# -*- 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, asin, fabs
)
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:: Saturn
:synopsis: Class to model Saturn planet
:license: GNU Lesser General Public License v3 (LGPLv3)
.. moduleauthor:: Dagoberto Salazar
"""
VSOP87_L = [
# L0
[
[87401354.029, 0.00000000000, 0.00000000000],
[11107659.780, 3.96205090194, 213.29909543800],
[1414150.958, 4.58581515873, 7.11354700080],
[398379.386, 0.52112025957, 206.18554843720],
[350769.223, 3.30329903015, 426.59819087600],
[206816.296, 0.24658366938, 103.09277421860],
[79271.288, 3.84007078530, 220.41264243880],
[23990.338, 4.66976934860, 110.20632121940],
[16573.583, 0.43719123541, 419.48464387520],
[14906.995, 5.76903283845, 316.39186965660],
[15820.300, 0.93808953760, 632.78373931320],
[14609.562, 1.56518573691, 3.93215326310],
[13160.308, 4.44891180176, 14.22709400160],
[15053.509, 2.71670027883, 639.89728631400],
[13005.305, 5.98119067061, 11.04570026390],
[10725.066, 3.12939596466, 202.25339517410],
[5863.207, 0.23657028777, 529.69096509460],
[5227.771, 4.20783162380, 3.18139373770],
[6126.308, 1.76328499656, 277.03499374140],
[5019.658, 3.17787919533, 433.71173787680],
[4592.541, 0.61976424374, 199.07200143640],
[4005.862, 2.24479893937, 63.73589830340],
[2953.815, 0.98280385206, 95.97922721780],
[3873.696, 3.22282692566, 138.51749687070],
[2461.172, 2.03163631205, 735.87651353180],
[3269.490, 0.77491895787, 949.17560896980],
[1758.143, 3.26580514774, 522.57741809380],
[1640.183, 5.50504966218, 846.08283475120],
[1391.336, 4.02331978116, 323.50541665740],
[1580.641, 4.37266314120, 309.27832265580],
[1123.515, 2.83726793572, 415.55249061210],
[1017.258, 3.71698151814, 227.52618943960],
[848.643, 3.19149825839, 209.36694217490],
[1087.237, 4.18343232481, 2.44768055480],
[956.752, 0.50740889886, 1265.56747862640],
[789.205, 5.00745123149, 0.96320784650],
[686.965, 1.74714407827, 1052.26838318840],
[654.470, 1.59889331515, 0.04818410980],
[748.811, 2.14398149298, 853.19638175200],
[633.980, 2.29889903023, 412.37109687440],
[743.584, 5.25276954625, 224.34479570190],
[852.677, 3.42141350697, 175.16605980020],
[579.857, 3.09259007048, 74.78159856730],
[624.904, 0.97046831256, 210.11770170030],
[529.861, 4.44938897119, 117.31986822020],
[542.643, 1.51824320514, 9.56122755560],
[474.279, 5.47527185987, 742.99006053260],
[448.542, 1.28990416161, 127.47179660680],
[546.358, 2.12678554211, 350.33211960040],
[478.054, 2.96488054338, 137.03302416240],
[354.944, 3.01286483030, 838.96928775040],
[451.827, 1.04436664241, 490.33408917940],
[347.413, 1.53928227764, 340.77089204480],
[343.475, 0.24604039134, 0.52126486180],
[309.001, 3.49486734909, 216.48048917570],
[322.185, 0.96137456104, 203.73786788240],
[372.308, 2.27819108625, 217.23124870110],
[321.543, 2.57182354537, 647.01083331480],
[330.196, 0.24715617844, 1581.95934828300],
[249.116, 1.47010534421, 1368.66025284500],
[286.688, 2.37043745859, 351.81659230870],
[220.225, 4.20422424873, 200.76892246580],
[277.775, 0.40020408926, 211.81462272970],
[204.500, 6.01082206600, 265.98929347750],
[207.663, 0.48349820488, 1162.47470440780],
[208.655, 1.34516255304, 625.67019231240],
[182.454, 5.49122292426, 2.92076130680],
[226.609, 4.91003163138, 12.53017297220],
[207.659, 1.28302218900, 39.35687591520],
[173.914, 1.86305806814, 0.75075952540],
[184.690, 3.50344404958, 149.56319713460],
[183.511, 0.97254952728, 4.19278569400],
[146.068, 6.23102544071, 195.13984817330],
[164.541, 0.44005517520, 5.41662597140],
[147.526, 1.53529320509, 5.62907429250],
[139.666, 4.29450260069, 21.34064100240],
[131.283, 4.06828961903, 10.29494073850],
[117.283, 2.67920400584, 1155.36115740700],
[149.299, 5.73594349789, 52.69019803950],
[122.373, 1.97588777199, 4.66586644600],
[113.747, 5.59427544714, 1059.38193018920],
[102.702, 1.19748124058, 1685.05212250160],
[118.156, 5.34072933900, 554.06998748280],
[109.275, 3.43812715686, 536.80451209540],
[110.399, 0.16604024090, 1.48447270830],
[124.969, 6.27737805832, 1898.35121793960],
[89.949, 5.80392934702, 114.13847448250],
[103.956, 2.19210363069, 88.86568021700],
[112.437, 1.10502663534, 191.20769491020],
[106.570, 4.01156608514, 956.28915597060],
[91.430, 1.87521577510, 38.13303563780],
[83.791, 5.48810655641, 0.11187458460],
[83.461, 2.28972767279, 628.85158605010],
[96.987, 4.53666595763, 302.16477565500],
[100.631, 4.96513666539, 269.92144674060],
[75.491, 2.18045274099, 728.76296653100],
[96.330, 2.83319189210, 275.55052103310],
[82.363, 3.05469876064, 440.82528487760],
[73.888, 5.08914205084, 1375.77379984580],
[71.633, 5.10940743430, 65.22037101170],
[70.409, 4.86846451411, 0.21244832110],
[69.760, 3.71029022489, 14.97785352700],
[88.772, 3.86334563977, 278.51946644970],
[68.090, 0.73415460990, 1478.86657406440],
[66.501, 0.02677580336, 70.84944530420],
[65.682, 2.02165559602, 142.44965013380],
[75.765, 1.61410487792, 284.14854074220],
[63.153, 3.49493353034, 479.28838891550],
[62.539, 2.58713611532, 422.66603761290],
[69.313, 3.43979731402, 515.46387109300],
[79.021, 4.45154941586, 35.42472265210],
[63.664, 3.31749528708, 62.25142559510],
[52.939, 5.51392725227, 0.26063243090],
[53.011, 3.18480701697, 8.07675484730],
[54.492, 2.45674090515, 22.09140052780],
[50.514, 4.26749346978, 99.16062095550],
[55.170, 0.96797446150, 942.06206196900],
[49.288, 2.38641424063, 1471.75302706360],
[47.199, 2.02515248245, 312.19908396260],
[61.080, 1.50295092063, 210.85141488320],
[45.126, 0.93109376473, 2001.44399215820],
[60.556, 2.68715551585, 388.46515523820],
[43.452, 2.52602011714, 288.08069400530],
[42.544, 3.81793980322, 330.61896365820],
[39.915, 5.71378652900, 408.43894361130],
[50.145, 6.03164759907, 2214.74308759620],
[45.860, 0.54229721801, 212.33588759150],
[54.165, 0.78154835399, 191.95845443560],
[47.016, 4.59934671151, 437.64389113990],
[42.362, 1.90070070955, 430.53034413910],
[39.722, 1.63259419913, 1066.49547719000],
[36.345, 0.84756992711, 213.34727954780],
[35.468, 4.18603772925, 215.74677599280],
[36.344, 3.93295730315, 213.25091132820],
[38.005, 0.31313803095, 423.41679713830],
[44.746, 1.12488341174, 6.15033915430],
[37.902, 1.19795851115, 2.70831298570],
[43.402, 1.37363944007, 563.63121503840],
[43.764, 3.93043802956, 525.49817940060],
[34.825, 1.01566605408, 203.00415469950],
[31.755, 1.69273634405, 0.16005869440],
[30.880, 6.13525703832, 417.03696332040],
[36.388, 6.00586032647, 18.15924726470],
[29.032, 1.19660544505, 404.50679034820],
[32.812, 0.53649479713, 107.02492748170],
[30.433, 0.72335287989, 222.86032299360],
[32.644, 0.81204701486, 1795.25844372100],
[37.769, 3.69666903716, 1272.68102562720],
[27.679, 1.45663979401, 7.16173111060],
[27.187, 1.89731951902, 1045.15483618760],
[37.699, 4.51997049537, 24.37902238820],
[34.885, 4.46095761791, 214.26230328450],
[32.650, 0.66372395761, 692.58748435350],
[30.324, 5.30369950147, 33.94024994380],
[27.480, 6.22702216249, 1.27202438720],
[26.657, 4.56713198392, 7.06536289100],
[31.745, 5.49798599565, 56.62235130260],
[28.050, 5.64447420566, 128.95626931510],
[24.277, 3.93966553574, 414.06801790380],
[32.017, 5.22260660455, 92.04707395470],
[26.976, 0.06705123981, 205.22234059070],
[22.974, 3.65817751770, 207.67002114550],
[31.775, 5.59198119173, 6069.77675455340],
[23.153, 2.10054506119, 1788.14489672020],
[31.025, 0.37190053329, 703.63318461740],
[29.376, 0.14742155778, 131.40394986990],
[22.562, 5.24009182383, 212.77783057620],
[26.185, 5.41311252822, 140.00196957900],
[25.673, 4.36038885283, 32.24332891440],
[20.392, 2.82413909260, 429.77958461370],
[20.659, 0.67091805084, 2317.83586181480],
[24.397, 3.08740396398, 145.63104387150],
[23.735, 2.54365387567, 76.26607127560],
[20.157, 5.06708675157, 617.80588578620],
[23.307, 3.97357729211, 483.22054217860],
[22.878, 6.10452832642, 177.87437278590],
[22.978, 3.20140795404, 208.63322899200],
[20.638, 5.22128727027, 6.59228213900],
[21.446, 0.72034565528, 1258.45393162560],
[18.034, 6.11382719947, 210.37833413120],
[22.380, 5.92299908546, 173.94221952280],
[19.128, 5.77772013766, 213.82036029980],
[20.871, 5.79126331864, 2531.13495725280],
[19.327, 1.64147367403, 565.11568774670],
[16.806, 3.27953583323, 98.89998852460],
[20.833, 2.01655935909, 860.30992875280],
[17.939, 3.14329498012, 831.85574074960],
[15.653, 3.10137669623, 106.27416795630],
[18.235, 5.22595172482, 73.29712585900],
[19.302, 5.93947114050, 425.11371816770],
[14.514, 2.75049388379, 1.22384027740],
[14.562, 5.18795088579, 305.34616939270],
[14.254, 3.88079504939, 54.17467074780],
[14.594, 3.25016810034, 78.71375183040],
[13.637, 2.55486219141, 405.25754987360],
[13.914, 1.72356993808, 69.15252427480],
[13.689, 2.37430586272, 125.98732389850],
[13.496, 0.82683590985, 99.91138048090],
[18.483, 0.73171264866, 9999.98645077300],
[13.542, 3.58584380924, 234.63973644040],
[13.741, 6.18458356845, 245.54242435240],
[16.944, 0.72200792996, 2111.65031337760],
[17.441, 0.23803796878, 134.58534360760],
[14.181, 4.51963935804, 59.80374504030],
[13.598, 2.53776983965, 1.69692102940],
[12.240, 2.11973445754, 28.31117565130],
[11.988, 1.62114832786, 1361.54670584420],
[11.974, 4.07378735120, 280.96714700450],
[12.758, 5.31146919749, 344.70304530790],
[16.051, 3.97093160336, 355.74874557180],
[11.427, 5.51123470805, 192.69216761850],
[13.133, 4.69168003518, 767.36908292080],
[14.746, 3.28998910617, 1589.07289528380],
[11.417, 1.81615681635, 2104.53676637680],
[11.626, 2.79410384978, 362.86229257260],
[13.234, 4.16642914717, 225.82926841020],
[10.599, 5.50554288376, 199.28444975750],
[10.558, 3.57501718639, 1.43628859850],
[10.485, 2.84462532686, 85.82729883120],
[10.296, 0.22225264071, 198.32124191100],
[10.552, 0.18716643576, 217.49188113200],
[11.853, 0.11584857323, 7.63481186260],
[10.248, 0.21904154170, 144.14657116320],
[10.403, 1.68776321208, 31.01948863700],
[10.313, 4.72132701805, 216.21985674480],
[10.719, 2.60869377832, 339.28641933650],
[9.636, 3.66746262954, 212.54833591260],
[9.631, 3.34275630477, 223.59403617650],
[9.684, 0.41556436593, 2634.22773147140],
[9.885, 4.01798130416, 207.14875628370],
[13.212, 6.00683506785, 214.78356814630],
[11.346, 2.61898383052, 7.86430652620],
[9.158, 5.39855118256, 342.25536475310],
[11.882, 4.00188476744, 267.47376618580],
[12.054, 3.59904816676, 124.43341522100],
[8.921, 4.22716773496, 6.36278747540],
[10.142, 3.60807025662, 14.01464568050],
[9.350, 0.72255756005, 347.88443904560],
[10.529, 2.36779614951, 831.10498122420],
[8.587, 4.48439552745, 1692.16566950240],
[10.142, 3.93620624488, 207.88246946660],
[9.147, 4.28032835242, 312.45971639350],
[8.088, 0.81225752596, 264.50482076920],
[9.241, 4.26402650779, 20.60692781950],
[9.614, 0.64291347187, 218.92816973050],
[8.537, 0.48756672382, 1574.84580128220],
[7.986, 4.71088791079, 333.65734504400],
[8.951, 0.90641577433, 497.44763618020],
[7.959, 2.73277594136, 4.14460158420],
[9.133, 5.08250578843, 241.61027108930],
[9.669, 1.60623316904, 0.89377187730],
[8.883, 5.55491009279, 2847.52682690940],
[8.926, 5.80857835271, 329.72519178090],
[7.226, 0.60164771281, 206.23373254700],
[7.655, 5.53676341721, 116.42609634290],
[7.118, 0.18747501525, 209.10630974400],
[7.507, 5.43555636173, 621.73803904930],
[8.885, 5.36210591059, 343.21857259960],
[7.056, 0.41911130648, 756.32338265690],
[8.124, 4.05571025939, 237.67811782620],
[8.964, 1.65023927130, 210.33015002140],
[6.961, 3.17855200943, 543.02428721890],
[8.916, 0.56503620503, 2428.04218303420],
[6.926, 3.66869171435, 247.23934538180],
[8.982, 4.25046722481, 46.47042291600],
[7.089, 5.14399672225, 231.45834270270],
[7.381, 1.25092810119, 217.96496188400],
[7.134, 2.83090354854, 1148.24761040620],
[6.353, 0.82582711056, 31.49256938900],
[7.558, 5.62617378543, 518.64526483070],
[6.383, 3.54809945181, 244.31858407500],
[6.914, 3.70012837706, 206.13736432740],
[6.286, 5.79144749096, 179.35884549420],
[6.639, 4.55197585824, 120.35824960600],
[5.823, 1.40737990571, 214.04985496340],
[5.850, 4.86725483749, 320.32402291970],
[6.213, 1.07959478499, 251.43213107580],
[7.730, 3.82244175824, 380.12776796000],
[5.716, 1.34909972549, 1677.93857550080],
[6.469, 1.34776801494, 188.92007304980],
[5.668, 2.28643368177, 20.44686912510],
[6.092, 3.62275289839, 1169.58825140860],
[5.711, 0.51687421521, 148.07872442630],
[5.804, 1.54831552984, 2420.92863603340],
[5.703, 5.05993483230, 2.96894541660],
[5.913, 1.66225477547, 842.15068148810],
[7.449, 1.36195943673, 166.82867252200],
[6.482, 1.94032041024, 357.44566660120],
[6.368, 2.44556930837, 654.12438031560],
[6.327, 0.40654591365, 168.05251279940],
[5.573, 2.69383455663, 750.10360753340],
[7.216, 2.22547711392, 488.84961647110],
[6.701, 6.03737590382, 160.60889739850],
[6.938, 5.78362034410, 700.66423920080],
[6.701, 3.14738404371, 491.81856188770],
[5.684, 2.59531540359, 1.64453140270],
[4.900, 2.03902856851, 0.80314915210],
[5.147, 4.10182033298, 196.62432088160],
[4.985, 2.96765983996, 258.87574647670],
[5.911, 1.81507526918, 252.65597135320],
[6.056, 3.33431010543, 182.27960680100],
[6.195, 5.01900871714, 273.10284047830],
[6.316, 5.49053160191, 206.70681329900],
[5.529, 3.31498938717, 1905.46476494040],
[5.102, 3.98171453610, 254.94359321360],
[4.762, 2.24463685255, 635.96513305090],
[5.213, 0.53609344278, 135.54855145410],
[4.639, 0.04466373027, 213.18722085340],
[5.951, 0.54565487490, 51.20572533120],
[4.535, 0.16088614438, 2950.61960112800],
[4.639, 4.73769153591, 213.41097002260],
[4.716, 3.13636467789, 28.57180808220],
[4.748, 1.12156952989, 6.21977512350],
[5.735, 0.04425142145, 348.84764689210],
[4.334, 2.68814219154, 81.75213321620],
[4.538, 3.83676888638, 487.36514376280],
[5.582, 3.63486861028, 248.72381809010],
[4.106, 3.39164360376, 50.40257617910],
[5.657, 3.59967787362, 282.45161971280],
[5.145, 1.33329458239, 173.68158709190],
[3.898, 4.11804949361, 213.51154375910],
[3.898, 0.66430577257, 213.08664711690],
[4.418, 0.10784811796, 905.88657979150],
[4.935, 2.19060382431, 189.72322220190],
[3.799, 2.60752583205, 546.95644048200],
[3.960, 1.60339889010, 218.71572140940],
[3.740, 3.30724497407, 274.06604832480],
[3.778, 0.26606330942, 636.71589257630],
[4.657, 0.37532078548, 2744.43405269080],
[3.682, 5.11587898667, 458.84151979040],
[4.230, 5.18313062329, 27.08733537390],
[5.181, 3.75590784411, 3127.31333126180],
[3.904, 2.21738744557, 358.93013930950],
[4.784, 4.60666675927, 72.07328558160],
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[0.186, 5.72093247348, 664.27630870220],
[0.184, 4.05878767739, 976.73602509570],
[0.159, 3.10978439502, 230.70758317730],
[0.154, 4.54479813612, 1239.54392483550],
[0.177, 4.68148789757, 2921.12778282460],
[0.158, 4.30854435851, 633.74694715970],
[0.195, 5.33376523453, 1130.23137549340],
[0.188, 2.04023570497, 1127.04998175570],
[0.174, 2.88817750136, 25668.41849769900],
[0.161, 2.96300008890, 152.74459087230],
[0.170, 1.70779560770, 493.30303459600],
[0.156, 3.05331862578, 913.75088631770],
[0.169, 3.18325334507, 757.80785536520],
[0.145, 0.89672198690, 632.83192342300],
[0.149, 2.69519361988, 203.26478713040],
[0.167, 2.96547549589, 1201.83158032300],
[0.187, 3.17592113403, 842.90144101350],
[0.173, 1.91528836350, 3487.42411322340],
[0.154, 0.37169915171, 285.11174858870],
[0.198, 3.14620903981, 640.86049416050],
[0.143, 3.42760427364, 520.12973753900],
[0.157, 2.34913118792, 5959.57043333400],
[0.178, 5.34566184657, 272.58157561650],
[0.171, 3.34185265551, 3067.93946934820],
[0.171, 4.87848878292, 354.52490529440],
[0.189, 0.07069084691, 1585.89150154610],
[0.137, 1.28925665885, 214.10224459010],
[0.137, 3.49438482900, 212.49594628590],
[0.174, 3.07450555579, 64.95973858080],
[0.181, 0.78652249647, 657.16276170140],
[0.158, 2.93809799392, 211.65456403530],
[0.133, 5.70724173596, 469.72716135990],
[0.140, 0.35530248121, 219.51887056150],
[0.132, 1.60614108449, 1372.59240610810],
[0.164, 1.68236348359, 707.56533788050],
[0.128, 1.49742950959, 45.24658263860],
[0.132, 4.98075995751, 238.57188970350],
[0.140, 3.62845435388, 423.88987789030],
[0.134, 1.41837795083, 3906.90875709860],
[0.127, 1.48966646069, 856.37777548970],
[0.158, 2.57990141197, 369.97583957340],
[0.132, 2.39662455993, 184.72728735580],
[0.140, 4.36785639279, 207.07932031450],
[0.157, 4.56655940808, 251.17149864490],
[0.125, 4.60433583965, 6076.89030155420],
[0.121, 1.59513269211, 184.84490743480],
[0.145, 5.85121885906, 221.89711514710],
[0.137, 0.76499603885, 476.10699517780],
[0.139, 6.02467582226, 429.30650386170],
[0.117, 0.23611722307, 426.75824957040],
[0.117, 3.13382984215, 426.43813218160],
[0.116, 4.34801448720, 418.96337901340],
[0.135, 2.69789181467, 455.16999895820],
[0.134, 1.19058772772, 502.86426215160],
[0.123, 3.97560160218, 499.89531673500],
[0.110, 2.37032413718, 439.93151300030],
[0.109, 6.20303291896, 220.30076785420],
[0.109, 1.38979633175, 325.95309721220],
[0.115, 0.05845336809, 631.82053146670],
[0.139, 2.21086387259, 9573.38825989700],
[0.142, 6.14666228712, 3340.61242669980],
[0.122, 4.77182119272, 604.47256366190],
[0.119, 3.03461367061, 528.20649238630],
[0.127, 2.97263950543, 498.93210888850],
[0.111, 5.01192320232, 220.20019411770],
[0.126, 3.95743516129, 566.60016045500],
[0.098, 2.36210526249, 634.26821202150],
[0.108, 2.46872857126, 83.37961827640],
[0.101, 4.88259474274, 425.32616648880],
[0.127, 4.89006771254, 162.09337010680],
[0.099, 0.90073463816, 586.31331639720],
[0.099, 0.16310526294, 394.35486196160],
[0.115, 0.49160291262, 517.16079212240],
[0.101, 3.86043866859, 198.10879358990],
[0.105, 3.48222097813, 5863.59120611620],
[0.104, 4.61148354671, 220.52451702340],
[0.101, 4.77041950285, 427.87021526320],
[0.098, 2.90784721214, 199.96577331370],
[0.127, 0.14136936897, 2332.06295581640],
[0.091, 6.22628300117, 211.29335786790],
[0.100, 5.14847283436, 226.79247625670],
[0.091, 4.84054379386, 215.30483300810],
[0.099, 4.37583492400, 640.41855117580],
[0.093, 5.30395179617, 222.70026429920],
[0.086, 4.57481701854, 636.97652500720],
[0.111, 0.61102669309, 1089.12939443900],
[0.086, 4.50969293872, 625.88264063350],
[0.088, 0.36828594935, 444.12429869430],
[0.093, 5.76287499885, 203.89792657680],
[0.082, 2.85558603378, 318.83955021140],
[0.082, 5.19618475111, 1467.82087380050],
[0.086, 0.97633784601, 200.03520928290],
[0.082, 4.78557953017, 195.77298761970],
[0.106, 2.29520624233, 799.61241183520],
[0.081, 3.57727166766, 205.97310011610],
[0.078, 5.50343512580, 262.80789973980],
[0.087, 0.76830756075, 201.99276274320],
[0.102, 2.11516755277, 206.93630796260],
[0.081, 5.29639775054, 111.16952906590],
[0.075, 2.77117107886, 255.83736509090],
[0.074, 5.81587984729, 316.44005376640],
[0.076, 1.78743197928, 171.65459766240],
[0.094, 4.99996904753, 378.64329525170],
[0.089, 5.85818860151, 807.94979911340],
[0.072, 0.99858616883, 280.21638747910],
[0.099, 0.15018241445, 186.21176006410],
[0.072, 5.15715918322, 110.15813710960],
],
# L1
[
[21354295595.986, 0.00000000000, 0.00000000000],
[1296855.005, 1.82820544701, 213.29909543800],
[564347.566, 2.88500136429, 7.11354700080],
[98323.030, 1.08070061328, 426.59819087600],
[107678.770, 2.27769911872, 206.18554843720],
[40254.586, 2.04128257090, 220.41264243880],
[19941.734, 1.27954662736, 103.09277421860],
[10511.706, 2.74880392800, 14.22709400160],
[6939.233, 0.40493079985, 639.89728631400],
[4803.325, 2.44194097666, 419.48464387520],
[4056.325, 2.92166618776, 110.20632121940],
[3768.630, 3.64965631460, 3.93215326310],
[3384.684, 2.41694251653, 3.18139373770],
[3302.200, 1.26256486715, 433.71173787680],
[3071.382, 2.32739317750, 199.07200143640],
[1953.036, 3.56394683300, 11.04570026390],
[1249.348, 2.62803737519, 95.97922721780],
[921.683, 1.96089834250, 227.52618943960],
[705.587, 4.41689249330, 529.69096509460],
[649.654, 6.17418093659, 202.25339517410],
[627.603, 6.11088227167, 309.27832265580],
[486.843, 6.03998200305, 853.19638175200],
[468.377, 4.61707843907, 63.73589830340],
[478.501, 4.98776987984, 522.57741809380],
[417.010, 2.11708169277, 323.50541665740],
[407.630, 1.29949556676, 209.36694217490],
[343.826, 3.95854178574, 412.37109687440],
[339.724, 3.63396398752, 316.39186965660],
[335.936, 3.77173072712, 735.87651353180],
[331.933, 2.86077699882, 210.11770170030],
[352.489, 2.31707079463, 632.78373931320],
[289.429, 2.73263080235, 117.31986822020],
[265.801, 0.54344631312, 647.01083331480],
[230.493, 1.64428879621, 216.48048917570],
[280.911, 5.74398845416, 2.44768055480],
[191.667, 2.96512946582, 224.34479570190],
[172.891, 4.07695221044, 846.08283475120],
[167.131, 2.59745202658, 21.34064100240],
[136.328, 2.28580246629, 10.29494073850],
[131.364, 3.44108355646, 742.99006053260],
[127.838, 4.09533471247, 217.23124870110],
[108.862, 6.16141072262, 415.55249061210],
[93.909, 3.48397279899, 1052.26838318840],
[92.482, 3.94755499926, 88.86568021700],
[97.584, 4.72845436677, 838.96928775040],
[86.600, 1.21951325061, 440.82528487760],
[83.463, 3.11269504725, 625.67019231240],
[77.588, 6.24408938835, 302.16477565500],
[61.557, 1.82789612597, 195.13984817330],
[61.900, 4.29344363385, 127.47179660680],
[67.106, 0.28961738595, 4.66586644600],
[56.919, 5.01889578112, 137.03302416240],
[54.160, 5.12628572382, 490.33408917940],
[54.585, 0.28356341456, 74.78159856730],
[51.425, 1.45766406064, 536.80451209540],
[65.843, 5.64757042732, 9.56122755560],
[57.780, 2.47630552035, 191.95845443560],
[44.444, 2.70873627665, 5.41662597140],
[46.799, 1.17721211050, 149.56319713460],
[40.380, 3.88870105683, 728.76296653100],
[37.768, 2.53379013859, 12.53017297220],
[46.649, 5.14818326902, 515.46387109300],
[45.891, 2.23198878761, 956.28915597060],
[40.400, 0.41281520440, 269.92144674060],
[37.191, 3.78239026411, 2.92076130680],
[33.778, 3.21070688046, 1368.66025284500],
[37.969, 0.64665967180, 422.66603761290],
[32.857, 0.30063884563, 351.81659230870],
[33.050, 5.43038091186, 1066.49547719000],
[30.276, 2.84067004928, 203.00415469950],
[35.116, 6.08421794089, 5.62907429250],
[29.667, 3.39052569135, 1059.38193018920],
[33.217, 4.64063092111, 277.03499374140],
[31.876, 4.38622923770, 1155.36115740700],
[28.913, 2.02614760507, 330.61896365820],
[28.264, 2.74178953996, 265.98929347750],
[30.089, 6.18684614308, 284.14854074220],
[31.329, 2.43455855525, 52.69019803950],
[26.493, 4.51214170121, 340.77089204480],
[21.983, 5.14437352579, 4.19278569400],
[22.230, 1.96481952451, 203.73786788240],
[20.824, 6.16048095923, 860.30992875280],
[21.690, 2.67578768862, 942.06206196900],
[22.552, 5.88579123000, 210.85141488320],
[19.807, 2.31345263487, 437.64389113990],
[19.447, 4.76573277668, 70.84944530420],
[19.310, 4.10209060369, 18.15924726470],
[22.662, 4.13732273379, 191.20769491020],
[18.209, 0.90310796389, 429.77958461370],
[17.667, 1.84954766042, 234.63973644040],
[17.547, 2.44735118493, 423.41679713830],
[15.428, 4.23790088205, 1162.47470440780],
[14.608, 3.59713247857, 1045.15483618760],
[14.111, 2.94262468353, 1685.05212250160],
[16.328, 4.05665272725, 949.17560896980],
[13.348, 6.24509592240, 38.13303563780],
[15.918, 1.06434204938, 56.62235130260],
[14.059, 1.43503954068, 408.43894361130],
[13.093, 5.75815864257, 138.51749687070],
[15.772, 5.59350835225, 6.15033915430],
[14.962, 5.77192239389, 22.09140052780],
[16.024, 1.93900586533, 1272.68102562720],
[16.751, 5.96673627422, 628.85158605010],
[12.843, 4.24658666814, 405.25754987360],
[13.628, 4.09892958087, 1471.75302706360],
[15.067, 0.74142807591, 200.76892246580],
[10.961, 1.55022573283, 223.59403617650],
[11.695, 1.81237511034, 124.43341522100],
[10.346, 3.46814088412, 1375.77379984580],
[12.056, 1.85655834555, 131.40394986990],
[10.123, 2.38221133049, 107.02492748170],
[9.855, 3.95166998848, 430.53034413910],
[9.803, 2.55389483994, 99.91138048090],
[10.614, 5.36692189034, 215.74677599280],
[12.080, 4.84549317054, 831.85574074960],
[10.210, 6.07692961370, 32.24332891440],
[9.245, 3.65417467270, 142.44965013380],
[8.984, 1.23808405498, 106.27416795630],
[9.336, 5.81062768434, 7.16173111060],
[9.717, 1.38703872827, 145.63104387150],
[8.394, 4.42341211111, 703.63318461740],
[8.370, 5.64015188458, 62.25142559510],
[8.244, 2.42225929772, 1258.45393162560],
[7.784, 0.52562994711, 654.12438031560],
[7.626, 3.75258725596, 312.19908396260],
[7.222, 0.28429555677, 0.75075952540],
[8.236, 6.22250515902, 14.97785352700],
[7.054, 0.53177810740, 388.46515523820],
[6.567, 3.48657341701, 35.42472265210],
[9.011, 4.94919626910, 208.63322899200],
[8.980, 0.08138173719, 288.08069400530],
[6.421, 3.32905264657, 1361.54670584420],
[6.489, 2.89389587598, 114.13847448250],
[6.244, 0.54973852782, 65.22037101170],
[6.154, 2.67885860584, 2001.44399215820],
[6.742, 0.23586769279, 8.07675484730],
[7.297, 4.85321224483, 222.86032299360],
[6.302, 3.80651124694, 1788.14489672020],
[5.824, 4.39327457448, 81.75213321620],
[6.102, 0.88585782895, 92.04707395470],
[6.914, 2.04631426723, 99.16062095550],
[5.363, 5.47995103139, 563.63121503840],
[5.172, 2.11968421583, 214.26230328450],
[5.117, 5.76987684107, 565.11568774670],
[6.197, 1.62553688800, 1589.07289528380],
[4.970, 0.41949366126, 76.26607127560],
[6.640, 5.82582210639, 483.22054217860],
[5.277, 4.57975789757, 134.58534360760],
[4.974, 4.20243895902, 404.50679034820],
[5.150, 4.67582673243, 212.33588759150],
[4.764, 4.59303997414, 554.06998748280],
[4.573, 3.24875415786, 231.45834270270],
[4.811, 0.46206327592, 362.86229257260],
[5.148, 3.33570646174, 1.48447270830],
[4.654, 5.80233066659, 217.96496188400],
[4.509, 5.37581684215, 497.44763618020],
[4.443, 0.11349392292, 295.05122865420],
[4.943, 3.78020789259, 1265.56747862640],
[4.211, 4.88306021960, 98.89998852460],
[4.252, 5.00120115113, 213.34727954780],
[4.774, 4.53259894142, 1148.24761040620],
[3.911, 0.58582192963, 750.10360753340],
[5.069, 2.20305668335, 207.88246946660],
[3.553, 0.35374030841, 333.65734504400],
[3.771, 0.98542435766, 24.37902238820],
[3.458, 1.84990273999, 225.82926841020],
[3.401, 5.31342401626, 347.88443904560],
[3.347, 0.21414641376, 635.96513305090],
[3.637, 1.61315058382, 245.54242435240],
[3.416, 2.19551489078, 1574.84580128220],
[3.655, 0.80544245690, 343.21857259960],
[4.260, 1.80258750109, 213.25091132820],
[3.110, 3.03815175282, 1677.93857550080],
[3.052, 1.33858964447, 543.91805909620],
[3.694, 0.81606028298, 344.70304530790],
[3.016, 3.36219319026, 7.86430652620],
[2.937, 4.86927342776, 144.14657116320],
[2.768, 2.42707131609, 2317.83586181480],
[3.059, 4.30820099442, 6062.66320755260],
[3.650, 5.12802531219, 218.92816973050],
[2.963, 3.53480751374, 2104.53676637680],
[3.230, 2.88057019783, 216.21985674480],
[2.984, 2.52971310583, 1692.16566950240],
[2.897, 5.73256482240, 9992.87290377220],
[2.591, 3.79880285744, 17.26547538740],
[3.495, 5.29902525443, 350.33211960040],
[2.859, 3.72804950659, 6076.89030155420],
[2.775, 0.23549396237, 357.44566660120],
[2.976, 2.48769315964, 46.47042291600],
[2.487, 4.37868078530, 217.49188113200],
[2.711, 5.15376840150, 10007.09999777380],
[3.127, 1.92343235583, 17.40848773930],
[3.181, 1.72419900322, 1169.58825140860],
[2.348, 0.77373103004, 414.06801790380],
[2.606, 3.42836913440, 31.01948863700],
[2.556, 0.91735028377, 479.28838891550],
[2.399, 4.82440545738, 1279.79457262800],
[2.245, 3.76323995584, 425.11371816770],
[3.020, 0.25310250109, 120.35824960600],
[2.503, 2.10679832121, 168.05251279940],
[2.564, 1.63158205055, 182.27960680100],
[2.221, 3.15472373256, 212.77783057620],
[2.357, 2.33145013714, 218.71572140940],
[2.510, 4.51903989011, 198.32124191100],
[2.715, 5.76330259543, 618.55664531160],
[2.204, 3.35952557362, 160.60889739850],
[2.648, 0.71962005233, 85.82729883120],
[2.029, 5.28642331696, 125.98732389850],
[2.497, 1.36671447252, 1905.46476494040],
[2.017, 1.11498225426, 447.93883187840],
[2.052, 1.27587874735, 14.01464568050],
[2.254, 3.22447674190, 273.10284047830],
[2.014, 0.39787014152, 358.93013930950],
[1.981, 2.33696859021, 28.45418800320],
[2.197, 5.93386789705, 13.33332212430],
[2.237, 3.64433751164, 213.82036029980],
[1.930, 1.85671740340, 1.27202438720],
[2.037, 5.05300562628, 424.15051032120],
[1.994, 1.35690802366, 20.60692781950],
[1.911, 3.44106886717, 69.15252427480],
[1.925, 3.75243031545, 28.31117565130],
[2.297, 4.24557050896, 1464.63948006280],
[2.117, 2.25897766314, 116.42609634290],
[1.847, 5.40631472802, 31.49256938900],
[1.841, 1.56916484272, 650.94298657790],
[1.884, 6.27233535258, 25.12978191360],
[1.960, 4.89484014840, 275.55052103310],
[2.016, 5.45791785675, 842.15068148810],
[2.282, 4.96276947440, 258.87574647670],
[1.709, 3.99098237135, 416.30325013750],
[2.176, 0.00746756006, 0.89377187730],
[1.634, 5.30978165487, 251.43213107580],
[1.687, 0.41586020065, 54.17467074780],
[1.910, 2.59825755790, 329.72519178090],
[2.113, 2.56582292726, 59.80374504030],
[1.921, 2.42279051938, 113.38771495710],
[1.658, 5.47323651540, 1073.60902419080],
[1.590, 2.77545297350, 1994.33044515740],
[1.936, 3.47558926847, 1581.95934828300],
[1.649, 1.82779010589, 128.95626931510],
[1.598, 1.71806465300, 129.91947716160],
[1.967, 1.25160413795, 621.73803904930],
[1.702, 1.91076102800, 278.51946644970],
[1.569, 0.16491194947, 643.07868005170],
[1.989, 5.28799230992, 508.35032409220],
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[0.129, 4.92592016162, 1286.90811962880],
[0.132, 3.44682160054, 156.67674413540],
[0.143, 0.67951827513, 425.84743135060],
[0.114, 5.46519773276, 552.58551477450],
[0.132, 1.76335093671, 432.01481684740],
[0.113, 0.68933513038, 450.97721326420],
[0.128, 2.13986068877, 2751.54759969160],
[0.123, 4.59695145319, 216.00740842370],
[0.119, 1.04688666457, 462.02291352810],
[0.108, 5.36873170289, 3377.21779200400],
[0.142, 6.24626256472, 299.12639426920],
[0.118, 0.63448253510, 369.97583957340],
[0.105, 2.31570619675, 200.55647414470],
[0.124, 1.87110815140, 850.01498801430],
[0.106, 0.55623662570, 114.39910691340],
[0.102, 3.95315219638, 361.37781986430],
[0.095, 4.10658529323, 10213.28554621100],
[0.097, 1.13534710734, 387.24131496080],
[0.096, 4.46689094543, 401.32539661050],
[0.119, 2.33636675091, 318.83955021140],
[0.115, 3.37508073115, 313.94418910180],
[0.106, 3.73586211650, 220.93390730060],
[0.090, 0.59788492023, 227.31374111850],
[0.103, 5.09172929383, 213.45915413240],
[0.097, 5.95268532215, 1044.40407666220],
[0.103, 1.70625660572, 213.13903674360],
[0.080, 0.86872596168, 233.90602325750],
[0.089, 5.35990932230, 214.19286731530],
[0.080, 2.69565238975, 540.73666535850],
[0.095, 1.19504849611, 460.53844081980],
[0.105, 0.58624363205, 481.73606947030],
[0.099, 2.68841109007, 219.89137757700],
[0.098, 1.59923557478, 484.70501488690],
[0.081, 1.12279793521, 420.44785172170],
[0.075, 4.58892231446, 394.35486196160],
[0.099, 4.68895851750, 448.68959140380],
[0.076, 1.66929798365, 196.03362005060],
[0.087, 3.12477195090, 857.12853501510],
[0.078, 5.59819387460, 364.34676528090],
[0.079, 3.53267171729, 969.62247809490],
],
# L2
[
[116441.181, 1.17987850633, 7.11354700080],
[91920.844, 0.07425261094, 213.29909543800],
[90592.251, 0.00000000000, 0.00000000000],
[15276.909, 4.06492007503, 206.18554843720],
[10631.396, 0.25778277414, 220.41264243880],
[10604.979, 5.40963595885, 426.59819087600],
[4265.368, 1.04595556630, 14.22709400160],
[1215.527, 2.91860042123, 103.09277421860],
[1164.684, 4.60942128971, 639.89728631400],
[1081.967, 5.69130351670, 433.71173787680],
[1020.079, 0.63369182642, 3.18139373770],
[1044.754, 4.04206453611, 199.07200143640],
[633.582, 4.38825410036, 419.48464387520],
[549.329, 5.57303134242, 3.93215326310],
[456.914, 1.26840971349, 110.20632121940],
[425.100, 0.20935499279, 227.52618943960],
[273.739, 4.28841011784, 95.97922721780],
[161.571, 1.38139149420, 11.04570026390],
[129.494, 1.56586884170, 309.27832265580],
[117.008, 3.88120915956, 853.19638175200],
[105.415, 4.90003203599, 647.01083331480],
[100.967, 0.89270493100, 21.34064100240],
[95.227, 5.62561150598, 412.37109687440],
[81.948, 1.02477558315, 117.31986822020],
[74.857, 4.76178468163, 210.11770170030],
[82.727, 6.05030934786, 216.48048917570],
[95.659, 2.91093561539, 316.39186965660],
[63.696, 0.35179804917, 323.50541665740],
[84.860, 5.73472777961, 209.36694217490],
[60.647, 4.87517850190, 632.78373931320],
[66.459, 0.48297940601, 10.29494073850],
[67.184, 0.45648612616, 522.57741809380],
[53.281, 2.74730541387, 529.69096509460],
[45.827, 5.69296621745, 440.82528487760],
[45.293, 1.66856699796, 202.25339517410],
[42.330, 5.70768187703, 88.86568021700],
[32.140, 0.07050050346, 63.73589830340],
[31.573, 1.67190022213, 302.16477565500],
[31.150, 4.16379537691, 191.95845443560],
[24.631, 5.65564728570, 735.87651353180],
[26.558, 0.83256214407, 224.34479570190],
[20.108, 5.94364609981, 217.23124870110],
[17.511, 4.90014736798, 625.67019231240],
[17.130, 1.62593421274, 742.99006053260],
[13.744, 3.76497167300, 195.13984817330],
[12.236, 4.71789723976, 203.00415469950],
[11.940, 0.12620714199, 234.63973644040],
[16.040, 0.57886320845, 515.46387109300],
[11.154, 5.92216844780, 536.80451209540],
[14.068, 0.20675293700, 838.96928775040],
[11.013, 5.60207982774, 728.76296653100],
[11.718, 3.12098483554, 846.08283475120],
[9.962, 4.15472049127, 860.30992875280],
[10.601, 3.20327613035, 1066.49547719000],
[10.072, 0.25709351996, 330.61896365820],
[9.490, 0.46379969328, 956.28915597060],
[10.240, 4.98736656070, 422.66603761290],
[8.287, 2.13990364272, 269.92144674060],
[7.238, 5.39724715258, 1052.26838318840],
[7.730, 5.24602742309, 429.77958461370],
[6.353, 4.46211130731, 284.14854074220],
[5.935, 5.40967847103, 149.56319713460],
[7.550, 4.03401153929, 9.56122755560],
[5.779, 4.29380891110, 415.55249061210],
[6.082, 5.93416924841, 405.25754987360],
[5.711, 0.01824076994, 124.43341522100],
[5.676, 6.02235682150, 223.59403617650],
[4.757, 4.92804854717, 654.12438031560],
[4.727, 2.27461984667, 18.15924726470],
[4.509, 4.40688707557, 942.06206196900],
[5.621, 0.29694719379, 127.47179660680],
[5.453, 5.53868222772, 949.17560896980],
[4.130, 4.68673560379, 74.78159856730],
[4.098, 5.30851262200, 1045.15483618760],
[4.223, 2.89014939299, 56.62235130260],
[4.887, 3.20022991216, 277.03499374140],
[3.905, 3.30270187305, 490.33408917940],
[3.923, 6.09732996823, 81.75213321620],
[3.755, 4.93065184796, 52.69019803950],
[4.602, 6.13908576681, 1155.36115740700],
[3.714, 0.40648076787, 137.03302416240],
[3.407, 4.28514461015, 99.91138048090],
[3.579, 0.20402442077, 1272.68102562720],
[3.946, 0.36500928968, 12.53017297220],
[3.246, 1.56761884227, 1059.38193018920],
[4.063, 0.29084229143, 831.85574074960],
[3.688, 0.15467406177, 437.64389113990],
[2.895, 3.13473183482, 70.84944530420],
[2.800, 0.32727938074, 191.20769491020],
[2.672, 1.87612402267, 295.05122865420],
[3.454, 4.77197610696, 423.41679713830],
[2.623, 5.15237415384, 1368.66025284500],
[2.457, 3.89612890177, 210.85141488320],
[2.461, 1.58522876760, 32.24332891440],
[2.595, 3.59007068361, 131.40394986990],
[2.289, 4.76825865118, 351.81659230870],
[2.357, 5.83099000562, 106.27416795630],
[2.221, 5.98277491515, 6062.66320755260],
[2.221, 2.05930402282, 6076.89030155420],
[2.183, 5.94985336393, 145.63104387150],
[2.718, 3.37801252354, 408.43894361130],
[2.288, 3.14000619320, 22.09140052780],
[2.090, 1.12304173562, 9992.87290377220],
[2.089, 3.48276230686, 10007.09999777380],
[2.570, 5.12167203704, 265.98929347750],
[1.835, 4.15379879659, 1258.45393162560],
[1.820, 5.05340615445, 1361.54670584420],
[1.760, 4.13532689228, 107.02492748170],
[1.921, 4.51790997496, 138.51749687070],
[1.707, 1.35864593280, 231.45834270270],
[1.956, 5.87006093798, 1471.75302706360],
[2.133, 5.23409848720, 1265.56747862640],
[1.595, 5.61962698786, 447.93883187840],
[1.609, 3.74893709671, 628.85158605010],
[1.490, 0.48352404940, 340.77089204480],
[1.560, 5.97095003614, 430.53034413910],
[1.352, 0.71405348653, 28.45418800320],
[1.355, 2.91219493604, 215.74677599280],
[1.298, 5.84254169775, 543.91805909620],
[1.664, 6.23834873469, 1148.24761040620],
[1.205, 2.83373725021, 200.76892246580],
[1.192, 3.52219428945, 497.44763618020],
[1.122, 2.60571030270, 1279.79457262800],
[1.217, 6.23528359211, 1589.07289528380],
[1.420, 0.85079202155, 6069.77675455340],
[1.120, 4.95656566453, 1685.05212250160],
[1.010, 3.39689646619, 1073.60902419080],
[1.352, 2.27575429523, 9999.98645077300],
[0.979, 1.58571463442, 1375.77379984580],
[1.159, 0.71823181781, 508.35032409220],
[1.014, 2.40759054741, 703.63318461740],
[0.956, 2.66256831556, 134.58534360760],
[1.110, 1.19713920197, 618.55664531160],
[0.945, 4.68155456977, 362.86229257260],
[0.953, 4.20749172571, 288.08069400530],
[1.033, 1.08781255146, 184.84490743480],
[0.942, 2.43465223460, 222.86032299360],
[0.909, 4.51769385360, 38.13303563780],
[1.002, 1.38543153271, 483.22054217860],
[1.082, 4.52832816548, 635.96513305090],
[1.008, 4.91325851448, 750.10360753340],
[0.862, 4.79998518474, 1677.93857550080],
[0.828, 2.21940849017, 333.65734504400],
[0.745, 3.97279299984, 1574.84580128220],
[0.903, 5.58963782799, 1788.14489672020],
[0.735, 2.28191723259, 1162.47470440780],
[0.773, 5.82270096882, 416.30325013750],
[0.734, 2.35356586018, 120.35824960600],
[0.745, 4.84266000843, 76.26607127560],
[0.765, 2.50840146722, 343.21857259960],
[0.908, 5.01046293458, 1581.95934828300],
[0.707, 3.66631544506, 347.88443904560],
[0.870, 0.77106152694, 113.38771495710],
[0.686, 2.88543836068, 92.04707395470],
[0.673, 3.75650667651, 203.73786788240],
[0.656, 3.77718582702, 217.96496188400],
[0.675, 5.62875135263, 17.26547538740],
[0.691, 0.21330089609, 99.16062095550],
[0.786, 4.49318079175, 643.07868005170],
[0.641, 0.67588390141, 46.47042291600],
[0.663, 5.74837848383, 721.64941953020],
[0.809, 5.94893988352, 1464.63948006280],
[0.638, 4.86195439622, 357.44566660120],
[0.740, 6.00053422445, 337.73251065900],
[0.555, 4.95858934298, 358.93013930950],
[0.581, 3.87669679805, 565.11568774670],
[0.541, 1.22296838713, 62.25142559510],
[0.697, 0.00715950269, 1169.58825140860],
[0.524, 1.53830423608, 195.89060769870],
[0.518, 5.41992758537, 312.19908396260],
[0.626, 5.26580317026, 436.89313161450],
[0.537, 6.17031657600, 182.27960680100],
[0.574, 5.98607898826, 1905.46476494040],
[0.541, 0.30589337713, 98.89998852460],
[0.603, 3.26888470585, 208.63322899200],
[0.504, 3.80930996688, 168.05251279940],
[0.477, 3.56642391994, 563.63121503840],
[0.511, 4.70719837179, 2001.44399215820],
[0.475, 1.06025557585, 5856.47765911540],
[0.540, 0.87230551412, 1692.16566950240],
[0.454, 2.48128029368, 9786.68735533500],
[0.456, 3.18303484133, 218.92816973050],
[0.462, 0.71358186864, 258.87574647670],
[0.424, 4.89778948357, 636.71589257630],
[0.537, 2.59376221736, 313.21047591890],
[0.410, 4.22147787617, 867.42347575360],
[0.408, 3.06057772788, 424.15051032120],
[0.407, 3.79376013938, 24.37902238820],
[0.569, 3.68547825941, 350.33211960040],
[0.404, 0.91401255827, 114.13847448250],
[0.395, 3.50478374207, 129.91947716160],
[0.395, 2.86309689622, 212.33588759150],
[0.386, 5.00762729432, 388.46515523820],
[0.393, 6.26835522096, 241.75328344120],
[0.401, 4.60258908692, 1994.33044515740],
[0.385, 0.91582119643, 160.60889739850],
[0.467, 0.54876489832, 404.50679034820],
[0.368, 0.35674031808, 214.26230328450],
[0.471, 0.67360047481, 207.88246946660],
[0.379, 0.92901327825, 767.36908292080],
[0.420, 5.69797398044, 225.82926841020],
[0.356, 3.10092792842, 842.15068148810],
[0.428, 5.35375368944, 2104.53676637680],
[0.422, 2.67975581832, 77.96299230500],
[0.370, 5.46144813372, 1038.04128918680],
[0.379, 5.56429091578, 131.54696222180],
[0.441, 5.68196668399, 1781.03134971940],
[0.361, 5.20616019966, 629.60234557550],
[0.341, 5.92928351979, 26.82670294300],
[0.419, 5.26851686707, 85.82729883120],
[0.322, 0.80223983857, 6283.07584999140],
[0.323, 3.86700993914, 576.16138801060],
[0.321, 2.17186032970, 10213.28554621100],
[0.355, 2.80560859177, 344.70304530790],
[0.311, 3.77477255556, 1891.23767093880],
[0.318, 5.22020784209, 142.44965013380],
[0.315, 0.52272202855, 5849.36411211460],
[0.428, 4.63722058283, 1898.35121793960],
[0.337, 0.68198429948, 45.57665103870],
[0.316, 0.54074780109, 444.75743814070],
[0.310, 1.41032075652, 273.10284047830],
[0.311, 3.53744556230, 251.43213107580],
[0.295, 1.93253015677, 436.15941843160],
[0.296, 1.97705648834, 9779.57380833420],
[0.326, 3.67854047003, 963.40270297140],
[0.389, 5.76841276132, 39.35687591520],
[0.277, 5.73995694175, 92.79783348010],
[0.315, 4.96371610197, 757.21715453420],
[0.295, 1.81638833900, 1493.09366806600],
[0.287, 0.97698377929, 685.47393735270],
[0.281, 2.66463042095, 1286.90811962880],
[0.330, 5.79776922760, 650.94298657790],
[0.292, 3.97858181479, 472.17484191470],
[0.266, 4.13716111320, 601.76425067620],
[0.262, 0.91887592474, 245.54242435240],
[0.278, 3.08964256591, 778.41478318470],
[0.277, 3.08750916880, 621.73803904930],
[0.255, 3.93981592051, 181.05576652360],
[0.333, 2.04835822938, 561.18353448360],
[0.247, 2.92754257675, 219.44943459230],
[0.306, 0.36127922606, 824.74219374880],
[0.253, 1.80130756458, 5643.17856367740],
[0.337, 4.97764462199, 175.16605980020],
[0.273, 0.66599369335, 2008.55753915900],
[0.227, 4.87285356383, 661.23792731640],
[0.249, 3.14202895058, 144.14657116320],
[0.220, 3.93526603081, 319.57326339430],
[0.212, 5.85248164087, 546.95644048200],
[0.234, 1.65314711167, 554.06998748280],
[0.204, 0.88373842674, 31.49256938900],
[0.205, 2.93169866171, 1596.18644228460],
[0.201, 3.36504567824, 1080.72257119160],
[0.224, 4.34612745705, 1382.88734684660],
[0.192, 5.13697232918, 329.72519178090],
[0.208, 3.08549771485, 41.64449777560],
[0.236, 0.07998742860, 1141.13406340540],
[0.203, 4.13011580915, 2627.11418447060],
[0.203, 0.13969067385, 1485.98012106520],
[0.204, 3.38137545713, 699.70103135430],
[0.212, 4.52370676085, 2310.72231481400],
[0.218, 5.79277335862, 2221.85663459700],
[0.213, 0.50441377637, 934.94851496820],
[0.210, 5.04017633795, 2420.92863603340],
[0.214, 4.64286758581, 2317.83586181480],
[0.178, 0.84588580004, 128.36556848410],
[0.170, 2.75006619605, 710.74673161820],
[0.171, 4.32615182967, 291.26208774300],
[0.172, 3.46971306920, 501.37978944330],
[0.170, 1.05408992106, 526.50957135690],
[0.162, 1.15683042950, 519.39602435610],
[0.180, 4.96266204107, 1670.82502850000],
[0.172, 1.65385549578, 916.93228005540],
[0.170, 2.30821101766, 429.04587143080],
[0.170, 5.98716489326, 643.82943957710],
[0.173, 5.19933564968, 1354.43315884340],
[0.195, 4.50165508529, 2214.74308759620],
[0.156, 4.16290662749, 572.22923474750],
[0.153, 1.23776248578, 2413.81508903260],
[0.150, 0.63076983213, 1478.86657406440],
[0.169, 4.28090123029, 305.34616939270],
[0.174, 6.23077892653, 3384.33133900480],
[0.149, 3.13274908516, 9573.38825989700],
[0.162, 6.25601818345, 213.25091132820],
[0.149, 4.81749019484, 945.99421523210],
[0.162, 0.88610129190, 216.21985674480],
[0.133, 2.31915371262, 156.67674413540],
[0.165, 6.06456216591, 732.69511979410],
[0.141, 6.14293754333, 1795.25844372100],
[0.133, 0.06530337135, 218.71572140940],
[0.162, 3.17058130506, 213.34727954780],
[0.125, 2.07143636845, 425.11371816770],
[0.146, 1.88627500632, 211.81462272970],
[0.113, 2.79541965778, 235.39049596580],
[0.117, 0.76464798684, 479.28838891550],
[0.108, 3.95650672786, 570.74476203920],
[0.106, 0.12820734703, 188.02630117250],
[0.134, 3.58244908862, 849.26422848890],
[0.114, 0.25990388555, 398.14400287280],
[0.112, 2.39181495831, 217.49188113200],
[0.091, 2.50716605179, 121.25202148330],
[0.091, 1.75367948574, 213.82036029980],
[0.088, 5.26121947108, 395.57870223900],
[0.096, 3.98832609364, 289.56516671360],
[0.091, 0.35318362186, 312.45971639350],
[0.112, 1.14387590923, 1802.37199072180],
[0.082, 3.73605217214, 207.67002114550],
[0.082, 6.06283262812, 210.37833413120],
[0.084, 3.34470673492, 67.66805156650],
[0.086, 2.73917300180, 5863.59120611620],
[0.083, 2.81499116485, 776.93031047640],
[0.091, 1.26160093170, 212.77783057620],
[0.090, 2.08722491981, 2111.65031337760],
[0.080, 2.13136842916, 421.93232443000],
[0.082, 4.16358350281, 9793.80090233580],
[0.077, 2.96973341607, 431.26405732200],
[0.079, 3.42790361067, 417.03696332040],
[0.079, 3.18693585419, 320.32402291970],
[0.080, 0.78975763683, 204.70107572890],
[0.077, 1.89354243952, 556.51766803760],
[0.073, 4.85923277221, 2118.76386037840],
[0.071, 3.64551577433, 198.32124191100],
],
# L3
[
[16038.734, 5.73945377424, 7.11354700080],
[4249.793, 4.58539675603, 213.29909543800],
[1906.524, 4.76082050205, 220.41264243880],
[1465.687, 5.91326678323, 206.18554843720],
[1162.041, 5.61973132428, 14.22709400160],
[1066.581, 3.60816533142, 426.59819087600],
[239.377, 3.86088273439, 433.71173787680],
[236.975, 5.76826451465, 199.07200143640],
[165.641, 5.11641150216, 3.18139373770],
[131.409, 4.74327544615, 227.52618943960],
[151.352, 2.73594641861, 639.89728631400],
[61.630, 4.74287052463, 103.09277421860],
[63.365, 0.22850089497, 419.48464387520],
[40.437, 5.47298059144, 21.34064100240],
[40.205, 5.96420266720, 95.97922721780],
[38.746, 5.83386199529, 110.20632121940],
[28.025, 3.01235311514, 647.01083331480],
[25.029, 0.98808170740, 3.93215326310],
[18.101, 1.02506397063, 412.37109687440],
[17.879, 3.31913418974, 309.27832265580],
[16.208, 3.89825272754, 440.82528487760],
[15.763, 5.61667809625, 117.31986822020],
[19.014, 1.91614237463, 853.19638175200],
[18.262, 4.96738415934, 10.29494073850],
[12.947, 1.18068953942, 88.86568021700],
[17.919, 4.20376505349, 216.48048917570],
[11.453, 5.57520615096, 11.04570026390],
[10.548, 5.92906266269, 191.95845443560],
[10.389, 3.94838736947, 209.36694217490],
[8.650, 3.39335369698, 302.16477565500],
[7.580, 4.87736913157, 323.50541665740],
[6.697, 0.38198725552, 632.78373931320],
[5.864, 1.05621157685, 210.11770170030],
[5.449, 4.64268475485, 234.63973644040],
[6.327, 2.25492722762, 522.57741809380],
[3.602, 2.30677010956, 515.46387109300],
[3.229, 2.20309400066, 860.30992875280],
[3.701, 3.14159265359, 0.00000000000],
[2.583, 4.93447677059, 224.34479570190],
[2.543, 0.42393884183, 625.67019231240],
[2.213, 3.19814958289, 202.25339517410],
[2.421, 4.76621391814, 330.61896365820],
[2.850, 0.58604395010, 529.69096509460],
[1.965, 4.39525359412, 124.43341522100],
[2.154, 1.35488209144, 405.25754987360],
[2.296, 3.34809165905, 429.77958461370],
[2.018, 3.06693569701, 654.12438031560],
[1.979, 1.02981005658, 728.76296653100],
[1.868, 3.09383546177, 422.66603761290],
[1.846, 4.15225985450, 536.80451209540],
[2.194, 1.18918501013, 1066.49547719000],
[2.090, 4.15631351317, 223.59403617650],
[1.481, 0.37916705169, 316.39186965660],
[1.720, 5.82865773356, 195.13984817330],
[1.460, 1.57663426355, 81.75213321620],
[1.623, 6.03706764648, 742.99006053260],
[1.286, 1.66154726117, 63.73589830340],
[1.304, 5.02409881054, 956.28915597060],
[1.446, 2.10575519127, 838.96928775040],
[1.245, 3.88109752770, 269.92144674060],
[1.018, 3.72599601656, 295.05122865420],
[1.323, 1.38492882986, 735.87651353180],
[1.318, 2.33460998999, 217.23124870110],
[0.943, 2.75813531246, 284.14854074220],
[0.906, 0.71155526266, 846.08283475120],
[0.886, 3.83754799777, 447.93883187840],
[0.943, 3.31480217015, 18.15924726470],
[0.800, 4.71386673963, 56.62235130260],
[0.908, 2.02119147951, 831.85574074960],
[0.787, 0.80410269937, 1045.15483618760],
[0.709, 4.27064410504, 437.64389113990],
[0.651, 6.17565900032, 942.06206196900],
[0.785, 2.40767785311, 203.00415469950],
[0.702, 1.64585301418, 423.41679713830],
[0.543, 2.86326941725, 184.84490743480],
[0.532, 6.25762144463, 1059.38193018920],
[0.521, 3.43013038466, 149.56319713460],
[0.484, 4.88366060720, 1272.68102562720],
[0.437, 5.40220619672, 408.43894361130],
[0.388, 2.57589594168, 508.35032409220],
[0.421, 4.05836524024, 543.91805909620],
[0.375, 1.22747948298, 2324.94940881560],
[0.347, 0.59237194522, 22.09140052780],
[0.433, 1.69090148012, 1155.36115740700],
[0.389, 1.46170367972, 1073.60902419080],
[0.307, 1.82185086955, 628.85158605010],
[0.409, 1.21858750514, 1052.26838318840],
[0.309, 0.33610530663, 6076.89030155420],
[0.309, 1.42279282226, 6062.66320755260],
[0.340, 1.83325770310, 1141.13406340540],
[0.303, 2.41584747330, 127.47179660680],
[0.305, 5.34154702988, 131.40394986990],
[0.298, 2.28594631393, 635.96513305090],
[0.372, 1.03723911390, 313.21047591890],
[0.338, 0.69100012338, 1361.54670584420],
[0.325, 1.78816356937, 1148.24761040620],
[0.322, 1.18628805010, 721.64941953020],
[0.271, 2.45663156460, 415.55249061210],
[0.251, 3.12046701975, 1382.88734684660],
[0.254, 3.00353256829, 618.55664531160],
[0.295, 0.35280179538, 2730.20695868920],
[0.242, 1.52154324392, 70.84944530420],
[0.296, 0.89576757167, 2104.53676637680],
[0.264, 3.00987438634, 661.23792731640],
[0.267, 0.31623829657, 1677.93857550080],
[0.270, 2.56774718753, 643.07868005170],
[0.261, 1.55058302472, 1457.52593306200],
[0.246, 2.29214585472, 867.42347575360],
[0.269, 3.18157515051, 750.10360753340],
[0.272, 1.12208982319, 1788.14489672020],
[0.256, 0.37673546414, 1279.79457262800],
[0.206, 1.81129778306, 497.44763618020],
[0.251, 0.61933213502, 2413.81508903260],
[0.237, 3.35941544147, 436.89313161450],
[0.247, 0.10102936687, 99.91138048090],
[0.247, 0.93125798111, 52.69019803950],
[0.221, 2.07880035795, 824.74219374880],
[0.197, 6.16682223437, 1258.45393162560],
[0.229, 5.57917534840, 2943.50605412720],
[0.227, 0.43324651601, 2737.32050569000],
[0.203, 4.12623986247, 337.73251065900],
[0.214, 3.57607524509, 934.94851496820],
[0.212, 1.25688162158, 1773.91780271860],
[0.215, 0.88867647880, 1038.04128918680],
[0.244, 5.51572084570, 231.45834270270],
[0.181, 2.13821830481, 416.30325013750],
[0.210, 4.19139167658, 2221.85663459700],
[0.178, 2.91685344537, 74.78159856730],
[0.201, 0.46214583002, 2854.64037391020],
[0.236, 4.64388694899, 1905.46476494040],
[0.199, 1.54991619669, 1471.75302706360],
[0.199, 0.70725247497, 2420.92863603340],
[0.162, 2.51488345020, 430.53034413910],
[0.160, 1.23508694599, 1596.18644228460],
[0.175, 4.14605894816, 2090.30967237520],
[0.152, 0.05796022559, 32.24332891440],
[0.176, 1.29002070623, 490.33408917940],
[0.154, 3.60622857548, 650.94298657790],
[0.185, 4.74969742128, 319.57326339430],
[0.154, 1.54587199996, 1464.63948006280],
[0.108, 4.25125786500, 145.63104387150],
[0.106, 1.04047809351, 1162.47470440780],
[0.114, 2.64055737100, 362.86229257260],
[0.093, 3.36746275886, 483.22054217860],
[0.091, 2.05796248692, 210.85141488320],
[0.091, 4.53336314765, 241.75328344120],
[0.072, 3.74361312157, 1485.98012106520],
[0.076, 3.33892447677, 195.89060769870],
],
# L4
[
[1661.894, 3.99826248978, 7.11354700080],
[257.107, 2.98436499013, 220.41264243880],
[236.344, 3.90241428075, 14.22709400160],
[149.418, 2.74110824208, 213.29909543800],
[109.598, 1.51515739251, 206.18554843720],
[113.953, 3.14159265359, 0.00000000000],
[68.390, 1.72120953337, 426.59819087600],
[37.699, 1.23795458356, 199.07200143640],
[40.060, 2.04644897412, 433.71173787680],
[31.219, 3.01094184090, 227.52618943960],
[15.111, 0.82897064529, 639.89728631400],
[9.444, 3.71485300868, 21.34064100240],
[5.690, 2.41995290633, 419.48464387520],
[4.470, 1.45120818748, 95.97922721780],
[5.608, 1.15607095740, 647.01083331480],
[4.463, 2.11783225176, 440.82528487760],
[3.229, 4.09278077834, 110.20632121940],
[2.871, 2.77203153866, 412.37109687440],
[2.796, 3.00730249564, 88.86568021700],
[2.638, 0.00255721254, 853.19638175200],
[2.574, 0.39246854091, 103.09277421860],
[1.862, 5.07955457727, 309.27832265580],
[2.225, 3.77689198137, 117.31986822020],
[1.769, 5.19176876406, 302.16477565500],
[1.921, 2.82884328662, 234.63973644040],
[1.805, 2.23816036743, 216.48048917570],
[1.211, 1.54685246534, 191.95845443560],
[0.765, 3.44501766503, 323.50541665740],
[0.763, 4.83197222448, 210.11770170030],
[0.613, 4.19052656353, 515.46387109300],
[0.648, 2.28591710303, 209.36694217490],
[0.616, 4.03194472161, 522.57741809380],
[0.630, 2.37952532019, 632.78373931320],
[0.639, 0.29772678242, 860.30992875280],
[0.559, 2.17110060530, 124.43341522100],
[0.442, 2.23500083592, 447.93883187840],
[0.407, 5.44515970990, 1066.49547719000],
[0.469, 1.26889429317, 654.12438031560],
[0.488, 3.20329778617, 405.25754987360],
[0.415, 3.12435410343, 330.61896365820],
[0.442, 3.38933498625, 81.75213321620],
[0.332, 4.12464206608, 838.96928775040],
[0.320, 3.18332026736, 529.69096509460],
[0.312, 1.40962796637, 429.77958461370],
[0.291, 3.18885372262, 1464.63948006280],
[0.333, 2.94355912397, 728.76296653100],
[0.235, 3.67049647573, 1148.24761040620],
[0.286, 2.57895004576, 1045.15483618760],
[0.223, 3.57980034401, 1155.36115740700],
[0.261, 2.04564143519, 1677.93857550080],
[0.218, 2.61967125327, 536.80451209540],
[0.262, 2.48322150677, 625.67019231240],
[0.191, 4.39064160974, 1574.84580128220],
[0.176, 1.26161895188, 422.66603761290],
[0.190, 2.32693171200, 223.59403617650],
[0.185, 1.08713469614, 742.99006053260],
[0.168, 0.69946458053, 824.74219374880],
[0.177, 5.02663339078, 203.00415469950],
[0.218, 0.40426546037, 867.42347575360],
[0.178, 3.67593243311, 831.85574074960],
[0.175, 5.75326979098, 1073.60902419080],
[0.156, 3.02120117572, 1781.03134971940],
[0.148, 2.28313808274, 295.05122865420],
[0.150, 3.48436135302, 956.28915597060],
[0.152, 1.91404443241, 942.06206196900],
[0.146, 6.16519696640, 316.39186965660],
[0.096, 2.93247663741, 224.34479570190],
[0.088, 4.48383632427, 423.41679713830],
],
# L5
[
[123.615, 2.25923345732, 7.11354700080],
[34.190, 2.16250652689, 14.22709400160],
[27.546, 1.19868150215, 220.41264243880],
[5.818, 1.21584270184, 227.52618943960],
[5.318, 0.23550400093, 433.71173787680],
[3.677, 6.22669694355, 426.59819087600],
[3.057, 2.97372046322, 199.07200143640],
[2.861, 4.28710932685, 206.18554843720],
[1.617, 6.25265362286, 213.29909543800],
[1.279, 5.27612561266, 639.89728631400],
[0.932, 5.56741549127, 647.01083331480],
[0.756, 6.17716234487, 191.95845443560],
[0.760, 0.69475544472, 302.16477565500],
[1.038, 0.23516951637, 440.82528487760],
[1.007, 3.14159265359, 0.00000000000],
[0.549, 4.87733288264, 88.86568021700],
[0.504, 4.77955496203, 419.48464387520],
[0.346, 4.31847547394, 853.19638175200],
[0.392, 5.69922389094, 654.12438031560],
[0.242, 2.05052677361, 323.50541665740],
[0.266, 1.11384528244, 234.63973644040],
[0.199, 0.88505901097, 309.27832265580],
[0.258, 5.10074489186, 95.97922721780],
[0.166, 2.40063312194, 515.46387109300],
[0.155, 4.70433216164, 860.30992875280],
[0.089, 1.36371070380, 412.37109687440],
[0.102, 0.49450039082, 117.31986822020],
],
]
"""This table contains Saturn's 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
435-440."""
VSOP87_B = [
# B0
[
[4330678.040, 3.60284428399, 213.29909543800],
[240348.303, 2.85238489390, 426.59819087600],
[84745.939, 0.00000000000, 0.00000000000],
[30863.357, 3.48441504465, 220.41264243880],
[34116.063, 0.57297307844, 206.18554843720],
[14734.070, 2.11846597870, 639.89728631400],
[9916.668, 5.79003189405, 419.48464387520],
[6993.564, 4.73604689179, 7.11354700080],
[4807.587, 5.43305315602, 316.39186965660],
[4788.392, 4.96512927420, 110.20632121940],
[3432.125, 2.73255752123, 433.71173787680],
[1506.129, 6.01304536144, 103.09277421860],
[1060.298, 5.63099292414, 529.69096509460],
[969.071, 5.20434966103, 632.78373931320],
[942.050, 1.39646678088, 853.19638175200],
[707.645, 3.80302329547, 323.50541665740],
[552.313, 5.13149109045, 202.25339517410],
[399.675, 3.35891413961, 227.52618943960],
[316.063, 1.99716764199, 647.01083331480],
[319.380, 3.62571550980, 209.36694217490],
[284.494, 4.88648481625, 224.34479570190],
[314.225, 0.46510272410, 217.23124870110],
[236.442, 2.13887472281, 11.04570026390],
[215.354, 5.94982610103, 846.08283475120],
[208.522, 2.12003893769, 415.55249061210],
[178.958, 2.95361514672, 63.73589830340],
[207.213, 0.73021462851, 199.07200143640],
[139.140, 1.99821990940, 735.87651353180],
[134.884, 5.24500819605, 742.99006053260],
[140.585, 0.64417620299, 490.33408917940],
[121.669, 3.11537140876, 522.57741809380],
[139.240, 4.59535168021, 14.22709400160],
[115.524, 3.10891547171, 216.48048917570],
[114.218, 0.96261442133, 210.11770170030],
[96.376, 4.48164339766, 117.31986822020],
[80.593, 1.31692750150, 277.03499374140],
[72.952, 3.05988482370, 536.80451209540],
[69.261, 4.92378633635, 309.27832265580],
[74.302, 2.89376539620, 149.56319713460],
[68.040, 2.18002263974, 351.81659230870],
[61.734, 0.67728106562, 1066.49547719000],
[56.598, 2.60963391288, 440.82528487760],
[48.864, 5.78725874107, 95.97922721780],
[48.243, 2.18211837430, 74.78159856730],
[38.304, 5.29151303843, 1059.38193018920],
[36.323, 1.63348365121, 628.85158605010],
[35.055, 1.71279210041, 1052.26838318840],
[34.270, 2.45740470599, 422.66603761290],
[34.313, 5.97994514798, 412.37109687440],
[33.787, 1.14073392951, 949.17560896980],
[31.633, 4.14722153007, 437.64389113990],
[36.833, 6.27769966148, 1162.47470440780],
[26.980, 1.27154816810, 860.30992875280],
[23.516, 2.74936525342, 838.96928775040],
[23.460, 0.98962849901, 210.85141488320],
[23.600, 4.11386961467, 3.93215326310],
[23.631, 3.07427204313, 215.74677599280],
[20.813, 3.51084686918, 330.61896365820],
[19.509, 2.81857577372, 127.47179660680],
[17.103, 3.89784279922, 214.26230328450],
[17.635, 6.19715516746, 703.63318461740],
[17.824, 2.28524493886, 388.46515523820],
[20.935, 0.14356167048, 430.53034413910],
[16.551, 1.66649120724, 38.13303563780],
[19.100, 2.97699096081, 137.03302416240],
[15.517, 4.54798410406, 956.28915597060],
[17.065, 0.16611115812, 212.33588759150],
[14.169, 0.48937283445, 213.34727954780],
[19.027, 6.27326062836, 423.41679713830],
[13.344, 2.37136126257, 429.77958461370],
[12.565, 1.03178071173, 563.63121503840],
[14.173, 3.57477564831, 213.25091132820],
[11.374, 1.45300927024, 1368.66025284500],
[10.585, 6.17633425930, 200.76892246580],
[10.600, 3.84358958373, 138.51749687070],
[10.263, 2.17423692422, 76.26607127560],
[10.072, 1.33197220789, 565.11568774670],
[12.058, 0.44149242700, 222.86032299360],
[10.367, 1.85278552549, 350.33211960040],
[8.706, 2.58144528603, 1155.36115740700],
[8.470, 1.97890349826, 625.67019231240],
[8.518, 4.51649648578, 3.18139373770],
[7.439, 4.92597321442, 212.77783057620],
[7.409, 2.03506679104, 288.08069400530],
[8.137, 3.98500592467, 85.82729883120],
[7.985, 2.20794292064, 362.86229257260],
[6.610, 6.14944028835, 417.03696332040],
[7.753, 6.23664549070, 1478.86657406440],
[6.318, 1.87388481013, 654.12438031560],
[6.319, 1.17328438271, 1265.56747862640],
[5.841, 2.35829915285, 750.10360753340],
[5.808, 5.01602242794, 479.28838891550],
[8.079, 0.42574715104, 554.06998748280],
[6.014, 5.58952234348, 425.11371816770],
[7.444, 5.41859596459, 213.82036029980],
[7.567, 2.68446523795, 191.20769491020],
[7.421, 4.19354269508, 9.56122755560],
[5.466, 3.21737829505, 234.63973644040],
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[0.118, 5.47495367121, 2957.73314812880],
[0.113, 2.57036693965, 462.02291352810],
[0.122, 4.96246567897, 638.93407846750],
[0.104, 1.91139383428, 472.17484191470],
[0.116, 2.82742160564, 450.97721326420],
[0.115, 2.26043201622, 1781.03134971940],
[0.110, 4.86686492403, 2914.01423582380],
[0.109, 4.43848727280, 405.99126305650],
[0.102, 5.90112611078, 99.91138048090],
[0.101, 2.53392410330, 640.86049416050],
[0.112, 5.53802838779, 381.35160823740],
[0.099, 5.92199927896, 411.62033734900],
[0.100, 5.21941099517, 426.48631629140],
[0.137, 2.20269111622, 7.16173111060],
[0.097, 1.27914551364, 2847.52682690940],
[0.115, 5.22953781515, 1119.18567522950],
[0.095, 4.26135357007, 540.73666535850],
[0.098, 5.27107833435, 639.94547042380],
[0.107, 4.38879925113, 412.58354519550],
[0.093, 5.35954173624, 334.55111692130],
[0.094, 1.16749092536, 5643.17856367740],
[0.106, 4.19443004843, 486.40193591630],
[0.096, 0.59816870672, 714.67888488130],
[0.094, 0.54205024076, 423.62924545940],
[0.109, 2.82817225044, 468.24268865160],
[0.083, 6.12100285205, 380.12776796000],
[0.084, 2.20217125255, 909.81873305460],
[0.085, 5.20920130934, 562.14674233010],
[0.105, 2.66415710279, 460.53844081980],
[0.084, 0.14646013561, 681.54178408960],
[0.080, 3.03551986945, 409.92341631960],
[0.097, 5.09373549436, 92.04707395470],
[0.110, 2.03622569317, 642.34496686880],
[0.080, 5.71035549752, 361.37781986430],
[0.084, 3.00961145133, 426.81063919710],
[0.085, 4.28770375688, 135.54855145410],
[0.093, 5.32943472274, 432.01481684740],
[0.086, 1.51247258028, 760.25553592000],
[0.084, 5.83905303748, 426.38574255490],
[0.100, 3.62925349363, 426.71006546060],
[0.094, 4.30151510535, 3377.21779200400],
[0.098, 2.07334671974, 639.84910220420],
[0.080, 4.11576173565, 774.48262992160],
[0.075, 2.89122656610, 806.72595883600],
[0.080, 0.88468467902, 856.37777548970],
[0.072, 4.85259171933, 392.65794093220],
[0.083, 0.11133738383, 402.21916848780],
],
# B1
[
[397554.998, 5.33289992556, 213.29909543800],
[49478.641, 3.14159265359, 0.00000000000],
[18571.607, 6.09919206378, 426.59819087600],
[14800.587, 2.30586060520, 206.18554843720],
[9643.981, 1.69674660120, 220.41264243880],
[3757.161, 1.25429514018, 419.48464387520],
[2716.647, 5.91166664787, 639.89728631400],
[1455.309, 0.85161616532, 433.71173787680],
[1290.595, 2.91770857090, 7.11354700080],
[852.630, 0.43572078997, 316.39186965660],
[284.386, 1.61881754773, 227.52618943960],
[292.185, 5.31574251270, 853.19638175200],
[275.090, 3.88864137336, 103.09277421860],
[297.726, 0.91909206723, 632.78373931320],
[172.359, 0.05215146556, 647.01083331480],
[127.731, 1.20711452525, 529.69096509460],
[166.237, 2.44351613165, 199.07200143640],
[158.220, 5.20850125766, 110.20632121940],
[109.839, 2.45695551627, 217.23124870110],
[81.759, 2.75839171353, 210.11770170030],
[81.010, 2.86038377187, 14.22709400160],
[68.658, 1.65537623146, 202.25339517410],
[59.281, 1.82410768234, 323.50541665740],
[65.161, 1.25527521313, 216.48048917570],
[61.024, 1.25273412095, 209.36694217490],
[46.386, 0.81534705304, 440.82528487760],
[36.163, 1.81851057689, 224.34479570190],
[34.041, 2.83971297997, 117.31986822020],
[32.164, 1.18676132343, 846.08283475120],
[33.114, 1.30557080010, 412.37109687440],
[27.282, 4.64744847591, 1066.49547719000],
[22.805, 4.12923703368, 415.55249061210],
[27.128, 4.44228739187, 11.04570026390],
[18.100, 5.56392353608, 860.30992875280],
[20.851, 1.40999273740, 309.27832265580],
[14.947, 1.34302610607, 95.97922721780],
[15.316, 1.22393617996, 63.73589830340],
[14.601, 1.00753704970, 536.80451209540],
[12.842, 2.27059911053, 742.99006053260],
[12.832, 4.88898877901, 522.57741809380],
[13.137, 2.45991904379, 490.33408917940],
[11.883, 1.87308666696, 423.41679713830],
[13.027, 3.21731634178, 277.03499374140],
[9.946, 3.11650057543, 625.67019231240],
[12.710, 0.29501589197, 422.66603761290],
[9.644, 1.74586356703, 330.61896365820],
[8.079, 2.41931187953, 430.53034413910],
[8.245, 4.68121931659, 215.74677599280],
[8.958, 0.46482448501, 429.77958461370],
[6.547, 3.01351967549, 949.17560896980],
[7.251, 5.97098186912, 149.56319713460],
[6.056, 1.49115011100, 234.63973644040],
[5.791, 5.36720639912, 735.87651353180],
[5.994, 0.02442871989, 654.12438031560],
[6.647, 3.90879134581, 351.81659230870],
[6.824, 1.52456408861, 437.64389113990],
[5.134, 3.81149834833, 74.78159856730],
[3.959, 5.63505813057, 210.85141488320],
[3.811, 2.63992803111, 3.18139373770],
[3.643, 1.73267151007, 1059.38193018920],
[3.554, 4.98621474362, 3.93215326310],
[4.568, 4.33599514584, 628.85158605010],
[3.145, 2.51404811765, 1162.47470440780],
[3.522, 1.16093567319, 223.59403617650],
[2.933, 2.06057834252, 956.28915597060],
[2.644, 5.62559379305, 203.73786788240],
[2.992, 5.06312015437, 515.46387109300],
[2.304, 2.73123930535, 21.34064100240],
[2.168, 2.91805928238, 203.00415469950],
[2.398, 3.99421633537, 1279.79457262800],
[2.146, 0.87500689888, 408.43894361130],
[2.074, 1.65731069687, 137.03302416240],
[1.797, 1.56879308343, 124.43341522100],
[2.088, 1.85721384366, 138.51749687070],
[1.769, 4.82294294946, 1073.60902419080],
[1.635, 1.20387813348, 88.86568021700],
[2.202, 5.93027042684, 1052.26838318840],
[1.843, 0.22126910774, 750.10360753340],
[1.851, 2.45470409290, 340.77089204480],
[1.890, 0.41025631859, 127.47179660680],
[1.582, 5.63360832372, 214.26230328450],
[1.920, 3.77935901504, 350.33211960040],
[1.786, 5.78644477326, 635.96513305090],
[1.497, 3.13026893210, 703.63318461740],
[1.583, 3.46882532865, 38.13303563780],
[1.577, 4.02973226017, 388.46515523820],
[1.645, 5.59115773632, 483.22054217860],
[1.405, 4.07880624509, 728.76296653100],
[1.498, 5.87094430469, 362.86229257260],
[1.317, 2.22386203585, 213.34727954780],
[1.321, 2.91534782718, 1265.56747862640],
[1.307, 5.41748323885, 217.96496188400],
[1.483, 0.91111666841, 543.91805909620],
[1.291, 2.62333801070, 554.06998748280],
[1.406, 0.34582712649, 85.82729883120],
[1.287, 2.82247279651, 231.45834270270],
[1.563, 4.88438049382, 208.63322899200],
[1.316, 5.30963570131, 213.25091132820],
[1.164, 1.39531381032, 210.37833413120],
[1.295, 2.46089213219, 200.76892246580],
[1.236, 3.03659580871, 838.96928775040],
[1.449, 4.00934078371, 195.13984817330],
[1.251, 1.46674521697, 218.71572140940],
[1.568, 1.89939852487, 212.33588759150],
[1.067, 5.34734443894, 207.67002114550],
[1.111, 0.70962013461, 447.93883187840],
[1.012, 1.37217220640, 636.71589257630],
[1.163, 6.00108996618, 191.20769491020],
[0.887, 2.84483069917, 191.95845443560],
[1.005, 2.72373040634, 1478.86657406440],
[0.879, 1.19585734916, 417.03696332040],
[0.829, 4.94182950387, 497.44763618020],
[0.878, 6.24981924813, 265.98929347750],
[0.781, 4.61973017912, 424.15051032120],
[0.924, 3.64210508536, 222.86032299360],
[0.971, 2.89404568581, 563.63121503840],
[0.946, 5.72987725592, 1368.66025284500],
[0.834, 6.12384852532, 209.10630974400],
[0.911, 1.06795057723, 650.94298657790],
[0.731, 0.81660632103, 142.44965013380],
[0.795, 5.54574074566, 76.26607127560],
[1.012, 5.97140626297, 643.07868005170],
[0.703, 2.41479303782, 10.29494073850],
[0.726, 4.52598413209, 565.11568774670],
[0.691, 2.31682364985, 160.60889739850],
[0.695, 0.37889317398, 212.77783057620],
[0.676, 4.43606270900, 842.15068148810],
[0.769, 4.47368582271, 52.69019803950],
[0.658, 0.32331118921, 621.73803904930],
[0.838, 4.68035046143, 288.08069400530],
[0.674, 5.63961963995, 867.42347575360],
[0.695, 1.32062509205, 1169.58825140860],
[0.841, 2.46995220838, 1375.77379984580],
[0.633, 3.46145143241, 18.15924726470],
[0.722, 0.04119071457, 269.92144674060],
[0.757, 2.15030650611, 207.88246946660],
[0.692, 0.87072324976, 213.82036029980],
[0.602, 0.85288769518, 225.82926841020],
[0.635, 4.76109030475, 831.85574074960],
[0.701, 1.20410854661, 479.28838891550],
[0.624, 2.30585779534, 643.82943957710],
[0.582, 0.18811617696, 1.48447270830],
[0.513, 2.56525967840, 404.50679034820],
[0.502, 4.97423814367, 212.54833591260],
[0.644, 2.10955154583, 1272.68102562720],
[0.467, 4.47217820662, 235.39049596580],
[0.566, 4.44740324446, 429.04587143080],
[0.448, 0.57491120802, 22.09140052780],
[0.520, 1.15131866397, 337.73251065900],
[0.476, 4.78513362967, 218.92816973050],
[0.519, 0.61616177345, 436.89313161450],
[0.442, 2.10204008144, 416.30325013750],
[0.536, 1.08779067908, 344.70304530790],
[0.477, 2.42483193385, 216.21985674480],
[0.469, 5.22622034028, 942.06206196900],
[0.392, 0.41137926465, 302.16477565500],
[0.400, 5.17216478470, 414.06801790380],
[0.383, 3.58419227076, 1045.15483618760],
[0.443, 1.11051326413, 425.11371816770],
[0.517, 3.44547026103, 12.53017297220],
[0.369, 1.60095273908, 56.62235130260],
[0.354, 2.79123486392, 1581.95934828300],
[0.405, 5.93402105921, 173.94221952280],
[0.319, 4.31850876624, 219.44943459230],
[0.330, 0.62529198264, 358.93013930950],
[0.305, 0.82404423420, 1485.98012106520],
[0.391, 2.59385552893, 1795.25844372100],
[0.291, 3.12019266878, 217.49188113200],
[0.294, 2.18552193901, 444.75743814070],
[0.281, 0.77791302266, 757.21715453420],
[0.355, 5.44570491928, 1685.05212250160],
[0.305, 2.65927043884, 355.74874557180],
[0.269, 6.00323720265, 934.94851496820],
[0.287, 2.60486363576, 113.38771495710],
[0.348, 0.98872551635, 70.84944530420],
[0.331, 5.62133883922, 9.56122755560],
[0.255, 4.14086605030, 284.14854074220],
[0.311, 6.27145060602, 207.14875628370],
[0.267, 4.72606312146, 696.51963761660],
[0.319, 4.68828119248, 1155.36115740700],
[0.227, 3.10352674343, 1361.54670584420],
[0.228, 1.19253095837, 1589.07289528380],
[0.244, 5.36327976010, 245.54242435240],
[0.218, 2.16069250901, 177.87437278590],
[0.254, 4.51652534648, 1148.24761040620],
[0.211, 2.82699627326, 106.27416795630],
[0.230, 4.63171743406, 107.02492748170],
[0.201, 4.52152562223, 508.35032409220],
[0.230, 5.93560798508, 618.55664531160],
[0.253, 2.08074949572, 252.65597135320],
[0.234, 2.43423283339, 1692.16566950240],
[0.196, 1.01284131123, 114.39910691340],
[0.196, 2.73629728926, 214.04985496340],
[0.191, 1.51642829677, 6069.77675455340],
[0.252, 5.10097595426, 1258.45393162560],
[0.240, 2.93712394928, 916.93228005540],
[0.224, 4.42406538277, 251.43213107580],
[0.223, 2.34400676548, 1677.93857550080],
[0.228, 5.00073557208, 1574.84580128220],
[0.183, 5.09056895026, 220.46082654860],
[0.178, 6.05669760153, 206.13736432740],
[0.185, 3.73859309582, 114.13847448250],
[0.200, 1.89409546254, 2420.92863603340],
[0.158, 2.78517362162, 2008.55753915900],
[0.191, 2.28724146195, 2435.15573003500],
[0.188, 4.29343910228, 1471.75302706360],
[0.155, 5.35194123420, 576.16138801060],
[0.174, 2.80423114755, 1781.03134971940],
[0.166, 5.32531835813, 2001.44399215820],
[0.165, 2.62993712087, 525.49817940060],
[0.141, 4.73916921092, 501.37978944330],
[0.161, 5.83368523750, 181.05576652360],
[0.137, 1.45135867137, 131.54696222180],
[0.157, 3.22870773657, 1493.09366806600],
[0.136, 4.20279658293, 710.74673161820],
[0.144, 4.61003572124, 121.25202148330],
[0.131, 5.85409245557, 175.16605980020],
[0.144, 0.96056164245, 214.78356814630],
[0.146, 3.95687956474, 421.93232443000],
[0.138, 1.03080573610, 4.66586644600],
[0.167, 1.97508934614, 62.25142559510],
[0.123, 2.28640485589, 1898.35121793960],
[0.168, 4.63122081226, 1891.23767093880],
[0.129, 0.05327999225, 211.81462272970],
[0.134, 3.49720535944, 488.84961647110],
[0.117, 3.43819501459, 436.15941843160],
[0.125, 5.87007326241, 963.40270297140],
[0.120, 0.70795300239, 81.75213321620],
[0.125, 4.50999471095, 2317.83586181480],
[0.116, 6.11600926571, 558.00214074590],
[0.117, 4.78666549046, 601.76425067620],
[0.108, 0.45464469172, 1802.37199072180],
[0.111, 1.44669239244, 2531.13495725280],
[0.109, 6.14289264597, 151.04766984290],
[0.113, 4.05600865495, 1286.90811962880],
[0.129, 5.13936946160, 849.26422848890],
[0.127, 3.88189432056, 98.89998852460],
[0.133, 2.38290634070, 2111.65031337760],
[0.122, 4.40757611742, 778.41478318470],
[0.095, 0.07909774752, 213.41097002260],
[0.095, 1.66925524906, 213.18722085340],
[0.103, 1.88058957173, 99.16062095550],
[0.119, 3.62785705509, 248.72381809010],
[0.090, 4.63029999228, 228.27694896500],
[0.092, 5.48700119144, 767.36908292080],
[0.089, 4.61331934339, 431.26405732200],
[0.099, 3.60670326134, 776.93031047640],
[0.085, 4.93878023673, 2.44768055480],
[0.089, 6.24541644164, 661.23792731640],
[0.085, 0.45896349060, 1382.88734684660],
[0.088, 3.81144552178, 1788.14489672020],
[0.103, 3.20558404998, 312.19908396260],
[0.080, 2.28889729136, 213.08664711690],
[0.080, 5.74264101239, 213.51154375910],
[0.082, 3.23546757052, 198.32124191100],
[0.078, 6.03841191050, 835.03713448730],
[0.080, 0.22601918692, 427.56139872250],
[0.072, 2.05164614795, 2634.22773147140],
[0.091, 5.97938003596, 556.51766803760],
[0.087, 2.71469794199, 617.80588578620],
],
# B2
[
[20629.977, 0.50482422817, 213.29909543800],
[3719.555, 3.99833475829, 206.18554843720],
[1627.158, 6.18189939500, 220.41264243880],
[1346.067, 0.00000000000, 0.00000000000],
[705.842, 3.03914308836, 419.48464387520],
[365.042, 5.09928680706, 426.59819087600],
[329.632, 5.27899210039, 433.71173787680],
[219.335, 3.82841533795, 639.89728631400],
[139.393, 1.04272623499, 7.11354700080],
[103.980, 6.15730992966, 227.52618943960],
[92.961, 1.97994412845, 316.39186965660],
[71.242, 4.14754353431, 199.07200143640],
[51.927, 2.88364833898, 632.78373931320],
[48.961, 4.43390206741, 647.01083331480],
[41.373, 3.15927770079, 853.19638175200],
[28.602, 4.52978327558, 210.11770170030],
[23.969, 1.11595912146, 14.22709400160],
[20.511, 4.35095844197, 217.23124870110],
[19.532, 5.30779711223, 440.82528487760],
[18.263, 0.85391476786, 110.20632121940],
[15.742, 4.25767226302, 103.09277421860],
[16.840, 5.68112084135, 216.48048917570],
[13.613, 2.99904334066, 412.37109687440],
[11.567, 2.52679928410, 529.69096509460],
[7.963, 3.31512423920, 202.25339517410],
[6.599, 0.28766025146, 323.50541665740],
[6.312, 1.16121321336, 117.31986822020],
[5.891, 3.58260177246, 309.27832265580],
[6.648, 5.55714129949, 209.36694217490],
[5.590, 2.47783944511, 1066.49547719000],
[6.192, 3.61231886519, 860.30992875280],
[4.231, 3.02212363572, 846.08283475120],
[3.612, 4.79935735435, 625.67019231240],
[3.398, 3.76732731354, 423.41679713830],
[3.387, 6.04222745633, 234.63973644040],
[2.578, 5.63610668746, 735.87651353180],
[2.831, 4.81642822334, 429.77958461370],
[2.817, 4.47516563908, 654.12438031560],
[2.573, 0.22467245054, 522.57741809380],
[2.610, 3.29126967191, 95.97922721780],
[2.419, 0.02986335489, 415.55249061210],
[2.112, 4.55964179603, 422.66603761290],
[2.304, 6.25081073546, 330.61896365820],
[1.758, 5.53430456858, 536.80451209540],
[1.814, 5.05675881426, 277.03499374140],
[1.550, 5.60375604692, 223.59403617650],
[1.457, 4.47767649852, 430.53034413910],
[1.607, 5.53599550100, 224.34479570190],
[1.172, 4.71017775994, 203.00415469950],
[1.231, 0.25115931880, 3.93215326310],
[1.105, 1.01595427676, 21.34064100240],
[0.868, 4.84623483952, 949.17560896980],
[0.939, 1.35429452093, 742.99006053260],
[0.693, 6.03599130692, 124.43341522100],
[0.712, 4.45550701473, 191.95845443560],
[0.690, 5.44243765037, 437.64389113990],
[0.810, 0.46198177342, 515.46387109300],
[0.694, 5.23748122403, 447.93883187840],
[0.604, 2.95749705544, 88.86568021700],
[0.669, 0.08457977809, 215.74677599280],
[0.579, 0.65329445948, 3.18139373770],
[0.712, 6.05964117622, 11.04570026390],
[0.698, 2.91371419321, 1073.60902419080],
[0.526, 2.24947851818, 1059.38193018920],
[0.511, 2.86838724347, 408.43894361130],
[0.589, 5.79268515755, 63.73589830340],
[0.519, 1.76641574095, 1279.79457262800],
[0.503, 5.73762297081, 728.76296653100],
[0.482, 4.68234512154, 838.96928775040],
[0.494, 4.04363805503, 490.33408917940],
[0.458, 1.17998315936, 210.85141488320],
[0.380, 5.28045750432, 1052.26838318840],
[0.404, 4.58953258519, 302.16477565500],
[0.377, 5.20131800999, 74.78159856730],
[0.328, 0.11893501088, 956.28915597060],
[0.290, 3.99300398632, 1162.47470440780],
[0.262, 2.04320741578, 1471.75302706360],
[0.259, 3.76206113036, 635.96513305090],
[0.254, 0.16694559092, 195.13984817330],
[0.309, 5.44921175960, 543.91805909620],
[0.237, 1.27761853769, 231.45834270270],
[0.288, 1.32449995239, 203.73786788240],
[0.229, 4.19748765966, 1265.56747862640],
[0.238, 4.02925601887, 643.07868005170],
[0.238, 0.49997895983, 10.29494073850],
[0.257, 3.69107889837, 867.42347575360],
[0.191, 0.17807919948, 628.85158605010],
[0.246, 5.62469599682, 351.81659230870],
[0.183, 3.38184740572, 636.71589257630],
[0.172, 3.83173494030, 1581.95934828300],
[0.220, 1.03443668151, 483.22054217860],
[0.217, 4.65210162713, 750.10360753340],
[0.143, 2.31969979791, 18.15924726470],
[0.137, 5.50046852846, 1169.58825140860],
[0.120, 3.70151294359, 416.30325013750],
[0.136, 3.38453909352, 1155.36115740700],
[0.149, 0.85459831932, 1375.77379984580],
[0.150, 5.71949902293, 618.55664531160],
[0.125, 4.82446274394, 436.89313161450],
[0.120, 3.26968058035, 1478.86657406440],
[0.131, 0.11496484259, 1898.35121793960],
[0.099, 4.57241894541, 643.82943957710],
[0.095, 4.92115458463, 650.94298657790],
[0.090, 2.09300085806, 621.73803904930],
[0.111, 0.11975665259, 831.85574074960],
[0.089, 2.54351587616, 85.82729883120],
[0.080, 5.09103451442, 340.77089204480],
[0.078, 3.17395501851, 497.44763618020],
[0.085, 0.18997660997, 1258.45393162560],
[0.081, 1.16732337173, 217.96496188400],
[0.072, 5.47328223678, 337.73251065900],
],
# B3
[
[666.252, 1.99006340181, 213.29909543800],
[632.350, 5.69778316807, 206.18554843720],
[398.051, 0.00000000000, 0.00000000000],
[187.838, 4.33779804809, 220.41264243880],
[91.884, 4.84104208217, 419.48464387520],
[42.369, 2.38073239056, 426.59819087600],
[51.548, 3.42149490328, 433.71173787680],
[25.661, 4.40167213109, 227.52618943960],
[20.551, 5.85313509872, 199.07200143640],
[18.081, 1.99321433229, 639.89728631400],
[10.874, 5.37344546547, 7.11354700080],
[9.590, 2.54901825866, 647.01083331480],
[7.085, 3.45518372721, 316.39186965660],
[6.002, 4.80055225135, 632.78373931320],
[5.778, 0.01680378777, 210.11770170030],
[4.881, 5.63719730884, 14.22709400160],
[4.501, 1.22424419010, 853.19638175200],
[5.542, 3.51756747774, 440.82528487760],
[3.548, 4.71299370890, 412.37109687440],
[2.851, 0.62679207578, 103.09277421860],
[2.173, 3.71982274459, 216.48048917570],
[1.991, 6.10867071657, 217.23124870110],
[1.435, 1.69177141453, 860.30992875280],
[1.217, 4.30778838827, 234.63973644040],
[1.157, 5.75027789902, 309.27832265580],
[0.795, 5.69026441157, 117.31986822020],
[0.733, 0.59842720676, 1066.49547719000],
[0.713, 0.21700311697, 625.67019231240],
[0.773, 5.48361981990, 202.25339517410],
[0.897, 2.65577866867, 654.12438031560],
[0.509, 2.86079833766, 429.77958461370],
[0.462, 4.17742567173, 529.69096509460],
[0.390, 6.11288036049, 191.95845443560],
[0.505, 4.51905764563, 323.50541665740],
[0.379, 3.74436004151, 223.59403617650],
[0.332, 5.49370890570, 21.34064100240],
[0.377, 5.25624813434, 95.97922721780],
[0.384, 4.48187414769, 330.61896365820],
[0.367, 5.03190929680, 846.08283475120],
[0.281, 1.14133888637, 735.87651353180],
[0.245, 5.81618253250, 423.41679713830],
[0.241, 1.70335120180, 522.57741809380],
[0.258, 3.69110118716, 447.93883187840],
[0.231, 4.15697626494, 110.20632121940],
[0.305, 5.97746884029, 302.16477565500],
[0.284, 0.66224572127, 203.00415469950],
[0.204, 1.54683820621, 209.36694217490],
[0.194, 4.21193801453, 124.43341522100],
[0.145, 4.79689259614, 88.86568021700],
[0.151, 3.82010884134, 536.80451209540],
[0.100, 0.03596545368, 949.17560896980],
[0.097, 0.91303450276, 1073.60902419080],
[0.110, 2.21197473966, 515.46387109300],
[0.084, 2.53842533109, 422.66603761290],
[0.085, 5.11102520704, 3.93215326310],
[0.077, 6.04074586787, 838.96928775040],
[0.085, 1.18898817378, 728.76296653100],
[0.084, 4.10158366806, 224.34479570190],
],
# B4
[
[80.384, 1.11918414679, 206.18554843720],
[31.660, 3.12218745098, 213.29909543800],
[17.143, 2.48073200414, 220.41264243880],
[11.844, 3.14159265359, 0.00000000000],
[9.005, 0.38441424927, 419.48464387520],
[6.164, 1.56186379537, 433.71173787680],
[4.660, 1.28235639570, 199.07200143640],
[4.775, 2.63498295487, 227.52618943960],
[1.487, 1.43096671616, 426.59819087600],
[1.424, 0.66988083613, 647.01083331480],
[1.075, 6.18092274059, 639.89728631400],
[1.145, 1.72041928134, 440.82528487760],
[0.682, 3.84841098180, 14.22709400160],
[0.655, 3.49486258327, 7.11354700080],
[0.456, 0.47338193402, 632.78373931320],
[0.509, 0.31432285584, 412.37109687440],
[0.343, 5.86413875355, 853.19638175200],
[0.270, 2.50125594913, 234.63973644040],
[0.197, 5.39156324804, 316.39186965660],
[0.236, 2.11084590211, 210.11770170030],
[0.172, 6.09682874401, 860.30992875280],
[0.159, 5.95049154821, 216.48048917570],
[0.100, 1.98534903594, 625.67019231240],
[0.112, 0.85526419268, 654.12438031560],
[0.115, 5.03884718594, 117.31986822020],
[0.115, 0.44589613974, 110.20632121940],
],
# B5
[
[7.895, 2.81927558645, 206.18554843720],
[1.014, 0.51187210270, 220.41264243880],
[0.772, 2.99484124049, 199.07200143640],
[0.967, 3.14159265359, 0.00000000000],
[0.583, 5.96456944075, 433.71173787680],
[0.588, 0.78008666397, 227.52618943960],
[0.445, 2.38630799074, 419.48464387520],
[0.098, 5.10622131539, 647.01083331480],
[0.091, 5.81659714144, 7.11354700080],
[0.088, 6.17828532308, 440.82528487760],
[0.089, 0.58396864530, 213.29909543800],
],
]
"""This table contains Saturn's 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
440-442."""
VSOP87_R = [
# R0
[
[955758135.801, 0.00000000000, 0.00000000000],
[52921382.465, 2.39226219733, 213.29909543800],
[1873679.934, 5.23549605091, 206.18554843720],
[1464663.959, 1.64763045468, 426.59819087600],
[821891.059, 5.93520025371, 316.39186965660],
[547506.899, 5.01532628454, 103.09277421860],
[371684.449, 2.27114833428, 220.41264243880],
[361778.433, 3.13904303264, 7.11354700080],
[140617.548, 5.70406652991, 632.78373931320],
[108974.737, 3.29313595577, 110.20632121940],
[69007.015, 5.94099622447, 419.48464387520],
[61053.350, 0.94037761156, 639.89728631400],
[48913.044, 1.55733388472, 202.25339517410],
[34143.794, 0.19518550682, 277.03499374140],
[32401.718, 5.47084606947, 949.17560896980],
[20936.573, 0.46349163993, 735.87651353180],
[20839.118, 1.52102590640, 433.71173787680],
[20746.678, 5.33255667599, 199.07200143640],
[15298.457, 3.05943652881, 529.69096509460],
[14296.479, 2.60433537909, 323.50541665740],
[11993.314, 5.98051421881, 846.08283475120],
[11380.261, 1.73105746566, 522.57741809380],
[12884.128, 1.64892310393, 138.51749687070],
[7752.769, 5.85191318903, 95.97922721780],
[9796.061, 5.20475863996, 1265.56747862640],
[6465.967, 0.17733160145, 1052.26838318840],
[6770.621, 3.00433479284, 14.22709400160],
[5850.443, 1.45519636076, 415.55249061210],
[5307.481, 0.59737534050, 63.73589830340],
[4695.746, 2.14919036956, 227.52618943960],
[4043.988, 1.64010323863, 209.36694217490],
[3688.132, 0.78016133170, 412.37109687440],
[3376.457, 3.69528478828, 224.34479570190],
[2885.348, 1.38764077631, 838.96928775040],
[2976.033, 5.68467931117, 210.11770170030],
[3419.551, 4.94549148887, 1581.95934828300],
[3460.943, 1.85088802878, 175.16605980020],
[3400.616, 0.55386747515, 350.33211960040],
[2507.630, 3.53851863255, 742.99006053260],
[2448.325, 6.18412386316, 1368.66025284500],
[2406.138, 2.96559220267, 117.31986822020],
[2881.181, 0.17960757891, 853.19638175200],
[2173.959, 0.01508587396, 340.77089204480],
[2024.483, 5.05411271271, 11.04570026390],
[1740.254, 2.34657043464, 309.27832265580],
[1861.397, 5.93361638244, 625.67019231240],
[1888.436, 0.02968443389, 3.93215326310],
[1610.859, 1.17302463549, 74.78159856730],
[1462.631, 1.92588134017, 216.48048917570],
[1474.547, 5.67670461130, 203.73786788240],
[1395.109, 5.93669404929, 127.47179660680],
[1781.165, 0.76314388077, 217.23124870110],
[1817.186, 5.77713225779, 490.33408917940],
[1472.392, 1.40064915651, 137.03302416240],
[1304.089, 0.77235613966, 647.01083331480],
[1149.773, 5.74021249703, 1162.47470440780],
[1126.667, 4.46707803791, 265.98929347750],
[1277.489, 2.98412586423, 1059.38193018920],
[1207.053, 0.75285933160, 351.81659230870],
[1071.399, 1.13567265104, 1155.36115740700],
[1020.922, 5.91233512844, 1685.05212250160],
[1315.042, 5.11202572637, 211.81462272970],
[1295.553, 4.69184139933, 1898.35121793960],
[1099.037, 1.81765118601, 149.56319713460],
[998.462, 2.63131596867, 200.76892246580],
[985.869, 2.25992849742, 956.28915597060],
[932.434, 3.66980793184, 554.06998748280],
[664.481, 0.60297724821, 728.76296653100],
[659.850, 4.66635439533, 195.13984817330],
[617.740, 5.62092000007, 942.06206196900],
[626.382, 5.94208232590, 1478.86657406440],
[482.230, 1.84070179496, 479.28838891550],
[487.689, 2.79373616806, 3.18139373770],
[470.086, 0.83847755040, 1471.75302706360],
[451.817, 5.64468459871, 2001.44399215820],
[553.128, 3.41088600844, 269.92144674060],
[534.397, 1.26443331367, 275.55052103310],
[472.572, 1.88198584660, 515.46387109300],
[405.434, 1.64001413521, 536.80451209540],
[517.196, 4.44310450526, 2214.74308759620],
[452.848, 3.00349117198, 302.16477565500],
[494.340, 2.28626675074, 278.51946644970],
[489.825, 5.80631420383, 191.20769491020],
[427.459, 0.05741344372, 284.14854074220],
[339.763, 1.40198657693, 440.82528487760],
[340.627, 0.89091104306, 628.85158605010],
[385.974, 1.99700402508, 1272.68102562720],
[288.298, 1.12160250272, 422.66603761290],
[294.444, 0.42577061903, 312.19908396260],
[262.490, 0.31753439818, 1045.15483618760],
[295.331, 0.67144493789, 88.86568021700],
[342.968, 5.85600322299, 1795.25844372100],
[341.117, 2.37585247250, 525.49817940060],
[234.018, 4.22756813216, 114.13847448250],
[223.729, 2.28129446763, 330.61896365820],
[275.814, 0.47832439352, 38.13303563780],
[224.592, 0.54754005675, 1788.14489672020],
[303.300, 0.87946670205, 6069.77675455340],
[292.103, 6.21420611920, 210.85141488320],
[226.121, 0.37495223398, 142.44965013380],
[277.257, 5.31917702012, 692.58748435350],
[242.911, 5.37187983246, 1258.45393162560],
[205.571, 0.95755250527, 288.08069400530],
[207.567, 5.38126259725, 2317.83586181480],
[186.835, 6.03591766061, 404.50679034820],
[218.536, 5.25607043545, 212.33588759150],
[222.155, 5.94588016768, 39.35687591520],
[179.673, 4.41045924362, 408.43894361130],
[241.440, 1.12525868110, 388.46515523820],
[197.093, 3.90141942850, 52.69019803950],
[236.639, 0.90802744873, 1375.77379984580],
[171.915, 5.56318632797, 213.34727954780],
[169.865, 2.85667554010, 99.16062095550],
[214.398, 4.20253525974, 2531.13495725280],
[172.010, 2.36537801012, 213.25091132820],
[165.707, 2.63679789706, 215.74677599280],
[230.892, 5.49463421262, 191.95845443560],
[177.585, 0.38155817719, 430.53034413910],
[191.514, 2.95906900704, 437.64389113990],
[163.250, 3.45832517280, 617.80588578620],
[162.305, 5.73050678664, 203.00415469950],
[175.108, 5.71404465044, 1066.49547719000],
[183.041, 5.66851947172, 2111.65031337760],
[150.077, 4.40663921925, 417.03696332040],
[187.935, 6.07916265661, 563.63121503840],
[145.127, 5.08176368814, 423.41679713830],
[137.491, 5.43912787991, 222.86032299360],
[172.824, 1.84920994090, 1589.07289528380],
[165.478, 2.89132196119, 214.26230328450],
[145.727, 1.56565192483, 831.85574074960],
[176.864, 2.30323752987, 9999.98645077300],
[128.877, 2.55338644107, 414.06801790380],
[120.093, 0.04329750542, 1361.54670584420],
[143.441, 0.99817357720, 76.26607127560],
[108.747, 2.09282278191, 207.67002114550],
[132.106, 2.85902597898, 312.45971639350],
[112.238, 0.26221759151, 2104.53676637680],
[125.186, 4.78354048063, 205.22234059070],
[104.427, 3.63671899047, 65.22037101170],
[107.447, 3.67064138701, 212.77783057620],
[108.642, 2.85492389024, 21.34064100240],
[97.743, 5.12231845599, 2634.22773147140],
[109.097, 1.63231061493, 208.63322899200],
[96.852, 4.19928280035, 305.34616939270],
[96.507, 2.56002066845, 1692.16566950240],
[85.829, 4.54545085982, 210.37833413120],
[99.249, 5.13816222131, 1574.84580128220],
[112.532, 5.03109281265, 703.63318461740],
[84.023, 1.18337717265, 429.77958461370],
[89.021, 5.38791571457, 107.02492748170],
[110.191, 2.43656081234, 355.74874557180],
[90.659, 4.20908809746, 213.82036029980],
[95.885, 5.44594259071, 2428.04218303420],
[94.109, 2.39786381418, 483.22054217860],
[85.609, 0.03354346966, 860.30992875280],
[88.796, 4.05766306750, 128.95626931510],
[81.951, 1.66499731549, 62.25142559510],
[91.240, 3.96942332591, 2847.52682690940],
[83.961, 4.60845858022, 177.87437278590],
[88.376, 3.86800515885, 140.00196957900],
[93.308, 0.73846639887, 831.10498122420],
[91.872, 2.94977605320, 35.42472265210],
[87.077, 1.33390590052, 1905.46476494040],
[96.584, 4.84438390997, 131.40394986990],
[71.010, 0.99334817658, 405.25754987360],
[95.266, 2.51506908152, 2.44768055480],
[72.514, 4.63213873657, 245.54242435240],
[82.580, 1.52823217919, 145.63104387150],
[76.693, 3.15240783008, 767.36908292080],
[70.317, 4.04253707270, 173.94221952280],
[86.015, 2.30103727270, 85.82729883120],
[66.529, 4.75053522835, 70.84944530420],
[65.835, 2.46869725001, 280.96714700450],
[64.824, 0.09343869325, 9.56122755560],
[71.557, 0.01212415296, 565.11568774670],
[66.533, 1.08034871114, 339.28641933650],
[63.488, 2.01740971153, 234.63973644040],
[60.786, 5.12026947473, 756.32338265690],
[58.123, 6.05732868566, 1677.93857550080],
[64.236, 1.28586474622, 1148.24761040620],
[73.124, 4.37810889148, 425.11371816770],
[55.012, 3.85865703217, 342.25536475310],
[57.101, 6.26689214029, 2420.92863603340],
[64.090, 4.09854757476, 327.43756992050],
[55.306, 1.60456896521, 543.02428721890],
[57.987, 5.47269124340, 347.88443904560],
[73.581, 3.72292337326, 92.04707395470],
[73.760, 3.57045342615, 1.48447270830],
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[1.408, 5.24970924980, 316.27999507200],
[1.724, 0.25483952164, 125.18417474640],
[1.426, 2.26871672572, 17.40848773930],
[1.881, 4.12588105003, 562.14674233010],
[1.370, 4.74474866880, 1357.61455258110],
[1.485, 2.18712736768, 9889.78012955360],
[1.369, 1.31846306523, 1160.83017300510],
[1.394, 5.66924517860, 1736.99156101570],
[1.375, 0.16983286236, 346.39996633730],
[1.525, 2.40244831911, 419.43645976540],
[1.359, 2.68668516027, 310.76279536410],
[1.396, 3.67055397940, 253.45912050530],
[1.454, 5.49356262440, 504.56118318100],
[1.813, 0.21882066860, 263.70167161710],
[1.330, 3.01736059716, 254.14044406150],
[1.498, 0.17578085903, 155.78297225810],
[1.509, 5.13129901759, 768.85355562910],
[1.550, 1.44225397189, 1894.41906467650],
[1.447, 1.44933809994, 893.35640681930],
[1.306, 5.76425101758, 714.67888488130],
[1.660, 1.34160526151, 322.61164478010],
[1.347, 3.00388920953, 843.63515419640],
[1.432, 3.43786149731, 251.17149864490],
[1.510, 4.39762427873, 25.27279426550],
[1.587, 5.17106904014, 141.69889060840],
[1.477, 5.47518377610, 226.04171673130],
[1.356, 4.24406292182, 332.17287233570],
[1.644, 1.74367211793, 67.88049988760],
[1.407, 5.79229630947, 188.16931352440],
[1.575, 0.09808372057, 702.14871190910],
[1.765, 4.93410889383, 201.51968199120],
[1.318, 4.91605557404, 17.52610781830],
[1.701, 4.47360878108, 384.27236954420],
[1.304, 6.04155032791, 25.86349509650],
[1.269, 4.91035989349, 354.99798604640],
[1.620, 5.54960841244, 260.36021918500],
[1.263, 1.16521999431, 255.83736509090],
[1.744, 3.70453251764, 147.11551657980],
[1.579, 4.31561365365, 2228.97018159780],
[1.557, 0.57740217353, 3178.14579056760],
[1.302, 0.32055726013, 119.76754877500],
[1.405, 3.20407486040, 395.10562148700],
[1.234, 2.34766954239, 318.67949151700],
[1.519, 4.74629629688, 100.17201291180],
[1.573, 4.00132484524, 1264.29545423920],
[1.222, 0.10709243166, 1372.59240610810],
[1.205, 0.24105241435, 466.75821594330],
[1.188, 1.27112537278, 1184.40604624120],
[1.280, 4.85454052139, 535.91074021810],
[1.482, 4.47166692910, 763.43692965770],
[1.233, 1.64803509193, 433.66355376700],
[1.476, 3.76634399110, 272.58157561650],
[1.199, 1.78020373551, 102.34201469320],
[1.186, 4.72162748523, 795.68025857210],
[1.291, 4.42697938285, 10220.39909321180],
[1.576, 2.40263038916, 348.63519857100],
[1.497, 3.44614317326, 3024.22055704320],
[1.175, 4.85145058205, 433.75992198660],
[1.262, 5.79416346069, 531.97858695500],
[1.486, 4.39599352105, 1055.44977692610],
[1.351, 0.46461977407, 707.56533788050],
[1.230, 5.18147817992, 752.39122939380],
[1.175, 4.35535063059, 3892.68166309700],
[1.581, 5.49361132323, 419.53282798500],
[1.247, 4.22328749428, 113.12708252620],
[1.145, 2.26067253357, 199.12018554620],
[1.385, 0.89711064123, 6073.70890781650],
[1.228, 4.55057016747, 680.05731138130],
[1.470, 1.58708185256, 409.18970313670],
[1.366, 3.99684537321, 6065.84460129030],
[1.131, 1.56474593118, 196.83676920270],
[1.163, 5.75528918663, 2303.60876781320],
[1.142, 4.35845106342, 1834.61531963620],
[1.244, 1.93187654929, 623.22251175760],
[1.136, 3.13253323524, 611.44309831080],
[1.425, 2.65840274172, 1253.77101883710],
[1.114, 3.43048279234, 771.30123618390],
[1.314, 0.15326588489, 493.30303459600],
[1.109, 2.95808402860, 1091.62525910360],
[1.177, 3.88159541809, 128.36556848410],
[1.150, 4.69140569690, 1.27202438720],
[1.527, 1.09983755253, 683.02625679790],
[1.304, 5.24544813643, 5650.29211067820],
[1.347, 4.11616699496, 97.46369992610],
[1.085, 0.70231952018, 1166.40685767090],
[1.224, 4.22994822530, 827.17282796110],
[1.142, 5.36157631813, 199.02381732660],
[1.373, 0.89371361814, 799.61241183520],
[1.085, 1.15969472512, 398.28701522470],
[1.098, 3.75659421786, 318.39760722670],
[1.136, 1.35127769399, 205.92491600630],
[1.108, 6.03201954623, 206.44618086810],
[1.146, 0.18236094571, 6386.16862421000],
[1.216, 0.49809632153, 1178.98942026980],
[1.295, 2.32056477953, 10003.91860403610],
[1.082, 1.96611069200, 3700.72320866140],
[1.094, 5.12244388591, 314.38613208650],
[1.464, 4.54056066665, 1248.14194454460],
[1.277, 5.42029902662, 9996.05429750990],
[1.248, 0.21625135029, 101.60830151030],
[1.055, 5.53725373260, 1578.77795454530],
[1.265, 5.85587479852, 82.85835341460],
[1.058, 0.73824266822, 670.91677495100],
[1.127, 3.63458498010, 582.38116313410],
[1.188, 2.10062104535, 423.88987789030],
[1.217, 2.49656109071, 311.72600321060],
[1.080, 3.96349373526, 118.87377689770],
[1.175, 0.91096377814, 740.06929922580],
[1.087, 5.46774426742, 494.47869076360],
[1.080, 3.49168860514, 847.04604259770],
[1.095, 0.97418295319, 1159.29331067010],
[1.078, 1.75579678521, 1457.52593306200],
[1.087, 4.81206824168, 109.68505635760],
[1.293, 0.02397468965, 2723.09341168840],
[1.190, 4.49552956868, 429.30650386170],
[1.127, 0.84707518843, 48.75804477640],
[1.047, 4.58416926615, 89.75945209430],
[1.251, 1.16783030789, 455.16999895820],
[1.122, 5.72161306640, 78263.70942472259],
[1.027, 0.16330222064, 229.76142167330],
[1.069, 2.37188773221, 848.53051530600],
[1.252, 5.28238896229, 6080.82245481730],
[1.181, 5.22299379363, 1459.95656727430],
[1.382, 0.51603096285, 774.00954916960],
[1.064, 5.95222326171, 1144.31545714310],
[1.083, 5.04862249728, 629.86297800640],
[1.061, 3.38604454777, 27.08733537390],
[1.415, 4.85796248007, 2332.06295581640],
[1.082, 4.07686503205, 1245.17299912800],
[1.112, 6.07617329506, 870.46185713940],
[1.072, 0.73647405514, 1482.79872732750],
[1.322, 2.81015928946, 223.33340374560],
[1.398, 1.55232715558, 25771.51127191760],
[1.065, 3.98884050015, 683.18631549230],
[1.008, 5.19594380826, 316.13123722570],
[1.197, 0.79148395839, 9580.50180689780],
[1.402, 4.82957073563, 883.79517926370],
[1.064, 4.65334775068, 201.99276274320],
[1.108, 5.88857586823, 657.16276170140],
[0.996, 4.99081076034, 426.75824957040],
[0.996, 1.60533807224, 426.43813218160],
[1.028, 5.92128319450, 108.50940019000],
[1.004, 3.54259597860, 754.03576079650],
[1.214, 0.81213286478, 1773.91780271860],
[1.318, 0.60269176130, 1123.11782849260],
[1.327, 4.75885008900, 321.80849562800],
[1.014, 5.79119811472, 6460.81221096080],
[1.178, 0.47169015111, 495.96316347190],
[0.999, 5.95030119388, 3906.90875709860],
[1.033, 3.75433174131, 414.81877742920],
[1.002, 1.39171012432, 1251.34038462480],
[0.990, 1.32621236288, 1268.74887236410],
[1.275, 1.95417923977, 757.80785536520],
[1.174, 6.04352585298, 225.07850888480],
[1.174, 5.43253033568, 849.26422848890],
[1.004, 5.33434806968, 46.20979048510],
[1.108, 1.28177889943, 294.30046912880],
[0.976, 1.83523959034, 5.88970672340],
[0.971, 3.38563950019, 306.09692891810],
[1.050, 3.88449467091, 632.26247445140],
[1.050, 3.26096036982, 159.71512552120],
[1.041, 2.36429894351, 821.54375366860],
[1.218, 4.61739999906, 990.22940591440],
[1.342, 1.55614528399, 498.93210888850],
[0.967, 3.84645372731, 604.47256366190],
[1.171, 0.42265751679, 10011.03215103690],
[0.965, 0.05396772193, 962.50893109410],
[1.096, 3.04685199735, 608.40471692500],
[1.166, 6.14999706886, 737.31280213030],
[0.986, 3.71830385737, 1235.61177157240],
[0.953, 0.79704964354, 16.46232623530],
[0.976, 1.05304205075, 8.33738727820],
[1.142, 1.06057209808, 369.97583957340],
[1.060, 4.36236322604, 633.30500417500],
[1.138, 4.31859245106, 98.42690777260],
[1.006, 5.89037944896, 10007.09999777380],
[0.967, 1.56852913547, 157.63995198190],
[1.082, 0.99548769517, 4.14460158420],
[1.009, 6.15037679495, 401.32539661050],
[0.981, 2.37620383333, 35.21227433100],
[1.011, 5.42685471402, 110.72758608120],
[0.989, 4.11575312649, 413.85556958270],
[1.024, 1.90798238649, 1175.80802653210],
[1.079, 4.95981991427, 631.82053146670],
[0.982, 3.02842195594, 347.41135829360],
[0.979, 3.74615289445, 700.45179087970],
[0.928, 5.22236951137, 1173.52040467170],
[0.912, 4.14451390992, 469.72716135990],
[0.938, 1.18273838991, 254.35289238260],
[0.977, 1.26684849112, 104.57724692690],
[1.134, 5.87478488618, 6058.73105428950],
[1.092, 4.51789158271, 532.13864564940],
[1.132, 4.55420027150, 1912.57831194120],
[0.915, 4.87266214195, 18.91000679010],
[0.915, 5.96624579967, 1987.21689815660],
[1.039, 2.40020830681, 6475.03930496240],
[0.965, 4.98927479154, 394.35486196160],
[0.964, 3.60903715900, 3281.23856478620],
[0.897, 2.81660605059, 316.23181096220],
[1.008, 5.78024010734, 502.86426215160],
[1.005, 6.12431717236, 6275.96230299060],
[0.895, 6.09245508513, 316.55192835100],
[1.224, 1.73535287415, 5120.60114558360],
[1.138, 2.92901543353, 1037.29052966140],
[0.924, 5.70601816488, 614.83694036960],
[0.893, 5.25155704274, 475.35623565240],
[1.042, 1.10027795842, 1518.22344997960],
[0.890, 4.03192782386, 1314.32552340280],
[0.926, 3.35110915055, 635.70450062000],
[1.130, 5.49282680494, 92.94084583200],
[0.890, 2.12933822393, 3384.33133900480],
[0.967, 5.86215202069, 13.33332212430],
[1.004, 1.73116475997, 10316.37832042960],
[1.226, 3.52834223937, 80.41067285980],
[1.029, 4.90620832171, 19.12245511120],
[0.996, 0.76740358631, 733.42883297700],
[0.910, 4.08904906301, 3333.49887969900],
[1.235, 1.23871819142, 357.23321828010],
[1.218, 0.18349810348, 1090.40141882620],
[0.864, 4.71917415767, 620.25356634100],
[0.935, 1.45887009044, 1042.91960395390],
[0.866, 4.04792682992, 522.52923398400],
[1.158, 5.43322209110, 1089.12939443900],
[0.860, 0.49220052417, 64.95973858080],
[1.190, 5.58965369650, 2810.92146160520],
[0.957, 3.12914047010, 628.59095361920],
[0.861, 5.69790389801, 103.84353374400],
[1.037, 5.91424823262, 11.30633269480],
[0.918, 0.21424702155, 373.01422095920],
[0.836, 3.02501867546, 387.24131496080],
[1.158, 3.33343863758, 6290.18939699220],
[0.856, 0.81593288669, 907.37105249980],
[1.036, 3.11936047271, 5429.87946823940],
[0.853, 6.23618175592, 938.88066823130],
[0.982, 3.39082880963, 521.61421024730],
[0.851, 5.14029961564, 802.79380557290],
[0.828, 0.28399876908, 338.48327018440],
[0.868, 1.89151676387, 627.15466502070],
[0.878, 2.67671626912, 688.65533109040],
[0.921, 0.18441593712, 3803.81598288000],
[0.821, 0.74694467095, 1152.17976366930],
[0.841, 2.42616504698, 625.88264063350],
[0.862, 3.35273419872, 425.32616648880],
[0.887, 3.46938383985, 1748.78802080500],
[0.815, 5.95428642326, 321.05773610260],
[0.958, 1.35525670354, 1201.83158032300],
[0.905, 5.43093361027, 236.87496867410],
[0.862, 3.24167644516, 427.87021526320],
[0.793, 5.01131700831, 109.99387289830],
[0.791, 2.21809404489, 110.41876954050],
[0.842, 5.04957483651, 444.12429869430],
[0.887, 4.23752031714, 3553.91152213780],
[0.851, 4.64229745145, 4105.98075853500],
[1.067, 4.69271921916, 559.69906177530],
[0.966, 4.55013458162, 9360.08916445900],
[0.977, 1.50925667031, 186.47239249500],
[1.092, 0.58153747940, 203.26478713040],
[0.997, 0.24589891452, 439.93151300030],
[0.786, 3.84829878956, 194.38908864790],
[0.774, 3.76050639310, 219.14061805160],
[0.845, 4.21602090805, 2648.45482547300],
[0.962, 0.30590569897, 229.34073054800],
[0.763, 0.05577842075, 846.13101886100],
[0.839, 5.68124142701, 2620.00063746980],
[0.818, 2.52609626540, 26301.20223701220],
[0.929, 0.71906225883, 740.28174754690],
[0.895, 5.83218231202, 4539.69249641180],
[0.939, 3.68460642343, 817.77165909990],
[0.755, 4.90024080821, 532.87235883230],
[0.784, 1.14096100609, 551.03160609700],
[0.899, 1.85252071775, 835.78789401270],
[0.753, 0.04254534997, 1534.73816584160],
[1.033, 1.00137993270, 134.11226285560],
[0.851, 6.12272864540, 1475.68518032670],
[0.797, 5.14322789256, 473.65931462300],
[0.729, 4.94931618796, 476.10699517780],
[0.852, 3.11058720799, 232.42155054920],
[0.783, 4.50805467439, 1151.42900414390],
[0.751, 0.92289775523, 1884.12412393800],
[0.832, 4.19686348297, 29.20494752860],
[0.720, 0.40961041030, 522.62560220360],
[0.722, 3.96121088528, 1474.93442080130],
[0.788, 0.99170388242, 121.84272231430],
[0.722, 4.16734185316, 232.20910222810],
[0.970, 2.32204039048, 566.60016045500],
[0.814, 5.19337022083, 948.21240112330],
[0.724, 2.30837674225, 949.12742486000],
[0.770, 5.89605163084, 156.67674413540],
[0.705, 5.40102118863, 1193.96727379680],
[0.809, 3.56474059969, 845.33207522580],
[0.755, 3.94580797273, 451.72797278960],
[0.731, 6.11847213487, 1239.54392483550],
[0.747, 1.40599730465, 782.34693644780],
[0.861, 1.84312374221, 984.60033162190],
[0.695, 4.78088165969, 10419.47109464820],
[0.804, 1.07998437400, 89.00869256890],
[0.828, 5.86080569334, 845.11962690470],
[0.692, 3.38736418117, 6489.26139842860],
[0.694, 3.07863807714, 316.60431797770],
[0.690, 5.86681311380, 316.17942133550],
[0.714, 5.38707933404, 567.82400073240],
[0.767, 0.12081849650, 485.88067105450],
[0.820, 1.87877245664, 499.89531673500],
[0.705, 0.57839934869, 1053.75285589670],
[0.684, 4.88442270630, 2545.36205125440],
[0.689, 6.14296395253, 622.48879857470],
[0.823, 3.50224755884, 877.57540414020],
[0.827, 2.59300433753, 232.94281541100],
[0.735, 3.05650026582, 66.91729204110],
],
# R1
[
[6182981.282, 0.25843515034, 213.29909543800],
[506577.574, 0.71114650941, 206.18554843720],
[341394.136, 5.79635773960, 426.59819087600],
[188491.375, 0.47215719444, 220.41264243880],
[186261.540, 3.14159265359, 0.00000000000],
[143891.176, 1.40744864239, 7.11354700080],
[49621.111, 6.01744469580, 103.09277421860],
[20928.189, 5.09245654470, 639.89728631400],
[19952.612, 1.17560125007, 419.48464387520],
[18839.639, 1.60819563173, 110.20632121940],
[12892.827, 5.94330258435, 433.71173787680],
[13876.565, 0.75886204364, 199.07200143640],
[5396.699, 1.28852405908, 14.22709400160],
[4869.308, 0.86793894213, 323.50541665740],
[4247.455, 0.39299384543, 227.52618943960],
[3252.084, 1.25853470491, 95.97922721780],
[2856.006, 2.16731405366, 735.87651353180],
[2909.411, 4.60679154788, 202.25339517410],
[3081.408, 3.43662557418, 522.57741809380],
[1987.689, 2.45054204795, 412.37109687440],
[1941.309, 6.02393385142, 209.36694217490],
[1581.446, 1.29191789712, 210.11770170030],
[1339.511, 4.30801821806, 853.19638175200],
[1315.590, 1.25296446023, 117.31986822020],
[1203.085, 1.86654673794, 316.39186965660],
[1091.088, 0.07527246854, 216.48048917570],
[954.403, 5.15173410519, 647.01083331480],
[966.012, 0.47991379141, 632.78373931320],
[881.827, 1.88471724478, 1052.26838318840],
[874.215, 1.40224683864, 224.34479570190],
[897.512, 0.98343776092, 529.69096509460],
[784.866, 3.06377517461, 838.96928775040],
[739.892, 1.38225356694, 625.67019231240],
[612.961, 3.03307306767, 63.73589830340],
[658.210, 4.14362930980, 309.27832265580],
[649.600, 1.72489486160, 742.99006053260],
[599.236, 2.54924174765, 217.23124870110],
[502.886, 2.12958819475, 3.93215326310],
[413.017, 4.59334402271, 415.55249061210],
[356.117, 2.30312127651, 728.76296653100],
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[2.192, 3.07202313269, 203.26478713040],
[2.424, 2.60715310452, 511.53171782990],
[2.126, 0.14811901148, 405.99126305650],
[2.306, 1.25068142377, 427.11945573780],
[2.121, 0.43505808954, 184.98791978670],
[2.755, 3.02380019321, 468.24268865160],
[2.333, 3.02634928771, 216.00740842370],
[2.182, 4.27912012069, 7.16173111060],
[2.101, 4.31781498012, 572.22923474750],
[2.362, 4.82914341110, 556.51766803760],
[2.218, 0.82936075453, 3370.10424500320],
[2.103, 5.25950154713, 661.23792731640],
[2.580, 1.03705340380, 213.41097002260],
[2.366, 6.14368355608, 205.43478891180],
[2.042, 0.21462094901, 3259.89792378380],
[2.547, 4.69969204009, 221.37585028530],
[1.987, 3.22670561632, 1382.88734684660],
[2.213, 0.89932827487, 286.59622129700],
[2.191, 0.08759174058, 259.76951835400],
[1.968, 0.57824086026, 180.16199464630],
[2.037, 2.35713099759, 610.69233878540],
[1.959, 2.18553775379, 72.07328558160],
[2.061, 1.68041202479, 1670.82502850000],
[1.940, 0.62951066481, 406.95447090300],
[2.043, 4.39130144045, 576.16138801060],
[1.936, 1.05286934530, 1262.38608488870],
[1.975, 0.31945835160, 938.12990870590],
[2.015, 1.66410213484, 193.65537546500],
[1.971, 0.72639439054, 200.55647414470],
[1.952, 6.25320630177, 241.75328344120],
[1.976, 1.31263772699, 135.54855145410],
[2.448, 0.52850194172, 429.51895218280],
[1.977, 3.13944703383, 421.93232443000],
[1.853, 0.17184530353, 196.03362005060],
[2.552, 5.39764879348, 2854.64037391020],
[1.830, 1.47821899466, 638.41281360570],
[2.245, 6.00427164270, 230.70758317730],
[1.822, 6.08626100417, 1261.63532536330],
[2.168, 0.41741136149, 213.51154375910],
[1.869, 3.67791368036, 403.02231763990],
[1.866, 1.59662677545, 391.17346822390],
[2.034, 1.21814866092, 3046.59882834580],
[1.929, 4.93193335031, 420.96911658350],
[1.746, 5.09757251683, 107.75864066460],
[2.168, 3.24685294764, 213.08664711690],
[2.178, 5.09777299346, 558.00214074590],
[1.992, 2.29524873043, 1773.91780271860],
[1.761, 2.88655624670, 141.69889060840],
[1.769, 5.47051542758, 206.13736432740],
[1.734, 2.11941015901, 430.79097657000],
[2.377, 1.07633521570, 59.80374504030],
[1.797, 2.90984583978, 92.79783348010],
[1.725, 5.22827286197, 757.21715453420],
[2.305, 5.88235807192, 426.55000676620],
[1.751, 5.28990803470, 87.31177153950],
[2.202, 1.28096946505, 624.91943278700],
[2.043, 0.46193065602, 831.10498122420],
[1.931, 1.26974971942, 219.89137757700],
[1.953, 2.96900002385, 398.14400287280],
[1.676, 4.81683149512, 181.80652604900],
[1.902, 2.74426125465, 4952.06359328620],
[2.133, 5.37177705284, 627.36711334180],
[1.962, 3.52111949662, 213.45915413240],
[1.709, 6.14073761844, 952.35700270750],
[1.784, 1.05243716682, 353.30106501700],
[1.700, 1.17418864170, 739.05790726950],
[1.609, 1.35009554392, 84.93352695390],
[2.038, 2.47570829812, 26.82670294300],
[1.870, 5.61729116529, 2957.73314812880],
[1.962, 0.13564680851, 213.13903674360],
[2.041, 3.31354526279, 1596.18644228460],
[1.612, 6.19495100885, 432.01481684740],
[1.742, 2.87947098602, 179.35884549420],
[1.964, 2.84253666387, 429.04587143080],
[1.805, 0.60932632638, 532.61172640140],
[1.647, 0.82347900016, 214.57111982520],
[1.893, 4.33962647901, 173.94221952280],
[1.689, 1.13037158144, 586.31331639720],
[1.523, 2.71561930244, 73.29712585900],
[1.524, 5.26558677448, 5429.87946823940],
[1.582, 2.79533721474, 842.90144101350],
[1.608, 2.33230359324, 418.52143602870],
[1.579, 1.15182102801, 731.94436026870],
[1.689, 1.91915438546, 630.33605875840],
[1.990, 5.23790221176, 550.13783421970],
[1.772, 2.95372411478, 172.24529849340],
[1.596, 0.99004701777, 953.10776223290],
[1.784, 3.91391032360, 159.12442469020],
[1.592, 2.99690086808, 45.57665103870],
[1.968, 0.23073879009, 220.36445832900],
[1.549, 5.88699595922, 60.55450456570],
[1.459, 5.51999778036, 273.85360000370],
[1.909, 2.78415262815, 418.00017116690],
[1.445, 3.25530914937, 453.42489381900],
[1.454, 0.16250693313, 115.62294719080],
[1.566, 2.24077018103, 1056.20053645150],
[1.412, 3.45442909885, 354.99798604640],
[1.564, 3.38591337689, 409.18970313670],
[1.631, 1.06286709889, 213.55972786890],
[1.415, 1.32091877590, 373.90799283650],
[1.389, 0.40584159469, 9360.08916445900],
[1.663, 2.33357114562, 188.02630117250],
[1.426, 5.44677783737, 864.24208201590],
[1.716, 3.96056093028, 1699.27921650320],
[1.682, 0.39747670320, 17.40848773930],
[1.368, 5.83289186692, 569.04784100980],
[1.416, 3.65464640816, 6.85291456990],
[1.469, 3.49069193830, 934.94851496820],
[1.330, 4.41794310534, 3914.02230409940],
[1.309, 1.29979865382, 428.08266358430],
[1.300, 1.57748627871, 238.57188970350],
[1.389, 1.31202796503, 6275.96230299060],
[1.384, 0.67585082323, 2751.54759969160],
[1.471, 1.21149871903, 2531.13495725280],
[1.334, 4.11154515525, 206.93630796260],
[1.601, 0.93356520728, 355.74874557180],
[1.259, 2.56678207309, 850.01498801430],
[1.277, 0.41764451386, 100.64509366380],
[1.436, 4.06045514506, 177.87437278590],
[1.308, 1.01324076289, 423.67742956920],
[1.541, 6.03020449918, 292.01284726840],
[1.307, 5.83815678434, 5863.59120611620],
[1.613, 2.45074803642, 1049.08698945070],
[1.249, 3.01518429832, 464.73122651380],
[1.250, 6.23516728885, 823.99143422340],
[1.275, 2.68217384213, 637.44960575920],
[1.249, 2.97028182853, 51749.20809227239],
[1.240, 2.66940683813, 2700.71514038580],
[1.456, 1.85558224828, 96.87299909510],
[1.491, 4.98649587341, 295.19424100610],
[1.230, 4.27283851216, 12139.55350910680],
[1.292, 2.73196017809, 10206.17199921020],
[1.247, 3.77399749791, 504.56118318100],
[1.408, 1.02955773079, 518.38463239980],
[1.223, 1.12202093840, 221.16340196420],
[1.420, 4.39795293289, 606.76018552230],
[1.190, 1.57292553631, 820.05928096030],
[1.247, 0.99102599652, 9793.80090233580],
[1.234, 1.10826361423, 2303.60876781320],
[1.186, 4.55984967028, 9808.53818466140],
[1.346, 4.94456950019, 384.05992122310],
[1.514, 3.60392291730, 2015.67108615980],
[1.432, 2.28704432909, 525.49817940060],
[1.129, 0.87100340620, 162.09337010680],
[1.196, 5.13485214850, 227.31374111850],
[1.339, 2.48923887712, 206.70681329900],
[1.421, 1.65379789078, 857.12853501510],
[1.162, 1.92099315083, 220.93390730060],
[1.277, 4.85435999187, 54.17467074780],
[1.153, 5.33028034679, 233.90602325750],
[1.214, 4.11324721963, 3377.21779200400],
[1.109, 5.68915582674, 162.89651925890],
[1.068, 4.85383480876, 611.44309831080],
[1.119, 1.40805686363, 1987.21689815660],
[1.085, 0.64208148190, 731.68372783780],
[1.435, 3.20880139888, 835.78789401270],
[1.184, 2.99776919968, 199.28444975750],
[1.281, 3.12245339510, 427.34895040140],
[1.058, 5.17851282929, 306.09692891810],
[1.152, 4.39244449554, 199.96577331370],
[1.036, 3.68027119804, 597.35901666110],
[1.055, 3.25561743426, 394.35486196160],
[1.127, 4.33255371960, 552.58551477450],
[1.213, 6.21447612110, 42.53826965290],
[1.117, 3.74367882111, 214.19286731530],
[1.023, 3.84199833949, 894.84087952760],
[1.042, 5.30120078590, 450.97721326420],
[1.290, 3.96221234564, 318.83955021140],
[1.073, 4.10012122884, 188.16931352440],
[1.204, 0.37702365750, 393.46109008430],
[1.214, 2.01826978554, 401.32539661050],
[1.018, 0.02946649279, 2840.41327990860],
[1.237, 5.41088851225, 425.84743135060],
[1.187, 5.16511890602, 838.21852822500],
[1.276, 2.93572146232, 1457.52593306200],
[0.994, 3.40079885702, 211.60217440860],
[1.042, 2.42209320898, 361.37781986430],
[1.093, 3.66289018246, 226.63241756230],
[0.978, 3.76334208607, 5856.47765911540],
[1.263, 2.09195268609, 78.71375183040],
[1.009, 5.85963705048, 1268.74887236410],
[1.148, 4.39543895068, 570.74476203920],
[1.051, 3.27272240682, 153.49535039770],
[0.975, 3.42924642244, 105.54045477340],
[0.997, 4.30943991893, 212.40532356070],
[0.954, 3.88548755058, 171.65459766240],
[0.960, 1.90180005280, 1159.29331067010],
[0.953, 3.40787141587, 244.79166482700],
[0.969, 1.93369993197, 525.75881183150],
[0.918, 1.73738789723, 223.33340374560],
[1.164, 5.05392864346, 263.70167161710],
[0.951, 4.23581224839, 92.94084583200],
[1.160, 5.80630916592, 460.53844081980],
[1.186, 4.46262000755, 465.95506679120],
[0.931, 2.09868057209, 205.66428357540],
[0.942, 3.86810837922, 238.42887735160],
[1.020, 5.53181822898, 0.04818410980],
[0.995, 2.03457885490, 6290.18939699220],
[0.888, 2.60957592990, 1912.57831194120],
[0.873, 5.78433393020, 480.77286162380],
[0.854, 1.63255087291, 328.24071907260],
[1.123, 4.07401922216, 3693.60966166060],
[0.934, 3.52355235083, 10220.39909321180],
[0.833, 3.03302227840, 532.87235883230],
[1.007, 2.73615455688, 4841.85727206680],
[0.870, 1.06968760644, 51.20572533120],
[0.891, 1.36817544763, 700.45179087970],
[0.833, 5.39754715806, 159.71512552120],
[0.854, 1.91765015557, 622.48879857470],
[0.976, 3.09106001923, 2332.06295581640],
[0.819, 5.55683690482, 462.02291352810],
[0.800, 1.47042677460, 969.62247809490],
[0.933, 1.40166917666, 287.93768165340],
[0.784, 1.69235162770, 477.80391620720],
[0.782, 3.98153416585, 702.14871190910],
[0.810, 5.87689161549, 561.93429400900],
[0.858, 4.02964773169, 41.64449777560],
[0.819, 0.98885784755, 960.22130923370],
[0.882, 1.49559638306, 760.25553592000],
[0.767, 2.46787654531, 402.21916848780],
[0.851, 3.64678001195, 348.63519857100],
[0.852, 1.03470840672, 2620.00063746980],
[0.770, 4.67090683753, 16.67477455640],
[0.849, 5.27994730935, 74.63858621540],
[0.854, 2.56811257488, 432.74853003030],
[0.767, 1.11806243753, 2847.52682690940],
[0.729, 0.44171990710, 898.77303279070],
[0.776, 5.54603607568, 3171.03224356680],
[0.721, 6.05392551158, 91.78644152380],
[0.739, 3.57172839746, 775.23338944700],
[0.730, 4.98865345688, 705.11765732570],
[0.705, 0.44942445750, 219.66188291340],
[0.708, 0.69014726046, 1048.33622992530],
[0.706, 2.22974712805, 29.20494752860],
[0.711, 0.00981284716, 2115.58246664070],
[0.722, 4.14075205197, 225.07850888480],
[0.735, 1.54083195463, 201.99276274320],
[0.746, 4.08997409526, 849.26422848890],
[0.729, 2.81779134868, 419.53282798500],
[0.837, 1.00844734156, 4127.32139953740],
[0.939, 0.46037763932, 5488.86810538160],
[0.939, 1.85473712038, 5062.26991450560],
[0.721, 1.62872794201, 2200.51599359460],
],
# R2
[
[436902.464, 4.78671673044, 213.29909543800],
[71922.760, 2.50069994874, 206.18554843720],
[49766.792, 4.97168150870, 220.41264243880],
[43220.894, 3.86940443794, 426.59819087600],
[29645.554, 5.96310264282, 7.11354700080],
[4141.650, 4.10670940823, 433.71173787680],
[4720.909, 2.47527992423, 199.07200143640],
[3789.370, 3.09771025067, 639.89728631400],
[2963.990, 1.37206248846, 103.09277421860],
[2556.363, 2.85065721526, 419.48464387520],
[2208.457, 6.27588858707, 110.20632121940],
[2187.621, 5.85545832218, 14.22709400160],
[1956.896, 4.92448618045, 227.52618943960],
[2326.801, 0.00000000000, 0.00000000000],
[923.840, 5.46392422737, 323.50541665740],
[705.936, 2.97081280098, 95.97922721780],
[546.115, 4.12854181522, 412.37109687440],
[373.838, 5.83435991809, 117.31986822020],
[360.882, 3.27703082368, 647.01083331480],
[356.350, 3.19152043942, 210.11770170030],
[390.627, 4.48106176893, 216.48048917570],
[431.485, 5.17825414612, 522.57741809380],
[325.598, 2.26867601656, 853.19638175200],
[405.018, 4.17294157872, 209.36694217490],
[204.494, 0.08774848590, 202.25339517410],
[206.854, 4.02188336738, 735.87651353180],
[178.474, 4.09716541453, 440.82528487760],
[180.143, 3.59704903955, 632.78373931320],
[153.656, 3.13470530382, 625.67019231240],
[147.779, 0.13614300541, 302.16477565500],
[123.189, 4.18895309647, 88.86568021700],
[133.076, 2.59350469420, 191.95845443560],
[100.367, 5.46056190585, 3.18139373770],
[131.975, 5.93293968941, 309.27832265580],
[97.235, 4.01832604356, 728.76296653100],
[110.709, 4.77853798276, 838.96928775040],
[119.053, 5.55385105975, 224.34479570190],
[93.852, 4.38395529912, 217.23124870110],
[108.701, 5.29310899841, 515.46387109300],
[78.609, 5.72525447528, 21.34064100240],
[81.468, 5.10897365253, 956.28915597060],
[96.412, 6.25859229567, 742.99006053260],
[69.228, 4.04901237761, 3.93215326310],
[65.168, 3.77713343518, 1052.26838318840],
[64.088, 5.81235002453, 529.69096509460],
[62.541, 2.18445116349, 195.13984817330],
[56.987, 3.14666549033, 203.00415469950],
[55.979, 4.84108422860, 234.63973644040],
[52.940, 5.07780548444, 330.61896365820],
[50.635, 2.77318570728, 942.06206196900],
[41.649, 4.79014211005, 63.73589830340],
[44.858, 0.56460613593, 269.92144674060],
[41.357, 3.73496404402, 316.39186965660],
[52.847, 3.92623831484, 949.17560896980],
[38.398, 3.73966157784, 1045.15483618760],
[37.583, 4.18924633757, 536.80451209540],
[35.285, 2.90795856092, 284.14854074220],
[33.576, 3.80465978802, 149.56319713460],
[41.073, 4.57870454147, 1155.36115740700],
[30.412, 2.48140171991, 860.30992875280],
[31.373, 4.84075951849, 1272.68102562720],
[30.218, 4.35186294470, 405.25754987360],
[39.430, 3.50858482049, 422.66603761290],
[29.658, 1.58886982096, 1066.49547719000],
[35.202, 5.94478241578, 1059.38193018920],
[25.829, 3.54946335477, 1368.66025284500],
[26.283, 4.81567477177, 124.43341522100],
[29.963, 3.66312205813, 429.77958461370],
[33.011, 4.96879544579, 831.85574074960],
[24.305, 5.31133255082, 10.29494073850],
[26.332, 4.45253273390, 223.59403617650],
[22.108, 2.76092021113, 415.55249061210],
[27.187, 1.66347897738, 277.03499374140],
[21.639, 1.03836302307, 11.04570026390],
[19.713, 2.52194629263, 1258.45393162560],
[17.062, 3.27669927228, 654.12438031560],
[17.261, 3.49414816663, 1361.54670584420],
[16.097, 1.73396878598, 490.33408917940],
[21.099, 3.62102032955, 1265.56747862640],
[17.692, 4.31141612385, 1471.75302706360],
[13.458, 0.32327889681, 295.05122865420],
[12.586, 3.13794576887, 74.78159856730],
[12.023, 2.32917797741, 210.85141488320],
[15.120, 3.59558424278, 265.98929347750],
[12.959, 4.62359706368, 1589.07289528380],
[15.424, 5.01335704925, 127.47179660680],
[11.193, 4.54981248285, 81.75213321620],
[13.449, 4.88710089777, 437.64389113990],
[10.673, 5.05234757424, 191.20769491020],
[13.963, 3.04990968366, 423.41679713830],
[10.614, 5.02845923229, 137.03302416240],
[14.382, 4.68720080027, 1148.24761040620],
[13.470, 1.90280407135, 408.43894361130],
[10.077, 5.20426583827, 340.77089204480],
[10.323, 3.34460279759, 1685.05212250160],
[9.563, 3.17317920222, 351.81659230870],
[11.295, 5.47808960704, 1375.77379984580],
[8.617, 2.81294528041, 99.91138048090],
[8.460, 3.22691940753, 1677.93857550080],
[7.914, 2.35624291874, 1574.84580128220],
[7.587, 6.08171425316, 231.45834270270],
[9.175, 3.40072244924, 1581.95934828300],
[7.337, 2.00393601815, 131.40394986990],
[8.240, 4.04095881407, 1788.14489672020],
[7.579, 3.68311134272, 846.08283475120],
[6.691, 4.37253800717, 145.63104387150],
[7.539, 3.29482043104, 750.10360753340],
[6.367, 4.00239137708, 447.93883187840],
[6.249, 4.55603671940, 106.27416795630],
[6.489, 1.33782087599, 215.74677599280],
[6.501, 3.78204726337, 313.21047591890],
[5.978, 0.55276980086, 18.15924726470],
[6.171, 2.84712795642, 138.51749687070],
[6.837, 4.83481646949, 319.57326339430],
[6.678, 5.43046031699, 508.35032409220],
[7.175, 4.37855723752, 1464.63948006280],
[5.753, 4.14268749228, 543.91805909620],
[5.727, 4.35383078313, 1905.46476494040],
[5.101, 2.63866058897, 288.08069400530],
[5.311, 3.62520849510, 6076.89030155420],
[5.498, 4.19972735173, 721.64941953020],
[5.089, 5.04845206653, 10007.09999777380],
[5.505, 1.13479635941, 56.62235130260],
[4.820, 3.30043078578, 76.26607127560],
[4.915, 6.17790518458, 483.22054217860],
[5.048, 2.44627820757, 628.85158605010],
[4.534, 1.19648682598, 200.76892246580],
[4.817, 3.11549733365, 2001.44399215820],
[4.712, 1.26507812515, 6062.66320755260],
[4.811, 5.78388270496, 184.84490743480],
[4.775, 0.76197795755, 333.65734504400],
[4.514, 0.95293919611, 343.21857259960],
[4.525, 2.68827745072, 9992.87290377220],
[4.378, 0.80241129896, 222.86032299360],
[4.873, 5.92092913946, 618.55664531160],
[4.142, 1.91878383159, 497.44763618020],
[5.112, 4.50449287745, 416.30325013750],
[4.125, 1.98204847532, 347.88443904560],
[4.045, 2.87666810085, 38.13303563780],
[4.133, 2.90478811425, 107.02492748170],
[4.035, 2.92972681787, 1994.33044515740],
[4.916, 3.12316267561, 1898.35121793960],
[3.657, 3.24680246734, 362.86229257260],
[3.753, 0.87719890943, 703.63318461740],
[3.576, 3.48080143501, 388.46515523820],
[3.555, 4.08436297683, 430.53034413910],
[3.598, 0.05255328597, 32.24332891440],
[3.561, 5.46414552453, 6283.07584999140],
[3.480, 1.81622589595, 70.84944530420],
[3.827, 3.12041228490, 635.96513305090],
[3.399, 0.54882815021, 10213.28554621100],
[3.399, 3.51833356080, 629.60234557550],
[3.364, 3.27821747958, 357.44566660120],
[3.260, 1.97623748027, 203.73786788240],
[3.118, 2.18465627368, 1891.23767093880],
[3.163, 1.26040995242, 134.58534360760],
[4.004, 5.45434102599, 1692.16566950240],
[3.180, 2.46319174788, 867.42347575360],
[3.389, 4.20503159673, 337.73251065900],
[3.026, 2.19331614526, 217.96496188400],
[3.573, 5.55097240810, 113.38771495710],
[3.682, 3.78966280284, 2104.53676637680],
[3.125, 4.09203641264, 1478.86657406440],
[2.881, 3.90810650240, 312.19908396260],
[3.199, 3.92123638342, 1038.04128918680],
[4.014, 5.17826893553, 404.50679034820],
[3.907, 4.11767191780, 1781.03134971940],
[3.144, 1.61185684069, 1073.60902419080],
[3.072, 5.00675625396, 312.45971639350],
[3.034, 5.46288652854, 258.87574647670],
[2.884, 2.38477237305, 181.05576652360],
[2.986, 0.88783591586, 1279.79457262800],
[2.683, 0.00956197492, 195.89060769870],
[3.081, 5.60034737330, 216.21985674480],
[2.626, 6.12701960244, 273.10284047830],
[2.665, 2.31576422128, 565.11568774670],
[3.245, 3.87540558646, 85.82729883120],
[2.740, 5.73784096806, 160.60889739850],
[2.876, 4.74720607366, 213.25091132820],
[2.523, 5.30458920892, 444.75743814070],
[2.752, 5.08984539930, 1169.58825140860],
[2.889, 1.66674437398, 213.34727954780],
[2.923, 4.21481009033, 650.94298657790],
[3.036, 2.55426675350, 6069.77675455340],
[3.116, 2.67220972004, 52.69019803950],
[2.371, 0.89591351822, 121.25202148330],
[2.993, 3.96957827454, 9999.98645077300],
[3.088, 0.40656113014, 561.18353448360],
[2.385, 4.74063881551, 218.71572140940],
[2.632, 1.12706218927, 344.70304530790],
[2.316, 4.08445262041, 131.54696222180],
[2.214, 3.37726228553, 22.09140052780],
[2.129, 3.32497715011, 358.93013930950],
[2.679, 1.68971401870, 208.63322899200],
[2.607, 5.10250482155, 824.74219374880],
[2.250, 2.60474848767, 305.34616939270],
[2.087, 3.37293958793, 320.32402291970],
[2.693, 3.62159456470, 436.89313161450],
[2.492, 2.96129217279, 2214.74308759620],
[2.704, 2.88483697319, 643.07868005170],
[2.124, 1.61210282593, 218.92816973050],
[2.037, 4.63481160778, 188.02630117250],
[2.394, 3.46386258552, 6275.96230299060],
[1.973, 2.28886138203, 2627.11418447060],
[1.937, 5.67082364247, 28.45418800320],
[1.920, 4.25647211328, 546.95644048200],
[2.498, 3.57572154405, 2420.92863603340],
[1.898, 1.30987536388, 212.33588759150],
[1.852, 1.58508015515, 424.15051032120],
[1.850, 3.57830449726, 329.72519178090],
[2.128, 3.95329215734, 1795.25844372100],
[2.236, 4.22073549375, 2221.85663459700],
[1.933, 1.68771499202, 350.33211960040],
[1.799, 2.06541260431, 144.14657116320],
[1.904, 4.60953896857, 182.27960680100],
[2.236, 5.17945392885, 99.16062095550],
[1.755, 2.73425330428, 291.26208774300],
[2.231, 5.42548168745, 207.88246946660],
[1.848, 2.24194286719, 168.05251279940],
[1.726, 1.31878655393, 219.44943459230],
[1.709, 5.55913931846, 92.79783348010],
[1.693, 1.95360003617, 129.91947716160],
[2.064, 4.84900344498, 1141.13406340540],
[1.758, 5.05088656436, 214.26230328450],
[1.781, 2.85880153340, 636.71589257630],
[1.900, 2.90295578617, 2310.72231481400],
[1.759, 5.34657858395, 45.57665103870],
[1.654, 6.14450664508, 554.06998748280],
[1.578, 4.50941374663, 210.37833413120],
[1.681, 3.55136706992, 1354.43315884340],
[1.862, 3.01276783582, 2317.83586181480],
[1.589, 1.15773448350, 235.39049596580],
[1.551, 2.15558953807, 207.67002114550],
[1.874, 4.12861627986, 225.82926841020],
[1.621, 3.29992957653, 1670.82502850000],
[1.911, 0.17724319140, 12.53017297220],
[1.477, 5.90270260570, 1.48447270830],
[1.618, 5.72513459206, 1485.98012106520],
[1.446, 1.78104589920, 1382.88734684660],
[1.683, 3.43534671475, 2428.04218303420],
[1.542, 5.51223038941, 204.70107572890],
[1.420, 2.07339356364, 198.32124191100],
[1.444, 5.56032454849, 128.36556848410],
[1.476, 6.12782257368, 212.77783057620],
[1.474, 0.33626790634, 213.82036029980],
[1.428, 3.25039966249, 945.99421523210],
[1.410, 0.68747644676, 429.04587143080],
[1.752, 2.70090942746, 12.74262129330],
[1.681, 4.97526853273, 2008.55753915900],
[1.408, 0.80461100746, 1585.14074202070],
[1.485, 0.49674043855, 120.35824960600],
[1.490, 2.68459799437, 207.14875628370],
[1.411, 4.36399216092, 5863.59120611620],
[1.315, 4.73430848989, 241.75328344120],
[1.516, 4.99488503706, 1162.47470440780],
[1.310, 1.98714265058, 563.63121503840],
[1.286, 2.12891372062, 251.43213107580],
[1.271, 5.70165238307, 2.92076130680],
[1.312, 1.68811514551, 2207.62954059540],
[1.259, 0.35924965717, 334.55111692130],
[1.252, 2.14513440216, 1055.44977692610],
[1.401, 6.13250261735, 1802.37199072180],
[1.343, 5.79995727295, 9793.80090233580],
[1.228, 3.29059284057, 661.23792731640],
[1.202, 2.88792018909, 2413.81508903260],
[1.286, 5.72360160371, 298.23262239190],
[1.357, 0.93175963411, 217.49188113200],
[1.356, 2.28121627817, 601.76425067620],
[1.190, 1.94993809928, 501.37978944330],
[1.304, 0.37337923280, 3473.19701922180],
[1.350, 2.87235622320, 142.44965013380],
[1.349, 3.21102203937, 175.16605980020],
[1.312, 3.70149813509, 2111.65031337760],
[1.129, 1.08860603834, 842.15068148810],
[1.237, 0.08698781252, 526.50957135690],
[1.217, 3.89835349840, 209.10630974400],
[1.467, 1.16228775027, 621.73803904930],
[1.044, 0.30512759901, 436.15941843160],
[1.140, 5.33720637097, 114.13847448250],
[1.295, 4.70261675421, 9786.68735533500],
[1.037, 4.07846687083, 156.67674413540],
[1.391, 4.73554028436, 398.14400287280],
[1.167, 5.68899703631, 479.28838891550],
[1.035, 5.34279429465, 327.43756992050],
[0.997, 1.19323192891, 710.74673161820],
[1.193, 5.17722376816, 98.89998852460],
[1.165, 4.58588490135, 732.69511979410],
[1.161, 4.90854984994, 10206.17199921020],
[1.144, 0.50394784140, 3906.90875709860],
[1.182, 3.69482624364, 2854.64037391020],
[0.970, 2.89031410383, 1987.21689815660],
[1.039, 0.48694895443, 525.49817940060],
[1.079, 3.61750956217, 2097.42321937600],
[1.148, 3.31015591733, 5856.47765911540],
[1.241, 4.31971543677, 230.70758317730],
[0.910, 4.59825926062, 380.12776796000],
[0.907, 1.34912454077, 685.47393735270],
[1.166, 1.61085609717, 5849.36411211460],
[0.882, 6.12045540405, 519.39602435610],
[0.963, 4.96065454054, 699.70103135430],
[1.062, 5.13323858077, 2751.54759969160],
[0.865, 6.12821112133, 245.54242435240],
[1.100, 2.18435744407, 1699.27921650320],
[0.822, 5.55083534581, 739.05790726950],
[0.926, 2.01158276144, 417.03696332040],
[0.813, 5.18401872205, 214.78356814630],
[1.033, 5.48677848094, 3995.77443731560],
[0.872, 3.02363724703, 306.09692891810],
[0.796, 0.44343664540, 486.40193591630],
[0.878, 1.82164034386, 135.33610313300],
[0.791, 2.14989417962, 2620.00063746980],
[0.881, 2.39697554334, 289.56516671360],
[0.782, 4.50471317138, 980.66817835880],
[0.783, 1.14229319753, 540.73666535850],
[0.831, 0.69937251013, 421.93232443000],
[0.770, 2.40292326155, 576.16138801060],
[0.950, 5.97621460162, 196.62432088160],
[0.814, 4.19303098086, 831.10498122420],
[0.969, 4.78071024754, 326.68681039510],
[0.760, 0.44860533530, 425.63498302950],
[0.907, 0.94781730418, 525.75881183150],
[0.788, 0.14287187051, 916.93228005540],
[0.801, 1.86383119100, 3039.48528134500],
[0.801, 0.46947170994, 3466.08347222100],
[0.747, 6.05374861925, 211.81462272970],
[0.968, 3.02618272726, 2634.22773147140],
[0.739, 2.27110740297, 2303.60876781320],
[0.750, 5.48554383902, 173.94221952280],
[1.024, 1.91564925560, 229.97386999440],
[0.816, 4.98990432666, 4209.07353275360],
[0.728, 1.30997967935, 511.53171782990],
[0.716, 3.74192651696, 3053.71237534660],
[0.727, 0.39191881243, 1493.09366806600],
[0.717, 2.68899513085, 228.27694896500],
[0.739, 2.12749199443, 1176.70179840940],
[0.805, 0.07187193910, 556.51766803760],
[0.835, 3.48287855700, 84.93352695390],
[0.790, 0.48073040004, 4017.11507831800],
[0.725, 1.96643065215, 220.46082654860],
[0.683, 2.68825142163, 151.04766984290],
[0.739, 3.33688408107, 953.10776223290],
[0.745, 6.22304530635, 1269.49963188950],
],
# R3
[
[20315.005, 3.02186626038, 213.29909543800],
[8923.581, 3.19144205755, 220.41264243880],
[6908.677, 4.35174889353, 206.18554843720],
[4087.129, 4.22406927376, 7.11354700080],
[3879.041, 2.01056445995, 426.59819087600],
[1070.788, 4.20360341236, 199.07200143640],
[907.332, 2.28344368029, 433.71173787680],
[606.121, 3.17458570534, 227.52618943960],
[596.639, 4.13455753351, 14.22709400160],
[483.181, 1.17345973258, 639.89728631400],
[393.174, 0.00000000000, 0.00000000000],
[229.472, 4.69838526383, 419.48464387520],
[188.250, 4.59003889007, 110.20632121940],
[149.508, 3.20199444400, 103.09277421860],
[121.442, 3.76831374104, 323.50541665740],
[101.215, 5.81884137755, 412.37109687440],
[102.146, 4.70974422803, 95.97922721780],
[93.078, 1.43531270909, 647.01083331480],
[72.601, 4.15395598507, 117.31986822020],
[84.347, 2.63462379693, 216.48048917570],
[62.198, 2.31239345505, 440.82528487760],
[45.145, 4.37317047297, 191.95845443560],
[49.536, 2.38854232908, 209.36694217490],
[54.829, 0.30526468471, 853.19638175200],
[40.498, 1.83836569765, 302.16477565500],
[38.089, 5.94455115525, 88.86568021700],
[32.243, 4.01146349387, 21.34064100240],
[40.671, 0.68845183210, 522.57741809380],
[28.209, 5.77193013961, 210.11770170030],
[24.976, 3.06249709014, 234.63973644040],
[20.824, 4.92570695678, 625.67019231240],
[25.070, 0.73137425284, 515.46387109300],
[17.485, 5.73135068691, 728.76296653100],
[18.009, 1.45593152612, 309.27832265580],
[16.927, 3.52771580455, 3.18139373770],
[13.437, 3.36479898106, 330.61896365820],
[11.090, 3.37212682914, 224.34479570190],
[11.082, 3.41719974793, 956.28915597060],
[9.978, 1.58791582772, 202.25339517410],
[11.551, 5.99093726182, 735.87651353180],
[10.500, 6.06911092266, 405.25754987360],
[9.144, 2.93557421591, 124.43341522100],
[8.737, 4.65432480769, 632.78373931320],
[10.023, 0.58247011625, 860.30992875280],
[7.482, 4.50669216436, 942.06206196900],
[10.091, 0.28268774007, 838.96928775040],
[9.243, 2.57034547708, 223.59403617650],
[8.652, 1.75808100881, 429.77958461370],
[7.564, 1.45635107202, 654.12438031560],
[7.058, 5.47394786065, 1045.15483618760],
[6.970, 1.51811695028, 422.66603761290],
[8.067, 4.48457709292, 742.99006053260],
[6.817, 4.83084424818, 316.39186965660],
[7.693, 0.43769724671, 831.85574074960],
[7.934, 4.20112367712, 195.13984817330],
[6.119, 2.33960392135, 269.92144674060],
[5.589, 1.14518720694, 284.14854074220],
[5.564, 4.18123189068, 529.69096509460],
[5.034, 2.12020038657, 295.05122865420],
[6.556, 3.42459866876, 10.29494073850],
[5.544, 2.46823271699, 536.80451209540],
[6.189, 6.01433827520, 1066.49547719000],
[5.649, 0.82784598388, 217.23124870110],
[4.264, 3.23245736673, 1272.68102562720],
[4.450, 0.92477808590, 203.00415469950],
[3.268, 4.32777516976, 1258.45393162560],
[3.655, 0.05832123987, 81.75213321620],
[3.951, 0.11124996745, 1155.36115740700],
[3.773, 6.01157059552, 1052.26838318840],
[2.915, 5.64342950039, 3.93215326310],
[3.019, 2.19411778004, 447.93883187840],
[2.977, 1.89387342550, 149.56319713460],
[3.146, 0.19215180096, 1148.24761040620],
[2.763, 0.92363342001, 508.35032409220],
[2.790, 4.97199778427, 1677.93857550080],
[2.608, 2.99591016813, 1589.07289528380],
[2.881, 5.40535671721, 1361.54670584420],
[2.337, 1.30362271569, 184.84490743480],
[2.536, 3.71412120849, 408.43894361130],
[2.450, 3.22118361135, 319.57326339430],
[2.585, 2.31346415454, 543.91805909620],
[2.324, 5.87500715503, 721.64941953020],
[1.990, 0.51565577383, 416.30325013750],
[2.490, 4.24017800021, 1059.38193018920],
[1.935, 2.41463084855, 337.73251065900],
[1.886, 0.53809070779, 635.96513305090],
[1.893, 5.62352727352, 11.04570026390],
[2.389, 5.73399981234, 313.21047591890],
[1.900, 2.41000566465, 131.54696222180],
[1.743, 4.57646237847, 1994.33044515740],
[1.913, 5.17436386408, 2854.64037391020],
[1.946, 6.23355845623, 1471.75302706360],
[1.963, 6.17814558628, 1464.63948006280],
[1.838, 5.59464577559, 1038.04128918680],
[1.541, 0.60765337379, 210.85141488320],
[1.617, 1.75479346067, 195.89060769870],
[1.577, 0.55789908488, 2324.94940881560],
[1.492, 0.26624235633, 497.44763618020],
[1.659, 2.57526072926, 2090.30967237520],
[1.809, 1.82317819973, 436.89313161450],
[1.566, 6.15328100324, 490.33408917940],
[1.771, 6.11741716855, 1073.60902419080],
[1.456, 0.85374460914, 415.55249061210],
[1.645, 2.95335775161, 437.64389113990],
[1.391, 4.12025028560, 1574.84580128220],
[1.585, 5.96841377266, 1781.03134971940],
[1.507, 3.84895122542, 1251.34038462480],
[1.442, 5.32547705924, 2538.24850425360],
[1.805, 1.50973093681, 750.10360753340],
[1.462, 3.28599831588, 1884.12412393800],
[1.482, 0.99340744053, 643.07868005170],
[1.312, 3.79347668996, 1567.73225428140],
[1.665, 0.02551523913, 423.41679713830],
[1.469, 5.35285153471, 1354.43315884340],
[1.352, 0.69945139243, 867.42347575360],
[1.124, 1.79624810407, 618.55664531160],
[1.126, 4.70052329245, 113.38771495710],
[1.122, 3.95537224270, 1891.23767093880],
[1.458, 1.50198846753, 430.53034413910],
[1.145, 5.13093399117, 25.27279426550],
[1.178, 2.97062300389, 241.75328344120],
[1.274, 2.29089799814, 2420.92863603340],
[1.071, 0.04888943982, 63.73589830340],
[1.377, 5.58271514873, 1382.88734684660],
[1.145, 3.10797488346, 2200.51599359460],
[1.076, 0.79465514815, 127.47179660680],
[1.046, 5.85060227045, 215.74677599280],
[1.082, 3.72589445510, 131.40394986990],
[1.218, 0.47504349592, 824.74219374880],
[1.116, 3.78039049056, 1375.77379984580],
[0.969, 5.90752273481, 265.98929347750],
[1.230, 1.41325962069, 2634.22773147140],
[1.070, 4.80334493874, 1987.21689815660],
[0.946, 6.25968535931, 2015.67108615980],
[1.030, 1.08973644893, 362.86229257260],
[1.072, 5.41838042079, 1279.79457262800],
[0.880, 1.92224908504, 483.22054217860],
[0.878, 2.96591300878, 934.94851496820],
[0.879, 2.65659265685, 145.63104387150],
[0.872, 6.26261969664, 2.44768055480],
[1.082, 4.48298283322, 2214.74308759620],
[0.959, 0.74479087918, 16.67477455640],
[1.035, 4.05664979327, 231.45834270270],
[0.851, 0.09360495322, 628.85158605010],
[0.888, 5.98816755324, 2524.02141025200],
[0.866, 3.16259265630, 2207.62954059540],
[0.843, 1.23731248821, 74.78159856730],
[0.809, 2.89742868175, 2008.55753915900],
[0.779, 2.28434811609, 1478.86657406440],
[0.990, 5.32604038017, 2428.04218303420],
[0.795, 2.38178135810, 2228.97018159780],
[0.765, 4.70033674940, 1670.82502850000],
[1.024, 4.23352869513, 1802.37199072180],
[0.831, 5.87457134912, 1368.66025284500],
[0.717, 5.92144324994, 1685.05212250160],
[0.772, 1.15596098579, 3053.71237534660],
[0.691, 3.13193109668, 56.62235130260],
],
# R4
[
[1202.050, 1.41499446465, 220.41264243880],
[707.796, 1.16153570102, 213.29909543800],
[516.121, 6.23973568330, 206.18554843720],
[426.664, 2.46924890293, 7.11354700080],
[267.736, 0.18659206741, 426.59819087600],
[170.171, 5.95926972384, 199.07200143640],
[145.113, 1.44211060143, 227.52618943960],
[150.339, 0.47970167140, 433.71173787680],
[121.033, 2.40527320817, 14.22709400160],
[47.332, 5.56857488676, 639.89728631400],
[15.745, 2.90112466278, 110.20632121940],
[16.668, 0.52920774279, 440.82528487760],
[18.954, 5.85626429118, 647.01083331480],
[14.074, 1.30343550656, 412.37109687440],
[12.708, 2.09349305926, 323.50541665740],
[14.724, 0.29905316786, 419.48464387520],
[11.133, 2.46304825990, 117.31986822020],
[11.320, 0.21785507019, 95.97922721780],
[9.233, 2.28127318068, 21.34064100240],
[9.246, 1.56496312830, 88.86568021700],
[8.970, 0.68301278041, 216.48048917570],
[7.674, 3.59367715368, 302.16477565500],
[7.823, 4.48688804175, 853.19638175200],
[8.360, 1.27239488455, 234.63973644040],
[9.552, 3.14159265359, 0.00000000000],
[4.834, 2.58836294602, 515.46387109300],
[6.059, 5.16774448740, 103.09277421860],
[4.410, 0.02211643085, 191.95845443560],
[4.364, 1.59622746023, 330.61896365820],
[3.676, 3.29899839673, 210.11770170030],
[4.364, 5.97349927933, 654.12438031560],
[4.447, 4.97415112184, 860.30992875280],
[3.220, 2.72684237392, 522.57741809380],
[4.005, 1.59858435636, 405.25754987360],
[3.099, 0.75235436533, 209.36694217490],
[2.464, 1.19167306488, 124.43341522100],
[3.088, 1.32258934286, 728.76296653100],
[2.220, 3.28087994088, 203.00415469950],
[2.127, 6.14648095022, 429.77958461370],
[2.110, 0.75462855247, 295.05122865420],
[2.020, 3.89394929749, 1066.49547719000],
[2.248, 0.49319150178, 447.93883187840],
[2.180, 0.72761059998, 625.67019231240],
[1.809, 0.09057839517, 942.06206196900],
[1.672, 1.39635398184, 224.34479570190],
[1.641, 3.02468307550, 184.84490743480],
[1.772, 0.81879250825, 223.59403617650],
[1.902, 2.00472814984, 831.85574074960],
[1.600, 5.41185167676, 824.74219374880],
[1.505, 5.95520747253, 422.66603761290],
[1.133, 1.11512973946, 838.96928775040],
[1.190, 1.89600567803, 956.28915597060],
[1.487, 2.11906469507, 529.69096509460],
[1.409, 0.72254420236, 536.80451209540],
[1.125, 0.89062692183, 721.64941953020],
[1.301, 1.64867038984, 17.40848773930],
[1.164, 5.96957981840, 195.13984817330],
[0.950, 5.36080713290, 316.39186965660],
[0.985, 3.05768671768, 1574.84580128220],
[1.050, 1.59202481523, 735.87651353180],
[0.817, 4.92838813598, 56.62235130260],
[0.780, 2.72125404102, 508.35032409220],
[0.969, 1.00708261792, 1045.15483618760],
[0.716, 1.11042181341, 1169.58825140860],
],
# R5
[
[128.612, 5.91282565136, 220.41264243880],
[32.273, 0.69256228602, 7.11354700080],
[26.698, 5.91428528629, 227.52618943960],
[19.923, 0.67370653385, 14.22709400160],
[20.223, 4.95136801768, 433.71173787680],
[13.537, 1.45669521408, 199.07200143640],
[14.097, 2.67074280191, 206.18554843720],
[13.364, 4.58826996370, 426.59819087600],
[7.257, 4.62966127155, 213.29909543800],
[4.876, 3.61448275002, 639.89728631400],
[3.136, 4.65661021909, 191.95845443560],
[2.917, 0.48665273315, 323.50541665740],
[3.759, 4.89624165044, 440.82528487760],
[3.303, 4.07190859545, 647.01083331480],
[2.883, 3.18003019204, 419.48464387520],
[2.338, 3.69553554327, 88.86568021700],
[1.950, 5.32729247780, 302.16477565500],
[2.052, 3.31663577368, 95.97922721780],
[1.591, 2.67009215574, 853.19638175200],
[2.028, 0.56025552769, 117.31986822020],
[1.560, 0.85608042681, 515.46387109300],
[1.678, 0.00000000000, 0.00000000000],
[1.102, 5.98011943842, 3.18139373770],
[1.285, 5.82563377753, 234.63973644040],
[0.896, 5.22791858719, 216.48048917570],
[1.141, 0.15741228205, 412.37109687440],
[0.798, 0.37452846153, 28.45418800320],
[0.837, 5.04769794123, 124.43341522100],
],
]
"""This table contains Saturn's 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 442-445."""
ORBITAL_ELEM = [
[50.077444, 1223.5110686, 0.00051908, -0.00000003], # L
[9.554909192, -0.000002139, 0.000000004, 0.0], # a
[0.05554814, -0.000346641, -0.0000006436, 0.0000000034], # e
[2.488879, -0.0037362, -0.00001519, 0.000000087], # i
[113.665503, 0.877088, -0.00012176, -0.000002249], # Omega
[93.057237, 1.9637613, 0.00083753, 0.000004928] # pie
]
"""This table contains the parameters to compute Saturn's orbital elements for
the mean equinox of date. Based in Table 31.A, page 213"""
ORBITAL_ELEM_J2000 = [
[50.077444, 1222.1138488, 0.00021004, -0.000000046], # L
[2.488879, 0.0025514, -0.00004906, 0.000000017], # i
[113.665503, -0.2566722, -0.00018399, 0.00000048], # Omega
[93.057237, 0.5665415, 0.0005285, 0.000004912] # pie
]
"""This table contains the parameters to compute Saturn's orbital elements for
the standard equinox J2000.0. Based on Table 31.B, page 215"""
[docs]class Saturn(object):
"""
Class Saturn models that planet.
"""
[docs] @staticmethod
def geometric_heliocentric_position(epoch, tofk5=True):
"""This method computes the geometric heliocentric position of planet
Saturn for a given epoch, using the VSOP87 theory.
:param epoch: Epoch to compute Saturn 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 = Saturn.geometric_heliocentric_position(epoch)
>>> print(round(l.to_positive(), 4))
279.5108
>>> print(round(b, 4))
0.6141
>>> print(round(r, 5))
10.06266
"""
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
Saturn for a given epoch, using the VSOP87 theory.
:param epoch: Epoch to compute Saturn 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 Saturn 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 = Saturn.orbital_elements_mean_equinox(epoch)
>>> print(round(l, 6))
131.196871
>>> print(round(a, 8))
9.55490779
>>> print(round(e, 7))
0.0553209
>>> print(round(i, 6))
2.486426
>>> print(round(ome, 5))
114.23974
>>> print(round(arg, 6))
-19.896331
"""
return orbital_elements(epoch, ORBITAL_ELEM, ORBITAL_ELEM)
[docs] @staticmethod
def orbital_elements_j2000(epoch):
"""This method computes the orbital elements of Saturn 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 = Saturn.orbital_elements_j2000(epoch)
>>> print(round(l, 6))
130.28188
>>> print(round(a, 8))
9.55490779
>>> print(round(e, 7))
0.0553209
>>> print(round(i, 6))
2.490529
>>> print(round(ome, 5))
113.49736
>>> print(round(arg, 6))
-20.068943
"""
return orbital_elements(epoch, ORBITAL_ELEM, ORBITAL_ELEM_J2000)
[docs] @staticmethod
def geocentric_position(epoch):
"""This method computes the geocentric position of Saturn (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 = Saturn.geocentric_position(epoch)
>>> print(ra.ra_str(n_dec=1))
21h 11' 41.8''
>>> print(dec.dms_str(n_dec=1))
-17d 15' 40.8''
>>> print(elon.dms_str(n_dec=1))
46d 51' 47.7''
"""
# First check that input value is of correct types
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input type")
# Compute the heliocentric position of Saturn
l, b, r = Saturn.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 Saturn coordinates with this correction
l, b, r = Saturn.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(2125, 6, 1.0)
>>> conj = Saturn.conjunction(epoch)
>>> y, m, d = conj.get_date()
>>> print(y)
2125
>>> print(m)
8
>>> print(round(d, 4))
26.4035
"""
# 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 Saturn's conjunction
a = 2451681.124
b = 378.091904
m0 = 131.6934
m1 = 12.647487
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
# Compute auxiliary angles
aa = 82.74 + 40.76 * t
bb = 29.86 + 1181.36 * t
cc = 14.13 + 590.68 * t
dd = 220.02 + 1262.87 * t
# Convert to radians
aa = Angle(aa).rad()
bb = Angle(bb).rad()
cc = Angle(cc).rad()
dd = Angle(dd).rad()
corr = (0.0172 + t * (-0.0006 + t * 0.00023)
+ sin(m) * (-8.5885 + t * (0.0411 + t * 0.0002))
+ cos(m) * (-1.147 + t * (0.0352 - t * 0.00011))
+ sin(2.0 * m) * (0.3331 + t * (-0.0034 - t * 0.00001))
+ cos(2.0 * m) * (0.1145 + t * (-0.0045 + t * 0.00002))
+ sin(3.0 * m) * (-0.0169 + t * 0.0002)
+ cos(3.0 * m) * (-0.0109 + t * 0.0004)
+ sin(aa) * (0.0 + t * (-0.0337 + t * 0.00018))
+ cos(aa) * (-0.851 + t * (0.0044 + t * 0.00068))
+ sin(bb) * (0.0 + t * (-0.0064 + t * 0.00004))
+ cos(bb) * (0.2397 + t * (-0.0012 - t * 0.00008))
+ sin(cc) * (0.0 - t * 0.001)
+ cos(cc) * (0.1245 + t * 0.0006)
+ sin(dd) * (0.0 + t * (0.0024 - t * 0.00003))
+ cos(dd) * (0.0477 + t * (-0.0005 - t * 0.00006)))
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(-6, 9, 1.0)
>>> oppo = Saturn.opposition(epoch)
>>> y, m, d = oppo.get_date()
>>> print(y)
-6
>>> print(m)
9
>>> print(round(d, 4))
14.3709
"""
# 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 Saturn's opposition
a = 2451870.17
b = 378.091904
m0 = 318.0172
m1 = 12.647487
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
# Compute an auxiliary angle
aa = 82.74 + 40.76 * t
bb = 29.86 + 1181.36 * t
cc = 14.13 + 590.68 * t
dd = 220.02 + 1262.87 * t
# Convert to radians
aa = Angle(aa).rad()
bb = Angle(bb).rad()
cc = Angle(cc).rad()
dd = Angle(dd).rad()
corr = (-0.0209 + t * (0.0006 + t * 0.00023)
+ sin(m) * (4.5795 + t * (-0.0312 - t * 0.00017))
+ cos(m) * (1.1462 + t * (-0.0351 + t * 0.00011))
+ sin(2.0 * m) * (0.0985 - t * 0.0015)
+ cos(2.0 * m) * (0.0733 + t * (-0.0031 + t * 0.00001))
+ sin(3.0 * m) * (0.0025 - t * 0.0001)
+ cos(3.0 * m) * (0.005 - t * 0.0002)
+ sin(aa) * (0.0 + t * (-0.0337 + t * 0.00018))
+ cos(aa) * (-0.851 + t * (0.0044 + t * 0.00068))
+ sin(bb) * (0.0 + t * (-0.0064 + t * 0.00004))
+ cos(bb) * (0.2397 + t * (-0.0012 - t * 0.00008))
+ sin(cc) * (0.0 - t * 0.001)
+ cos(cc) * (0.1245 + t * 0.0006)
+ sin(dd) * (0.0 + t * (0.0024 - t * 0.00003))
+ cos(dd) * (0.0477 + t * (-0.0005 - t * 0.00006)))
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(2018, 11, 1.0)
>>> sta1 = Saturn.station_longitude_1(epoch)
>>> y, m, d = sta1.get_date()
>>> print(y)
2018
>>> print(m)
4
>>> print(round(d, 4))
17.9433
"""
# 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 Saturn's opposition
a = 2451870.17
b = 378.091904
m0 = 318.0172
m1 = 12.647487
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
# Compute an auxiliary angle
aa = 82.74 + 40.76 * t
bb = 29.86 + 1181.36 * t
cc = 14.13 + 590.68 * t
dd = 220.02 + 1262.87 * t
# Convert to radians
aa = Angle(aa).rad()
bb = Angle(bb).rad()
cc = Angle(cc).rad()
dd = Angle(dd).rad()
corr = (-68.884 + t * (0.0009 + t * 0.00023)
+ sin(m) * (5.5452 + t * (-0.0279 - t * 0.0002))
+ cos(m) * (3.0727 + t * (-0.043 + t * 0.00007))
+ sin(2.0 * m) * (0.1101 + t * (-0.0006 - t * 0.00001))
+ cos(2.0 * m) * (0.1654 + t * (-0.0043 + t * 0.00001))
+ sin(3.0 * m) * (0.001 + t * 0.0001)
+ cos(3.0 * m) * (0.0095 - t * 0.0003)
+ sin(aa) * (0.0 + t * (-0.0337 + t * 0.00018))
+ cos(aa) * (-0.851 + t * (0.0044 + t * 0.00068))
+ sin(bb) * (0.0 + t * (-0.0064 + t * 0.00004))
+ cos(bb) * (0.2397 + t * (-0.0012 - t * 0.00008))
+ sin(cc) * (0.0 - t * 0.001)
+ cos(cc) * (0.1245 + t * 0.0006)
+ sin(dd) * (0.0 + t * (0.0024 - t * 0.00003))
+ cos(dd) * (0.0477 + t * (-0.0005 - t * 0.00006)))
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(2018, 11, 1.0)
>>> sta2 = Saturn.station_longitude_2(epoch)
>>> y, m, d = sta2.get_date()
>>> print(y)
2018
>>> print(m)
9
>>> print(round(d, 4))
6.4175
"""
# 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 Saturn's opposition
a = 2451870.17
b = 378.091904
m0 = 318.0172
m1 = 12.647487
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
# Compute an auxiliary angle
aa = 82.74 + 40.76 * t
bb = 29.86 + 1181.36 * t
cc = 14.13 + 590.68 * t
dd = 220.02 + 1262.87 * t
# Convert to radians
aa = Angle(aa).rad()
bb = Angle(bb).rad()
cc = Angle(cc).rad()
dd = Angle(dd).rad()
corr = (68.872 + t * (-0.0007 + t * 0.00023)
+ sin(m) * (5.9399 + t * (-0.04 - t * 0.00015))
+ cos(m) * (-0.7998 + t * (-0.0266 + t * 0.00014))
+ sin(2.0 * m) * (0.1738 - t * 0.0032)
+ cos(2.0 * m) * (-0.0039 + t * (-0.0024 + t * 0.00001))
+ sin(3.0 * m) * (0.0073 - t * 0.0002)
+ cos(3.0 * m) * (0.002 - t * 0.0002)
+ sin(aa) * (0.0 + t * (-0.0337 + t * 0.00018))
+ cos(aa) * (-0.851 + t * (0.0044 + t * 0.00068))
+ sin(bb) * (0.0 + t * (-0.0064 + t * 0.00004))
+ cos(bb) * (0.2397 + t * (-0.0012 - t * 0.00008))
+ sin(cc) * (0.0 - t * 0.001)
+ cos(cc) * (0.1245 + t * 0.0006)
+ sin(dd) * (0.0 + t * (0.0024 - t * 0.00003))
+ cos(dd) * (0.0477 + t * (-0.0005 - t * 0.00006)))
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(1944, 1, 1.0)
>>> e = Saturn.perihelion_aphelion(epoch)
>>> y, m, d, h, mi, s = e.get_full_date()
>>> print(y)
1944
>>> print(m)
9
>>> print(d)
8
>>> print(h)
1
>>> epoch = Epoch(2047, 1, 1.0)
>>> e = Saturn.perihelion_aphelion(epoch, perihelion=False)
>>> y, m, d, h, mi, s = e.get_full_date()
>>> print(y)
2047
>>> print(m)
7
>>> print(d)
15
>>> print(h)
0
"""
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input value")
# First approximation
k = 0.03393 * (epoch.year() - 2003.52)
if perihelion:
k = round(k)
else:
k = round(k + 0.5) - 0.5
jde = 2452830.12 + k * (10764.21676 - k * 0.000827)
# Compute the epochs three months before and after
jde_before = jde - 90.0
jde_after = jde + 90.0
# Compute the Sun-Saturn distance for each epoch
l, b, r_b = Saturn.geometric_heliocentric_position(Epoch(jde_before))
l, b, r = Saturn.geometric_heliocentric_position(Epoch(jde))
l, b, r_a = Saturn.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 Saturn, 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 = Saturn.passage_nodes(epoch)
>>> year, month, day = time.get_date()
>>> print(year)
2034
>>> print(month)
5
>>> print(round(day, 1))
30.2
>>> print(round(r, 4))
9.0546
"""
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input types")
# Get the orbital parameters
l, a, e, i, ome, arg = Saturn.orbital_elements_mean_equinox(epoch)
# Compute the time of passage through perihelion
t = Saturn.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, delta_U, B):
"""This function computes the approximate magnitude of Saturn.
:param sun_dist: Distance from Saturn to the Sun, in Astronomical Units
:type sun_dist: float
:param earth_dist: Distance from Saturn to Earth, in Astronomical Units
:type earth_dist: float
:param delta_U: Difference between the Saturnicentric longitudes of the
Sun and the Earth, measured in the plane of the ring, in degrees
:type delta_U: float, :py:class:`Angle`
:param B: Saturnicentric latitude of the Earth refered to the plane of
the ring, positive towards the north, in degrees
:type B: float, :py:class:`Angle`
:returns: Saturn's magnitude
:rtype: float
:raises: TypeError if input values are of wrong type.
.. note::
In order to obtain ``delta_U`` and ``B``, please see method
``ring_parameters()``.
>>> sun_dist = 9.867882
>>> earth_dist = 10.464606
>>> delta_U = Angle(16.442)
>>> B = Angle(4.198)
>>> m = Saturn.magnitude(sun_dist, earth_dist, delta_U, B)
>>> print(m)
1.9
"""
# WARNING: According to Example 41.d in page 286 of Meeus book, the
# result for the example above is 0.9 (instead of 1.9). However, after
# carefully checking the formula implemented here, I'm sure that the
# book has an error
if not (isinstance(sun_dist, float) and isinstance(earth_dist, float)
and isinstance(delta_U, (float, Angle))
and isinstance(B, (float, Angle))):
raise TypeError("Invalid input types")
delta_U = float(delta_U)
B = Angle(B).rad()
m = (-8.68 + 5.0 * log10(sun_dist * earth_dist) + 0.044 * abs(delta_U)
- 2.6 * sin(abs(B)) + 1.25 * sin(B) * sin(B))
return round(m, 1)
[docs] @staticmethod
def ring_inclination(epoch):
"""This function computes the inclination of the plane of Saturn's
ring, referred to the ecliptic and mean equinox of the date.
:param epoch: Epoch to compute the ring inclination
:type epoch: :py:class:`Epoch`
:returns: Inclination of the ring referred to the ecliptic and mean
equinox of the date
:rtype: :py:class:`Angle`
:raises: TypeError if input value is of wrong type.
>>> epoch = Epoch(1992, 12, 16.00068)
>>> i = Saturn.ring_inclination(epoch)
>>> print(round(i, 6))
28.076131
"""
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input type")
# Get the time from J2000.0 in Julian centuries
t = (epoch - JDE2000) / 36525.0
# Compute the inclination
i = Angle(28.075216 + (-0.012998 + 0.000004 * t) * t)
return i
[docs] @staticmethod
def ring_logitude_ascending_node(epoch):
"""This function computes the longitude of the ascending node of the
plane of Saturn's ring, referred to the ecliptic and mean equinox of
the date.
:param epoch: Epoch to compute the ring longitude of ascending node
:type epoch: :py:class:`Epoch`
:returns: Longitude of the ascending node of the ring, referred to the
ecliptic and mean equinox of the date
:rtype: :py:class:`Angle`
:raises: TypeError if input value is of wrong type.
>>> epoch = Epoch(1992, 12, 16.00068)
>>> omega = Saturn.ring_logitude_ascending_node(epoch)
>>> print(round(omega, 6))
169.410243
"""
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input type")
# Get the time from J2000.0 in Julian centuries
t = (epoch - JDE2000) / 36525.0
# Compute the longitude of the ascending node
omega = Angle(169.50847 + (1.394681 + 0.000412 * t) * t)
return omega
[docs] @staticmethod
def ring_parameters(epoch):
"""This function computes the parameters related to Saturn's ring, like
geocentric position angle of the semiminor axis, the size of the major
and minor axes of the outer edge, etc.
:param epoch: Epoch closest to the node passage
:type epoch: :py:class:`Epoch`
:returns: Tuple containing:
* Saturnicentic latitude of the Earth referred to the plane
of the ring (B), positive towards the north (:py:class:`Angle`).
* Saturnicentric latitude of the Sun referred to the plane
of the ring (B'), positive towards the north (:py:class:`Angle`).
* Geocentric position angle of the northern semiminor axis
of the apparent ellipse of the ring (P), measured from the north
towards the east. This is also the position angle of the north
pole of rotation of the planet (:py:class:`Angle`).
* Difference between the Saturnicentric longitudes of the Sun and
the Earth (delta_U), measured in the plane of the ring
(:py:class:`Angle`).
* The size of major axis of the outer edge of the outer
ring ('a'), in arcseconds (float).
* The size of minor axis of the outer edge of the outer
ring ('b'), in arcseconds (float).
:rtype: tuple
:raises: TypeError if input value is of wrong type.
.. note:: Factors by which the axes 'a' and 'b' of the outer edge of
the outer ring are to be multiplied to obtain the axes of:
* Inner edge of outer ring: 0.8801
* Outer edge of inner ring: 0.8599
* Inner edge of inner ring: 0.6650
* Inner edge of dusky ring: 0.5486
>>> epoch = Epoch(1992, 12, 16.00068)
>>> B, Bprime, P, delta_U, a, b = Saturn.ring_parameters(epoch)
>>> print(round(B, 3))
16.442
>>> print(round(Bprime, 3))
14.679
>>> print(round(P, 3))
6.741
>>> print(round(delta_U, 3))
4.198
>>> print(round(a, 2))
35.87
>>> print(round(b, 2))
10.15
"""
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input type")
# Get inclination and longitude of the ascending node of the ring
i = Saturn.ring_inclination(epoch)
Omega = Saturn.ring_logitude_ascending_node(epoch)
# Compute the geometric heliocentric position of the Earth
l0, b0, R = Earth.geometric_heliocentric_position(epoch)
l0r = l0.rad()
b0r = b0.rad()
# Set an initial value to the distance between Earth and Saturn, in UA.
delta = 9.0
# Compute the approximate light-time from Saturn to Earth
tau = 0.0057755183 * delta
oldtau = 0.0
ll = Angle(0.0)
b = Angle(0.0)
r = 0.0
while fabs(tau - oldtau) > 0.000001:
newEpoch = epoch - tau
ll, bl, r = Saturn.geometric_heliocentric_position(newEpoch)
# Convert to radians
lr = ll.rad()
br = bl.rad()
# Compute the rectangular position of Saturn w.r.t. Earth
x = r * cos(br) * cos(lr) - R * cos(l0r)
y = r * cos(br) * sin(lr) - R * sin(l0r)
z = r * sin(br) - R * sin(b0r)
# Compute the distance Earth-Saturn
delta = sqrt((x * x) + (y * y) + (z * z))
oldtau = tau
tau = 0.0057755183 * delta
# Compute geocentric longitude and latitude of Saturn, in radians
lambdar = atan2(y, x)
betar = atan2(z, sqrt(x * x + y * y))
# Get the Saturnicentic latitude of the Earth
ir = i.rad()
Omegar = Omega.rad()
B = asin(sin(ir) * cos(betar) * sin(lambdar - Omegar)
- (cos(ir) * sin(betar)))
# Compute the size of the ring, in arcseconds
a = 375.35 / delta
b = a * sin(fabs(B))
# Get the time from J2000.0 in Julian centuries
T = (epoch - JDE2000) / 36525.0
# Calculate the longitude N of the ascending node of Saturn's orbit
N = Angle(113.6655 + 0.8771 * T)
# Correct l and b for the Sun's aberration as seen from Saturn
lprime = Angle(ll() - 0.01759 / r)
bprime = bl - (0.000764 * cos(lr - N.rad())) / r
Bprime = asin(sin(ir) * cos(bprime.rad()) * sin(lprime.rad() - Omegar)
- cos(ir) * sin(bprime.rad()))
Bprime = Angle(Bprime, radians=True)
# Let's calculate the quantity delta_U, needed to compute the magnitude
bprimer = bprime.rad()
diff1 = lprime.rad() - Omegar
U1r = atan2((sin(ir) * sin(bprimer) + cos(ir) * cos(bprimer)
* sin(diff1)), (cos(bprimer) * cos(diff1)))
diff2 = lambdar - Omegar
U2r = atan2((sin(ir) * sin(betar) + cos(ir) * cos(bprimer)
* sin(diff2)), (cos(betar) * cos(diff2)))
delta_U = Angle(fabs(U1r - U2r), radians=True)
B = Angle(B, radians=True)
dpsi = nutation_longitude(epoch)
epsilon = true_obliquity(epoch)
Lambda0 = Omega - 90.0
Beta0 = 90.0 - i
corrLambda = 0.005693 * cos(l0r - lambdar) / cos(betar)
corrBeta = 0.005693 * sin(l0r - lambdar) * sin(betar)
Lambda = Angle(lambdar, radians=True).to_positive() + corrLambda
Beta = Angle(betar, radians=True) + corrBeta
Lambda += dpsi
Lambda0 += dpsi
alpha0, delta0 = ecliptical2equatorial(Lambda0, Beta0, epsilon)
alpha0r = alpha0.rad()
delta0r = delta0.rad()
alpha, delta = ecliptical2equatorial(Lambda, Beta, epsilon)
alphar = alpha.rad()
deltar = delta.rad()
P = atan2((cos(delta0r) * sin(alpha0r - alphar)),
(sin(delta0r) * cos(deltar)
- cos(delta0r) * sin(deltar) * cos(alpha0r - alphar)))
P = Angle(P, radians=True)
return B, Bprime, P, delta_U, a, b
def main():
# Let's define a small helper function
def print_me(msg, val):
print("{}: {}".format(msg, val))
# Let's show some uses of Saturn class
print("\n" + 35 * "*")
print("*** Use of Saturn class")
print(35 * "*" + "\n")
# Let's now compute the heliocentric position for a given epoch
epoch = Epoch(2018, 10, 27.0)
lon, lat, r = Saturn.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 = Saturn.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 Saturn at 2065.6.24
epoch = Epoch(2065, 6, 24.0)
l, a, e, i, ome, arg = Saturn.orbital_elements_mean_equinox(epoch)
print_me("Mean longitude of the planet", round(l, 6)) # 131.196871
print_me("Semimajor axis of the orbit (UA)", round(a, 8)) # 9.55490779
print_me("Eccentricity of the orbit", round(e, 7)) # 0.0553209
print_me("Inclination on plane of the ecliptic", round(i, 6)) # 2.486426
print_me("Longitude of the ascending node", round(ome, 5)) # 114.23974
print_me("Argument of the perihelion", round(arg, 6)) # -19.896331
print("")
# Compute the time of the conjunction close to 2125/6/1
epoch = Epoch(2125, 6, 1.0)
conj = Saturn.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 -6/9/1
epoch = Epoch(-6, 9, 1.0)
oppo = Saturn.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 2018/11/1
epoch = Epoch(2018, 11, 1.0)
sta1 = Saturn.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 2018/11/1
epoch = Epoch(2018, 11, 1.0)
sta2 = Saturn.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 Perihelion closer to 2000/1/1
epoch = Epoch(2000, 1, 1.0)
e = Saturn.perihelion_aphelion(epoch)
y, m, d, h, mi, s = e.get_full_date()
peri = str(y) + '/' + str(m) + '/' + str(d) + ' at ' + str(h) + ' hours'
print_me("The Perihelion closest to 2000/1/1 happened on", peri)
print("")
# Compute the time of passage through an ascending node
epoch = Epoch(2019, 1, 1)
time, r = Saturn.passage_nodes(epoch)
y, m, d = time.get_date()
d = round(d, 1)
print("Time of passage through ascending node: {}/{}/{}".format(y, m, d))
# 2034/5/30.2
print_me("Radius vector at ascending node", round(r, 4)) # 9.0546
print("")
# Compute the approximate magnitude of Saturn::
sun_dist = 9.867882
earth_dist = 10.464606
delta_u = Angle(16.442)
b = Angle(4.198)
m = Saturn.magnitude(sun_dist, earth_dist, delta_u, b)
print_me("Approximate magnitude of Saturn", m)
# 1.9
print("")
# Compute the ring inclination
epoch = Epoch(1992, 12, 16.00068)
i = Saturn.ring_inclination(epoch)
print_me("Saturn's ring inclination", round(i, 6))
# 28.076131
print("")
# Compute the longitude of the ascending node of the ring
epoch = Epoch(1992, 12, 16.00068)
omega = Saturn.ring_logitude_ascending_node(epoch)
print_me("Saturn's ring longitude of the ascending node", round(omega, 6))
# 169.410243
print("")
# Compute the parameters related to the ring
epoch = Epoch(1992, 12, 16.00068)
B, Bprime, P, delta_U, a, b = Saturn.ring_parameters(epoch)
print_me("Saturnicentric latitude of the Earth", round(B, 3)) # 16.442
print_me("Saturnicentric latitude of the Sun", round(Bprime, 3)) # 14.679
print_me("Geocentric position angle of nothern semiminor axis",
round(P, 3)) # 6.741
print_me("Difference in Saturnicentric longitudes of Sun and Earth",
round(delta_U, 3)) # 4.198
print_me("Size of major axis of outer ring", round(a, 2)) # 35.87
print_me("Size of minor axis of outer ring", round(b, 2)) # 10.15
if __name__ == "__main__":
main()