[0.069, 1.10040627005, 2544.33167353560],
[0.063, 6.05841309176, 6453.74872061060],
[0.069, 2.67053540192, 2641.34127847220],
[0.086, 1.73112264739, 6286.59896834040],
[0.062, 5.49002783256, 4957.08687808040],
[0.072, 3.38857910283, 3184.21170619740],
[0.069, 5.35281990892, 2544.29716623120],
[0.064, 4.79175268505, 3181.66890891660],
[0.060, 6.18449904353, 3361.94806716680],
[0.065, 1.48236627574, 4819.47900076420],
[0.054, 3.66018290396, 2917.53735417280],
[0.064, 4.72286914683, 2281.16318620780],
[0.053, 4.65521663671, 3448.27595063840],
[0.060, 0.77450276964, 3319.27678623280],
[0.051, 1.45142985881, 3547.31316399640],
[0.051, 4.81258158513, 4403.51747523800],
[0.050, 0.37366902835, 3322.79990458180],
[0.050, 4.68787711774, 3253.30422216000],
[0.067, 4.63578431535, 4694.00295470760],
[0.049, 3.17471347671, 5452.26274007740],
[0.051, 2.54791773443, 4001.84535348080],
[0.048, 2.81171553464, 3372.58473251660],
[0.054, 4.45945188023, 10284.92120347220],
[0.053, 3.85131213520, 9758.75335672660],
[0.051, 1.11244863072, 6901.63749583840],
[0.062, 1.42198009630, 6830.78805053420],
[0.055, 5.61672988180, 45494.58142974879],
[0.054, 0.61701959453, 4716.38622654560],
[0.054, 4.28556326526, 2910.49111747480],
[0.045, 3.14626081312, 13951.51453380740],
[0.050, 4.16235480519, 12979.55317457600],
[0.046, 1.66182208107, 7768.00833968560],
[0.045, 5.07701425888, 14951.52260208300],
[0.043, 4.31723459530, 5881.40372823420],
[0.045, 2.39713581676, 8852.24902869080],
[0.043, 2.10202660495, 3337.15661865360],
[0.048, 0.19934255781, 1905.46476494040],
[0.056, 5.25687695855, 12808.88030395680],
[0.049, 2.06320966659, 4296.90158267040],
[0.042, 6.07282126953, 4295.85395129940],
[0.043, 1.74571613780, 3130.83644961080],
[0.050, 2.27112469544, 3427.92063123960],
[0.050, 0.30214747765, 3358.42494881780],
[0.043, 5.05297177283, 3229.42578441220],
[0.054, 6.11998016428, 16894.51039961060],
[0.043, 1.90603004035, 3451.79906898740],
[0.039, 0.50727886431, 10011.20061474960],
[0.052, 3.17851184154, 2324.94940881560],
[0.038, 4.88249540246, 3499.55594448300],
[0.039, 5.28113083211, 3343.15522398060],
[0.039, 4.98185580267, 3468.56395973440],
[0.047, 2.16244218985, 10027.36020440680],
[0.037, 5.84953090935, 6791.43117461900],
[0.048, 5.03779546898, 7064.10413197060],
[0.038, 0.58076516432, 8966.38750317330],
[0.051, 3.36181117037, 8976.68244391180],
[0.042, 4.13725767158, 8336.78515759780],
[0.038, 5.75425648893, 4531.53631857540],
[0.038, 3.55681323215, 5351.71276313960],
[0.040, 2.79414141035, 3067.93946934820],
[0.040, 4.99798468494, 10042.19259949820],
[0.037, 1.82286411009, 10017.95594474140],
[0.036, 6.02115369796, 6474.52411610300],
[0.044, 3.01299253859, 7417.10136693140],
[0.045, 2.33470159894, 3123.79021291280],
[0.039, 4.91767933978, 8034.61538140740],
],
# L1
[
[334085627474.342, 0.00000000000, 0.00000000000],
[1458227.051, 3.60426053609, 3340.61242669980],
[164901.343, 3.92631250962, 6681.22485339960],
[19963.338, 4.26594061030, 10021.83728009940],
[3452.399, 4.73210386365, 3.52311834900],
[2485.480, 4.61277567318, 13362.44970679920],
[841.551, 4.45858256765, 2281.23049651060],
[537.566, 5.01589727492, 398.14900340820],
[521.041, 4.99422678175, 3344.13554504880],
[432.614, 2.56066402860, 191.44826611160],
[429.656, 5.31646162367, 155.42039943420],
[381.747, 3.53881289437, 796.29800681640],
[314.129, 4.96335266049, 16703.06213349900],
[282.804, 3.15967518204, 2544.31441988340],
[205.664, 4.56891455660, 2146.16541647520],
[168.805, 1.32894813366, 3337.08930835080],
[157.587, 4.18501035954, 1751.53953141600],
[133.686, 2.23325104196, 0.98032106820],
[116.561, 2.21347652545, 1059.38193018920],
[117.591, 6.02407213861, 6151.53388830500],
[113.595, 5.42803224317, 3738.76143010800],
[133.563, 5.97421903927, 1748.01641306700],
[91.098, 1.09627836591, 1349.86740965880],
[83.301, 5.29636626272, 6684.74797174860],
[113.876, 2.12869455089, 1194.44701022460],
[80.776, 4.42813405865, 529.69096509460],
[79.531, 2.24864266330, 8962.45534991020],
[72.505, 5.84208163240, 242.72860397400],
[72.946, 2.50189460554, 951.71840625060],
[71.487, 3.85636094435, 2914.01423582380],
[85.342, 3.90854841008, 553.56940284240],
[67.582, 5.02327686473, 382.89653222320],
[65.089, 1.01802439311, 3340.59517304760],
[65.089, 3.04879603978, 3340.62968035200],
[61.508, 4.15183159800, 3149.16416058820],
[48.477, 4.87362121538, 213.29909543800],
[46.584, 1.31452419914, 3185.19202726560],
[56.520, 3.88813699320, 4136.91043351620],
[47.613, 1.18238046057, 3333.49887969900],
[41.343, 0.71385375517, 1592.59601363280],
[40.055, 5.31611875491, 20043.67456019880],
[40.272, 2.72542480614, 7.11354700080],
[32.886, 5.41067411968, 6283.07584999140],
[28.244, 0.04534124888, 9492.14631500480],
[22.294, 5.88516997273, 3870.30339179440],
[22.431, 5.46592525433, 20.35531939880],
[22.612, 0.83775884934, 3097.88382272579],
[21.418, 5.37934044204, 3340.54511639700],
[23.335, 6.16762213077, 3532.06069281140],
[26.579, 3.88960724782, 1221.84856632140],
[22.797, 1.54504711003, 2274.11694950980],
[20.431, 2.36353950189, 1589.07289528380],
[20.186, 3.36375535766, 5088.62883976680],
[26.554, 5.11271747607, 2700.71514038580],
[19.675, 2.57805423988, 12303.06777661000],
[19.468, 0.49216434489, 6677.70173505060],
[21.104, 3.52525428062, 15.25247118500],
[21.425, 4.97081508139, 3340.67973700260],
[18.505, 5.57863503922, 1990.74501704100],
[17.811, 6.12537931996, 4292.33083295040],
[16.472, 2.60291845066, 3341.59274776800],
[16.599, 1.25519718278, 3894.18182954220],
[19.455, 2.53112676345, 4399.99435688900],
[15.000, 1.03464802434, 2288.34404351140],
[20.029, 4.73119428749, 4690.47983635860],
[15.381, 2.47009470350, 4535.05943692440],
[19.964, 5.78652958398, 7079.37385680780],
[15.307, 2.26515985343, 3723.50895892300],
[14.705, 3.36979890389, 6681.24210705180],
[13.535, 2.12334410410, 5486.77784317500],
[12.950, 5.61929676688, 10025.36039844840],
[12.682, 2.95022113262, 3496.03282613400],
[13.644, 1.97739547259, 5614.72937620960],
[13.013, 1.51424752315, 5628.95647021120],
[14.705, 1.33902715586, 6681.20759974740],
[11.353, 6.23438193885, 135.06508003540],
[13.275, 3.42243595774, 5621.84292321040],
[10.867, 5.28184140482, 2818.03500860600],
[11.850, 3.12701832949, 426.59819087600],
[10.472, 2.73581537999, 2787.04302385740],
[11.132, 5.84178807242, 2803.80791460440],
[11.764, 2.58551521265, 8432.76438481560],
[11.854, 5.47630686910, 3553.91152213780],
[8.490, 1.91378007528, 11773.37681151540],
[9.708, 4.52957217749, 6489.77658728800],
[8.562, 3.16141186861, 162.46663613220],
[10.958, 4.15771850822, 2388.89402044920],
[8.133, 1.61295625304, 2957.71589447660],
[8.840, 4.23294294197, 7477.52286021600],
[8.034, 5.69983564288, 6041.32756708560],
[8.344, 2.18273563186, 23.87843774780],
[7.696, 5.71877332978, 9623.68827669120],
[8.695, 4.43542512603, 5092.15195811580],
[8.434, 3.16292250873, 3347.72597370060],
[6.664, 5.07517838003, 8031.09226305840],
[8.650, 4.33256981793, 3339.63210563160],
[7.372, 6.17831593269, 3583.34103067380],
[5.726, 3.68120120299, 8429.24126646660],
[6.186, 3.54165967734, 692.15760122680],
[5.438, 1.05129689580, 4933.20844033260],
[6.108, 1.66240879939, 6525.80445396540],
[5.154, 1.14703246368, 28.44918746780],
[4.850, 5.29254832907, 6681.29216370240],
[5.467, 6.12511022569, 2487.41604494780],
[4.866, 3.10475368803, 5.52292430740],
[6.360, 2.11896608283, 5884.92684658320],
[5.223, 0.37446264120, 12832.75874170460],
[4.710, 0.23326120326, 36.02786667740],
[4.954, 2.44806818502, 5099.26550511660],
[4.861, 5.60505298870, 6467.92575796160],
[4.706, 0.02998416568, 7210.91581849420],
[4.845, 5.70115105957, 6681.15754309680],
[5.496, 2.01006612503, 522.57741809380],
[4.964, 1.51006845561, 1744.42598441520],
[4.443, 0.31208413867, 10018.31416175040],
[5.381, 0.18359380473, 2942.46342329160],
[4.075, 3.95582108330, 3.88133535800],
[5.462, 0.19274227117, 7632.94325965020],
[4.110, 1.59535768711, 7234.79425624200],
[4.287, 2.87635993968, 2810.92146160520],
[5.276, 2.22638595594, 3127.31333126180],
[4.450, 4.17005729081, 2906.90068882300],
[5.144, 5.66878565669, 23384.28698689860],
[3.844, 2.26442183160, 2699.73481931760],
[3.514, 1.76463961051, 1758.65307841680],
[3.351, 2.66194137496, 4929.68532198360],
[4.299, 4.43057446968, 640.87760738220],
[3.140, 1.75866226873, 9595.23908922340],
[3.716, 2.91969220147, 15643.68020330980],
[3.249, 6.13937134379, 10419.98628350760],
[3.077, 2.56115174488, 7064.12138562280],
[3.208, 2.32519453080, 5085.03841111500],
[2.930, 1.27797225349, 574.34479833480],
[2.771, 1.75664216142, 639.89728631400],
[3.325, 2.58945297384, 2118.76386037840],
[3.187, 2.86646751510, 7740.60678358880],
[2.780, 0.43157089331, 5828.02847164760],
[2.824, 0.98500544471, 3191.04922956520],
[3.016, 1.86555882509, 7.04623669800],
[3.364, 1.52847138842, 6674.11130639880],
[2.672, 3.70855172347, 10021.85453375160],
[2.636, 3.11790581052, 6836.64525283380],
[2.672, 1.67778079449, 10021.82002644720],
[2.563, 3.77294986894, 2921.12778282460],
[2.509, 0.30454165124, 3475.67750673520],
[2.400, 0.96972421975, 3319.83703120740],
[2.262, 2.81394314950, 7875.67186362420],
[2.395, 2.96002707485, 6682.20517446780],
[2.210, 0.61263930586, 10973.55568635000],
[2.248, 4.12382007742, 59.37386191360],
[2.426, 5.91508357946, 5331.35744374080],
[2.158, 2.17583545077, 15113.98923821520],
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[0.118, 0.29322259611, 2945.98654164060],
[0.089, 4.49875865671, 21947.11137270000],
[0.104, 1.36766858693, 4032.77002792660],
[0.116, 4.67476277278, 272.67295735160],
[0.105, 3.73327973850, 4989.05918389720],
[0.095, 0.34653808205, 13517.80279593060],
[0.086, 2.70925448214, 7218.02936549500],
[0.112, 5.27572276726, 17499.36014031540],
[0.114, 3.37335971932, 2938.94030494260],
[0.090, 0.26623024836, 9485.03276800400],
[0.086, 3.66786582491, 6997.61672305620],
[0.087, 4.07823608680, 18606.49894600020],
[0.117, 5.61863859185, 16511.61386738740],
[0.084, 2.80171829534, 8584.66166590080],
[0.086, 5.87459621301, 73.60095591520],
[0.090, 1.07789160729, 10721.10842832700],
[0.084, 0.78729386249, 146.81168652360],
[0.112, 2.31690430881, 9638.94074787620],
[0.083, 5.90575201511, 16858.41522263039],
[0.082, 4.31690557700, 9374.82644678460],
[0.083, 1.41315204958, 22854.59602180400],
[0.084, 0.90320571725, 2171.02417529120],
[0.082, 1.59442952041, 9947.05568153210],
[0.082, 0.44163602941, 4782.87363546000],
[0.086, 5.18335054161, 12410.73130054860],
[0.085, 3.61669636863, 8965.97846825920],
[0.097, 5.35511765140, 4996.17273089800],
[0.085, 2.36814442737, 1062.90504853820],
[0.078, 1.75580354602, 2060.81785407180],
[0.087, 0.98702744399, 10156.90236013480],
[0.098, 0.35294347682, 23546.75362303080],
[0.101, 1.03298143418, 20040.15144184979],
[0.088, 0.56201084357, 17101.21113690720],
[0.082, 2.65765057749, 12979.55317457600],
[0.085, 1.07007237991, 10706.88133432540],
[0.082, 0.80588396320, 20735.83216142559],
[0.092, 4.87180501294, 9389.05354078620],
[0.078, 3.22869264518, 11925.27409260060],
[0.074, 5.59171946181, 8535.85715903420],
[0.080, 0.42260849968, 956.28915597060],
[0.082, 1.47379060963, 16.83220104979],
[0.073, 3.76950560688, 8859.36257569160],
[0.073, 4.59130182630, 362.12113673080],
[0.072, 5.15373872266, 9872.27408296480],
[0.098, 2.47740242208, 5401.43028077160],
[0.071, 0.08395696279, 15849.86575174700],
[0.078, 0.04212599783, 16703.12944380180],
[0.075, 3.77172360793, 4845.90023579280],
[0.072, 2.01742377451, 1329.51209026000],
[0.076, 0.30413402871, 72.05573335480],
[0.097, 5.15109318550, 1.48447270830],
[0.070, 0.33648335823, 23141.55838292460],
[0.068, 0.34828385806, 20047.19767854780],
[0.078, 1.42772075938, 16063.16484718500],
[0.081, 2.37498404818, 16703.04487984680],
[0.069, 3.66727984195, 13363.43002786740],
[0.067, 1.77194706681, 18451.07854656599],
[0.073, 0.41181711796, 33406.12426699800],
[0.067, 3.15946840380, 8799.98871377800],
[0.067, 4.07602260745, 10448.43547097540],
[0.068, 1.78981361818, 224.34479570190],
[0.066, 1.01449371817, 4193.80880845180],
[0.067, 4.89249339125, 12082.65513417120],
[0.081, 0.61914094848, 949.17560896980],
[0.066, 3.39914635235, 10184.30391623160],
[0.064, 5.50528849889, 4936.79886898440],
[0.064, 1.82608235490, 3077.52850332700],
[0.069, 2.48571574894, 10018.24685144760],
[0.064, 2.80447322320, 20809.46762464520],
[0.068, 0.97907335430, 6717.25272007700],
[0.087, 2.45966764758, 7321.12213971360],
[0.062, 1.69131771765, 632.78373931320],
[0.081, 4.40575713075, 16703.07938715119],
[0.063, 3.63625395496, 25685.87280280800],
[0.075, 5.54907590704, 16872.64231663200],
[0.061, 0.33159827734, 12012.58229714040],
[0.063, 3.16314818302, 11670.28403729680],
[0.062, 0.23148800541, 7314.00859271280],
[0.078, 1.65377731167, 11614.43329373220],
[0.068, 1.10866475394, 6155.05700665400],
[0.068, 4.45713540461, 9175.75444534820],
[0.081, 3.66553577428, 15265.88651930040],
[0.068, 5.59792852411, 377.37360791580],
[0.059, 6.25689995147, 41427.48698317880],
[0.072, 3.39739853142, 685.11136452880],
[0.062, 0.11206359088, 14047.49376102520],
[0.057, 4.31819630987, 95.97922721780],
[0.070, 5.98596344975, 6531.66165626500],
[0.066, 5.93804470886, 3490.17562383440],
[0.056, 5.11205539684, 7322.10246078180],
[0.056, 3.36788837326, 4379.63903749020],
[0.056, 2.20908914878, 6688.27109009760],
[0.057, 4.57828186723, 10037.08975128440],
[0.057, 0.04695703833, 24889.57479599160],
[0.065, 2.70973517401, 19617.07636932279],
[0.068, 3.51423189318, 14556.89671702380],
[0.056, 5.94452825242, 21548.96236929180],
[0.056, 3.94541346495, 25665.51748340920],
[0.055, 0.45166365461, 16702.99482319620],
[0.062, 0.05229160039, 14061.72085502680],
[0.055, 1.14774475393, 4459.36821880260],
[0.065, 6.21442820689, 6947.83189512140],
[0.056, 5.01712943722, 485.97205278960],
[0.065, 1.51615558729, 5511.63660199100],
[0.072, 4.90742373357, 25287.72379939980],
[0.057, 5.31542907454, 28628.33622609960],
[0.055, 4.02023620788, 4005.36847182980],
[0.054, 5.51196184505, 44.65383324020],
[0.053, 0.46840976995, 19645.52555679060],
[0.053, 4.51539970261, 9886.77220006400],
[0.069, 3.37092084432, 41.55079098480],
[0.072, 4.66520155151, 6685.10618875760],
[0.052, 2.05209599225, 7366.26890762560],
[0.052, 6.25882226723, 12509.25332504720],
[0.060, 0.33350021257, 13575.74880223720],
[0.059, 5.94433755684, 625.67019231240],
[0.050, 2.65624501709, 10124.93005431800],
[0.068, 2.92105834159, 10025.42770875120],
[0.051, 2.88289068067, 39601.89191244960],
[0.069, 1.09637075565, 24076.44458812540],
[0.052, 2.65290577481, 15650.79375031060],
[0.052, 3.28683313010, 6756.00645196690],
[0.054, 5.34683925496, 6578.13207918100],
[0.054, 2.77410607136, 6705.10329114740],
[0.049, 2.65700209900, 6944.30877677240],
[0.053, 5.67436244967, 1883.08149310240],
[0.048, 5.68336050679, 8646.06348025360],
[0.051, 0.11390643300, 17402.33328172660],
[0.065, 1.03099992649, 4106.40549114620],
[0.060, 1.00159365247, 151.89728108520],
[0.050, 3.84651247899, 45494.58142974879],
[0.047, 3.03959709242, 5408.54382777240],
[0.063, 4.16165369755, 8186.51266249260],
[0.046, 2.69368087378, 16547.64173406480],
[0.051, 2.99576014378, 3774.32416457660],
[0.044, 2.00664763411, 6418.14093002680],
[0.045, 4.01853755929, 19406.67828817460],
[0.058, 3.14474753550, 4025.65648092580],
[0.050, 2.59881540437, 6621.85099148600],
[0.043, 4.87912487459, 6414.61781167780],
[0.042, 5.20400092044, 4447.75123238460],
[0.051, 1.99634375899, 5032.77809620220],
[0.043, 1.28813888865, 6643.09181776180],
[0.040, 0.96801618560, 14591.41182012140],
[0.039, 1.84985100829, 10001.48196070061],
[0.039, 5.69967200167, 6106.88005506480],
[0.038, 3.27498743518, 18052.92954315780],
[0.039, 2.84167905068, 6652.77566593180],
[0.044, 0.57891618854, 16865.52876963120],
[0.043, 4.61937364869, 3341.03250279340],
[0.042, 6.02555835659, 6691.86151874940],
[0.034, 4.97734992350, 6670.58818804980],
[0.033, 1.39167727215, 4825.54491639400],
[0.035, 6.02955363644, 3568.08855948880],
[0.035, 0.31961016732, 6645.19698672220],
[0.032, 5.63043769073, 3511.28529731900],
[0.031, 5.42978464210, 9945.57120882380],
[0.038, 5.66461657503, 3416.87849797540],
[0.030, 0.98518793666, 20426.57109242200],
[0.038, 0.12870962242, 6604.95878212400],
[0.037, 5.48374357342, 3311.18291816379],
[0.032, 6.11106979810, 4392.88080988820],
[0.031, 3.18481282781, 3341.04230982650],
[0.034, 2.32358226279, 9072.66167112960],
[0.039, 4.11042361929, 3312.16323923200],
[0.027, 0.57810321636, 3391.89276456221],
[0.029, 2.48646403166, 9815.65173166220],
[0.031, 0.44265747667, 3451.79906898740],
[0.027, 6.13498177783, 3362.46325602620],
[0.027, 6.21846173482, 5223.69391980220],
[0.027, 2.94945830517, 7203.80227149340],
[0.027, 3.26179855800, 8756.26980147300],
[0.027, 3.94385271700, 23958.63178523340],
[0.033, 3.77237326006, 12808.88030395680],
[0.030, 4.75096367323, 15906.76412668260],
[0.031, 0.88248871193, 3340.18254357310],
[0.025, 0.31303295413, 6571.01853218020],
[0.031, 4.29076841627, 10020.85695903120],
[0.026, 2.22427360058, 10050.28646756720],
[0.025, 0.67881122439, 23937.85638974100],
[0.031, 1.72899093511, 13745.34623902240],
[0.024, 0.20355912395, 3229.42578441220],
[0.032, 3.37195631109, 2284.75361485960],
],
# L2
[
[58015.791, 2.04979463279, 3340.61242669980],
[54187.645, 0.00000000000, 0.00000000000],
[13908.426, 2.45742359888, 6681.22485339960],
[2465.104, 2.80000020929, 10021.83728009940],
[398.379, 3.14118428289, 13362.44970679920],
[222.022, 3.19436080019, 3.52311834900],
[120.957, 0.54325292454, 155.42039943420],
[61.517, 3.48529427371, 16703.06213349900],
[53.638, 3.54191121461, 3344.13554504880],
[34.268, 6.00188499119, 2281.23049651060],
[31.665, 4.14015171788, 191.44826611160],
[29.839, 1.99870679845, 796.29800681640],
[23.168, 4.33403365928, 242.72860397400],
[21.659, 3.44532466378, 398.14900340820],
[16.044, 6.11000472441, 2146.16541647520],
[20.370, 5.42191375400, 553.56940284240],
[14.927, 6.09541783564, 3185.19202726560],
[16.227, 0.65678953303, 0.98032106820],
[14.317, 2.61851897591, 1349.86740965880],
[14.416, 4.01923812101, 951.71840625060],
[11.934, 3.86122163021, 6684.74797174860],
[15.648, 1.22086121940, 1748.01641306700],
[11.260, 4.71822363671, 2544.31441988340],
[13.352, 0.60189008414, 1194.44701022460],
[10.396, 0.25038714677, 382.89653222320],
[9.468, 0.68170713564, 1059.38193018920],
[9.229, 3.83209092321, 20043.67456019880],
[9.005, 3.88271826102, 3738.76143010800],
[7.501, 5.46498630412, 1751.53953141600],
[6.497, 5.47773072872, 1592.59601363280],
[6.311, 2.34104793674, 3097.88382272579],
[6.859, 2.57522504136, 3149.16416058820],
[5.870, 1.14783576679, 7.11354700080],
[6.681, 2.37843690339, 4136.91043351620],
[4.647, 4.42957708526, 6151.53388830500],
[4.166, 3.68631477611, 5614.72937620960],
[4.764, 2.89684755585, 3333.49887969900],
[4.045, 6.12493402657, 5628.95647021120],
[3.653, 4.06679068397, 1990.74501704100],
[3.618, 2.46868561769, 529.69096509460],
[3.277, 0.68101740787, 8962.45534991020],
[3.253, 2.79565340390, 3894.18182954220],
[3.091, 4.56861203364, 3496.03282613400],
[2.921, 5.41458945995, 2914.01423582380],
[2.921, 1.23050883841, 2787.04302385740],
[2.784, 1.38911141844, 4292.33083295040],
[2.620, 1.04061894134, 3341.59274776800],
[2.888, 3.41062353663, 3337.08930835080],
[2.418, 0.96341462666, 4535.05943692440],
[2.357, 4.84628239765, 9492.14631500480],
[2.593, 5.74934234498, 3340.59517304760],
[2.191, 3.26449527357, 213.29909543800],
[2.594, 1.49510566123, 3340.62968035200],
[2.344, 4.18104725028, 10025.36039844840],
[2.630, 4.67640929857, 3583.34103067380],
[2.602, 2.64911714813, 2388.89402044920],
[1.830, 0.97181050149, 1589.07289528380],
[2.416, 1.04749173375, 4399.99435688900],
[2.386, 4.27072575550, 7079.37385680780],
[2.187, 0.16036551231, 6525.80445396540],
[2.344, 0.01425578204, 4690.47983635860],
[1.617, 4.95614491689, 5088.62883976680],
[1.633, 1.10703599922, 12303.06777661000],
[2.126, 0.48290227706, 2700.71514038580],
[1.629, 4.94267977718, 1221.84856632140],
[1.504, 0.11031912519, 2957.71589447660],
[1.759, 3.81170701376, 3723.50895892300],
[1.401, 3.85907867678, 6283.07584999140],
[1.338, 5.29685392418, 6677.70173505060],
[1.763, 2.51660121293, 2810.92146160520],
[1.392, 2.73498041122, 7477.52286021600],
[1.431, 2.97747408389, 6489.77658728800],
[1.236, 3.77245965590, 2699.73481931760],
[1.234, 1.88931735265, 6681.24210705180],
[1.513, 2.92614134711, 640.87760738220],
[1.234, 6.14168429036, 6681.20759974740],
[1.408, 1.54395721611, 3347.72597370060],
[1.038, 5.82880072933, 4933.20844033260],
[1.156, 1.50825464304, 426.59819087600],
[1.362, 4.17794297520, 23384.28698689860],
[1.135, 3.77506455273, 3870.30339179440],
[0.916, 3.81726339298, 5092.15195811580],
[0.853, 3.82520490669, 3340.54511639700],
[1.077, 5.05062828760, 5621.84292321040],
[1.074, 3.81446920470, 3553.91152213780],
[0.847, 3.41702696402, 3340.67973700260],
[0.920, 1.91108056416, 3532.06069281140],
[0.738, 4.25786145387, 9623.68827669120],
[0.908, 4.12911006922, 162.46663613220],
[0.647, 3.10301033831, 7234.79425624200],
[0.800, 5.20674574801, 87.30820453981],
[0.657, 1.57895580467, 2487.41604494780],
[0.650, 2.78932995437, 574.34479833480],
[0.659, 5.16655918817, 12832.75874170460],
[0.712, 5.79288230676, 3339.63210563160],
[0.660, 0.25125103909, 8969.56889691100],
[0.527, 4.62218528897, 10419.98628350760],
[0.607, 3.84724721085, 5486.77784317500],
[0.500, 4.66323134619, 6836.64525283380],
[0.509, 0.32548381735, 8031.09226305840],
[0.613, 1.72250879737, 7632.94325965020],
[0.516, 1.37906978509, 7740.60678358880],
[0.469, 1.31324778369, 7875.67186362420],
[0.442, 5.34515135225, 10018.31416175040],
[0.496, 4.49656852602, 692.15760122680],
[0.544, 1.44465369200, 15643.68020330980],
[0.467, 1.40928870138, 6682.20517446780],
[0.547, 4.42021065522, 5331.35744374080],
[0.433, 1.25048504108, 4929.68532198360],
[0.409, 3.80689273098, 6681.29216370240],
[0.403, 1.57190239310, 6127.65545055720],
[0.401, 4.59976459753, 7210.91581849420],
[0.406, 0.60945437905, 11773.37681151540],
[0.367, 0.97726583907, 6041.32756708560],
[0.361, 0.13117924893, 639.89728631400],
[0.411, 4.21323421517, 6681.15754309680],
[0.441, 4.49050100878, 13365.97282514820],
[0.474, 5.18562524130, 2301.58581590939],
[0.334, 2.21001303889, 10021.85453375160],
[0.370, 5.02880065186, 6923.95345737360],
[0.333, 0.18229887483, 10021.82002644720],
[0.342, 2.49988747611, 6438.49624942560],
[0.320, 1.32374476890, 2118.76386037840],
[0.330, 2.98027481579, 5729.50644714900],
[0.340, 0.51409045792, 9866.41688066520],
[0.283, 4.03219455446, 8955.34180290940],
[0.281, 3.33891891806, 9830.38901398780],
[0.271, 1.53144358045, 1039.02661079040],
[0.252, 3.04356928941, 10818.13528691580],
[0.270, 2.22972724035, 5828.02847164760],
[0.259, 4.24406546278, 6894.52394883760],
[0.237, 5.07818982743, 8429.24126646660],
[0.263, 2.00552313665, 3767.21061757580],
[0.241, 4.06396704332, 7064.12138562280],
[0.250, 0.45422818547, 6298.32832117640],
[0.240, 1.94655459341, 6688.33840040040],
[0.209, 0.03043017984, 3914.95722503460],
[0.218, 4.53201818250, 26724.89941359840],
[0.246, 3.85272742042, 4562.46099302120],
[0.254, 1.19313236635, 8432.76438481560],
[0.231, 1.70340106651, 2942.46342329160],
[0.209, 3.82345999055, 6467.92575796160],
[0.175, 3.26444055581, 3981.49003408200],
[0.210, 3.55052707697, 10575.40668294180],
[0.162, 5.95176683701, 310.84079886840],
[0.165, 5.04267055142, 10177.25767953360],
[0.198, 0.80464315638, 15113.98923821520],
[0.188, 1.99007233842, 3127.31333126180],
[0.188, 4.55406803143, 12964.30070339100],
[0.163, 2.14874886056, 10973.55568635000],
[0.154, 4.35708331036, 3360.96774609859],
[0.169, 2.40504327781, 3355.86489788480],
[0.164, 5.53875620970, 16173.37116840440],
[0.144, 0.30186831602, 1903.43681250120],
[0.161, 3.18977924032, 6674.11130639880],
[0.135, 1.65570006128, 3325.35995551480],
[0.143, 6.25825818399, 9595.23908922340],
[0.158, 6.14255608340, 8273.82086703240],
[0.170, 5.98413937993, 3320.25710730100],
[0.124, 1.74571336137, 11081.21921028860],
[0.146, 2.22851709304, 3178.14579056760],
[0.126, 5.02927593525, 3475.67750673520],
[0.123, 4.99342648375, 13760.59871020740],
[0.141, 4.56735815490, 10021.76996979660],
[0.118, 5.42945437851, 13358.92658845020],
[0.116, 4.22080571309, 5884.92684658320],
[0.119, 4.09962692144, 10021.90459040220],
[0.124, 1.79723243306, 18984.29263000960],
[0.135, 1.00085140609, 18454.60166491500],
[0.106, 5.76342924005, 2288.34404351140],
[0.103, 0.63812052706, 12310.18132361080],
[0.100, 4.37946945260, 9808.53818466140],
[0.104, 4.01151451052, 13916.01910964160],
[0.125, 4.94825577002, 10551.52824519400],
[0.098, 5.91086068785, 14584.29827312060],
[0.126, 1.55752034021, 8270.29774868340],
[0.098, 2.52869810530, 3191.04922956520],
[0.095, 5.50808311620, 3319.83703120740],
[0.108, 1.67115668669, 11216.28429032400],
[0.090, 1.71281301325, 1505.28780909299],
[0.088, 0.42472333366, 11371.70468975820],
[0.089, 4.83867235269, 16706.58525184800],
[0.106, 1.78998252916, 10022.81760116760],
[0.087, 5.89602688150, 16858.48253293320],
[0.085, 0.55423657166, 13362.43245314700],
[0.091, 1.61117547913, 24093.27678917520],
[0.083, 0.55328893146, 3344.20285535160],
[0.083, 1.06830368571, 3364.49086444760],
[0.084, 6.22980173043, 3369.06161416760],
[0.085, 2.58442459869, 13362.46696045140],
[0.079, 3.08636079495, 2818.03500860600],
[0.077, 1.53791408869, 5459.37628707820],
[0.075, 3.34890581175, 9070.11887384880],
[0.097, 2.99973987655, 3316.73398895200],
[0.084, 5.55309637085, 3427.92063123960],
[0.089, 4.16432726564, 6158.64743530580],
[0.078, 3.72375730390, 13171.00144068760],
[0.083, 0.11917380846, 3337.02199804800],
[0.073, 4.91632010974, 13362.38239649640],
[0.076, 4.52961122356, 708.98980227659],
[0.071, 5.37905772348, 10264.56588407340],
[0.084, 1.93007660929, 9468.26787725700],
[0.073, 5.28498987702, 4845.90023579280],
[0.080, 4.81193020727, 13149.15061136120],
[0.076, 4.77873149036, 8671.96987044060],
[0.069, 0.86312560839, 13207.02930736500],
[0.070, 1.22001285505, 2274.11694950980],
[0.070, 0.53977528244, 13119.72110282519],
[0.070, 0.09801356525, 1437.17561419860],
[0.069, 2.23597403243, 7107.82304427560],
[0.074, 0.67876411085, 16460.33352952499],
[0.068, 0.54393617190, 12935.85151592320],
[0.084, 5.11617356640, 13892.14067189380],
[0.078, 5.27206373031, 853.19638175200],
[0.065, 4.74504626032, 6144.42034130420],
[0.065, 2.89744951086, 7903.07341972100],
[0.089, 5.44755326514, 13517.87010623340],
[0.073, 3.81554166604, 3503.07906283200],
[0.066, 0.47312197978, 3980.50971301380],
[0.065, 1.38901912957, 3253.30422216000],
[0.086, 5.44050231013, 6816.28993343500],
[0.072, 3.44697351738, 14158.74771361560],
[0.086, 4.50213985772, 13362.51701710200],
[0.074, 1.34701853675, 3361.38782219220],
[0.076, 6.04002959430, 5085.03841111500],
[0.065, 0.07623776004, 5099.26550511660],
[0.066, 2.09160717290, 14421.83163698840],
[0.077, 2.75740817982, 19402.79695281660],
[0.059, 3.61679189501, 7322.10246078180],
[0.060, 4.67079289372, 10235.13637553740],
[0.064, 6.17220244155, 9381.93999378540],
[0.066, 0.35824154106, 7255.56965173440],
[0.059, 4.52818219212, 9499.25986200560],
[0.065, 1.86765892646, 11610.91017538320],
[0.074, 3.12276411101, 1107.13880568480],
[0.060, 1.35069679183, 19800.94595622480],
[0.055, 0.64581579779, 6677.63442474780],
[0.055, 0.65206957868, 7373.38245462640],
[0.055, 0.41979092764, 9779.10867612540],
[0.074, 3.85276242820, 2766.26762836500],
[0.056, 2.49261586879, 5642.19824260920],
[0.055, 2.62555306434, 14314.16811304980],
[0.054, 3.95212835807, 4032.77002792660],
[0.055, 0.51062350773, 15110.46611986620],
[0.053, 5.88757767795, 21265.52312652020],
[0.051, 5.99253934388, 21947.11137270000],
[0.049, 5.16723732129, 20047.19767854780],
[0.067, 1.53758821512, 9380.95967271720],
[0.057, 5.34893894346, 17101.21113690720],
[0.049, 1.92678602770, 12721.57209941700],
[0.046, 2.31590320480, 10028.95082710020],
[0.052, 4.92463460288, 16304.91313009080],
[0.050, 1.69803302925, 9225.53927328300],
[0.045, 2.91271003676, 8982.81066930900],
[0.044, 4.38728556203, 12168.00269657460],
[0.047, 4.44933635857, 6872.67311951120],
[0.043, 2.13295656057, 22324.90505670940],
[0.050, 1.34759191325, 8439.87793181640],
[0.044, 0.89037464728, 20752.66436247540],
[0.041, 2.76164156557, 6696.47732458460],
[0.042, 4.45031185062, 10404.73381232260],
[0.044, 3.20262780268, 22743.40937951640],
[0.042, 3.54559408987, 30376.35263916660],
[0.042, 0.82118836477, 20597.24396304120],
[0.052, 4.59037852162, 22345.26037610820],
[0.042, 3.79872109079, 28628.33622609960],
[0.041, 2.36253602080, 16062.18452611680],
[0.050, 1.48377570574, 6040.34724601740],
[0.041, 5.33088551342, 765.79306444640],
[0.039, 1.57984331116, 24889.57479599160],
[0.038, 0.21571600948, 9168.64089834740],
[0.038, 3.47667842127, 1066.49547719000],
[0.052, 0.81427285458, 9638.94074787620],
[0.041, 0.04356010851, 6660.86953400080],
[0.046, 0.89345529755, 16703.04487984680],
[0.044, 0.85335841824, 17468.85519794540],
[0.039, 0.27098916103, 11614.43329373220],
[0.036, 3.93388136028, 33716.96506586640],
[0.047, 3.90896957151, 5244.04923920100],
[0.034, 2.37310468308, 10213.28554621100],
[0.034, 4.85454495742, 14469.58851248400],
[0.035, 1.96497348634, 6702.00024889200],
[0.033, 2.14488758889, 13363.43002786740],
[0.046, 2.92422266239, 16703.07938715119],
[0.035, 1.78692835372, 2648.45482547300],
[0.033, 4.24484480826, 8584.66166590080],
[0.043, 6.09391349922, 6660.44945790720],
[0.035, 5.72426647579, 16699.53901514999],
[0.031, 1.95254273311, 6665.97238221460],
[0.028, 5.88548900893, 19513.98359510420],
[0.030, 4.38908125588, 12295.95422960920],
[0.029, 6.25276686131, 17924.91069982040],
[0.025, 4.89000247975, 30065.51184029820],
[0.026, 2.43119321236, 6518.75821726740],
[0.028, 3.97032105354, 4407.10790388980],
[0.025, 1.88631752737, 4379.63903749020],
[0.028, 3.06196380356, 6247.51311552280],
[0.029, 5.98057498931, 6680.24453233140],
[0.032, 4.65556810177, 6701.58017279840],
[0.026, 0.76018385758, 3863.18984479360],
[0.023, 0.31107548102, 8827.39026987480],
[0.022, 1.11553014451, 6684.81528205140],
[0.020, 4.81193192299, 15508.61512327440],
[0.019, 5.11656455993, 12012.58229714040],
[0.026, 1.07254469525, 8425.65083781480],
[0.021, 2.68436255141, 6261.74020952440],
[0.022, 2.15631095909, 3335.08950239240],
[0.017, 0.03684125273, 3877.41693879520],
[0.017, 2.84467149903, 3344.49376205780],
[0.020, 5.41519706836, 3205.54734666440],
],
# L3
[
[1482.423, 0.44434694876, 3340.61242669980],
[662.095, 0.88469178686, 6681.22485339960],
[188.268, 1.28799982497, 10021.83728009940],
[41.474, 1.64850786997, 13362.44970679920],
[22.661, 2.05267665262, 155.42039943420],
[25.994, 0.00000000000, 0.00000000000],
[8.024, 1.99858757687, 16703.06213349900],
[10.454, 1.58006906385, 3.52311834900],
[4.900, 2.82452457966, 242.72860397400],
[3.782, 2.01914272515, 3344.13554504880],
[3.176, 4.59144897927, 3185.19202726560],
[3.134, 0.65044714325, 553.56940284240],
[1.684, 5.53835848782, 951.71840625060],
[1.511, 5.71795850828, 191.44826611160],
[1.448, 0.45869142895, 796.29800681640],
[1.442, 2.34368495577, 20043.67456019880],
[1.302, 5.36284013048, 0.98032106820],
[1.169, 4.14601161433, 1349.86740965880],
[1.133, 2.38180830662, 6684.74797174860],
[1.037, 1.76892750558, 382.89653222320],
[0.894, 5.33688328934, 1194.44701022460],
[0.807, 2.74798886181, 1748.01641306700],
[0.640, 6.10665147849, 3496.03282613400],
[0.558, 1.85212342360, 398.14900340820],
[0.567, 5.85922384979, 7.11354700080],
[0.647, 3.17645475605, 3583.34103067380],
[0.452, 5.98109989317, 2787.04302385740],
[0.508, 1.01139298015, 3149.16416058820],
[0.519, 4.93376176788, 6525.80445396540],
[0.405, 1.27295444059, 2281.23049651060],
[0.399, 2.32888685659, 3738.76143010800],
[0.472, 0.84411483892, 4136.91043351620],
[0.333, 5.42704539231, 1059.38193018920],
[0.313, 3.70599897858, 3097.88382272579],
[0.281, 5.74581724084, 3341.59274776800],
[0.287, 2.69304799864, 10025.36039844840],
[0.237, 5.68519881994, 4535.05943692440],
[0.215, 2.49494803822, 1990.74501704100],
[0.260, 2.67996877129, 23384.28698689860],
[0.269, 1.10390153866, 2388.89402044920],
[0.186, 4.86408411823, 2957.71589447660],
[0.176, 3.86618588087, 1592.59601363280],
[0.177, 0.85374318134, 3894.18182954220],
[0.191, 4.58805692093, 3337.08930835080],
[0.185, 5.80899316550, 4399.99435688900],
[0.143, 1.15592612974, 7477.52286021600],
[0.173, 2.70622920014, 7079.37385680780],
[0.146, 1.37569151302, 6489.77658728800],
[0.121, 3.24333934982, 9492.14631500480],
[0.116, 5.71639819530, 12303.06777661000],
[0.111, 2.69566947038, 6151.53388830500],
[0.103, 3.53587741373, 6923.95345737360],
[0.097, 5.23712981002, 8962.45534991020],
[0.089, 0.05951324220, 6127.65545055720],
[0.093, 5.29818155587, 9866.41688066520],
[0.084, 5.68544044325, 4292.33083295040],
[0.091, 6.16223680965, 6682.20517446780],
[0.081, 4.32723330620, 4933.20844033260],
[0.077, 5.63189824170, 1589.07289528380],
[0.102, 6.26937663026, 3347.72597370060],
[0.076, 3.05724276091, 13365.97282514820],
[0.063, 3.12770931753, 10419.98628350760],
[0.062, 1.45647168723, 7234.79425624200],
[0.069, 4.82266605869, 6677.70173505060],
[0.064, 1.73713448446, 3870.30339179440],
[0.058, 4.85723088492, 5486.77784317500],
[0.058, 6.09849516790, 7875.67186362420],
[0.063, 4.14716431158, 3340.59517304760],
[0.065, 6.17932665318, 3340.62968035200],
[0.057, 1.48905992502, 5729.50644714900],
[0.060, 6.08710604997, 7740.60678358880],
[0.056, 1.96253427165, 3553.91152213780],
[0.059, 0.89874385953, 3339.63210563160],
[0.053, 3.04776975379, 26724.89941359840],
[0.061, 3.63390789623, 12832.75874170460],
[0.059, 0.22989746040, 6681.24210705180],
[0.053, 3.97996929188, 5092.15195811580],
[0.059, 4.48255178273, 6681.20759974740],
[0.045, 3.88055745121, 10264.56588407340],
[0.058, 4.85371375265, 5621.84292321040],
[0.049, 4.03623343126, 16173.37116840440],
[0.061, 2.90942510134, 5331.35744374080],
[0.043, 1.80990718340, 9830.38901398780],
[0.044, 4.10828944542, 4690.47983635860],
[0.044, 3.49332765553, 13760.59871020740],
[0.048, 1.81207342615, 3723.50895892300],
[0.041, 1.59906754314, 10818.13528691580],
[0.041, 2.05797417369, 6681.29216370240],
[0.038, 3.38619280993, 16706.58525184800],
[0.041, 2.53336616026, 6681.15754309680],
[0.041, 1.79026132252, 3340.54511639700],
[0.050, 4.70324784090, 8273.82086703240],
[0.037, 3.37898394417, 30065.51184029820],
[0.039, 2.65566008587, 6894.52394883760],
[0.035, 2.58475025674, 9623.68827669120],
[0.037, 6.07442797404, 4929.68532198360],
[0.042, 3.04642561189, 12964.30070339100],
[0.037, 5.23784488646, 6298.32832117640],
[0.043, 6.17835198533, 15643.68020330980],
[0.034, 2.44806511268, 7210.91581849420],
[0.038, 0.26295105909, 10022.81760116760],
[0.028, 0.74281728305, 10021.85453375160],
[0.028, 4.99536302577, 10021.82002644720],
[0.034, 5.04118058624, 8969.56889691100],
[0.025, 2.59849002421, 8955.34180290940],
[0.030, 1.14354290938, 2146.16541647520],
[0.027, 0.26980783576, 18984.29263000960],
[0.025, 0.39810308575, 6688.33840040040],
[0.024, 5.64558695441, 13207.02930736500],
[0.027, 6.24398988438, 5088.62883976680],
[0.024, 0.25455613132, 11081.21921028860],
[0.023, 0.53673547304, 3333.49887969900],
[0.024, 1.80155161992, 6674.11130639880],
[0.029, 4.39953507920, 10018.31416175040],
[0.023, 2.91040060956, 10551.52824519400],
[0.022, 1.20895727897, 529.69096509460],
[0.026, 0.08254324904, 7632.94325965020],
[0.026, 1.81668969835, 6283.07584999140],
[0.021, 0.67232850824, 6836.64525283380],
[0.017, 5.19518401928, 2914.01423582380],
[0.017, 5.16488977775, 8031.09226305840],
[0.021, 3.62973082412, 5884.92684658320],
[0.018, 5.06870872024, 2544.31441988340],
[0.014, 2.50522181917, 7064.12138562280],
[0.017, 0.41835598950, 9468.26787725700],
[0.011, 2.21363101654, 6438.49624942560],
[0.013, 1.38424462832, 3340.67973700260],
[0.012, 3.28248484262, 8671.96987044060],
[0.014, 0.23027665815, 3767.21061757580],
],
# L4
[
[113.969, 3.14159265359, 0.00000000000],
[28.725, 5.63662412043, 6681.22485339960],
[24.447, 5.13868481454, 3340.61242669980],
[11.187, 6.03161074431, 10021.83728009940],
[3.190, 3.56267988299, 155.42039943420],
[3.252, 0.13228350651, 13362.44970679920],
[0.787, 0.49340783377, 16703.06213349900],
[0.776, 1.31734531594, 242.72860397400],
[0.494, 3.06356214498, 3185.19202726560],
[0.374, 2.15785846355, 553.56940284240],
[0.331, 6.23159792887, 3.52311834900],
[0.197, 0.44350153983, 3344.13554504880],
[0.181, 0.81531283571, 20043.67456019880],
[0.168, 3.73509781785, 3496.03282613400],
[0.086, 0.79259553758, 6684.74797174860],
[0.115, 1.66898531261, 3583.34103067380],
[0.092, 3.40530361815, 6525.80445396540],
[0.064, 4.47443580658, 2787.04302385740],
[0.045, 5.17216217058, 3097.88382272579],
[0.041, 1.21875027733, 23384.28698689860],
[0.036, 5.53975653407, 3149.16416058820],
[0.039, 5.40966345885, 4136.91043351620],
[0.028, 4.85378781404, 6127.65545055720],
[0.027, 0.42811091036, 3738.76143010800],
[0.032, 1.22337093927, 10025.36039844840],
[0.025, 1.56348878811, 26724.89941359840],
[0.029, 2.40178626971, 3894.18182954220],
[0.023, 4.16371253947, 3341.59274776800],
[0.022, 5.98429191667, 7477.52286021600],
[0.019, 2.03228980685, 6923.95345737360],
[0.020, 3.79275573433, 9866.41688066520],
[0.021, 4.27532111122, 6836.64525283380],
[0.015, 1.56315497374, 13365.97282514820],
[0.011, 1.33261955275, 2281.23049651060],
[0.009, 6.15390464542, 6489.77658728800],
[0.007, 4.23894194106, 4535.05943692440],
],
# L5
[
[0.710, 4.04089996521, 6681.22485339960],
[0.868, 3.14159265359, 0.00000000000],
[0.510, 4.49214901625, 10021.83728009940],
[0.357, 5.07435505061, 155.42039943420],
[0.223, 3.51351884241, 3340.61242669980],
[0.199, 4.85313666795, 13362.44970679920],
[0.100, 6.09089356066, 242.72860397400],
[0.069, 5.19017483537, 16703.06213349900],
[0.064, 1.55783055571, 3185.19202726560],
[0.035, 3.68246171643, 553.56940284240],
[0.025, 5.22079788019, 3496.03282613400],
[0.024, 0.17861991485, 3583.34103067380],
[0.019, 5.59184714460, 20043.67456019880],
[0.014, 5.95565787085, 23384.28698689860],
[0.012, 1.93859256739, 6525.80445396540],
],
]
"""This table contains Mars' periodic terms (all of them) from the planetary
theory VSOP87 for the heliocentric longitude at the equinox of date (taken from
the 'D' solution). In Meeus' book a shortened version can be found in pages
421-424."""
VSOP87_B = [
# B0
[
[3197134.986, 3.76832042432, 3340.61242669980],
[298033.234, 4.10616996243, 6681.22485339960],
[289104.742, 0.00000000000, 0.00000000000],
[31365.538, 4.44651052853, 10021.83728009940],
[3484.100, 4.78812547889, 13362.44970679920],
[442.999, 5.65233015876, 3337.08930835080],
[443.401, 5.02642620491, 3344.13554504880],
[399.109, 5.13056814700, 16703.06213349900],
[292.506, 3.79290644595, 2281.23049651060],
[181.982, 6.13648011704, 6151.53388830500],
[163.159, 4.26399626634, 529.69096509460],
[159.678, 2.23194610246, 1059.38193018920],
[139.323, 2.41796344238, 8962.45534991020],
[149.297, 2.16501209917, 5621.84292321040],
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[0.087, 2.11654357529, 3450.81874791920],
[0.072, 3.89476829327, 9380.95967271720],
[0.075, 2.59340305340, 1964.83862685400],
[0.098, 4.01577665825, 6843.69148953180],
[0.074, 5.32032289064, 11766.26326451460],
[0.068, 0.04775525953, 2125.87740737920],
[0.069, 6.07427052412, 26482.17080962440],
[0.069, 2.05018999200, 29424.63423291600],
[0.084, 0.16960920719, 263.08392337280],
[0.068, 5.03013252197, 9070.11887384880],
[0.076, 2.00296087293, 224.34479570190],
[0.078, 2.17362706851, 30220.93223973240],
[0.066, 3.85497672006, 19406.67828817460],
[0.066, 5.70059718737, 33561.54466643220],
[0.067, 0.16600936321, 22743.40937951640],
[0.065, 4.65423392949, 2807.39834325620],
[0.069, 3.34387224268, 11670.28403729680],
[0.087, 4.97838021880, 1118.75579210280],
[0.063, 0.18907106180, 30065.51184029820],
[0.064, 4.61909647015, 9886.77220006400],
[0.073, 0.93706647938, 20735.83216142559],
[0.060, 5.83757395809, 8646.06348025360],
[0.062, 4.81389895867, 20199.09495963300],
[0.059, 5.00150762621, 6414.61781167780],
[0.068, 3.84252763135, 6571.01853218020],
[0.062, 2.81689634717, 6944.30877677240],
[0.065, 4.49078808776, 632.78373931320],
[0.058, 5.64889513615, 9945.57120882380],
[0.070, 2.51605694403, 9638.94074787620],
[0.057, 3.28105791201, 206.18554843720],
[0.057, 2.97448265957, 21795.21409161479],
[0.056, 2.23565630779, 20995.39296644940],
[0.057, 1.88614831237, 18451.07854656599],
[0.071, 4.82445647307, 8542.97070603500],
[0.061, 3.65945073900, 14421.83163698840],
[0.056, 3.13789031275, 8799.98871377800],
[0.057, 4.89927831599, 9602.35263622420],
[0.065, 3.37109873211, 11610.91017538320],
[0.067, 1.92945007459, 21265.52312652020],
[0.055, 1.95164531764, 9588.12554222260],
[0.057, 2.82240075154, 10124.93005431800],
[0.057, 6.10407356832, 19800.94595622480],
[0.055, 5.20976473824, 3237.51965248120],
[0.057, 4.12235760406, 10028.95082710020],
[0.055, 1.41700952855, 15906.76412668260],
[0.053, 2.16328741039, 6418.14093002680],
[0.060, 2.64683840328, 10018.24685144760],
[0.068, 5.36539876845, 1228.96211332220],
[0.051, 5.73824213507, 6048.44111408640],
[0.053, 0.31937174553, 12721.57209941700],
[0.051, 0.06312524105, 20206.14119633100],
[0.049, 4.53401402385, 6675.70192909220],
[0.051, 1.15475560534, 10156.90236013480],
[0.064, 4.56332268770, 16703.07938715119],
[0.060, 3.61007443614, 9468.26787725700],
[0.059, 3.08413561767, 10025.42770875120],
[0.064, 2.53229538141, 16703.04487984680],
[0.056, 3.31988072467, 6518.75821726740],
[0.047, 1.44559165677, 6643.09181776180],
[0.050, 1.92342238827, 11614.43329373220],
[0.047, 4.03794177027, 23958.63178523340],
[0.046, 3.70927352724, 8859.36257569160],
[0.060, 2.55506470511, 11780.49035851620],
[0.047, 1.69256878711, 6660.86953400080],
[0.044, 6.09481217162, 6460.81221096080],
[0.044, 2.63040622140, 13936.79450513400],
[0.053, 0.77878945764, 16865.52876963120],
[0.049, 1.83368544550, 17654.78053974960],
[0.048, 0.52828042378, 6686.74777770700],
[0.042, 4.30347553493, 9065.54812412880],
[0.042, 5.71964550673, 7203.80227149340],
[0.041, 0.98427208931, 20426.57109242200],
[0.051, 3.54335413699, 20597.24396304120],
[0.041, 0.21219617682, 7314.00859271280],
[0.038, 2.53074981011, 13207.02930736500],
[0.039, 5.15577369902, 6670.58818804980],
[0.051, 3.25271478667, 7799.98064550240],
[0.049, 0.77060706107, 17101.21113690720],
[0.038, 6.06684699984, 9389.05354078620],
[0.043, 0.51983815091, 16489.76303806100],
[0.036, 0.84102576439, 23937.85638974100],
],
# B1
[
[350068.845, 5.36847836211, 3340.61242669980],
[14116.030, 3.14159265359, 0.00000000000],
[9670.755, 5.47877786506, 6681.22485339960],
[1471.918, 3.20205766795, 10021.83728009940],
[425.864, 3.40843812875, 13362.44970679920],
[102.039, 0.77617286189, 3337.08930835080],
[78.848, 3.71768293865, 16703.06213349900],
[26.171, 2.48293558065, 2281.23049651060],
[32.708, 3.45803723682, 5621.84292321040],
[20.712, 1.44120802297, 6151.53388830500],
[18.294, 6.03102943125, 529.69096509460],
[15.680, 3.93075566599, 8962.45534991020],
[16.975, 4.81115186866, 3344.13554504880],
[13.067, 0.97324736181, 6677.70173505060],
[15.622, 2.78241383265, 3340.59517304760],
[15.622, 4.81318636318, 3340.62968035200],
[13.771, 1.67983063909, 3532.06069281140],
[12.711, 4.04546734935, 20043.67456019880],
[14.268, 0.24640247719, 2942.46342329160],
[12.493, 2.25620513522, 5884.92684658320],
[8.800, 0.34079528233, 398.14900340820],
[8.637, 1.75213704409, 2544.31441988340],
[8.903, 5.95437916504, 2810.92146160520],
[8.102, 0.84279830287, 6283.07584999140],
[9.250, 4.35071778619, 3496.03282613400],
[8.085, 4.29614034209, 6684.74797174860],
[5.811, 3.55479498415, 5092.15195811580],
[5.864, 3.69652093329, 5486.77784317500],
[5.618, 0.03475872145, 3185.19202726560],
[5.148, 0.85886443528, 3340.54511639700],
[5.145, 0.45169791514, 3340.67973700260],
[4.898, 4.12922007874, 1059.38193018920],
[3.471, 5.07253485267, 5088.62883976680],
[3.102, 3.11487063736, 3339.63210563160],
[3.013, 1.00910437496, 2914.01423582380],
[3.171, 1.24730004776, 3738.76143010800],
[3.194, 2.86899092087, 1751.53953141600],
[2.304, 1.38460565999, 3870.30339179440],
[2.233, 2.91238180064, 3894.18182954220],
[2.792, 4.27117916474, 8432.76438481560],
[2.431, 0.14615904873, 4690.47983635860],
[2.577, 2.78651098185, 6254.62666252360],
[1.996, 1.51200589223, 4292.33083295040],
[1.860, 5.15222219319, 796.29800681640],
[2.014, 5.48528849094, 3127.31333126180],
[1.922, 4.37668623732, 23384.28698689860],
[2.248, 4.46756441051, 10025.36039844840],
[1.782, 2.70229954651, 4136.91043351620],
[1.621, 2.26742355334, 3149.16416058820],
[1.452, 1.53948251192, 9492.14631500480],
[1.373, 3.20232312108, 2146.16541647520],
[1.332, 5.67966837010, 1592.59601363280],
[1.378, 4.12087865376, 3723.50895892300],
[1.215, 0.33914405698, 6674.11130639880],
[1.168, 3.52407129935, 11773.37681151540],
[1.179, 6.15475441355, 213.29909543800],
[1.173, 1.26036608440, 3341.59274776800],
[1.211, 0.97241747335, 6467.92575796160],
[1.204, 0.95200561837, 10018.31416175040],
[1.107, 1.44142157852, 2787.04302385740],
[1.194, 0.84501638145, 1194.44701022460],
[1.043, 3.98123209815, 12303.06777661000],
[1.029, 1.21951732572, 4535.05943692440],
[0.939, 2.99716248257, 7477.52286021600],
[1.303, 1.12409937702, 4399.99435688900],
[1.032, 4.26592917807, 1990.74501704100],
[1.230, 0.37904885593, 6525.80445396540],
[0.989, 2.37220445455, 9225.53927328300],
[0.946, 3.14940196742, 6489.77658728800],
[1.013, 5.90131661122, 3097.88382272579],
[0.913, 2.86098924372, 2388.89402044920],
[0.954, 4.90448639106, 3583.34103067380],
[0.866, 4.92421595837, 6681.24210705180],
[0.797, 4.53307543814, 7079.37385680780],
[0.866, 2.89344915945, 6681.20759974740],
[0.659, 0.33901474348, 2957.71589447660],
[0.670, 3.23650405278, 9595.23908922340],
[0.782, 1.56739177814, 3333.49887969900],
[0.641, 4.46918721250, 6836.64525283380],
[0.611, 3.97393774087, 6041.32756708560],
[0.738, 3.78715624780, 4562.46099302120],
[0.558, 2.92718433901, 1589.07289528380],
[0.513, 0.96852780537, 9623.68827669120],
[0.508, 4.07262127921, 7.11354700080],
[0.512, 1.53960708348, 7740.60678358880],
[0.481, 3.51023225206, 155.42039943420],
[0.528, 6.06190721770, 4933.20844033260],
[0.558, 2.09491968451, 2288.34404351140],
[0.445, 3.42439886280, 6680.24453233140],
[0.482, 4.73460866232, 13365.97282514820],
[0.534, 4.88536251621, 3361.38782219220],
[0.520, 6.19100285186, 6438.49624942560],
[0.441, 1.82408206251, 3325.35995551480],
[0.487, 2.72879191049, 3319.83703120740],
[0.417, 4.48716253276, 7903.07341972100],
[0.430, 0.62845892205, 5614.72937620960],
[0.395, 4.89021898045, 10419.98628350760],
[0.380, 1.91138845097, 3553.91152213780],
[0.358, 4.21584518245, 426.59819087600],
[0.409, 4.53421956625, 3360.96774609859],
[0.426, 5.47172830908, 3205.54734666440],
[0.330, 1.00078638665, 8955.34180290940],
[0.322, 2.42607399606, 2274.11694950980],
[0.316, 3.22064089430, 1221.84856632140],
[0.312, 3.66073476074, 3337.02199804800],
[0.310, 4.09100416919, 3344.20285535160],
[0.295, 2.87635162282, 7210.91581849420],
[0.329, 5.64440592793, 12832.75874170460],
[0.306, 1.52567836482, 7875.67186362420],
[0.284, 0.56373187712, 6681.29216370240],
[0.358, 4.21258737082, 1052.26838318840],
[0.347, 1.52200237477, 10213.28554621100],
[0.268, 3.57749600251, 9830.38901398780],
[0.346, 1.65247014273, 6682.20517446780],
[0.269, 4.45182417080, 9381.93999378540],
[0.285, 0.97118840317, 6681.15754309680],
[0.256, 3.67744143301, 1066.49547719000],
[0.269, 1.78448639785, 6127.65545055720],
[0.312, 4.63751658715, 5331.35744374080],
[0.317, 6.15274242841, 3320.25710730100],
[0.245, 4.71030710599, 26724.89941359840],
[0.249, 3.31328995337, 10818.13528691580],
[0.240, 4.87364672707, 6144.42034130420],
[0.239, 1.35709001659, 7064.12138562280],
[0.237, 3.19837233399, 5729.50644714900],
[0.278, 1.50842060340, 4929.68532198360],
[0.274, 3.61160906396, 191.44826611160],
[0.248, 3.93789974497, 11243.68584642080],
[0.242, 2.57630671866, 3355.86489788480],
[0.241, 1.89683861728, 15643.68020330980],
[0.228, 0.71217112323, 9866.41688066520],
[0.246, 0.16913226579, 2700.71514038580],
[0.219, 0.03864812268, 522.57741809380],
[0.215, 3.44260776071, 8827.39026987480],
[0.206, 5.23615052385, 6923.95345737360],
[0.202, 0.60277862639, 10021.82002644720],
[0.226, 2.43332503270, 8429.24126646660],
[0.202, 2.63373646725, 10021.85453375160],
[0.199, 3.26545613445, 382.89653222320],
[0.198, 4.50685315424, 242.72860397400],
[0.215, 2.12744795327, 553.56940284240],
[0.177, 3.92599588022, 8031.09226305840],
[0.162, 3.94498519498, 2921.12778282460],
[0.199, 4.22948972595, 3312.16323923200],
[0.188, 0.67072289565, 6298.32832117640],
[0.160, 2.90951395323, 6872.67311951120],
[0.155, 1.24529852403, 3364.49086444760],
[0.186, 2.44723831367, 3503.07906283200],
[0.139, 5.75493557040, 7632.94325965020],
[0.149, 0.49665393273, 8969.56889691100],
[0.132, 4.97828413367, 1748.01641306700],
[0.130, 0.66881298338, 10014.72373309860],
[0.128, 2.80753554051, 14584.29827312060],
[0.176, 2.37291314099, 2118.76386037840],
[0.127, 1.76223414864, 11081.21921028860],
[0.127, 0.26234206855, 13358.92658845020],
[0.163, 5.83356697025, 639.89728631400],
[0.129, 2.02607662846, 3346.13535100720],
[0.155, 1.57189307640, 3767.21061757580],
[0.133, 4.20989922795, 11371.70468975820],
[0.114, 2.12636383988, 6688.33840040040],
[0.130, 1.33114943655, 3347.72597370060],
[0.110, 5.78893316282, 16173.37116840440],
[0.105, 3.27202438053, 15113.98923821520],
[0.117, 5.66812806862, 536.80451209540],
[0.106, 1.21268139587, 7234.79425624200],
[0.108, 0.94652521237, 9808.53818466140],
[0.121, 4.22204758443, 6158.64743530580],
[0.124, 4.92495255567, 12964.30070339100],
[0.142, 3.85764234922, 6894.52394883760],
[0.099, 5.62543167000, 10973.55568635000],
[0.100, 2.56456804207, 3178.14579056760],
[0.131, 0.08971075365, 8273.82086703240],
[0.112, 3.14240135508, 3316.73398895200],
[0.095, 0.64723185059, 2487.41604494780],
[0.087, 4.14322802003, 3603.69635007260],
[0.087, 3.50260474148, 3077.52850332700],
[0.096, 5.13010621713, 3304.58456002240],
[0.082, 4.87880877413, 5828.02847164760],
[0.083, 2.04400907684, 18984.29263000960],
[0.085, 3.33671991814, 1758.65307841680],
[0.099, 3.28955694324, 17654.78053974960],
[0.078, 0.89238228021, 2699.73481931760],
[0.095, 0.32948273562, 3863.18984479360],
[0.083, 0.80327899268, 5085.03841111500],
[0.091, 1.48623539837, 8270.29774868340],
[0.075, 4.91191036053, 10021.76996979660],
[0.079, 4.25171159471, 7373.38245462640],
[0.084, 2.16662156833, 12566.15169998280],
[0.088, 2.78893554858, 11769.85369316640],
[0.095, 0.29428946155, 5628.95647021120],
[0.076, 5.23354729169, 13760.59871020740],
[0.092, 1.40883592065, 3336.73109134180],
[0.069, 3.50477916910, 10713.99488132620],
[0.079, 0.61833410504, 951.71840625060],
[0.070, 1.93458925881, 3475.67750673520],
[0.066, 5.01996258363, 16706.58525184800],
[0.067, 3.68731475523, 4032.77002792660],
[0.071, 1.71691035008, 10575.40668294180],
[0.086, 1.82073461894, 10404.73381232260],
[0.064, 2.43149744819, 2648.45482547300],
[0.062, 0.25250107112, 3980.50971301380],
[0.062, 3.16420520010, 13517.87010623340],
[0.078, 1.41762772678, 3.52311834900],
[0.086, 3.34935714534, 1581.95934828300],
[0.064, 3.75812808116, 1596.18644228460],
[0.061, 1.37421861116, 419.48464387520],
[0.055, 1.11154560464, 433.71173787680],
[0.061, 5.33515994167, 853.19638175200],
[0.059, 0.80382380790, 13362.43245314700],
[0.055, 0.37478855406, 149.56319713460],
[0.053, 0.55329112916, 14314.16811304980],
[0.059, 0.07234691744, 6531.66165626500],
[0.059, 2.83458587563, 13362.46696045140],
[0.059, 4.13409540555, 4407.10790388980],
[0.057, 5.57913927474, 3376.64029337720],
[0.049, 4.58036235824, 10551.52824519400],
[0.050, 2.01769015785, 10022.81760116760],
[0.055, 1.36081433917, 21393.54196985760],
[0.048, 1.59939595487, 18052.92954315780],
[0.045, 4.97928157994, 8671.96987044060],
[0.044, 2.58542985685, 13916.01910964160],
[0.047, 1.40206686464, 8425.65083781480],
[0.043, 0.21864618144, 9779.10867612540],
[0.042, 6.22365857047, 3914.95722503460],
[0.048, 3.44104044998, 692.15760122680],
[0.043, 3.21191030055, 6247.51311552280],
[0.055, 4.01321481700, 10177.25767953360],
[0.053, 2.93285711320, 3981.49003408200],
[0.039, 5.54634215618, 6702.00024889200],
[0.041, 2.46188112193, 6660.44945790720],
[0.049, 3.04236065330, 640.87760738220],
[0.039, 1.62689158397, 3335.08950239240],
[0.038, 3.31198341709, 1744.42598441520],
[0.038, 6.16317067723, 2818.03500860600],
[0.038, 4.03534957207, 103.09277421860],
[0.044, 0.91040525278, 5459.37628707820],
[0.049, 1.88325571471, 11216.28429032400],
[0.046, 5.62762941168, 9168.64089834740],
[0.035, 1.65976191407, 12168.00269657460],
[0.047, 4.52334272666, 10021.90459040220],
[0.039, 2.08367076229, 13745.34623902240],
[0.039, 4.76186135572, 20597.24396304120],
[0.039, 3.00951950244, 3344.49376205780],
[0.037, 1.33065895739, 12295.95422960920],
[0.040, 3.96893429107, 13171.00144068760],
[0.032, 0.91212661789, 12310.18132361080],
[0.032, 2.22618836835, 7107.82304427560],
[0.032, 4.96078703650, 24734.15439655740],
[0.037, 3.30085609301, 20995.39296644940],
[0.033, 3.70858397913, 10020.85695903120],
[0.031, 4.18674524484, 17256.63153634140],
[0.034, 3.25657016622, 14054.60730802600],
[0.032, 5.75360661734, 6546.15977336420],
[0.031, 3.16209740784, 12935.85151592320],
[0.037, 2.14901622101, 6665.97238221460],
[0.030, 0.21926429217, 6660.86953400080],
[0.030, 3.55459460301, 9070.11887384880],
[0.029, 2.97927335664, 2766.26762836500],
[0.029, 4.65051930186, 10235.13637553740],
[0.030, 5.16882435400, 16304.91313009080],
[0.032, 5.01760544488, 3191.04922956520],
[0.029, 2.93988761068, 6696.47732458460],
[0.029, 5.06447742493, 5099.26550511660],
[0.029, 5.68073325802, 3329.97576135000],
[0.029, 0.43949269085, 3351.24909204960],
[0.032, 1.37056688814, 6040.34724601740],
[0.032, 1.42334455474, 76.26607127560],
[0.033, 0.36423446435, 6604.95878212400],
[0.033, 4.85478789063, 6701.58017279840],
[0.030, 3.33348460172, 3369.06161416760],
[0.028, 0.60182098585, 11766.26326451460],
[0.026, 1.05197848649, 13207.02930736500],
[0.026, 5.03535225585, 30065.51184029820],
[0.034, 3.65553061498, 14158.74771361560],
[0.025, 4.60925601393, 8329.67161059700],
[0.025, 2.05970140678, 17395.21973472580],
[0.030, 5.22285260441, 9485.03276800400],
[0.025, 4.84964369679, 1648.44675719740],
[0.026, 5.47626814223, 3074.00538497800],
[0.024, 2.45239543931, 17085.95866572220],
[0.029, 5.36428737888, 2707.82868738660],
[0.024, 5.57488544800, 10264.56588407340],
[0.025, 4.22744782935, 1692.16566950240],
[0.023, 6.09244870438, 20199.09495963300],
[0.028, 1.30366587075, 8439.87793181640],
[0.032, 2.13597148493, 9468.26787725700],
],
# B2
[
[16726.690, 0.60221392419, 3340.61242669980],
[4986.799, 3.14159265359, 0.00000000000],
[302.141, 5.55871276021, 6681.22485339960],
[25.767, 1.89662673499, 13362.44970679920],
[21.452, 0.91749968618, 10021.83728009940],
[11.820, 2.24240738700, 3337.08930835080],
[7.985, 2.24892866611, 16703.06213349900],
[2.960, 5.89425825808, 3496.03282613400],
[2.445, 5.18770525274, 5621.84292321040],
[1.428, 1.25238140580, 2281.23049651060],
[1.779, 2.58759968520, 20043.67456019880],
[1.501, 3.18533003542, 3532.06069281140],
[1.259, 4.80695172904, 3185.19202726560],
[1.029, 2.35029907056, 6677.70173505060],
[1.109, 3.80982317372, 5884.92684658320],
[0.928, 0.29719160927, 3344.13554504880],
[0.860, 3.11698318930, 6151.53388830500],
[0.853, 1.33003321402, 529.69096509460],
[0.883, 5.18681316017, 5486.77784317500],
[1.100, 1.82962075794, 2942.46342329160],
[0.815, 3.40910567373, 2544.31441988340],
[0.702, 5.49076132554, 8962.45534991020],
[0.644, 0.31400306761, 5088.62883976680],
[0.745, 4.30248377111, 3340.59517304760],
[0.586, 4.48071459693, 3894.18182954220],
[0.681, 5.40951261308, 2810.92146160520],
[0.745, 0.05006463495, 3340.62968035200],
[0.542, 4.68895461946, 3339.63210563160],
[0.497, 4.65665197749, 5092.15195811580],
[0.460, 1.06670343610, 3097.88382272579],
[0.423, 3.08034568777, 4292.33083295040],
[0.381, 2.24933115190, 6283.07584999140],
[0.429, 1.70668733378, 4690.47983635860],
[0.339, 2.92195933142, 23384.28698689860],
[0.310, 5.63324402105, 3723.50895892300],
[0.287, 1.98619629868, 398.14900340820],
[0.298, 2.58990636818, 6684.74797174860],
[0.323, 5.15230144390, 6525.80445396540],
[0.247, 2.36923535528, 3340.54511639700],
[0.247, 1.96071951597, 3340.67973700260],
[0.223, 4.75562842441, 2146.16541647520],
[0.240, 3.53331653789, 3583.34103067380],
[0.238, 4.69268478666, 6254.62666252360],
[0.198, 6.21548965568, 2787.04302385740],
[0.202, 4.25439775032, 3333.49887969900],
[0.158, 1.89216973387, 6674.11130639880],
[0.185, 2.99350590687, 10025.36039844840],
[0.177, 1.41002572971, 6438.49624942560],
[0.138, 1.23172102079, 3127.31333126180],
[0.153, 5.93528616595, 6836.64525283380],
[0.106, 5.35414400998, 3738.76143010800],
[0.102, 3.67040445208, 1059.38193018920],
[0.136, 1.06039656714, 2388.89402044920],
[0.093, 5.04434801864, 155.42039943420],
[0.093, 2.70817394910, 8955.34180290940],
[0.108, 6.13917250674, 1748.01641306700],
[0.116, 5.97739483530, 2914.01423582380],
[0.099, 1.50221319099, 1751.53953141600],
[0.092, 2.68470906437, 1990.74501704100],
[0.077, 4.01966292109, 1592.59601363280],
[0.076, 4.49660101731, 4562.46099302120],
[0.076, 5.67354102576, 6041.32756708560],
[0.078, 0.79220883728, 2288.34404351140],
[0.074, 5.84795427965, 3341.59274776800],
[0.080, 5.48556941416, 8432.76438481560],
[0.065, 2.11705931744, 10018.31416175040],
[0.066, 5.08073805943, 2957.71589447660],
[0.059, 3.79695096075, 6923.95345737360],
[0.061, 4.51116100631, 4933.20844033260],
[0.059, 0.27765984344, 6127.65545055720],
[0.052, 5.84885902302, 4535.05943692440],
[0.051, 1.45495904398, 7477.52286021600],
[0.054, 1.50278239577, 6489.77658728800],
[0.056, 5.23212313891, 9866.41688066520],
[0.057, 4.73711357046, 2274.11694950980],
[0.051, 2.48654805044, 6467.92575796160],
[0.047, 3.25899585469, 26724.89941359840],
[0.048, 1.12255878532, 1349.86740965880],
[0.048, 2.87122326236, 242.72860397400],
[0.045, 1.61358524585, 5729.50644714900],
[0.043, 2.24334731490, 7.11354700080],
[0.044, 4.61065704096, 11773.37681151540],
[0.042, 3.32038536161, 13365.97282514820],
[0.047, 5.10736479739, 8969.56889691100],
[0.044, 4.64194663616, 4399.99435688900],
[0.039, 5.45779680648, 8031.09226305840],
[0.044, 5.21409542420, 4136.91043351620],
[0.045, 4.26206063790, 796.29800681640],
[0.048, 3.04342098072, 5331.35744374080],
[0.042, 2.12882700518, 213.29909543800],
[0.038, 2.49365585516, 951.71840625060],
[0.037, 3.44816851943, 3325.35995551480],
[0.038, 3.13981385980, 3149.16416058820],
[0.039, 3.64984946180, 553.56940284240],
[0.036, 0.54858124109, 7632.94325965020],
[0.032, 4.29985057106, 3355.86489788480],
[0.037, 6.26349600634, 6682.20517446780],
[0.037, 3.83188032092, 3870.30339179440],
[0.031, 4.94959395405, 6680.24453233140],
[0.035, 6.14813219827, 3360.96774609859],
[0.029, 0.54115054572, 6681.29216370240],
[0.035, 1.49899662719, 3320.25710730100],
[0.033, 0.19183878029, 3347.72597370060],
[0.036, 3.28055425527, 1589.07289528380],
[0.031, 5.66015228291, 1066.49547719000],
[0.028, 4.18178455540, 7210.91581849420],
[0.025, 1.21627749818, 9492.14631500480],
[0.029, 2.02283118033, 7234.79425624200],
[0.024, 2.96777681837, 7064.12138562280],
[0.024, 2.16823248221, 10419.98628350760],
[0.022, 4.67496434823, 1194.44701022460],
[0.022, 5.01797528499, 9595.23908922340],
[0.028, 4.19843924702, 8429.24126646660],
[0.023, 6.21195010050, 7740.60678358880],
[0.025, 1.45100528915, 6872.67311951120],
[0.024, 1.93342510858, 2699.73481931760],
[0.028, 5.87009898150, 1052.26838318840],
[0.025, 2.49707182259, 2118.76386037840],
[0.020, 0.15682384975, 3205.54734666440],
[0.019, 3.82087005916, 12303.06777661000],
[0.020, 6.26534330674, 7875.67186362420],
[0.019, 0.99282533197, 522.57741809380],
[0.018, 4.11668144665, 426.59819087600],
[0.020, 3.28531167827, 9225.53927328300],
[0.019, 5.72169822815, 11371.70468975820],
[0.018, 4.76871968197, 382.89653222320],
[0.017, 0.96519535826, 191.44826611160],
[0.017, 0.86184324841, 10973.55568635000],
[0.018, 6.22706341047, 9381.93999378540],
[0.015, 0.54135050421, 640.87760738220],
],
# B3
[
[606.506, 1.98050633529, 3340.61242669980],
[42.611, 0.00000000000, 0.00000000000],
[13.652, 1.79588228800, 6681.22485339960],
[2.730, 3.45377082121, 10021.83728009940],
[0.929, 3.75226159072, 3337.08930835080],
[0.607, 0.10618486408, 13362.44970679920],
[0.617, 1.14471772765, 3496.03282613400],
[0.479, 0.70504966293, 16703.06213349900],
[0.185, 3.28778562029, 3185.19202726560],
[0.169, 0.29980532608, 5621.84292321040],
[0.158, 1.09025317222, 20043.67456019880],
[0.123, 2.55664973413, 3097.88382272579],
[0.126, 4.74517022983, 3532.06069281140],
[0.093, 6.03607685759, 3894.18182954220],
[0.099, 4.92257049901, 2544.31441988340],
[0.106, 3.41315845439, 2942.46342329160],
[0.062, 6.25738949900, 3339.63210563160],
[0.058, 4.64867983361, 4292.33083295040],
[0.050, 3.75358626972, 6677.70173505060],
[0.050, 1.89408668049, 5088.62883976680],
[0.058, 3.65295480755, 6525.80445396540],
[0.045, 0.38295906298, 5486.77784317500],
[0.052, 3.25535694335, 4690.47983635860],
[0.044, 1.89342588822, 3583.34103067380],
[0.037, 0.04871920725, 2146.16541647520],
[0.039, 0.91787211117, 3723.50895892300],
[0.051, 5.24063514394, 5884.92684658320],
[0.036, 2.79633276263, 529.69096509460],
[0.032, 1.44641701752, 23384.28698689860],
[0.024, 5.41362501363, 3340.59517304760],
[0.023, 4.70639896508, 2787.04302385740],
[0.021, 1.12581894224, 3340.62968035200],
[0.021, 0.51744721589, 8962.45534991020],
[0.018, 0.36433365806, 155.42039943420],
[0.018, 5.53170427847, 3333.49887969900],
[0.019, 4.34401282378, 6151.53388830500],
[0.021, 2.94765501590, 398.14900340820],
[0.020, 5.96181389299, 5092.15195811580],
[0.017, 0.80891817293, 1194.44701022460],
[0.011, 0.43817745316, 1059.38193018920],
[0.014, 1.06654064248, 6836.64525283380],
],
# B4
[
[11.334, 3.45724352586, 3340.61242669980],
[13.369, 0.00000000000, 0.00000000000],
[0.744, 0.50445805257, 6681.22485339960],
[0.148, 1.05056602649, 10021.83728009940],
[0.102, 2.66185835593, 3496.03282613400],
[0.053, 5.27888218929, 3337.08930835080],
[0.022, 4.09971603267, 3097.88382272579],
[0.023, 1.72422342130, 3185.19202726560],
[0.013, 5.41704779112, 16703.06213349900],
[0.013, 2.06957065662, 13362.44970679920],
[0.010, 0.95989595600, 3894.18182954220],
],
# B5
[
[0.457, 4.86794125358, 3340.61242669980],
[0.053, 5.30547050586, 6681.22485339960],
[0.012, 5.75114070583, 10021.83728009940],
[0.013, 4.17736925293, 3496.03282613400],
[0.007, 0.00000000000, 0.00000000000],
],
]
"""This table contains Mars' periodic terms (all of them) from the planetary
theory VSOP87 for the heliocentric latitude at the equinox of date (taken from
the 'D' solution). In Meeus' book a shortened version can be found in pages
424-425."""
VSOP87_R = [
# R0
[
[153033488.276, 0.00000000000, 0.00000000000],
[14184953.153, 3.47971283519, 3340.61242669980],
[660776.357, 3.81783442097, 6681.22485339960],
[46179.117, 4.15595316284, 10021.83728009940],
[8109.738, 5.55958460165, 2810.92146160520],
[7485.315, 1.77238998069, 5621.84292321040],
[5523.193, 1.36436318880, 2281.23049651060],
[3825.160, 4.49407182408, 13362.44970679920],
[2306.539, 0.09081742493, 2544.31441988340],
[1999.399, 5.36059605227, 3337.08930835080],
[2484.385, 4.92545577893, 2942.46342329160],
[1960.198, 4.74249386323, 3344.13554504880],
[1167.115, 2.11261501155, 5092.15195811580],
[1102.828, 5.00908264160, 398.14900340820],
[899.077, 4.40790433994, 529.69096509460],
[992.252, 5.83862401067, 6151.53388830500],
[807.348, 2.10216647104, 1059.38193018920],
[797.910, 3.44839026172, 796.29800681640],
[740.980, 1.49906336892, 2146.16541647520],
[692.340, 2.13378814785, 8962.45534991020],
[633.144, 0.89353285018, 3340.59517304760],
[725.583, 1.24516913473, 8432.76438481560],
[633.140, 2.92430448169, 3340.62968035200],
[574.352, 0.82896196337, 2914.01423582380],
[526.187, 5.38292276228, 3738.76143010800],
[629.976, 1.28738135858, 1751.53953141600],
[472.776, 5.19850457873, 3127.31333126180],
[348.095, 4.83219198908, 16703.06213349900],
[283.702, 2.90692294913, 3532.06069281140],
[279.552, 5.25749247548, 6283.07584999140],
[233.827, 5.10546492529, 5486.77784317500],
[219.428, 5.58340248784, 191.44826611160],
[269.891, 3.76394728622, 5884.92684658320],
[208.333, 5.25476080773, 3340.54511639700],
[275.224, 2.90818883832, 1748.01641306700],
[275.501, 1.21767967781, 6254.62666252360],
[239.133, 2.03669896238, 1194.44701022460],
[223.190, 4.19861593779, 3149.16416058820],
[182.686, 5.08062683355, 6684.74797174860],
[186.213, 5.69871555748, 6677.70173505060],
[175.995, 5.95341786369, 3870.30339179440],
[178.613, 4.18423025538, 3333.49887969900],
[208.336, 4.84626442122, 3340.67973700260],
[228.128, 3.25529020620, 6872.67311951120],
[144.286, 0.21296012258, 5088.62883976680],
[163.534, 3.79889068111, 4136.91043351620],
[133.120, 1.53910106710, 7903.07341972100],
[141.759, 2.47790321309, 4562.46099302120],
[114.941, 4.31745088059, 1349.86740965880],
[118.781, 2.12178071222, 1589.07289528380],
[102.096, 6.18138550087, 9492.14631500480],
[128.555, 5.49883294915, 8827.39026987480],
[111.538, 0.55339169625, 11243.68584642080],
[82.498, 1.62227044590, 11773.37681151540],
[83.212, 0.61553380568, 8429.24126646660],
[84.470, 0.62274593110, 1592.59601363280],
[86.659, 1.74988330093, 2700.71514038580],
[71.826, 2.47489899385, 12303.06777661000],
[85.312, 1.61621097912, 4690.47983635860],
[63.641, 2.67334126661, 426.59819087600],
[68.599, 2.40197828418, 4399.99435688900],
[58.559, 4.72052787516, 213.29909543800],
[62.015, 1.10065866221, 1221.84856632140],
[66.509, 2.21307705185, 6041.32756708560],
[55.811, 1.23288325946, 3185.19202726560],
[54.989, 5.72691385306, 951.71840625060],
[52.418, 3.02366828926, 4292.33083295040],
[55.686, 5.44686699242, 3723.50895892300],
[58.959, 3.26242666052, 6681.24210705180],
[44.629, 2.01473640390, 8031.09226305840],
[58.959, 1.23165502899, 6681.20759974740],
[42.444, 2.26551590902, 155.42039943420],
[38.956, 2.57760416009, 3341.59274776800],
[51.561, 5.72326937712, 7079.37385680780],
[48.939, 5.61614696751, 3553.91152213780],
[45.414, 5.43290921705, 6467.92575796160],
[36.435, 4.43921812388, 3894.18182954220],
[35.980, 1.15966567007, 2288.34404351140],
[35.265, 5.49029710802, 1990.74501704100],
[42.191, 1.63253742760, 5628.95647021120],
[44.292, 5.00341366850, 5614.72937620960],
[33.623, 5.17029029766, 20043.67456019880],
[43.256, 1.03732072925, 11769.85369316640],
[39.237, 1.24237122859, 3339.63210563160],
[31.943, 4.59258406791, 2274.11694950980],
[30.345, 2.44177670130, 11371.70468975820],
[32.259, 2.38215172582, 4535.05943692440],
[31.870, 4.37521442752, 3.52311834900],
[29.350, 4.06034813442, 3097.88382272579],
[31.972, 1.93970478412, 382.89653222320],
[26.166, 5.58466944895, 9623.68827669120],
[27.904, 4.25805969214, 3191.04922956520],
[33.065, 0.85467740581, 553.56940284240],
[27.543, 1.57668567401, 9595.23908922340],
[25.159, 0.81355213242, 10713.99488132620],
[22.070, 0.85747723964, 3319.83703120740],
[24.772, 5.38970742761, 2818.03500860600],
[23.359, 6.01453778225, 3496.03282613400],
[24.732, 2.58034797703, 2803.80791460440],
[19.365, 5.18528750472, 6681.29216370240],
[19.122, 5.41968559451, 10025.36039844840],
[19.364, 5.59378382138, 6681.15754309680],
[18.330, 5.79567324240, 7064.12138562280],
[18.193, 5.61307426173, 7.11354700080],
[20.392, 4.53637816869, 6489.77658728800],
[21.260, 6.19160142215, 14054.60730802600],
[17.094, 1.55004739305, 2957.71589447660],
[22.791, 3.41709388606, 7632.94325965020],
[20.585, 2.98697279083, 3361.38782219220],
[18.005, 2.81431094394, 4032.77002792660],
[17.049, 6.15528099726, 10404.73381232260],
[16.488, 3.84534700818, 10973.55568635000],
[16.052, 0.92823508003, 14584.29827312060],
[21.027, 2.38474290907, 4989.05918389720],
[16.267, 1.92321585819, 7373.38245462640],
[16.291, 6.28233085307, 7210.91581849420],
[18.585, 4.07325116588, 2388.89402044920],
[15.977, 4.58368417141, 3264.34635542420],
[19.913, 2.73518445950, 5099.26550511660],
[19.661, 1.86285979000, 3443.70520091840],
[16.500, 4.14061745086, 7477.52286021600],
[19.495, 6.03778234182, 10018.31416175040],
[15.104, 2.65433427561, 2787.04302385740],
[19.099, 0.22623441108, 13745.34623902240],
[17.163, 3.18825562972, 3347.72597370060],
[13.423, 2.12818658793, 3344.20285535160],
[15.410, 2.20773507960, 2118.76386037840],
[17.238, 3.67067776368, 3205.54734666440],
[13.113, 4.27490214998, 14314.16811304980],
[16.451, 2.86641622696, 14712.31711645800],
[13.734, 1.68629769646, 3337.02199804800],
[16.659, 4.52130808861, 6674.11130639880],
[11.830, 0.19684525299, 3475.67750673520],
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[0.123, 3.58787674774, 3318.76159737340],
[0.153, 0.37199746202, 6533.14612897330],
[0.145, 1.73326841661, 6637.50594109460],
[0.133, 3.27553306809, 11876.46958573400],
[0.119, 5.15087396729, 15636.56665630900],
[0.117, 3.70999224131, 3343.15522398060],
[0.115, 5.99541570797, 11986.67590695340],
[0.152, 5.66662339960, 6530.17718355670],
[0.123, 0.05231448642, 9801.42463766060],
[0.130, 1.42377926040, 16063.16484718500],
[0.120, 4.19579234337, 604.84974070480],
[0.126, 1.38788085609, 169.58018313300],
[0.122, 0.18785107006, 18849.22754997420],
[0.113, 4.67731144918, 24491.42579258340],
[0.122, 1.21803689218, 3067.93946934820],
[0.118, 3.92389195187, 2963.23881878400],
[0.137, 0.80076862963, 3123.79021291280],
[0.124, 0.77274469912, 12465.53441274220],
[0.132, 4.73888023892, 2267.00340250900],
[0.122, 3.66231014052, 8756.26980147300],
[0.113, 3.74955221887, 21393.54196985760],
[0.153, 5.00596002145, 15906.76412668260],
[0.109, 1.46394078440, 2854.64037391020],
[0.125, 6.00744459186, 1442.26120876020],
[0.140, 0.64532646558, 13532.02988993220],
[0.108, 2.11691804278, 43.71891230500],
[0.130, 1.43185911960, 3370.10424500320],
[0.133, 2.31239626151, 9072.66167112960],
[0.107, 5.68864833782, 4878.85286267780],
[0.116, 3.91262234002, 11904.91877320180],
[0.106, 1.99989592271, 3497.01314720220],
[0.106, 5.79020088316, 1.48447270830],
[0.105, 1.79751699456, 3517.30615683360],
[0.130, 0.80396347034, 3397.51080163540],
[0.107, 5.29449090921, 10.63666534980],
[0.137, 0.47037516401, 13575.74880223720],
[0.104, 5.03145022037, 1751.52227776380],
[0.146, 2.57659804831, 3308.64012088300],
[0.103, 3.29589452622, 4379.63903749020],
[0.104, 0.77903634693, 1751.55678506820],
[0.118, 4.11892224522, 10927.29397676420],
[0.106, 2.25714927822, 13207.02930736500],
[0.126, 1.10289326962, 6680.79497027290],
[0.105, 1.41449747957, 10081.21114201300],
[0.110, 6.16072219971, 3338.06962941900],
[0.113, 0.61947991056, 13421.82356871280],
[0.139, 2.21345603147, 1954.71715036360],
[0.102, 3.81767069895, 6670.17915313570],
[0.101, 3.44583422545, 1505.28780909299],
[0.105, 2.46134952447, 5525.86369599260],
[0.119, 5.64454862995, 8425.71814811760],
[0.101, 1.87446179141, 9161.52735134660],
[0.111, 5.46183253107, 7214.43893684320],
[0.123, 0.14056284625, 16489.76303806100],
[0.128, 0.00452525697, 2185.25126929280],
[0.106, 6.20225179330, 3717.98603461560],
[0.099, 1.70554147455, 1655.56030419820],
[0.100, 1.76373681853, 3002.36972771680],
[0.101, 0.55693458655, 3337.15661865360],
[0.101, 0.56441794685, 30774.50164257480],
[0.098, 1.93983799659, 5562.46906129680],
[0.130, 5.65255471249, 2735.76268599500],
[0.125, 6.18575288406, 9698.33186344200],
[0.100, 2.35767934317, 3337.07205469860],
[0.100, 3.76317527562, 3344.15279870100],
[0.105, 5.33897491215, 5096.08411137890],
[0.103, 1.24189801298, 1385.89527633620],
[0.101, 1.42727612221, 37455.72649597440],
[0.096, 2.55328478399, 4466.48176580340],
[0.097, 5.86779127410, 5220.17080145320],
[0.101, 2.61513508379, 16858.41522263039],
[0.107, 4.23943588615, 8823.86715152580],
[0.100, 4.38845221965, 3337.10656200300],
[0.100, 1.73240240188, 3344.11829139661],
[0.101, 3.51764169063, 4694.00295470760],
[0.096, 3.16895015703, 12825.64519470380],
[0.101, 6.24060604565, 2942.53073359440],
[0.103, 1.09500325425, 12089.76868117200],
[0.106, 5.57931664756, 39048.32250960720],
[0.126, 3.40521738550, 6681.65473652630],
[0.105, 2.52404371984, 1755.06264976500],
[0.115, 6.10031030713, 3145.64104223920],
[0.092, 5.06385191401, 5085.10572141780],
[0.097, 1.11670836674, 3341.79306935190],
[0.092, 5.83209800268, 6682.70932610790],
[0.121, 2.39411154886, 18208.34994259200],
[0.110, 2.51677822824, 1045.15483618760],
[0.091, 1.07173725022, 927.83996850280],
[0.096, 3.60155667418, 13363.43002786740],
[0.097, 5.34224904711, 7636.46637799920],
[0.094, 1.20811080231, 9495.66943335380],
[0.090, 4.17568982529, 0.06731030280],
[0.097, 3.20862890174, 5298.33750655300],
[0.092, 3.20029831258, 4403.51747523800],
[0.090, 3.79900428724, 685.04405422600],
[0.101, 2.12778329280, 10050.28646756720],
[0.098, 3.89390262307, 2373.64154926420],
[0.090, 4.49046504054, 6453.74872061060],
[0.096, 5.13129666936, 7792.86709850160],
[0.089, 4.51228904794, 10037.08975128440],
[0.098, 0.65689906709, 2810.98877190800],
[0.114, 4.15908543927, 9090.47419324760],
[0.094, 4.78960145866, 35707.71008290740],
[0.087, 6.26525215858, 34554.81386366760],
[0.087, 1.50181194995, 9983.70424446160],
[0.087, 1.43790822626, 9488.62319665580],
[0.090, 2.79573736864, 47477.56377607380],
[0.094, 5.68919291448, 6106.88005506480],
[0.087, 0.74049208991, 41990.78593289880],
[0.101, 0.99308133443, 6614.73744448520],
[0.115, 3.49732055752, 4.50343941720],
[0.086, 0.18628425275, 216.82221378700],
[0.099, 1.06539589813, 2810.85415130240],
[0.087, 3.02856210899, 7218.02936549500],
[0.085, 4.58476007089, 1699.27921650320],
[0.088, 4.47996444588, 21957.68072774700],
[0.106, 6.12011880730, 4819.47900076420],
[0.089, 3.88600719587, 12199.97500239140],
[0.097, 2.70091698598, 3339.43178404770],
[0.118, 1.02739527200, 34115.11406927460],
[0.101, 0.36591831115, 2942.39611298880],
[0.084, 5.66081869654, 1169.58825140860],
[0.086, 1.91214909013, 55516.41870984820],
[0.084, 4.30909434949, 4150.08989614680],
[0.094, 1.36645151323, 9093.99731159660],
[0.097, 2.26544245706, 13361.46938573100],
[0.099, 1.16054562056, 128.01884333740],
[0.094, 1.10573952457, 4591.44262300060],
[0.092, 0.74386387542, 4845.90023579280],
[0.101, 1.51570299040, 7807.09419250320],
[0.096, 1.02187746571, 2899.78714182220],
[0.086, 0.66787658068, 2957.73314812880],
[0.087, 3.49676189640, 4061.75165790600],
[0.095, 3.35452781355, 661.23292678100],
[0.087, 0.04840436087, 23546.75362303080],
[0.114, 2.83270741566, 394.62588505920],
[0.081, 3.44420073782, 148.07872442630],
[0.081, 1.27062968985, 4893.07995667940],
[0.083, 5.48462687348, 4349.16189758320],
[0.105, 3.47842036130, 3413.90955255880],
[0.084, 4.33209852801, 51449.32426327820],
[0.093, 1.59775582035, 5088.21980485270],
[0.088, 3.29950478012, 2655.50106217100],
[0.081, 1.65543714666, 78263.70942472259],
[0.086, 1.19342535692, 4029.24690957760],
[0.079, 4.41964678009, 151.04766984290],
[0.084, 1.96289182788, 14867.73751589219],
[0.091, 5.76229906142, 2544.33167353560],
[0.086, 3.78659802914, 1481.40937134520],
[0.082, 2.85633413428, 14164.81362924540],
[0.078, 4.29426812598, 187.92514776260],
[0.078, 5.38566529072, 2655.56837247380],
[0.084, 2.15121245434, 3311.12060839640],
[0.078, 2.01651247942, 9124.92198604240],
[0.083, 4.28280129037, 74923.09699802278],
[0.077, 1.45903147715, 2544.38173018620],
[0.081, 3.62204400197, 12306.59089495900],
[0.100, 1.33498371324, 9278.84721956680],
[0.089, 2.62080312892, 24341.52831745660],
[0.098, 3.78877505378, 3198.43379966360],
[0.081, 4.34306418828, 10177.19036923080],
[0.080, 5.80054348103, 2751.01515718000],
[0.092, 2.80228448795, 3707.83675566220],
[0.082, 2.45812896240, 9815.65173166220],
[0.076, 3.03616461584, 9993.38809263160],
[0.076, 3.92674885488, 2910.08208256070],
[0.076, 3.20004040720, 7733.49323658800],
[0.098, 3.28574616663, 3289.33208883739],
[0.077, 2.05948930010, 12928.73796892240],
[0.075, 0.85784191736, 28638.90558114660],
[0.078, 0.29690749181, 10654.62101941260],
[0.101, 0.72388999452, 48827.43118573260],
[0.085, 5.19438010130, 2146.14816282300],
[0.083, 4.42475849926, 2060.81785407180],
[0.075, 5.19097428778, 1055.44977692610],
[0.096, 6.24132708357, 11.04570026390],
[0.074, 3.37882325472, 8006.16619393960],
[0.101, 0.95332927487, 8186.51266249260],
[0.092, 0.96173005100, 151.89728108520],
[0.074, 2.22716630210, 272.67295735160],
[0.092, 5.56705883046, 27873.58901026800],
[0.091, 3.73152787182, 2544.29716623120],
[0.084, 0.41493230617, 4296.90158267040],
[0.074, 5.09669613096, 9755.23023837760],
[0.078, 1.79565224435, 3564.95722240170],
[0.075, 4.58345774133, 9153.90361602180],
[0.074, 3.88658218247, 25298.29315444680],
[0.085, 5.31472029744, 4716.38622654560],
[0.074, 1.46907693289, 11527.12508919240],
[0.101, 2.94847804254, 12032.93761653920],
[0.072, 0.24413748615, 1324.94134054000],
[0.078, 0.17721609024, 3391.89276456221],
[0.073, 1.65072742864, 5452.26274007740],
[0.073, 4.91730083470, 10787.63034454580],
[0.073, 3.28285909319, 8830.91338822380],
[0.081, 5.46340742050, 3856.07629779280],
[0.073, 4.61913155968, 3288.35211178700],
[0.096, 5.71767221046, 206.70073729660],
[0.080, 4.47918417138, 12299.54465826100],
[0.071, 4.98130328330, 12942.96506292400],
[0.073, 2.86057567032, 4960.60999642940],
[0.072, 5.14120362338, 4665.55376723980],
[0.076, 0.00928867041, 6534.41316687600],
[0.090, 5.38224594245, 2125.81009707640],
[0.085, 0.94196641948, 2146.18267012740],
[0.096, 0.68069708134, 10006.58480891440],
[0.073, 1.06048379839, 3866.78027344540],
[0.072, 0.84342376295, 3334.54651107000],
[0.091, 5.12701600437, 3392.87274161260],
[0.076, 5.96038992872, 3482.79105373600],
[0.090, 1.46230169383, 5092.16921176800],
[0.071, 1.16745785331, 1574.84580128220],
[0.072, 3.86137692169, 16762.43599541260],
[0.070, 0.07310763691, 12839.87228870540],
[0.073, 0.11725123446, 10507.80933288900],
[0.081, 5.86817748181, 3495.96551583120],
[0.071, 2.07963275673, 1063.31408345230],
[0.068, 3.30993028662, 4106.40549114620],
[0.069, 0.33467954461, 5.52292430740],
[0.068, 1.56404561711, 2398.55036473080],
[0.090, 2.61953849393, 3346.67834232960],
[0.068, 1.06108185791, 191.38095580880],
[0.077, 0.87794040199, 2917.94638908690],
[0.067, 0.29712068423, 12012.58229714040],
[0.067, 2.55451787747, 11567.19126307820],
[0.083, 1.82578570364, 3511.28529731900],
[0.068, 2.68247854175, 20213.25474333179],
[0.086, 2.79273636804, 367.22432896240],
[0.086, 0.81171860574, 209.77597708900],
[0.067, 5.28035928877, 8966.38750317330],
[0.067, 0.20258020424, 27433.88921587499],
[0.071, 2.76410148218, 15650.79375031060],
[0.090, 0.71593793107, 3451.79906898740],
[0.067, 6.18148420146, 3966.28261901220],
[0.074, 3.61959120765, 7064.10413197060],
[0.068, 2.69550405031, 12725.45343477500],
[0.074, 1.24854309783, 8027.56914470940],
[0.084, 2.47006028699, 3738.74417645580],
[0.077, 5.89874180572, 4307.58330413540],
[0.067, 0.33285041428, 19645.52555679060],
[0.083, 3.79134493696, 2472.67876262220],
[0.064, 0.43216125634, 1994.26813539000],
[0.071, 0.65707804543, 860.30992875280],
[0.064, 0.98960038205, 3376.17516116840],
[0.070, 0.96227192685, 8428.83223155250],
[0.066, 0.65425879867, 8219.46528937760],
[0.070, 4.36060455306, 8436.69653807870],
[0.084, 4.50083253887, 3738.77868376020],
[0.073, 5.69670871544, 14687.39104733920],
[0.071, 0.36334330253, 2619.47319549360],
[0.080, 5.85771861744, 7747.72033058960],
[0.068, 3.06409889136, 8446.99147881720],
[0.066, 1.07137364271, 1987.22189869200],
[0.061, 3.71171429905, 1055.85881184020],
[0.079, 0.06487001849, 6286.59896834040],
[0.075, 1.54177744365, 1059.39918384140],
[0.061, 1.47350010728, 1685.05212250160],
[0.061, 0.46897959303, 1727.66109366820],
[0.064, 2.11869877898, 3305.04969223120],
[0.060, 1.17940250396, 97670.38771289718],
[0.060, 5.13953821352, 1898.33396428740],
[0.064, 4.04058406722, 3945.46216740460],
[0.063, 5.20562384814, 24606.13555322000],
[0.061, 0.55428968913, 7082.89697515680],
[0.075, 4.81208819076, 27299.24421193320],
[0.059, 1.75511446129, 12082.65513417120],
[0.061, 5.88333855610, 6901.63749583840],
[0.074, 3.46408580786, 14556.89671702380],
[0.074, 4.40649822049, 9360.60435331840],
[0.058, 4.22827613192, 4531.53631857540],
[0.080, 2.14103357856, 7917.30051372260],
[0.075, 1.85618011420, 52566.19261584059],
[0.075, 5.15830659680, 45884.96776244100],
[0.068, 2.06915254754, 8958.52319664710],
[0.056, 3.77847713307, 299.12639426920],
[0.062, 2.25564130818, 9758.75335672660],
[0.059, 2.68657637673, 6283.05859633920],
[0.056, 5.54148283448, 13286.18363552360],
[0.056, 3.89200811600, 8962.38803960740],
[0.063, 2.07254352069, 7593.79509706520],
[0.061, 4.31994402891, 4709.27267954480],
[0.075, 5.79419108898, 1059.36467653700],
[0.056, 0.18569912415, 7768.00833968560],
[0.059, 5.49627068572, 7322.10246078180],
[0.064, 3.95992112220, 3050.12694723020],
[0.055, 2.19506741266, 7.04623669800],
[0.057, 4.05252695300, 3930.20969621960],
[0.075, 3.99788100837, 5483.25472482600],
[0.060, 4.61703903739, 6990.50317605540],
[0.073, 4.20362525534, 21150.81336588360],
[0.066, 2.82009591985, 8771.00708379860],
[0.054, 0.38782719267, 360.11078196160],
[0.059, 4.71734799803, 6283.09310364360],
[0.068, 5.74655335863, 987.74627292800],
],
# R1
[
[1107433.340, 2.03250524950, 3340.61242669980],
[103175.886, 2.37071845682, 6681.22485339960],
[12877.200, 0.00000000000, 0.00000000000],
[10815.880, 2.70888093803, 10021.83728009940],
[1194.550, 3.04702182503, 13362.44970679920],
[438.579, 2.88835072628, 2281.23049651060],
[395.698, 3.42324611291, 3344.13554504880],
[182.572, 1.58428644001, 2544.31441988340],
[135.850, 3.38507017993, 16703.06213349900],
[128.204, 0.62991220570, 1059.38193018920],
[127.068, 1.95389775740, 796.29800681640],
[118.443, 2.99761345074, 2146.16541647520],
[128.362, 6.04343360441, 3337.08930835080],
[87.537, 3.42052758979, 398.14900340820],
[83.026, 3.85574986653, 3738.76143010800],
[75.598, 4.45101839349, 6151.53388830500],
[71.999, 2.76442180680, 529.69096509460],
[66.542, 2.54892602695, 1751.53953141600],
[54.314, 0.67750943459, 8962.45534991020],
[51.035, 3.72585409207, 6684.74797174860],
[66.430, 4.40597549957, 1748.01641306700],
[47.863, 2.28527896843, 2914.01423582380],
[49.428, 5.72959428364, 3340.59517304760],
[49.424, 1.47717922226, 3340.62968035200],
[57.518, 0.54354327916, 1194.44701022460],
[48.318, 2.58061691301, 3149.16416058820],
[36.384, 6.02728752344, 3185.19202726560],
[37.176, 5.81439911546, 1349.86740965880],
[36.036, 5.89508336048, 3333.49887969900],
[31.115, 0.97832506960, 191.44826611160],
[38.953, 2.31900090554, 4136.91043351620],
[27.244, 5.41367977087, 1592.59601363280],
[24.300, 3.75843924498, 155.42039943420],
[22.804, 1.74830773908, 5088.62883976680],
[22.324, 0.93932040730, 951.71840625060],
[21.708, 3.83571581352, 6283.07584999140],
[21.304, 0.78049229782, 1589.07289528380],
[21.631, 4.56895741061, 3532.06069281140],
[17.956, 4.21930481803, 3870.30339179440],
[18.237, 0.41328624131, 5486.77784317500],
[16.251, 3.80760134974, 3340.54511639700],
[16.803, 5.54857987615, 3097.88382272579],
[16.850, 4.53690440252, 4292.33083295040],
[15.755, 4.75736730681, 9492.14631500480],
[15.746, 3.72356090283, 20043.67456019880],
[20.428, 3.13540712557, 4690.47983635860],
[14.699, 5.95325006816, 3894.18182954220],
[16.251, 3.39910907599, 3340.67973700260],
[14.259, 3.99897353022, 1990.74501704100],
[16.528, 0.96752074938, 4399.99435688900],
[13.010, 5.14230107067, 6677.70173505060],
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[0.102, 5.38933965862, 13892.14067189380],
[0.108, 4.33438895790, 3490.17562383440],
[0.095, 2.32591017464, 10028.95082710020],
[0.113, 1.74323945160, 11610.91017538320],
[0.119, 4.94578003013, 3443.70520091840],
[0.096, 1.63239207663, 11925.27409260060],
[0.124, 0.82697196609, 9638.94074787620],
[0.101, 1.51065535085, 1062.90504853820],
[0.107, 4.36653716080, 6531.66165626500],
[0.090, 2.01534774170, 22324.90505670940],
[0.094, 4.85202869277, 14047.49376102520],
[0.089, 1.23714034226, 20809.46762464520],
[0.095, 5.69916785631, 6717.25272007700],
[0.095, 2.15038299943, 8013.27974094040],
[0.111, 3.91313035726, 3311.18291816379],
[0.089, 1.37925538521, 74.78159856730],
[0.094, 3.24872875047, 6657.34641565180],
[0.089, 0.70324117212, 23.87843774780],
[0.087, 0.40376031248, 2221.85663459700],
[0.092, 3.33165786190, 2540.79130153440],
[0.120, 3.09344469205, 6685.10618875760],
[0.087, 4.92694309070, 1505.28780909299],
[0.091, 1.66121998822, 24150.08005134500],
[0.090, 5.47687082598, 16699.53901514999],
[0.119, 2.53709230647, 3312.16323923200],
[0.118, 5.56523997231, 2814.44457995420],
[0.093, 1.61394240489, 3341.04230982650],
[0.084, 1.19439840758, 3450.81874791920],
[0.085, 4.95060410388, 7314.00859271280],
[0.084, 3.92244493446, 170.67287061920],
[0.096, 5.49205832489, 3427.92063123960],
[0.106, 1.61703818023, 3774.32416457660],
[0.101, 6.18535119914, 5511.63660199100],
[0.081, 3.16562241132, 52175.80628314840],
[0.093, 5.15512549422, 3451.79906898740],
[0.108, 0.33314004399, 6709.67404086740],
[0.078, 2.38080208142, 13553.89797291080],
[0.085, 1.18588430640, 6705.10329114740],
[0.098, 3.24856024758, 25287.72379939980],
[0.080, 2.54327778068, 6675.70192909220],
[0.078, 4.70533248161, 24889.57479599160],
[0.095, 1.59916172961, 4271.97551355160],
[0.076, 0.90799171644, 2675.85638156980],
[0.091, 3.80728044706, 2125.87740737920],
[0.093, 5.59480359619, 3340.18254357310],
[0.095, 2.06299921822, 6518.75821726740],
[0.100, 6.02550501045, 3313.21087060300],
[0.075, 6.16095890090, 3370.04193523580],
[0.077, 4.92444879515, 3229.42578441220],
[0.090, 4.55063359845, 6701.58017279840],
[0.078, 2.01202524407, 14421.83163698840],
[0.079, 5.92142974185, 6155.05700665400],
[0.101, 2.07923317336, 15265.88651930040],
[0.082, 6.04078010866, 3760.09707057500],
[0.073, 3.01106366205, 206.18554843720],
[0.078, 1.71095661489, 3399.98628861340],
[0.073, 3.32824316241, 9588.12554222260],
[0.076, 1.74030672711, 6756.00645196690],
[0.073, 1.44980946324, 5408.54382777240],
[0.077, 5.64501410813, 3209.07046501340],
[0.080, 5.70272305344, 10156.90236013480],
[0.075, 3.83222347813, 39048.32250960720],
[0.072, 0.82629826575, 7366.26890762560],
[0.083, 4.71804515025, 14061.72085502680],
[0.072, 4.35767091893, 21548.96236929180],
[0.086, 1.50107043029, 5989.06725217280],
[0.073, 3.77377582806, 28628.33622609960],
[0.082, 0.78740181090, 16276.46394262300],
[0.070, 2.69225539304, 3296.89351439480],
[0.069, 1.01941228196, 12295.95422960920],
[0.081, 4.64227979982, 6947.83189512140],
[0.094, 0.74502278458, 5244.04923920100],
[0.067, 4.47328871650, 20206.14119633100],
[0.091, 2.95968633697, 3326.38533269820],
[0.076, 2.86128350856, 8542.97070603500],
[0.065, 1.31079130285, 23546.75362303080],
[0.065, 3.31422850411, 6414.61781167780],
[0.064, 3.98415414793, 3368.01398279660],
[0.065, 4.15810281695, 3340.19235060619],
[0.071, 3.82044323862, 6578.13207918100],
[0.080, 1.02128994578, 7321.12213971360],
[0.064, 1.07965886113, 6944.30877677240],
[0.064, 1.20215520018, 38.13303563780],
[0.070, 5.11166911478, 9485.03276800400],
[0.067, 2.22216014849, 4845.90023579280],
[0.083, 1.86067842148, 931.36308685180],
[0.063, 0.45029141698, 6418.14093002680],
[0.062, 5.68207205878, 4459.36821880260],
[0.062, 0.62454636835, 6688.27109009760],
[0.076, 0.41820625869, 5032.77809620220],
[0.062, 5.72811519809, 2008.55753915900],
[0.060, 1.98790201827, 12199.97500239140],
[0.078, 2.18035217615, 3232.94890276120],
[0.060, 1.08971396071, 10124.93005431800],
[0.072, 4.08555524166, 3416.87849797540],
[0.061, 2.49066420507, 4005.36847182980],
[0.059, 2.93755144370, 9886.77220006400],
[0.069, 1.02371083242, 6621.85099148600],
[0.061, 4.57446273568, 2277.70737816160],
[0.059, 4.74745481720, 16865.52876963120],
[0.069, 3.62576981720, 15906.76412668260],
[0.058, 4.15993379336, 1854.63230563460],
[0.060, 4.92798256747, 3391.89276456221],
[0.070, 4.51699340219, 16304.91313009080],
[0.056, 3.59354639280, 7322.10246078180],
[0.068, 0.81217091970, 16703.04487984680],
[0.056, 3.19997567622, 4140.43355186520],
[0.058, 1.73479637157, 2409.24933984800],
[0.054, 5.54310937490, 2604.73591316800],
[0.059, 2.02922256380, 45486.81875903279],
[0.063, 5.29505507594, 17101.21113690720],
[0.054, 4.88230660750, 48300.16010269000],
[0.071, 4.84381041200, 3289.33208883739],
[0.054, 1.76917054114, 3510.19260983280],
[0.063, 2.80175814276, 16894.51039961060],
[0.058, 0.91631357427, 10018.24685144760],
[0.054, 1.06826755543, 8948.22825590860],
[0.072, 1.36121375974, 10025.42770875120],
[0.061, 0.92427393171, 17468.85519794540],
[0.068, 2.84271358352, 16703.07938715119],
[0.053, 3.42679182927, 14867.73751589219],
[0.054, 0.41070672545, 18451.07854656599],
[0.060, 5.86922287544, 7447.01791784600],
[0.051, 1.64684042106, 3472.15438838620],
[0.057, 6.13250399703, 17085.95866572220],
[0.053, 4.16969434701, 6106.88005506480],
[0.050, 3.17196717347, 2111.65031337760],
[0.055, 5.72607545560, 10706.88133432540],
[0.062, 0.57333106196, 3171.03224356680],
[0.053, 1.29007833025, 6652.77566593180],
[0.050, 2.96441858632, 10037.08975128440],
[0.065, 5.11165617529, 3113.13629391080],
[0.053, 4.87447079015, 1485.98012106520],
[0.050, 2.52848298042, 10448.43547097540],
[0.059, 1.69623653028, 4025.65648092580],
[0.047, 5.15559748285, 12012.58229714040],
[0.049, 1.19473362353, 3448.27595063840],
[0.063, 1.01191427607, 11769.85369316640],
[0.064, 3.86219786087, 18208.34994259200],
[0.059, 2.96261275062, 14071.43950907579],
[0.049, 1.41657179779, 2938.94030494260],
[0.048, 2.95878690387, 11527.12508919240],
[0.052, 0.01971915447, 8226.57883637840],
[0.045, 5.07966377852, 3318.76159737340],
[0.043, 1.23879381294, 7218.02936549500],
[0.058, 5.58121433163, 6643.09181776180],
[0.048, 5.02446939402, 6645.19698672220],
[0.043, 0.69492704598, 20995.39296644940],
[0.044, 4.02272101657, 9389.05354078620],
[0.055, 4.38138154697, 1478.86657406440],
[0.051, 4.24292455428, 792.77488846740],
[0.042, 2.74826708762, 14577.18472611980],
[0.044, 4.18397905503, 8535.85715903420],
[0.047, 1.33588473182, 632.78373931320],
[0.042, 5.05676915852, 3397.51080163540],
[0.042, 0.28204510006, 10001.48196070061],
[0.042, 0.75310918544, 6357.71943674220],
[0.042, 4.94532732982, 18052.92954315780],
[0.052, 4.09912687749, 5835.14201864840],
[0.054, 2.46533302314, 8186.51266249260],
[0.043, 4.77713978044, 32124.36905223359],
[0.053, 6.08293348275, 3377.21779200400],
[0.041, 2.51168269556, 4186.69526145100],
[0.041, 1.24482327948, 3212.59358336240],
[0.041, 5.42003026893, 685.04405422600],
[0.041, 5.04768364997, 6571.01853218020],
[0.042, 2.08904552145, 13363.43002786740],
[0.048, 4.82888746454, 1835.32461760680],
[0.043, 4.17203713456, 43340.65334255760],
[0.046, 0.81640935106, 45884.96776244100],
[0.042, 2.26773068307, 12729.66596748600],
[0.039, 5.85791936573, 846.08283475120],
[0.043, 2.90976420757, 6872.67311951120],
[0.045, 1.98725045807, 1861.74585263540],
[0.045, 0.50053853542, 14128.24277124560],
[0.046, 2.86512929328, 38650.17350619900],
[0.038, 3.65846461938, 29698.28751133580],
[0.039, 4.57679716458, 6901.63749583840],
[0.039, 3.85504465583, 9945.57120882380],
[0.040, 0.06127203284, 9947.05568153210],
[0.043, 5.28854105201, 3274.12501778540],
[0.047, 6.25707790441, 24606.13555322000],
[0.037, 5.02115296017, 11128.97608578420],
[0.039, 1.71421919870, 7696.88787128380],
[0.037, 4.34652985120, 3283.71405176420],
[0.037, 0.05572748092, 21150.81336588360],
[0.042, 4.97872041460, 13575.74880223720],
[0.050, 4.24170332288, 7747.72033058960],
[0.037, 4.07496312186, 8646.06348025360],
[0.038, 0.44080908793, 24491.42579258340],
[0.036, 1.73681874925, 3468.63127003720],
[0.041, 5.69294900686, 26087.90314157420],
[0.036, 1.80256389689, 8756.26980147300],
[0.036, 3.37374689465, 48429.28218232440],
[0.035, 0.10555289345, 8742.04270747140],
[0.041, 4.26832466355, 21000.91589075680],
[0.038, 0.73199792046, 26084.02180621620],
],
# R2
[
[44242.247, 0.47930603943, 3340.61242669980],
[8138.042, 0.86998398093, 6681.22485339960],
[1274.915, 1.22594050809, 10021.83728009940],
[187.387, 1.57298991982, 13362.44970679920],
[40.744, 1.97080175060, 3344.13554504880],
[52.396, 3.14159265359, 0.00000000000],
[26.616, 1.91665615762, 16703.06213349900],
[17.825, 4.43499505333, 2281.23049651060],
[11.713, 4.52510453730, 3185.19202726560],
[10.209, 5.39143469548, 1059.38193018920],
[9.950, 0.41870577185, 796.29800681640],
[9.237, 4.53579272961, 2146.16541647520],
[7.299, 3.14218509183, 2544.31441988340],
[7.217, 2.29300859074, 6684.74797174860],
[6.808, 5.26702580055, 155.42039943420],
[6.528, 2.30781369329, 3738.76143010800],
[7.785, 5.93369079547, 1748.01641306700],
[5.840, 1.05191350362, 1349.86740965880],
[6.749, 5.30194395749, 1194.44701022460],
[4.695, 0.76880586144, 3097.88382272579],
[5.391, 1.00223256041, 3149.16416058820],
[4.406, 2.45556303355, 951.71840625060],
[4.286, 3.89643520638, 1592.59601363280],
[3.514, 1.85168391963, 398.14900340820],
[3.699, 2.26043707772, 20043.67456019880],
[3.377, 3.81683532672, 1751.53953141600],
[4.585, 0.80787441740, 4136.91043351620],
[3.201, 2.11657635165, 5614.72937620960],
[3.622, 1.32395191387, 3333.49887969900],
[2.916, 1.19337460559, 529.69096509460],
[2.979, 2.86481008776, 6151.53388830500],
[3.057, 4.55276793064, 5628.95647021120],
[2.906, 1.20295377623, 3894.18182954220],
[3.850, 3.86055626689, 553.56940284240],
[2.820, 2.48683324916, 1990.74501704100],
[2.657, 6.07411629964, 4292.33083295040],
[2.700, 2.92139773350, 3496.03282613400],
[2.395, 5.94175921617, 2787.04302385740],
[2.264, 2.56219866409, 191.44826611160],
[2.167, 5.36812435483, 8962.45534991020],
[2.149, 2.74950075397, 242.72860397400],
[2.217, 1.85265984462, 3337.08930835080],
[1.996, 5.76429928131, 3341.59274776800],
[1.999, 3.82349238481, 2914.01423582380],
[1.835, 5.68592723044, 1589.07289528380],
[1.812, 3.32042068028, 5088.62883976680],
[2.413, 4.68291336853, 4690.47983635860],
[1.970, 4.17480610904, 3340.59517304760],
[1.970, 6.20643855008, 3340.62968035200],
[1.627, 5.67733051452, 4535.05943692440],
[2.160, 1.07452599834, 2388.89402044920],
[1.964, 3.10805316088, 3583.34103067380],
[1.985, 5.75850351840, 4399.99435688900],
[1.507, 4.95936409838, 382.89653222320],
[1.278, 4.82232889938, 2957.71589447660],
[1.475, 2.22707926559, 3723.50895892300],
[1.196, 3.26724458920, 9492.14631500480],
[1.349, 4.87573224485, 6525.80445396540],
[1.433, 2.69734916443, 7079.37385680780],
[1.224, 2.62012336714, 10025.36039844840],
[1.404, 5.19056026479, 2700.71514038580],
[1.202, 0.93472783088, 2810.92146160520],
[0.869, 5.81340811635, 12303.06777661000],
[0.867, 2.20046640409, 2699.73481931760],
[0.830, 2.01484544773, 5092.15195811580],
[0.855, 5.96220147975, 426.59819087600],
[0.848, 2.26407047301, 6283.07584999140],
[0.917, 1.40295785881, 6489.77658728800],
[0.833, 1.17384197174, 7477.52286021600],
[1.041, 6.27171470048, 3347.72597370060],
[0.965, 3.39855816541, 5621.84292321040],
[0.722, 4.26304776331, 4933.20844033260],
[0.706, 2.34131594714, 7.11354700080],
[0.768, 2.06208352904, 5486.77784317500],
[0.953, 2.11123497948, 3870.30339179440],
[0.844, 2.23931963240, 3553.91152213780],
[0.646, 2.24669034469, 3340.54511639700],
[0.653, 3.99043329363, 6677.70173505060],
[0.714, 0.29739480601, 6681.24210705180],
[0.828, 0.22863617670, 3532.06069281140],
[0.612, 1.55388376751, 7234.79425624200],
[0.714, 4.54969883976, 6681.20759974740],
[0.586, 3.30118433303, 1221.84856632140],
[0.646, 1.83853693231, 3340.67973700260],
[0.560, 5.05848353328, 8031.09226305840],
[0.651, 0.15897472160, 7632.94325965020],
[0.488, 3.08086378649, 6836.64525283380],
[0.534, 4.25727954634, 3339.63210563160],
[0.504, 2.59990772815, 23384.28698689860],
[0.372, 6.27186983164, 2487.41604494780],
[0.343, 4.71059403854, 639.89728631400],
[0.449, 1.34123846614, 640.87760738220],
[0.342, 5.96338023755, 4929.68532198360],
[0.329, 2.65955258770, 9623.68827669120],
[0.352, 6.09567212646, 7740.60678358880],
[0.326, 6.05498346093, 2118.76386037840],
[0.403, 4.96465831103, 8969.56889691100],
[0.402, 2.84624835384, 5331.35744374080],
[0.319, 1.44545457475, 5729.50644714900],
[0.303, 0.01918776551, 6127.65545055720],
[0.297, 5.74070606294, 6041.32756708560],
[0.297, 3.06763224975, 10419.98628350760],
[0.282, 6.04069352017, 7875.67186362420],
[0.278, 5.11654962157, 11773.37681151540],
[0.259, 2.89786343627, 7210.91581849420],
[0.273, 3.83181794308, 8429.24126646660],
[0.256, 1.08862226474, 2288.34404351140],
[0.288, 6.13572687680, 6682.20517446780],
[0.302, 3.61490647715, 12832.75874170460],
[0.235, 2.21413387615, 6681.29216370240],
[0.317, 3.60634897209, 2301.58581590939],
[0.289, 5.08223311018, 2274.11694950980],
[0.254, 0.36603904729, 3767.21061757580],
[0.235, 2.62434481550, 6681.15754309680],
[0.226, 3.45305949713, 6923.95345737360],
[0.205, 3.88943452829, 10018.31416175040],
[0.206, 3.44453113177, 10177.25767953360],
[0.210, 0.57926734389, 10973.55568635000],
[0.194, 1.57870686859, 10818.13528691580],
[0.190, 2.42312911773, 8955.34180290940],
[0.194, 2.45887376159, 7064.12138562280],
[0.193, 0.58793888724, 5828.02847164760],
[0.183, 1.68247271963, 213.29909543800],
[0.236, 1.98863774162, 10575.40668294180],
[0.245, 2.17761779228, 4562.46099302120],
[0.177, 0.66379705293, 10021.85453375160],
[0.176, 4.91607557961, 10021.82002644720],
[0.217, 2.93968443649, 13365.97282514820],
[0.167, 4.74764434327, 3914.95722503460],
[0.213, 0.15734917857, 2942.46342329160],
[0.155, 1.78776991092, 9830.38901398780],
[0.180, 5.21088564787, 9866.41688066520],
[0.161, 5.17683861380, 6298.32832117640],
[0.159, 2.68980684850, 6894.52394883760],
[0.149, 6.26524493469, 1039.02661079040],
[0.147, 0.36939961702, 6688.33840040040],
[0.151, 1.22272892290, 574.34479833480],
[0.137, 2.09492296067, 1066.49547719000],
[0.165, 6.15952050903, 15643.68020330980],
[0.163, 4.66507592292, 8273.82086703240],
[0.124, 0.67855210339, 6438.49624942560],
[0.128, 1.69206367749, 3981.49003408200],
[0.116, 2.78191248964, 3360.96774609859],
[0.128, 0.84461423001, 3355.86489788480],
[0.124, 1.63253732557, 6674.11130639880],
[0.120, 0.31762150109, 3127.31333126180],
[0.129, 2.26678583645, 6467.92575796160],
[0.104, 0.07355376701, 3325.35995551480],
[0.130, 4.41777190830, 3320.25710730100],
[0.095, 1.31957248342, 7903.07341972100],
[0.114, 0.65681602343, 3178.14579056760],
[0.092, 4.98392367746, 9779.10867612540],
[0.101, 4.10670787374, 536.80451209540],
[0.106, 5.41622566807, 15113.98923821520],
[0.096, 3.52561014696, 3475.67750673520],
[0.101, 2.91169549546, 692.15760122680],
[0.093, 3.21464368291, 8671.96987044060],
[0.087, 5.24375873119, 13119.72110282519],
[0.106, 3.76804681559, 13517.87010623340],
[0.089, 5.73652101746, 11371.70468975820],
[0.104, 5.90078964406, 8432.76438481560],
[0.099, 3.61425346453, 853.19638175200],
[0.078, 0.95802015551, 3191.04922956520],
[0.089, 2.50872076312, 1052.26838318840],
[0.078, 2.98115354616, 26724.89941359840],
[0.079, 5.91514993930, 6040.34724601740],
[0.090, 3.00950470302, 12964.30070339100],
[0.075, 1.31512531841, 17924.91069982040],
[0.073, 5.01153593776, 1903.43681250120],
[0.075, 2.57969241717, 10021.90459040220],
[0.073, 4.09954161905, 3319.83703120740],
[0.070, 5.37678396256, 12310.18132361080],
[0.071, 0.98422998240, 13362.46696045140],
[0.068, 4.69140248943, 522.57741809380],
[0.068, 3.24217441291, 16706.58525184800],
[0.069, 2.53964193741, 5884.92684658320],
[0.070, 2.38237948321, 13916.01910964160],
[0.066, 3.48443797546, 13760.59871020740],
[0.068, 5.27435069681, 3980.50971301380],
[0.076, 0.12288413214, 11216.28429032400],
[0.073, 3.94785759909, 16173.37116840440],
[0.062, 0.15518975647, 11081.21921028860],
[0.074, 2.99926779692, 10021.76996979660],
[0.080, 6.18812323827, 9380.95967271720],
[0.064, 3.99294283669, 13358.92658845020],
[0.061, 2.56817782412, 149.56319713460],
[0.059, 3.80850908229, 10264.56588407340],
[0.060, 4.79879360562, 1437.17561419860],
[0.068, 2.07515658228, 1596.18644228460],
[0.060, 2.26503107747, 28628.33622609960],
[0.058, 6.10782258899, 5459.37628707820],
[0.063, 0.24407077742, 18984.29263000960],
[0.058, 5.22738430747, 13362.43245314700],
[0.056, 1.88708253797, 9070.11887384880],
[0.055, 5.72587156499, 433.71173787680],
[0.056, 1.18238857561, 6696.47732458460],
[0.062, 3.98214740104, 3427.92063123960],
[0.056, 5.37129176649, 5099.26550511660],
[0.057, 0.86204712032, 5642.19824260920],
[0.055, 1.31787605222, 8982.81066930900],
[0.056, 5.49808236951, 24093.27678917520],
[0.054, 3.77562154746, 10213.28554621100],
[0.054, 2.36294643031, 33716.96506586640],
[0.063, 3.53402427573, 3205.54734666440],
[0.066, 6.25810929981, 8270.29774868340],
[0.067, 0.58592813080, 3335.08950239240],
[0.055, 4.74995645767, 6660.86953400080],
[0.053, 0.31930032532, 12721.57209941700],
[0.069, 2.42905593362, 6158.64743530580],
[0.055, 5.03192783121, 7255.56965173440],
[0.051, 5.45351947711, 13207.02930736500],
[0.050, 0.23368526162, 4379.63903749020],
[0.053, 2.12826344020, 13171.00144068760],
[0.049, 2.35512151368, 4032.77002792660],
[0.049, 2.81773050890, 9808.53818466140],
[0.067, 2.26295786556, 2766.26762836500],
[0.049, 0.72597680486, 10028.95082710020],
[0.050, 6.10119450350, 3253.30422216000],
[0.059, 0.27861398526, 9225.53927328300],
[0.053, 1.27330874549, 3344.49376205780],
[0.049, 2.91499389416, 10404.73381232260],
[0.047, 0.48598973231, 17395.21973472580],
[0.049, 3.40240207389, 3304.58456002240],
[0.060, 3.40554368741, 10551.52824519400],
[0.050, 1.83471955355, 30376.35263916660],
[0.046, 3.04980996832, 6144.42034130420],
[0.049, 0.33200904496, 6702.00024889200],
[0.053, 0.35820094732, 9468.26787725700],
[0.050, 0.15378507249, 2648.45482547300],
[0.044, 0.79762157297, 7107.82304427560],
[0.050, 2.41332661328, 4407.10790388980],
[0.054, 0.21682940856, 10022.81760116760],
[0.044, 5.78502737591, 3364.49086444760],
[0.044, 0.75508636274, 16062.18452611680],
[0.043, 3.10581037685, 10235.13637553740],
[0.044, 5.21252098878, 7373.38245462640],
[0.058, 4.51680312444, 6660.44945790720],
[0.043, 0.15523355839, 1505.28780909299],
[0.055, 5.93371026829, 8439.87793181640],
[0.042, 5.40417232308, 3344.20285535160],
[0.056, 3.87534582911, 6816.28993343500],
[0.049, 5.57153056447, 17468.85519794540],
[0.046, 3.07783299049, 12722.55242048520],
[0.045, 1.49303542795, 6247.51311552280],
[0.055, 6.26098836404, 3361.38782219220],
[0.042, 4.74455545491, 3369.06161416760],
[0.040, 1.58676666294, 2818.03500860600],
[0.043, 4.97295184315, 3337.02199804800],
[0.055, 3.80215638520, 3376.64029337720],
[0.047, 1.97367775421, 1581.95934828300],
[0.045, 2.03598705348, 5244.04923920100],
[0.049, 4.43182954044, 9595.23908922340],
[0.043, 0.38914582094, 6665.97238221460],
[0.040, 1.06953099245, 23695.12778576700],
[0.038, 0.59996214864, 10713.99488132620],
[0.039, 3.79055778605, 33318.81606245820],
[0.041, 5.54542347834, 3863.18984479360],
[0.037, 5.27208151144, 20752.66436247540],
[0.039, 3.15412760412, 14469.58851248400],
[0.041, 0.55705920174, 3346.13535100720],
[0.048, 1.42210748234, 3316.73398895200],
[0.049, 5.44942247991, 9638.94074787620],
[0.038, 2.11846271943, 15664.03552270859],
[0.035, 5.30782933148, 6677.63442474780],
[0.036, 2.68151450016, 8584.66166590080],
[0.046, 3.09450395763, 6701.58017279840],
[0.038, 1.81885395671, 14158.74771361560],
[0.037, 5.80483071722, 6684.81528205140],
[0.047, 2.60317702777, 162.46663613220],
[0.038, 2.22559377525, 3503.07906283200],
[0.035, 0.84358942718, 6518.75821726740],
[0.033, 4.92302322062, 23141.55838292460],
[0.043, 0.95148893985, 34115.11406927460],
[0.046, 4.99457196207, 9381.93999378540],
[0.043, 1.73832102244, 12323.42309600880],
[0.032, 2.92741580696, 9499.25986200560],
[0.043, 1.50296327105, 27035.74021246680],
[0.033, 5.41731109688, 20597.24396304120],
[0.032, 4.13881058425, 31570.79964939120],
[0.040, 5.84463069180, 16460.33352952499],
[0.035, 5.50083743557, 8425.65083781480],
[0.038, 5.91991985929, 3336.73109134180],
[0.030, 5.09155042811, 5085.03841111500],
[0.031, 4.27211180916, 36659.42848915800],
[0.030, 4.87389489592, 1692.16566950240],
[0.030, 3.75494646937, 4845.90023579280],
[0.034, 3.71030605417, 8827.39026987480],
[0.030, 0.01599456850, 11243.68584642080],
[0.029, 2.66198696023, 12295.95422960920],
[0.028, 3.12114207206, 11925.27409260060],
[0.036, 1.16568750904, 18052.92954315780],
[0.032, 1.72704226918, 12566.15169998280],
[0.028, 2.80254457895, 3607.21946842160],
[0.032, 4.04390839531, 6680.24453233140],
[0.027, 2.53565904393, 19004.64794940840],
[0.036, 3.33518515689, 29978.20363575840],
[0.028, 0.58104982217, 20354.51535906720],
[0.029, 5.85207825749, 31172.65064598300],
[0.026, 2.22598820379, 3.52311834900],
[0.033, 5.15903548241, 10596.18207843420],
[0.028, 1.89792803028, 3333.56619000180],
[0.027, 2.25129832716, 76.26607127560],
[0.026, 4.32703172263, 17085.95866572220],
[0.026, 5.12847780702, 11766.26326451460],
[0.028, 0.80926596905, 20735.83216142559],
[0.026, 5.06814803493, 17412.05193577560],
[0.024, 4.47399155600, 3134.42687826260],
[0.024, 4.35557152695, 14584.29827312060],
[0.027, 4.98717355201, 3877.41693879520],
[0.025, 5.63712701265, 14054.60730802600],
[0.024, 4.12573657295, 4193.80880845180],
[0.025, 1.40880282063, 8186.51266249260],
[0.024, 4.96463811748, 26087.90314157420],
],
# R3
[
[1113.107, 5.14987350142, 3340.61242669980],
[424.446, 5.61343766478, 6681.22485339960],
[100.044, 5.99726827028, 10021.83728009940],
[19.606, 0.07633062094, 13362.44970679920],
[3.477, 0.42951907576, 16703.06213349900],
[4.693, 3.14159265359, 0.00000000000],
[2.869, 0.44711842697, 3344.13554504880],
[2.428, 3.02115527957, 3185.19202726560],
[0.688, 0.80693359444, 6684.74797174860],
[0.540, 3.86836515672, 1059.38193018920],
[0.577, 0.77853275120, 20043.67456019880],
[0.468, 4.52450786544, 3496.03282613400],
[0.487, 1.60862391345, 3583.34103067380],
[0.362, 4.42397903418, 2787.04302385740],
[0.397, 5.71967986581, 3149.16416058820],
[0.299, 0.75640033535, 3738.76143010800],
[0.350, 5.55691984889, 4136.91043351620],
[0.314, 3.37632898783, 6525.80445396540],
[0.233, 2.13965262306, 3097.88382272579],
[0.212, 4.20487494011, 3341.59274776800],
[0.214, 0.56779556947, 155.42039943420],
[0.201, 2.35284464564, 1592.59601363280],
[0.204, 0.96723315302, 1990.74501704100],
[0.230, 5.82959057146, 2388.89402044920],
[0.160, 4.14974194757, 4535.05943692440],
[0.156, 5.13345210285, 796.29800681640],
[0.146, 3.29541339704, 2957.71589447660],
[0.156, 1.13805508457, 10025.36039844840],
[0.159, 3.76174286126, 1194.44701022460],
[0.136, 5.58293924642, 3894.18182954220],
[0.145, 3.02112488974, 3337.08930835080],
[0.146, 4.25359617225, 4399.99435688900],
[0.100, 4.26740096115, 1589.07289528380],
[0.091, 6.12108227231, 6489.77658728800],
[0.101, 1.17242141914, 7079.37385680780],
[0.098, 1.12613498307, 23384.28698689860],
[0.075, 6.02182689533, 529.69096509460],
[0.078, 5.93418069229, 7477.52286021600],
[0.068, 1.70775041911, 9492.14631500480],
[0.070, 3.67253155189, 8962.45534991020],
[0.062, 4.14954627063, 4292.33083295040],
[0.067, 0.15092246550, 3870.30339179440],
[0.066, 1.12578506413, 6151.53388830500],
[0.062, 1.93984222091, 6923.95345737360],
[0.060, 4.30641513096, 12303.06777661000],
[0.074, 4.72156358149, 3347.72597370060],
[0.055, 2.75742802464, 4933.20844033260],
[0.053, 4.77894621871, 6127.65545055720],
[0.050, 2.57807944338, 3340.59517304760],
[0.048, 3.72532068729, 9866.41688066520],
[0.042, 6.15391373101, 7234.79425624200],
[0.043, 3.43955584179, 5486.77784317500],
[0.050, 4.60885064189, 3340.62968035200],
[0.044, 4.47943289816, 426.59819087600],
[0.045, 6.24485207500, 2274.11694950980],
[0.040, 0.73805316471, 7.11354700080],
[0.038, 1.06497784748, 9623.68827669120],
[0.041, 4.60954640493, 6682.20517446780],
[0.038, 4.60963924082, 7740.60678358880],
[0.036, 3.15129246169, 639.89728631400],
[0.037, 6.14629970622, 5729.50644714900],
[0.040, 1.47395544850, 13365.97282514820],
[0.035, 2.60772245492, 4690.47983635860],
[0.035, 2.45077931900, 2288.34404351140],
[0.034, 4.50544497582, 7875.67186362420],
[0.042, 2.11383330882, 12832.75874170460],
[0.033, 3.97655860802, 191.44826611160],
[0.032, 4.06047154083, 3532.06069281140],
[0.034, 5.06671994554, 6681.24210705180],
[0.042, 4.67024017441, 15643.68020330980],
[0.036, 0.29140871479, 3723.50895892300],
[0.033, 4.52588149629, 4929.68532198360],
[0.034, 2.74499072890, 6677.70173505060],
[0.030, 1.57743012295, 10419.98628350760],
[0.040, 1.31713176335, 5331.35744374080],
[0.034, 3.03490000148, 6681.20759974740],
[0.031, 1.25306164576, 242.72860397400],
[0.029, 5.44118048011, 10021.85453375160],
[0.029, 3.41037097794, 10021.82002644720],
[0.028, 4.81855060968, 6836.64525283380],
[0.028, 0.72745302325, 6283.07584999140],
[0.030, 3.06267495632, 2281.23049651060],
[0.027, 0.62535799761, 6681.29216370240],
[0.030, 3.56389476096, 8969.56889691100],
[0.032, 5.31078691958, 553.56940284240],
[0.033, 2.00753799963, 5884.92684658320],
[0.027, 1.18001479303, 8955.34180290940],
[0.025, 2.94122791628, 2544.31441988340],
[0.025, 0.17808889827, 9830.38901398780],
[0.031, 5.73384204593, 3339.63210563160],
[0.028, 3.70436008855, 6298.32832117640],
[0.024, 0.07739730466, 10818.13528691580],
[0.027, 1.03401737006, 6681.15754309680],
[0.024, 0.09987383242, 382.89653222320],
[0.027, 0.60053652251, 3553.91152213780],
[0.027, 4.97107900859, 3767.21061757580],
[0.024, 3.36621347824, 8031.09226305840],
[0.026, 4.80509833364, 7632.94325965020],
[0.022, 1.43966107077, 26724.89941359840],
[0.020, 0.36901153144, 398.14900340820],
[0.019, 1.00325306041, 7064.12138562280],
[0.020, 0.19821371186, 6674.11130639880],
[0.018, 1.07169297658, 7210.91581849420],
[0.021, 2.69512140340, 10018.31416175040],
[0.023, 3.25670295081, 5621.84292321040],
[0.018, 0.24542781929, 3981.49003408200],
[0.018, 5.14428605713, 6688.33840040040],
[0.020, 0.97539014916, 6894.52394883760],
[0.024, 4.42156401638, 1748.01641306700],
[0.016, 0.65389503440, 3340.54511639700],
[0.016, 5.28427106012, 3333.49887969900],
],
# R4
[
[19.552, 3.58211650473, 3340.61242669980],
[16.323, 4.05116076923, 6681.22485339960],
[5.848, 4.46383962094, 10021.83728009940],
[1.532, 4.84374321619, 13362.44970679920],
[0.375, 1.50962233608, 3185.19202726560],
[0.339, 5.20684967613, 16703.06213349900],
[0.151, 5.16472931648, 3344.13554504880],
[0.125, 2.19233532803, 3496.03282613400],
[0.148, 0.00000000000, 0.00000000000],
[0.087, 0.10275067375, 3583.34103067380],
[0.070, 5.55303619365, 20043.67456019880],
[0.048, 2.91797786512, 2787.04302385740],
[0.049, 5.57038514830, 6684.74797174860],
[0.057, 1.86867280743, 6525.80445396540],
[0.034, 3.63370917313, 3097.88382272579],
[0.021, 2.30677637991, 1059.38193018920],
[0.021, 4.03682122005, 4136.91043351620],
[0.018, 4.17438755890, 3149.16416058820],
[0.013, 1.97805475719, 155.42039943420],
[0.017, 5.94856414690, 10025.36039844840],
[0.012, 0.51097435253, 6923.95345737360],
[0.012, 3.27945299261, 6127.65545055720],
[0.013, 2.22938285522, 9866.41688066520],
[0.016, 2.64206771227, 4399.99435688900],
[0.013, 2.75813969974, 6836.64525283380],
[0.013, 4.51988349676, 6489.77658728800],
[0.014, 0.76591550754, 3894.18182954220],
[0.011, 5.47381242145, 3738.76143010800],
],
# R5
[
[0.476, 2.47617204701, 6681.22485339960],
[0.268, 2.91510547706, 10021.83728009940],
[0.115, 1.76888962311, 3340.61242669980],
[0.096, 3.31378377179, 13362.44970679920],
[0.048, 6.27457828287, 3185.19202726560],
[0.027, 3.69380877066, 16703.06213349900],
[0.013, 3.72005807206, 3496.03282613400],
[0.012, 4.88179002689, 3583.34103067380],
[0.012, 3.14159265359, 0.00000000000],
],
]
"""This table contains Mars' periodic terms (all of them) from the planetary
theory VSOP87 for the radius vector at the equinox of date (taken from the 'D'
solution). In Meeus' book a shortened version can be found in pages 425-426."""
ORBITAL_ELEM = [
[355.433, 19141.6964471, 0.00031052, 0.000000016], # L
[1.523679342, 0.0, 0.0, 0.0], # a
[0.09340065, 0.000090484, -0.0000000806, -0.00000000025], # e
[1.849726, -0.0006011, 0.00001276, -0.000000007], # i
[49.558093, 0.7720959, 0.00001557, 0.000002267], # Omega
[336.060234, 1.8410449, 0.00013477, 0.000000536] # pie
]
"""This table contains the parameters to compute Mars' orbital elements for
the mean equinox of date. Based in Table 31.A, page 212"""
ORBITAL_ELEM_J2000 = [
[355.433, 19140.2993039, 0.00000262, -0.000000003], # L
[1.849726, -0.0081477, -0.00002255, -0.000000029], # i
[49.558093, -0.295025, -0.00064048, -0.000001964], # Omega
[336.060234, 0.4439016, -0.00017313, 0.000000518] # pie
]
"""This table contains the parameters to compute Mars' orbital elements for
the standard equinox J2000.0. Based on Table 31.B, page 214"""
[docs]class Mars(object):
"""
Class Mars models that planet.
"""
[docs] @staticmethod
def geometric_heliocentric_position(epoch, tofk5=True):
"""This method computes the geometric heliocentric position of planet
Mars for a given epoch, using the VSOP87 theory.
:param epoch: Epoch to compute Mars position, as an Epoch object
:type epoch: :py:class:`Epoch`
:param tofk5: Whether or not the small correction to convert to the FK5
system will be applied or not
:type tofk5: bool
:returns: A tuple with the heliocentric longitude and latitude (as
:py:class:`Angle` objects), and the radius vector (as a float,
in astronomical units), in that order
:rtype: tuple
:raises: TypeError if input values are of wrong type.
>>> epoch = Epoch(2018, 10, 27.0)
>>> l, b, r = Mars.geometric_heliocentric_position(epoch)
>>> print(round(l.to_positive(), 4))
2.0015
>>> print(round(b, 4))
-1.3683
>>> print(round(r, 5))
1.39306
"""
return geometric_vsop_pos(epoch, VSOP87_L, VSOP87_B, VSOP87_R, tofk5)
[docs] @staticmethod
def apparent_heliocentric_position(epoch):
"""This method computes the apparent heliocentric position of planet
Mars for a given epoch, using the VSOP87 theory.
:param epoch: Epoch to compute Mars position, as an Epoch object
:type epoch: :py:class:`Epoch`
:returns: A tuple with the heliocentric longitude and latitude (as
:py:class:`Angle` objects), and the radius vector (as a float,
in astronomical units), in that order
:rtype: tuple
:raises: TypeError if input values are of wrong type.
"""
return apparent_vsop_pos(epoch, VSOP87_L, VSOP87_B, VSOP87_R)
[docs] @staticmethod
def orbital_elements_mean_equinox(epoch):
"""This method computes the orbital elements of Mars for the mean
equinox of the date for a given epoch.
:param epoch: Epoch to compute orbital elements, as an Epoch object
:type epoch: :py:class:`Epoch`
:returns: A tuple containing the following six orbital elements:
- Mean longitude of the planet (Angle)
- Semimajor axis of the orbit (float, astronomical units)
- eccentricity of the orbit (float)
- inclination on the plane of the ecliptic (Angle)
- longitude of the ascending node (Angle)
- argument of the perihelion (Angle)
:rtype: tuple
:raises: TypeError if input values are of wrong type.
>>> epoch = Epoch(2065, 6, 24.0)
>>> l, a, e, i, ome, arg = Mars.orbital_elements_mean_equinox(epoch)
>>> print(round(l, 6))
288.855211
>>> print(round(a, 8))
1.52367934
>>> print(round(e, 7))
0.0934599
>>> print(round(i, 6))
1.849338
>>> print(round(ome, 5))
50.06365
>>> print(round(arg, 6))
287.202108
"""
return orbital_elements(epoch, ORBITAL_ELEM, ORBITAL_ELEM)
[docs] @staticmethod
def orbital_elements_j2000(epoch):
"""This method computes the orbital elements of Mars for the
standard equinox J2000.0 for a given epoch.
:param epoch: Epoch to compute orbital elements, as an Epoch object
:type epoch: :py:class:`Epoch`
:returns: A tuple containing the following six orbital elements:
- Mean longitude of the planet (Angle)
- Semimajor axis of the orbit (float, astronomical units)
- eccentricity of the orbit (float)
- inclination on the plane of the ecliptic (Angle)
- longitude of the ascending node (Angle)
- argument of the perihelion (Angle)
:rtype: tuple
:raises: TypeError if input values are of wrong type.
>>> epoch = Epoch(2065, 6, 24.0)
>>> l, a, e, i, ome, arg = Mars.orbital_elements_j2000(epoch)
>>> print(round(l, 6))
287.94027
>>> print(round(a, 8))
1.52367934
>>> print(round(e, 7))
0.0934599
>>> print(round(i, 6))
1.844381
>>> print(round(ome, 5))
49.36464
>>> print(round(arg, 6))
286.98617
"""
return orbital_elements(epoch, ORBITAL_ELEM, ORBITAL_ELEM_J2000)
[docs] @staticmethod
def geocentric_position(epoch):
"""This method computes the geocentric position of Mars (right
ascension and declination) for the given epoch, as well as the
elongation angle.
:param epoch: Epoch to compute geocentric position, as an Epoch object
:type epoch: :py:class:`Epoch`
:returns: A tuple containing the right ascension, the declination and
the elongation angle as Angle objects
:rtype: tuple
:raises: TypeError if input value is of wrong type.
>>> epoch = Epoch(1992, 12, 20.0)
>>> ra, dec, elon = Mars.geocentric_position(epoch)
>>> print(ra.ra_str(n_dec=1))
7h 48' 35.4''
>>> print(dec.dms_str(n_dec=1))
24d 35' 33.9''
>>> print(elon.dms_str(n_dec=1))
153d 35' 1.6''
"""
# First check that input value is of correct types
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input type")
# Compute the heliocentric position of Mars
l, b, r = Mars.geometric_heliocentric_position(epoch, tofk5=False)
# Compute the heliocentric position of the Earth
l0, b0, r0 = Earth.geometric_heliocentric_position(epoch, tofk5=False)
# Convert to radians
lr = l.rad()
br = b.rad()
l0r = l0.rad()
b0r = b0.rad()
# Compute first iteration
x = r * cos(br) * cos(lr) - r0 * cos(b0r) * cos(l0r)
y = r * cos(br) * sin(lr) - r0 * cos(b0r) * sin(l0r)
z = r * sin(br) - r0 * sin(b0r)
delta = sqrt(x * x + y * y + z * z)
tau = 0.0057755183 * delta
# Adjust the epoch for light-time
epoch -= tau
# Compute again Mars coordinates with this correction
l, b, r = Mars.geometric_heliocentric_position(epoch, tofk5=False)
# Compute second iteration
lr = l.rad()
br = b.rad()
x = r * cos(br) * cos(lr) - r0 * cos(b0r) * cos(l0r)
y = r * cos(br) * sin(lr) - r0 * cos(b0r) * sin(l0r)
z = r * sin(br) - r0 * sin(b0r)
# Compute longitude and latitude
lamb = atan2(y, x)
beta = atan2(z, sqrt(x * x + y * y))
# Now, let's compute the aberration effect
t = (epoch - JDE2000) / 36525
e = 0.016708634 + t * (-0.000042037 - t * 0.0000001267)
pie = 102.93735 + t * (1.71946 + t * 0.00046)
pie = radians(pie)
lon = l0 + 180.0
lon = lon.rad()
k = 20.49552 # The constant of aberration
deltal1 = k * (-cos(lon - lamb) + e * cos(pie - lamb)) / cos(beta)
deltab1 = -k * sin(beta) * (sin(lon - lamb) - e * sin(pie - lamb))
deltal1 = Angle(0, 0, deltal1)
deltab1 = Angle(0, 0, deltab1)
# Correction to FK5 system
lamb = Angle(lamb, radians=True)
lamb = lamb.to_positive()
beta = Angle(beta, radians=True)
l_prime = lamb - t * (1.397 + t * 0.00031)
deltal2 = Angle(0, 0, -0.09033)
a = 0.03916 * (cos(l_prime.rad()) + sin(l_prime.rad()))
a = a * tan(b.rad())
deltal2 += Angle(0, 0, a)
deltab2 = 0.03916 * (cos(l_prime.rad()) - sin(l_prime.rad()))
deltab2 = Angle(0, 0, deltab2)
# Apply the corrections
lamb = lamb + deltal1 + deltal2
beta = beta + deltab1 + deltab2
# Correction for nutation
dpsi = nutation_longitude(epoch)
lamb += dpsi
e = true_obliquity(epoch)
ra, dec = ecliptical2equatorial(lamb, beta, e)
# Let's compute the elongation angle
lons, lats, rs = Sun.apparent_geocentric_position(epoch)
lambr = lamb.rad()
lsr = lons.rad()
betar = beta.rad()
elon = acos(cos(betar) * cos(lambr - lsr))
elon = Angle(elon, radians=True)
return ra, dec, elon
[docs] @staticmethod
def conjunction(epoch):
"""This method computes the time of the conjunction closest to the
given epoch.
:param epoch: Epoch close to the desired conjunction
:type epoch: :py:class:`Epoch`
:returns: The time when the conjunction happens, as an Epoch
:rtype: :py:class:`Epoch`
:raises: TypeError if input value is of wrong type.
:raises: ValueError if input epoch outside the -2000/4000 range.
>>> epoch = Epoch(1993, 10, 1.0)
>>> conj = Mars.conjunction(epoch)
>>> y, m, d = conj.get_date()
>>> print(y)
1993
>>> print(m)
12
>>> print(round(d, 4))
27.0898
"""
# First check that input value is of correct types
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input type")
# Check that the input epoch is within valid range
y = epoch.year()
if y < -2000.0 or y > 4000.0:
raise ValueError("Epoch outside the -2000/4000 range")
# Set some specific constants for Mars' conjunction
a = 2451707.414
b = 779.936104
m0 = 157.6047
m1 = 48.705244
k = round((365.2425 * y + 1721060.0 - a) / b)
jde0 = a + k * b
m = m0 + k * m1
m = Angle(m).to_positive()
m = m.rad()
t = (jde0 - 2451545.0) / 36525.0
corr = (0.3102 + t * (-0.0001 + t * 0.00001)
+ sin(m) * (9.7273 + t * (-0.0156 + t * 0.00001))
+ cos(m) * (-18.3195 + t * (-0.0467 + t * 0.00009))
+ sin(2.0 * m) * (-1.6488 + t * (-0.0133 + t * 0.00001))
+ cos(2.0 * m) * (-2.6117 + t * (-0.002 + t * 0.00004))
+ sin(3.0 * m) * (-0.6827 + t * (-0.0026 + t * 0.00001))
+ cos(3.0 * m) * (0.0281 + t * (0.0035 + t * 0.00001))
+ sin(4.0 * m) * (-0.0823 + t * (0.0006 + t * 0.00001))
+ cos(4.0 * m) * (0.1584 + t * 0.0013)
+ sin(5.0 * m) * (0.027 + t * 0.0005)
+ cos(5.0 * m) * (0.0433))
to_return = jde0 + corr
return Epoch(to_return)
[docs] @staticmethod
def opposition(epoch):
"""This method computes the time of the opposition closest to the given
epoch.
:param epoch: Epoch close to the desired opposition
:type epoch: :py:class:`Epoch`
:returns: The time when the opposition happens, as an Epoch
:rtype: :py:class:`Epoch`
:raises: TypeError if input value is of wrong type.
:raises: ValueError if input epoch outside the -2000/4000 range.
>>> epoch = Epoch(2729, 10, 1.0)
>>> oppo = Mars.opposition(epoch)
>>> y, m, d = oppo.get_date()
>>> print(y)
2729
>>> print(m)
9
>>> print(round(d, 4))
9.1412
"""
# First check that input value is of correct types
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input type")
# Check that the input epoch is within valid range
y = epoch.year()
if y < -2000.0 or y > 4000.0:
raise ValueError("Epoch outside the -2000/4000 range")
# Set some specific constants for Mars' opposition
a = 2452097.382
b = 779.936104
m0 = 181.9573
m1 = 48.705244
k = round((365.2425 * y + 1721060.0 - a) / b)
jde0 = a + k * b
m = m0 + k * m1
m = Angle(m).to_positive()
m = m.rad()
t = (jde0 - 2451545.0) / 36525.0
corr = (-0.3088 + t * t * 0.00002
+ sin(m) * (-17.6965 + t * (0.0363 + t * 0.00005))
+ cos(m) * (18.3131 + t * (0.0467 - t * 0.00006))
+ sin(2.0 * m) * (-0.2162 + t * (-0.0198 - t * 0.00001))
+ cos(2.0 * m) * (-4.5028 + t * (-0.0019 + t * 0.00007))
+ sin(3.0 * m) * (0.8987 + t * (0.0058 - t * 0.00002))
+ cos(3.0 * m) * (0.7666 + t * (-0.005 - t * 0.00003))
+ sin(4.0 * m) * (-0.3636 + t * (-0.0001 + t * 0.00002))
+ cos(4.0 * m) * (0.0402 + t * 0.0032)
+ sin(5.0 * m) * (0.0737 - t * 0.0008)
+ cos(5.0 * m) * (-0.098 - t * 0.0011))
to_return = jde0 + corr
return Epoch(to_return)
[docs] @staticmethod
def station_longitude_1(epoch):
"""This method computes the time of the 1st station in longitude
(i.e. when the planet is stationary and begins to move westward -
retrograde - among the starts) closest to the given epoch.
:param epoch: Epoch close to the desired opposition
:type epoch: :py:class:`Epoch`
:returns: Time when the 1st station in longitude happens, as an Epoch
:rtype: :py:class:`Epoch`
:raises: TypeError if input value is of wrong type.
:raises: ValueError if input epoch outside the -2000/4000 range.
>>> epoch = Epoch(1997, 3, 1.0)
>>> sta1 = Mars.station_longitude_1(epoch)
>>> y, m, d = sta1.get_date()
>>> print(y)
1997
>>> print(m)
2
>>> print(round(d, 4))
6.033
"""
# First check that input value is of correct types
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input type")
# Check that the input epoch is within valid range
y = epoch.year()
if y < -2000.0 or y > 4000.0:
raise ValueError("Epoch outside the -2000/4000 range")
# Set some specific constants for Mars' opposition
a = 2452097.382
b = 779.936104
m0 = 181.9573
m1 = 48.705244
k = round((365.2425 * y + 1721060.0 - a) / b)
jde0 = a + k * b
m = m0 + k * m1
m = Angle(m).to_positive()
m = m.rad()
t = (jde0 - 2451545.0) / 36525.0
corr = (-37.079 + t * (-0.0009 + t * 0.00002)
+ sin(m) * (-20.0651 + t * (0.0228 + t * 0.00004))
+ cos(m) * (14.5205 + t * (0.0504 - t * 0.00001))
+ sin(2.0 * m) * (1.1737 - t * 0.0169)
+ cos(2.0 * m) * (-4.255 + t * (-0.0075 + t * 0.00008))
+ sin(3.0 * m) * (0.4897 + t * (0.0074 - t * 0.00001))
+ cos(3.0 * m) * (1.1151 + t * (-0.0021 - t * 0.00005))
+ sin(4.0 * m) * (-0.3636 + t * (-0.002 + t * 0.00001))
+ cos(4.0 * m) * (-0.1769 + t * (0.0028 + t * 0.00002))
+ sin(5.0 * m) * (0.1437 - t * 0.0004)
+ cos(5.0 * m) * (-0.0383 - t * 0.0016))
to_return = jde0 + corr
return Epoch(to_return)
[docs] @staticmethod
def station_longitude_2(epoch):
"""This method computes the time of the 2nd station in longitude
(i.e. when the planet is stationary and begins to move eastward -
prograde - among the starts) closest to the given epoch.
:param epoch: Epoch close to the desired opposition
:type epoch: :py:class:`Epoch`
:returns: Time when the 2nd station in longitude happens, as an Epoch
:rtype: :py:class:`Epoch`
:raises: TypeError if input value is of wrong type.
:raises: ValueError if input epoch outside the -2000/4000 range.
>>> epoch = Epoch(1997, 3, 1.0)
>>> sta2 = Mars.station_longitude_2(epoch)
>>> y, m, d = sta2.get_date()
>>> print(y)
1997
>>> print(m)
4
>>> print(round(d, 4))
27.7553
"""
# First check that input value is of correct types
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input type")
# Check that the input epoch is within valid range
y = epoch.year()
if y < -2000.0 or y > 4000.0:
raise ValueError("Epoch outside the -2000/4000 range")
# Set some specific constants for Mars' opposition
a = 2452097.382
b = 779.936104
m0 = 181.9573
m1 = 48.705244
k = round((365.2425 * y + 1721060.0 - a) / b)
jde0 = a + k * b
m = m0 + k * m1
m = Angle(m).to_positive()
m = m.rad()
t = (jde0 - 2451545.0) / 36525.0
corr = (36.7191 + t * (0.0016 + t * 0.00003)
+ sin(m) * (-12.6163 + t * (0.0417 - t * 0.00001))
+ cos(m) * (20.1218 + t * (0.0379 - t * 0.00006))
+ sin(2.0 * m) * (-1.636 - t * 0.019)
+ cos(2.0 * m) * (-3.9657 + t * (0.0045 + t * 0.00007))
+ sin(3.0 * m) * (1.1546 + t * (0.0029 - t * 0.00003))
+ cos(3.0 * m) * (0.2888 + t * (-0.0073 - t * 0.00002))
+ sin(4.0 * m) * (-0.3128 + t * (0.0017 + t * 0.00002))
+ cos(4.0 * m) * (0.2513 + t * (0.0026 - t * 0.00002))
+ sin(5.0 * m) * (-0.0021 - t * 0.0016)
+ cos(5.0 * m) * (-0.1497 - t * 0.0006))
to_return = jde0 + corr
return Epoch(to_return)
[docs] @staticmethod
def perihelion_aphelion(epoch, perihelion=True):
"""This method computes the time of Perihelion (or Aphelion) closer to
a given epoch.
:param epoch: Epoch close to the desired Perihelion (or Aphelion)
:type epoch: :py:class:`Epoch`
:param peihelion: If True, the epoch of the closest Perihelion is
computed, if False, the epoch of the closest Aphelion is found.
:type bool:
:returns: The epoch of the desired Perihelion (or Aphelion)
:rtype: :py:class:`Epoch`
:raises: TypeError if input values are of wrong type.
>>> epoch = Epoch(2019, 2, 23.0)
>>> e = Mars.perihelion_aphelion(epoch)
>>> y, m, d, h, mi, s = e.get_full_date()
>>> print(y)
2018
>>> print(m)
9
>>> print(d)
16
>>> print(h)
12
>>> epoch = Epoch(2032, 1, 1.0)
>>> e = Mars.perihelion_aphelion(epoch, perihelion=False)
>>> y, m, d, h, mi, s = e.get_full_date()
>>> print(y)
2032
>>> print(m)
10
>>> print(d)
24
>>> print(h)
22
"""
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input value")
# First approximation
k = 0.53166 * (epoch.year() - 2001.78)
if perihelion:
k = round(k)
else:
k = round(k + 0.5) - 0.5
jde = 2452195.026 + k * (686.9957857 - k * 0.0000001187)
# Compute the epochs half a day before and after
jde_before = jde - 0.5
jde_after = jde + 0.5
# Compute the Sun-Mars distance for each epoch
l, b, r_b = Mars.geometric_heliocentric_position(Epoch(jde_before))
l, b, r = Mars.geometric_heliocentric_position(Epoch(jde))
l, b, r_a = Mars.geometric_heliocentric_position(Epoch(jde_after))
# Call an interpolation object
m = Interpolation([jde_before, jde, jde_after], [r_b, r, r_a])
sol = m.minmax()
return Epoch(sol)
[docs] @staticmethod
def passage_nodes(epoch, ascending=True):
"""This function computes the time of passage by the nodes (ascending
or descending) of Mars, nearest to the given epoch.
:param epoch: Epoch closest to the node passage
:type epoch: :py:class:`Epoch`
:param ascending: Whether the time of passage by the ascending (True)
or descending (False) node will be computed
:type ascending: bool
:returns: Tuple containing:
- Time of passage through the node (:py:class:`Epoch`)
- Radius vector when passing through the node (in AU, float)
:rtype: tuple
:raises: TypeError if input values are of wrong type.
>>> epoch = Epoch(2019, 1, 1)
>>> time, r = Mars.passage_nodes(epoch)
>>> year, month, day = time.get_date()
>>> print(year)
2019
>>> print(month)
1
>>> print(round(day, 1))
15.2
>>> print(round(r, 4))
1.4709
"""
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input types")
# Get the orbital parameters
l, a, e, i, ome, arg = Mars.orbital_elements_mean_equinox(epoch)
# Compute the time of passage through perihelion
t = Mars.perihelion_aphelion(epoch)
# Get the time of passage through the node
time, r = passage_nodes_elliptic(arg, e, a, t, ascending)
return time, r
[docs] @staticmethod
def magnitude(sun_dist, earth_dist, phase_angle):
"""This function computes the approximate magnitude of Mars.
:param sun_dist: Distance from Mars to the Sun, in Astronomical Units
:type sun_dist: float
:param earth_dist: Distance from Mars to Earth, in Astronomical Units
:type earth_dist: float
:param phase_angle: Mars phase angle
:type phase_angle: float, :py:class:`Angle`
:returns: Mars' magnitude
:rtype: float
:raises: TypeError if input values are of wrong type.
"""
if not (isinstance(sun_dist, float) and isinstance(earth_dist, float)
and isinstance(phase_angle, (float, Angle))):
raise TypeError("Invalid input types")
i = float(phase_angle)
m = -1.3 + 5.0 * log10(sun_dist * earth_dist) + 0.01486 * i
return round(m, 1)
def main():
# Let's define a small helper function
def print_me(msg, val):
print("{}: {}".format(msg, val))
# Let's show some uses of Mars class
print("\n" + 35 * "*")
print("*** Use of Mars class")
print(35 * "*" + "\n")
# Let's now compute the heliocentric position for a given epoch
epoch = Epoch(2018, 10, 27.0)
lon, lat, r = Mars.geometric_heliocentric_position(epoch)
print_me("Geometric Heliocentric Longitude", lon.to_positive())
print_me("Geometric Heliocentric Latitude", lat)
print_me("Radius vector", r)
print("")
# Compute the geocentric position for 1992/12/20:
epoch = Epoch(1992, 12, 20.0)
ra, dec, elon = Mars.geocentric_position(epoch)
print_me("Right ascension", ra.ra_str(n_dec=1))
print_me("Declination", dec.dms_str(n_dec=1))
print_me("Elongation", elon.dms_str(n_dec=1))
print("")
# Print mean orbital elements for Mars at 2065.6.24
epoch = Epoch(2065, 6, 24.0)
l, a, e, i, ome, arg = Mars.orbital_elements_mean_equinox(epoch)
print_me("Mean longitude of the planet", round(l, 6)) # 288.855211
print_me("Semimajor axis of the orbit (UA)", round(a, 8)) # 1.52367934
print_me("Eccentricity of the orbit", round(e, 7)) # 0.0934599
print_me("Inclination on plane of the ecliptic", round(i, 6)) # 1.849338
print_me("Longitude of the ascending node", round(ome, 5)) # 50.06365
print_me("Argument of the perihelion", round(arg, 6)) # 287.202108
print("")
# Compute the time of the conjunction close to 1993/10/1
epoch = Epoch(1993, 10, 1.0)
conj = Mars.conjunction(epoch)
y, m, d = conj.get_date()
d = round(d, 4)
date = "{}/{}/{}".format(y, m, d)
print_me("Conjunction date", date)
# Compute the time of the opposition close to 2729/10/1
epoch = Epoch(2729, 10, 1.0)
oppo = Mars.opposition(epoch)
y, m, d = oppo.get_date()
d = round(d, 4)
date = "{}/{}/{}".format(y, m, d)
print_me("Opposition date", date)
print("")
# Compute the time of the station in longitude #1 close to 1997/3/1
epoch = Epoch(1997, 3, 1.0)
sta1 = Mars.station_longitude_1(epoch)
y, m, d = sta1.get_date()
d = round(d, 4)
date = "{}/{}/{}".format(y, m, d)
print_me("Date of station in longitude #1", date)
# Compute the time of the station in longitude #2 close to 1997/3/1
epoch = Epoch(1997, 3, 1.0)
sta2 = Mars.station_longitude_2(epoch)
y, m, d = sta2.get_date()
d = round(d, 4)
date = "{}/{}/{}".format(y, m, d)
print_me("Date of station in longitude #2", date)
print("")
# Find the epoch of the Aphelion closer to 2032/1/1
epoch = Epoch(2032, 1, 1.0)
e = Mars.perihelion_aphelion(epoch, perihelion=False)
y, m, d, h, mi, s = e.get_full_date()
peri = str(y) + '/' + str(m) + '/' + str(d) + ' at ' + str(h) + ' hours'
print_me("The Aphelion closest to 2032/1/1 will happen on", peri)
print("")
# Compute the time of passage through an ascending node
epoch = Epoch(2019, 1, 1)
time, r = Mars.passage_nodes(epoch)
y, m, d = time.get_date()
d = round(d, 1)
print("Time of passage through ascending node: {}/{}/{}".format(y, m, d))
# 2019/1/15.2
print("Radius vector at ascending node: {}".format(round(r, 4))) # 1.4709
if __name__ == "__main__":
main()