# -*- coding: utf-8 -*-
# PyMeeus: Python module implementing astronomical algorithms.
# Copyright (C) 2018 Dagoberto Salazar
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
from math import sin, cos, tan, acos, atan2, sqrt, radians, log10
from pymeeus.Angle import Angle
from pymeeus.Epoch import Epoch, JDE2000
from pymeeus.Interpolation import Interpolation
from pymeeus.Coordinates import (
geometric_vsop_pos, apparent_vsop_pos, orbital_elements,
nutation_longitude, true_obliquity, ecliptical2equatorial,
passage_nodes_elliptic
)
from pymeeus.Earth import Earth
from pymeeus.Sun import Sun
"""
.. module:: Jupiter
:synopsis: Class to model Jupiter planet
:license: GNU Lesser General Public License v3 (LGPLv3)
.. moduleauthor:: Dagoberto Salazar
"""
VSOP87_L = [
# L0
[
[59954691.495, 0.00000000000, 0.00000000000],
[9695898.711, 5.06191793105, 529.69096509460],
[573610.145, 1.44406205976, 7.11354700080],
[306389.180, 5.41734729976, 1059.38193018920],
[97178.280, 4.14264708819, 632.78373931320],
[72903.096, 3.64042909255, 522.57741809380],
[64263.986, 3.41145185203, 103.09277421860],
[39806.051, 2.29376744855, 419.48464387520],
[38857.780, 1.27231724860, 316.39186965660],
[27964.622, 1.78454589485, 536.80451209540],
[13589.738, 5.77481031590, 1589.07289528380],
[8246.362, 3.58227961655, 206.18554843720],
[8768.686, 3.63000324417, 949.17560896980],
[7368.057, 5.08101125612, 735.87651353180],
[6263.171, 0.02497643742, 213.29909543800],
[6114.050, 4.51319531666, 1162.47470440780],
[4905.419, 1.32084631684, 110.20632121940],
[5305.283, 1.30671236848, 14.22709400160],
[5305.457, 4.18625053495, 1052.26838318840],
[4647.249, 4.69958109497, 3.93215326310],
[3045.009, 4.31675960318, 426.59819087600],
[2610.001, 1.56667594850, 846.08283475120],
[2028.191, 1.06376547379, 3.18139373770],
[1764.768, 2.14148077766, 1066.49547719000],
[1722.983, 3.88036008872, 1265.56747862640],
[1920.959, 0.97168928755, 639.89728631400],
[1633.217, 3.58201089758, 515.46387109300],
[1431.997, 4.29683690269, 625.67019231240],
[973.278, 4.09764957065, 95.97922721780],
[884.439, 2.43701426123, 412.37109687440],
[732.875, 6.08534113239, 838.96928775040],
[731.072, 3.80591233956, 1581.95934828300],
[691.928, 6.13368222939, 2118.76386037840],
[709.190, 1.29272573658, 742.99006053260],
[614.464, 4.10853496756, 1478.86657406440],
[495.224, 3.75567461379, 323.50541665740],
[581.902, 4.53967717552, 309.27832265580],
[375.657, 4.70299124833, 1368.66025284500],
[389.864, 4.89716105852, 1692.16566950240],
[341.006, 5.71452525783, 533.62311835770],
[330.458, 4.74049819491, 0.04818410980],
[440.854, 2.95818460943, 454.90936652730],
[417.266, 1.03554430161, 2.44768055480],
[244.170, 5.22020878900, 728.76296653100],
[261.540, 1.87652461032, 0.96320784650],
[256.568, 3.72410724159, 199.07200143640],
[261.009, 0.82047246448, 380.12776796000],
[220.382, 1.65115015995, 543.91805909620],
[201.996, 1.80684574186, 1375.77379984580],
[207.327, 1.85461666594, 525.75881183150],
[197.046, 5.29252149016, 1155.36115740700],
[235.141, 1.22693908124, 909.81873305460],
[174.809, 5.90973505276, 956.28915597060],
[149.368, 4.37745104275, 1685.05212250160],
[175.184, 3.22634903433, 1898.35121793960],
[175.191, 3.72966554761, 942.06206196900],
[157.909, 4.36483921766, 1795.25844372100],
[137.871, 1.31797920785, 1169.58825140860],
[117.495, 2.50022140890, 1596.18644228460],
[150.502, 3.90625022622, 74.78159856730],
[116.757, 3.38920921041, 0.52126486180],
[105.895, 4.55439798236, 526.50957135690],
[130.531, 4.16867945489, 1045.15483618760],
[141.445, 3.13568357861, 491.55792945680],
[99.511, 1.42117395747, 532.87235883230],
[96.137, 1.18156870005, 117.31986822020],
[91.758, 0.85756633461, 1272.68102562720],
[87.695, 1.21738140813, 453.42489381900],
[68.507, 2.35242959478, 2.92076130680],
[66.098, 5.34386149468, 1471.75302706360],
[77.401, 4.42676337124, 39.35687591520],
[72.006, 4.23834923691, 2111.65031337760],
[63.406, 4.97665525033, 0.75075952540],
[59.427, 4.11130498612, 2001.44399215820],
[62.481, 0.51211384012, 220.41264243880],
[66.532, 2.98864358135, 2214.74308759620],
[60.194, 4.12628179571, 4.19278569400],
[56.012, 1.15493222602, 21.34064100240],
[52.854, 0.91207215543, 10.29494073850],
[70.297, 5.14180555282, 835.03713448730],
[51.916, 4.10048180020, 1258.45393162560],
[46.442, 4.66531163524, 5.62907429250],
[58.190, 5.86646380344, 5753.38488489680],
[40.103, 4.68801114087, 0.16005869440],
[46.654, 4.79394835282, 305.34616939270],
[39.298, 4.25448423697, 853.19638175200],
[46.042, 5.10983515150, 4.66586644600],
[54.459, 1.57072704127, 983.11585891360],
[38.920, 6.07592905580, 518.64526483070],
[38.450, 2.43836870888, 433.71173787680],
[46.800, 3.54640538283, 5.41662597140],
[41.830, 4.67982493646, 302.16477565500],
[35.920, 2.45088036239, 430.53034413910],
[37.888, 0.21127448431, 2648.45482547300],
[39.190, 1.71835571629, 11.04570026390],
[37.567, 6.19481310233, 831.85574074960],
[35.828, 4.61459907698, 2008.55753915900],
[43.402, 0.14992289081, 528.20649238630],
[31.598, 5.14073450755, 1788.14489672020],
[29.849, 5.34441117167, 2221.85663459700],
[32.811, 5.28907118836, 88.86568021700],
[27.686, 1.85227036207, 0.21244832110],
[25.820, 3.85920882494, 2317.83586181480],
[24.705, 2.63495214991, 114.13847448250],
[33.844, 1.00563073268, 9683.59458111640],
[24.266, 3.82355417268, 1574.84580128220],
[27.111, 2.80845435102, 18.15924726470],
[26.837, 1.77586123775, 532.13864564940],
[26.064, 2.74361318804, 2531.13495725280],
[30.765, 0.42330537728, 1.48447270830],
[30.476, 3.66677894407, 508.35032409220],
[23.282, 3.24372142416, 984.60033162190],
[19.445, 0.52370214471, 14.97785352700],
[19.332, 4.86314494382, 1361.54670584420],
[22.910, 3.84914895064, 2428.04218303420],
[21.617, 6.01696940024, 1063.31408345230],
[20.155, 5.59582008789, 527.24328453980],
[23.732, 2.52766031921, 494.26624244250],
[20.189, 1.01560227681, 628.85158605010],
[15.994, 5.09003530653, 529.73914920440],
[16.134, 5.27095037302, 142.44965013380],
[20.697, 4.03443281612, 355.74874557180],
[21.479, 1.28668134295, 35.42472265210],
[14.964, 4.86039684390, 2104.53676637680],
[17.242, 1.59187913206, 1439.50969814920],
[15.994, 1.89222417794, 529.64278098480],
[17.958, 4.30178016003, 6.15033915430],
[13.279, 2.18943981644, 1055.44977692610],
[14.148, 2.71597731671, 0.26063243090],
[14.689, 0.87944553412, 99.16062095550],
[14.202, 2.41335693735, 530.65417294110],
[15.320, 6.07703092728, 149.56319713460],
[15.832, 4.11682440678, 636.71589257630],
[12.398, 2.61042299578, 405.25754987360],
[16.199, 2.77035044582, 760.25553592000],
[13.665, 3.56039678310, 217.23124870110],
[15.261, 2.81824770887, 621.73803904930],
[14.681, 6.26423732742, 569.04784100980],
[12.529, 1.39077179081, 7.06536289100],
[11.677, 3.60447374272, 2634.22773147140],
[11.603, 4.60461756191, 7.16173111060],
[12.152, 0.24540531919, 1485.98012106520],
[11.347, 2.00818458261, 1073.60902419080],
[11.242, 2.48000947870, 423.41679713830],
[10.942, 5.03602448252, 458.84151979040],
[11.117, 4.04973271023, 519.39602435610],
[12.256, 4.30153222783, 604.47256366190],
[13.149, 2.72189077702, 1364.72809958190],
[10.604, 3.11518747072, 1.27202438720],
[9.874, 1.70200068743, 1699.27921650320],
[10.851, 5.08554552028, 2324.94940881560],
[10.692, 2.51401681528, 2847.52682690940],
[12.640, 4.75572797691, 528.72775724810],
[10.084, 4.05599810206, 38.13303563780],
[11.536, 2.35034215745, 643.82943957710],
[10.247, 3.63479911496, 2744.43405269080],
[10.105, 3.65845333837, 107.02492748170],
[10.121, 1.31482648275, 1905.46476494040],
[9.341, 5.92176693887, 1148.24761040620],
[8.796, 2.77421822809, 6.59228213900],
[8.420, 4.52537756809, 1677.93857550080],
[10.128, 2.09034472544, 511.53171782990],
[8.272, 2.98682673354, 540.73666535850],
[9.753, 1.22438911827, 32.24332891440],
[10.630, 2.07777800288, 92.04707395470],
[7.850, 0.98996894618, 408.43894361130],
[8.811, 3.46911754939, 1021.24889455140],
[7.946, 2.86682926070, 2125.87740737920],
[8.575, 5.29590411702, 415.55249061210],
[7.841, 6.08025056721, 70.84944530420],
[7.706, 1.69832954219, 8.07675484730],
[7.265, 4.65503563919, 629.60234557550],
[7.164, 4.93400217968, 1056.20053645150],
[7.247, 4.61607677560, 2420.92863603340],
[7.753, 2.12871653382, 33.94024994380],
[6.645, 0.45647460873, 635.96513305090],
[9.377, 4.03158388202, 2810.92146160520],
[8.263, 1.23558676139, 1802.37199072180],
[6.341, 0.07278001580, 202.25339517410],
[6.383, 3.54310669809, 1891.23767093880],
[7.902, 2.32510002614, 230.56457082540],
[6.214, 4.54560345237, 2.70831298570],
[7.347, 1.24457237337, 24.37902238820],
[7.451, 3.02719199239, 330.61896365820],
[6.220, 1.77687561489, 1062.56332392690],
[5.674, 5.14132196367, 746.92221379570],
[5.855, 5.42130172896, 28.31117565130],
[5.629, 3.24348217277, 529.16970023280],
[7.652, 0.52813391052, 672.14061522840],
[5.456, 3.34716871364, 2950.61960112800],
[7.127, 1.43497795005, 6.21977512350],
[5.388, 4.90175095580, 69.15252427480],
[5.618, 4.97903783721, 2641.34127847220],
[5.844, 2.95364118152, 490.33408917940],
[4.943, 5.37597740579, 721.64941953020],
[5.062, 4.84282906467, 31.01948863700],
[5.163, 5.07410777073, 67.66805156650],
[4.739, 6.10248862834, 106.27416795630],
[4.879, 0.07095292379, 78.71375183040],
[4.854, 5.63875661096, 1.69692102940],
[5.629, 3.73871604865, 530.21222995640],
[4.471, 4.49152882547, 505.31194270640],
[4.313, 4.79369370451, 535.10759106600],
[4.280, 0.54783823710, 1.43628859850],
[4.453, 0.50551854591, 524.06189080210],
[4.936, 4.82992988255, 422.66603761290],
[4.701, 3.41634869046, 3060.82592234740],
[4.261, 2.67044686458, 561.93429400900],
[4.156, 4.00660658688, 99.91138048090],
[4.561, 2.29650164054, 3163.91869656600],
[4.414, 5.67224020329, 1464.63948006280],
[5.345, 0.31513851830, 1289.94650101460],
[5.269, 3.89116469022, 191.95845443560],
[3.855, 4.28942301453, 1994.33044515740],
[4.210, 5.32763589447, 2538.24850425360],
[3.949, 4.56507101172, 1382.88734684660],
[3.885, 1.56778786810, 647.01083331480],
[4.227, 5.51697599030, 5223.69391980220],
[4.129, 2.81119457666, 416.30325013750],
[3.663, 4.35187510477, 2737.32050569000],
[3.566, 5.48243943375, 750.10360753340],
[4.330, 0.84941756640, 531.17543780290],
[4.093, 0.19980340452, 525.02509864860],
[4.022, 1.92293311337, 1512.80682400820],
[3.400, 6.00302355875, 1.22384027740],
[3.496, 0.31252921473, 597.35901666110],
[3.299, 4.27596694481, 526.77020378780],
[3.226, 2.90455264496, 963.40270297140],
[3.150, 3.81061764181, 280.96714700450],
[4.129, 4.74946631331, 0.89377187730],
[3.840, 1.91064405186, 378.64329525170],
[3.057, 1.65589659685, 528.94020556920],
[3.011, 1.59276337369, 224.34479570190],
[3.196, 5.86588452873, 4.14460158420],
[3.628, 0.07930225897, 558.00214074590],
[2.932, 0.41424445089, 7.86430652620],
[3.316, 2.70211697795, 532.61172640140],
[2.925, 4.47580363425, 533.88375078860],
[3.690, 0.39897023849, 685.47393735270],
[3.223, 2.45833032883, 960.22130923370],
[3.059, 5.32616140812, 530.44172462000],
[3.383, 4.42170370028, 312.45971639350],
[3.320, 2.71417812514, 495.75071515080],
[2.697, 5.23146633437, 739.80866679490],
[3.590, 2.30999595873, 908.33426034630],
[3.677, 5.07337955976, 73.29712585900],
[2.618, 3.09118499149, 3267.01147078460],
[2.796, 2.98942316119, 483.22054217860],
[3.398, 3.29598270278, 911.30320576290],
[3.352, 1.44391979336, 593.42686339800],
[2.563, 3.35080110279, 2207.62954059540],
[2.553, 0.36892288645, 1048.33622992530],
[2.620, 3.82769874340, 520.12973753900],
[3.356, 1.08315053878, 46.47042291600],
[3.035, 5.52230028113, 618.55664531160],
[3.397, 3.83084746522, 210.11770170030],
[2.497, 0.47917884538, 945.24345570670],
[2.341, 5.87941292649, 2751.54759969160],
[2.656, 0.49713061045, 1057.89745748090],
[2.581, 0.03759881914, 1.64453140270],
[2.900, 2.50019054587, 525.49817940060],
[3.153, 2.30900986177, 457.61767951300],
[2.201, 3.94367109739, 31.49256938900],
[2.381, 6.19252134885, 327.43756992050],
[2.458, 0.65614291954, 9153.90361602180],
[2.111, 5.61905648764, 16.46232623530],
[2.130, 3.75880734109, 724.83081326790],
[2.406, 2.29315649755, 195.13984817330],
[2.166, 5.43262641046, 534.35683154060],
[2.057, 1.49875151278, 551.03160609700],
[2.676, 5.06374981112, 456.39383923560],
[2.078, 5.28920097886, 76.26607127560],
[2.261, 5.38117230692, 1781.03134971940],
[2.356, 0.67392574097, 227.52618943960],
[2.240, 3.18006978517, 3377.21779200400],
[2.183, 3.08384250950, 524.27433912320],
[2.119, 2.70107659927, 387.24131496080],
[2.056, 4.82779196994, 2957.73314812880],
[2.116, 6.20263841494, 209.36694217490],
[2.712, 3.18157754631, 1474.67378837040],
[2.127, 1.24424012514, 539.98590583310],
[2.424, 3.57595925853, 953.10776223290],
[1.947, 1.94468082546, 529.53090640020],
[1.896, 4.01406242800, 2310.72231481400],
[1.935, 4.10051493950, 3053.71237534660],
[2.056, 6.27074148550, 245.54242435240],
[2.108, 3.22886474225, 252.65597135320],
[2.596, 2.77467278614, 177.87437278590],
[1.919, 3.14834694111, 381.61224066830],
[2.217, 1.92368906925, 535.91074021810],
[1.947, 5.03751780002, 529.85102378900],
[2.025, 4.82814272957, 17.26547538740],
[1.945, 2.10611582568, 3480.31056622260],
[1.899, 0.05104263891, 560.71045373160],
[2.221, 0.58365090630, 3178.14579056760],
[2.271, 1.67360565619, 731.94436026870],
[1.706, 5.40277333462, 20.44686912510],
[2.295, 4.20863103004, 1038.04128918680],
[2.218, 3.65982280555, 282.45161971280],
[2.181, 4.87369503022, 535.32003938710],
[1.745, 1.34021867874, 25.12978191360],
[1.601, 3.92730015840, 17.52610781830],
[1.651, 0.63598292839, 17.40848773930],
[1.826, 0.31592311031, 124.43341522100],
[2.041, 0.15617294873, 598.84348936940],
[1.494, 3.81418025130, 319.57326339430],
[1.551, 5.25201528605, 437.64389113990],
[1.852, 2.36130812462, 37.87240320690],
[1.466, 1.72926380881, 59.80374504030],
[1.417, 5.82273267086, 81.75213321620],
[1.430, 1.17528806260, 440.82528487760],
[1.906, 4.06896022692, 1819.63746610920],
[1.397, 0.26383366743, 50.40257617910],
[1.756, 2.32977483716, 938.12990870590],
[1.487, 2.24866746540, 10.03430830760],
[1.368, 3.56691602771, 1514.29129671650],
[1.400, 4.84502200703, 295.05122865420],
[1.344, 2.20177702122, 529.90341341570],
[1.464, 1.42648716568, 1158.54255114470],
[1.341, 1.15693423225, 2435.15573003500],
[1.786, 5.44716330146, 2854.64037391020],
[1.677, 6.22875777048, 833.55266177900],
[1.471, 4.80574535807, 696.51963761660],
[1.436, 1.45810957330, 537.76771994190],
[1.657, 0.02890651793, 138.51749687070],
[1.300, 3.14074420421, 547.85021235930],
[1.343, 6.14827138025, 988.53248488500],
[1.344, 4.78042160426, 529.47851677350],
[1.234, 2.83294330979, 3583.40334044120],
[1.651, 2.12056447005, 1061.82961074400],
[1.479, 0.24646493075, 1593.00504854690],
[1.413, 3.07444632745, 6283.07584999140],
[1.246, 5.94882321661, 1056.93424963440],
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[0.158, 5.00063628575, 650.94298657790],
[0.159, 5.37530499642, 20426.57109242200],
[0.218, 0.27875408082, 175.16605980020],
[0.155, 0.83696849428, 1474.93442080130],
[0.154, 2.62839957291, 683.18631549230],
[0.171, 1.79511736017, 1123.11782849260],
[0.188, 5.24747110812, 25565.32572348040],
[0.168, 4.14907553818, 946.72792841500],
[0.203, 2.83699715530, 1489.91227432830],
[0.173, 4.34546063838, 3046.59882834580],
[0.190, 5.67865607835, 1060.13268971460],
[0.201, 2.38524182920, 419.53282798500],
[0.152, 5.89088685790, 208.63322899200],
[0.206, 4.46933127349, 2654.67460059650],
[0.156, 2.37819796438, 2758.66114669240],
[0.203, 0.70565514297, 498.19839570560],
[0.205, 3.05468636546, 1062.30269149600],
[0.174, 3.50824761708, 2004.36475346500],
[0.148, 4.73961194393, 1799.19059698410],
[0.188, 3.62315953725, 3156.80514956520],
[0.183, 2.35011338194, 25551.09862947879],
[0.162, 1.58053710589, 628.59095361920],
[0.162, 3.99983876824, 1482.79872732750],
[0.181, 2.85489861839, 1055.18914449520],
[0.151, 3.43198157222, 629.86297800640],
[0.157, 3.15195826490, 1025.44168024540],
[0.194, 5.13049187783, 1818.15299340090],
[0.193, 1.92287052164, 1140.38330388000],
[0.137, 4.22335221970, 1049.82070263360],
[0.167, 2.85163087563, 5746.27133789600],
[0.167, 5.73970282991, 5760.49843189760],
[0.138, 2.23519776527, 1176.70179840940],
[0.151, 4.89507270899, 532.39927808030],
[0.147, 2.65931838448, 987.30864460760],
[0.135, 0.12836417770, 991.71387862270],
[0.166, 3.12682515439, 580.09354127370],
[0.118, 5.98810576300, 531.38788612400],
[0.135, 5.26601313643, 1065.01100448170],
[0.138, 3.18511244397, 707.56533788050],
[0.122, 1.34377059565, 446.31134681820],
[0.120, 2.29717714347, 1059.22187149480],
[0.121, 0.58145552537, 5621.84292321040],
[0.103, 4.75645235023, 1226.21060271120],
[0.104, 6.08481630139, 528.25467649610],
[0.119, 1.06475523307, 527.99404406520],
[0.104, 0.89730746841, 531.12725369310],
[0.120, 5.39001411803, 1059.54198888360],
[0.104, 0.44849170648, 1128.53445446400],
[0.117, 5.42449214711, 986.08480433020],
[0.101, 5.09893554462, 530.58473697190],
[0.102, 0.26948040239, 450.97721326420],
[0.107, 1.58724086516, 1069.67687092770],
[0.086, 2.28711702506, 2498.89162833840],
[0.101, 1.88318822518, 528.79719321730],
[0.086, 1.37568728263, 970.51624997220],
[0.083, 0.06930748288, 530.91480537200],
[0.085, 3.22094000094, 1553.64817263170],
[0.083, 0.62963097974, 528.46712481720],
[0.083, 4.16314675511, 849.26422848890],
[0.079, 3.46688102340, 1077.54117745390],
[0.097, 0.87886975916, 9690.70812811720],
[0.097, 4.27398311206, 9676.48103411560],
[0.101, 0.29639798579, 857.12853501510],
[0.083, 2.55427333923, 1059.59437851030],
[0.078, 0.06461496210, 521.82665856840],
[0.078, 0.76677000862, 525.54636351040],
[0.096, 0.33631035749, 1090.40141882620],
[0.098, 1.42815294497, 757.21715453420],
[0.077, 0.85066773729, 537.55527162080],
[0.084, 5.04765104413, 1160.02702385300],
[0.076, 3.62264327413, 782.34693644780],
[0.085, 1.86831145784, 25028.52121138500],
[0.079, 2.90602202890, 2114.83170711530],
],
# L1
[
[52993480757.497, 0.00000000000, 0.00000000000],
[489741.194, 4.22066689928, 529.69096509460],
[228918.538, 6.02647464016, 7.11354700080],
[27655.380, 4.57265956824, 1059.38193018920],
[20720.943, 5.45938936295, 522.57741809380],
[12105.732, 0.16985765041, 536.80451209540],
[6068.051, 4.42419502005, 103.09277421860],
[5433.924, 3.98478382565, 419.48464387520],
[4237.795, 5.89009351271, 14.22709400160],
[2211.854, 5.26771446618, 206.18554843720],
[1295.769, 5.55132765087, 3.18139373770],
[1745.919, 4.92669378486, 1589.07289528380],
[1163.411, 0.51450895328, 3.93215326310],
[1007.216, 0.46478398551, 735.87651353180],
[1173.129, 5.85647304350, 1052.26838318840],
[847.678, 5.75805850450, 110.20632121940],
[827.329, 4.80312015734, 213.29909543800],
[1003.574, 3.15040301822, 426.59819087600],
[1098.735, 5.30704981594, 515.46387109300],
[816.397, 0.58643054886, 1066.49547719000],
[725.447, 5.51827471473, 639.89728631400],
[567.845, 5.98867049451, 625.67019231240],
[474.181, 4.13245269168, 412.37109687440],
[412.930, 5.73652891261, 95.97922721780],
[335.817, 3.73248749046, 1162.47470440780],
[345.249, 4.24159565410, 632.78373931320],
[234.066, 6.24302226646, 309.27832265580],
[194.784, 2.21879010911, 323.50541665740],
[234.340, 4.03469970332, 949.17560896980],
[183.938, 6.27963588822, 543.91805909620],
[198.525, 1.50458442825, 838.96928775040],
[186.899, 6.08620565908, 742.99006053260],
[171.380, 5.41655983845, 199.07200143640],
[130.771, 0.62643377351, 728.76296653100],
[107.575, 4.49282760117, 956.28915597060],
[115.393, 0.68019050174, 846.08283475120],
[115.047, 5.28641699144, 2118.76386037840],
[66.824, 5.73365126533, 21.34064100240],
[69.618, 5.97263450278, 532.87235883230],
[64.850, 6.08803490288, 1581.95934828300],
[79.686, 5.82412400273, 1045.15483618760],
[57.939, 0.99453087342, 1596.18644228460],
[65.635, 0.12924191430, 526.50957135690],
[58.509, 0.58626971028, 1155.36115740700],
[56.600, 1.41198438841, 533.62311835770],
[71.643, 5.34162650321, 942.06206196900],
[57.368, 5.96851304799, 1169.58825140860],
[54.935, 5.42806383723, 10.29494073850],
[52.016, 0.22981299129, 1368.66025284500],
[52.309, 5.72661448388, 117.31986822020],
[50.418, 6.08075147811, 525.75881183150],
[47.418, 3.62611843241, 1478.86657406440],
[39.888, 4.16158013600, 1692.16566950240],
[46.678, 0.51144073175, 1265.56747862640],
[32.827, 5.03596689455, 220.41264243880],
[33.558, 0.09913904872, 302.16477565500],
[29.379, 3.35927241533, 4.66586644600],
[29.307, 0.75907909735, 88.86568021700],
[32.449, 5.37492530697, 508.35032409220],
[29.483, 5.42208897099, 1272.68102562720],
[21.802, 6.15054054070, 1685.05212250160],
[25.195, 1.60723063387, 831.85574074960],
[21.133, 5.86346824200, 1258.45393162560],
[19.747, 2.17205957814, 316.39186965660],
[17.871, 0.82841413516, 433.71173787680],
[17.703, 5.95527049039, 5.41662597140],
[17.230, 2.76395560958, 853.19638175200],
[17.453, 0.70749901224, 1471.75302706360],
[17.508, 0.49799925173, 1375.77379984580],
[14.368, 0.91459831140, 18.15924726470],
[14.107, 0.63031082833, 2.92076130680],
[11.559, 4.30379009964, 405.25754987360],
[11.728, 1.76426582357, 380.12776796000],
[11.054, 5.56735602213, 1574.84580128220],
[10.425, 0.31355034390, 1361.54670584420],
[9.804, 5.90363777277, 519.39602435610],
[9.805, 0.38648727979, 1073.60902419080],
[9.285, 3.21842287530, 1795.25844372100],
[8.864, 0.53776257958, 1788.14489672020],
[8.370, 5.88484552222, 2001.44399215820],
[8.148, 5.10162311410, 1485.98012106520],
[7.658, 5.64890060131, 2648.45482547300],
[6.690, 2.41093459420, 4.19278569400],
[5.840, 4.22347896053, 2008.55753915900],
[7.256, 6.19384525651, 11.04570026390],
[6.266, 1.36137786945, 1148.24761040620],
[5.141, 5.23083932012, 628.85158605010],
[5.140, 2.92955981951, 518.64526483070],
[4.765, 0.16838181862, 629.60234557550],
[4.603, 0.78529559911, 721.64941953020],
[4.575, 6.24794935732, 1677.93857550080],
[4.537, 4.95096707833, 635.96513305090],
[4.518, 2.06523915453, 453.42489381900],
[4.414, 0.15381186059, 1699.27921650320],
[5.593, 5.57489981207, 191.95845443560],
[5.403, 1.46004886198, 330.61896365820],
[4.285, 0.23949868127, 2104.53676637680],
[4.223, 1.44087555881, 2125.87740737920],
[4.101, 6.19274358942, 636.71589257630],
[4.432, 4.35811524051, 423.41679713830],
[4.132, 0.50170694173, 1056.20053645150],
[4.398, 4.14280286969, 511.53171782990],
[5.406, 4.40429493698, 2221.85663459700],
[4.467, 0.08534650684, 1062.56332392690],
[3.569, 5.66540477010, 2317.83586181480],
[4.007, 2.54845549248, 74.78159856730],
[3.515, 0.25495124831, 1055.44977692610],
[3.687, 2.93378008847, 32.24332891440],
[2.883, 5.72793010505, 99.91138048090],
[2.969, 5.50054720569, 107.02492748170],
[2.720, 1.25222590925, 540.73666535850],
[2.808, 3.30714813896, 0.75075952540],
[2.768, 1.61339487804, 1063.31408345230],
[2.666, 4.28662288102, 106.27416795630],
[2.704, 3.03615556153, 422.66603761290],
[3.290, 5.89081682150, 1802.37199072180],
[2.578, 3.60390367979, 750.10360753340],
[2.661, 0.35249312659, 1898.35121793960],
[2.486, 5.28950877719, 1891.23767093880],
[2.936, 1.09052029450, 1464.63948006280],
[3.190, 4.60740643547, 416.30325013750],
[2.390, 6.01779736611, 551.03160609700],
[2.214, 5.24450923180, 621.73803904930],
[2.319, 5.82920300130, 305.34616939270],
[2.089, 5.99310370434, 1994.33044515740],
[2.042, 0.75008788531, 142.44965013380],
[2.121, 0.01537599023, 2420.92863603340],
[2.114, 6.25308371567, 647.01083331480],
[2.020, 4.17560390841, 569.04784100980],
[2.109, 5.18682321403, 227.52618943960],
[2.283, 5.80043809222, 539.98590583310],
[1.977, 3.99197009651, 24.37902238820],
[1.960, 1.35288793079, 963.40270297140],
[1.903, 2.78349628184, 2428.04218303420],
[1.915, 4.22134509685, 2324.94940881560],
[1.971, 5.88715684267, 217.23124870110],
[1.917, 3.03728154374, 1382.88734684660],
[2.026, 3.08606488714, 408.43894361130],
[1.834, 5.61474110217, 430.53034413910],
[1.838, 1.25467410218, 81.75213321620],
[2.460, 4.63268678998, 1905.46476494040],
[1.820, 5.97497926120, 114.13847448250],
[2.043, 4.34047514845, 70.84944530420],
[1.959, 4.03116026306, 92.04707395470],
[1.768, 0.33097462499, 35.42472265210],
[2.334, 5.87042638470, 1038.04128918680],
[1.835, 4.81326127892, 124.43341522100],
[2.269, 1.02549350754, 618.55664531160],
[1.919, 5.01297395549, 99.16062095550],
[1.923, 0.28688549585, 31.01948863700],
[1.878, 5.69299116574, 210.11770170030],
[1.679, 0.25635730278, 295.05122865420],
[1.656, 5.46039280732, 2634.22773147140],
[1.675, 6.15609073315, 643.82943957710],
[1.953, 5.09846435548, 17.40848773930],
[1.539, 2.75316078346, 415.55249061210],
[1.467, 0.54812675158, 458.84151979040],
[1.482, 3.76736278426, 534.35683154060],
[1.446, 3.15802770791, 25.12978191360],
[1.667, 0.26406950755, 835.03713448730],
[1.472, 0.83054329617, 28.31117565130],
[1.655, 0.88908548504, 1781.03134971940],
[1.294, 5.76241191046, 440.82528487760],
[1.348, 2.49823510924, 984.60033162190],
[1.352, 5.10869562455, 149.56319713460],
[1.344, 0.01942249067, 2214.74308759620],
[1.188, 2.24279457878, 31.49256938900],
[1.166, 0.80686346228, 739.80866679490],
[1.322, 4.25691184168, 2538.24850425360],
[1.094, 6.02985819406, 2737.32050569000],
[1.112, 4.38204360670, 561.93429400900],
[1.346, 3.20575848870, 525.02509864860],
[1.056, 5.76507115032, 2310.72231481400],
[1.159, 0.46189564970, 67.66805156650],
[1.027, 0.20709586018, 7.86430652620],
[1.143, 5.56626418636, 46.47042291600],
[1.012, 0.54293005597, 532.13864564940],
[0.978, 5.13939194101, 2207.62954059540],
[0.993, 2.03698185233, 319.57326339430],
[1.035, 2.90231353535, 611.44309831080],
[1.021, 4.75651217048, 527.24328453980],
[1.308, 1.78809336431, 824.74219374880],
[0.964, 2.82269601958, 2111.65031337760],
[0.896, 2.54505998806, 2744.43405269080],
[0.890, 5.41036782817, 28.45418800320],
[0.906, 0.76565238554, 1439.50969814920],
[0.985, 0.88687623770, 5760.49843189760],
[0.983, 1.42102343372, 5746.27133789600],
[0.892, 5.87250060663, 203.00415469950],
[0.942, 2.31049430734, 9690.70812811720],
[0.941, 2.84331157527, 9676.48103411560],
[0.867, 0.81020362547, 524.27433912320],
[0.829, 2.35178495412, 312.45971639350],
[0.912, 2.80494184378, 6.21977512350],
[0.809, 1.05148218513, 529.64278098480],
[0.779, 4.80009242059, 945.24345570670],
[0.878, 5.76532521399, 1.64453140270],
[0.953, 4.30945738629, 209.36694217490],
[0.772, 5.25607113566, 2950.61960112800],
[0.745, 0.03810558502, 535.10759106600],
[0.744, 0.58381523987, 25.27279426550],
[0.734, 0.20800485100, 1049.08698945070],
[0.747, 2.71772840871, 38.13303563780],
[0.728, 5.97210358938, 945.99421523210],
[0.769, 4.51394016967, 952.35700270750],
[0.710, 0.38016353553, 69.15252427480],
[0.760, 3.07033779824, 39.35687591520],
[0.802, 1.14191463412, 532.61172640140],
[0.704, 1.25447308120, 547.85021235930],
[0.721, 0.73855379162, 2228.97018159780],
[0.794, 4.25051539085, 2641.34127847220],
[0.795, 3.20588363820, 604.47256366190],
[0.818, 1.05229815343, 909.81873305460],
[0.724, 5.68281830264, 953.10776223290],
[0.836, 0.60410469174, 2097.42321937600],
[0.669, 5.75757140051, 2015.67108615980],
[0.682, 1.19994890339, 387.24131496080],
[0.640, 3.91546675664, 528.72775724810],
[0.809, 4.24929331276, 529.73914920440],
[0.819, 4.91540072376, 2751.54759969160],
[0.692, 2.51162384766, 916.93228005540],
[0.784, 4.23651511312, 195.13984817330],
[0.762, 1.12201139619, 732.69511979410],
[0.617, 5.80920925081, 739.05790726950],
[0.727, 4.24401822698, 760.25553592000],
[0.591, 3.26075006572, 202.25339517410],
[0.552, 5.83533550039, 526.77020378780],
[0.640, 1.38530872949, 530.65417294110],
[0.577, 6.09100925678, 2531.13495725280],
[0.620, 3.01917904435, 902.70518605380],
[0.722, 5.18171159557, 1.48447270830],
[0.540, 3.78809230820, 2957.73314812880],
[0.523, 3.63882376000, 437.64389113990],
[0.527, 5.80796427555, 3053.71237534660],
[0.488, 4.99103190309, 483.22054217860],
[0.557, 4.11381202161, 2854.64037391020],
[0.492, 0.76371083106, 1603.29998928540],
[0.487, 5.55383951779, 2627.11418447060],
[0.487, 5.86510858429, 724.83081326790],
[0.453, 0.61375011101, 1159.29331067010],
[0.450, 2.28121042355, 3060.82592234740],
[0.515, 4.78126059280, 447.79581952650],
[0.449, 4.70231576312, 934.94851496820],
[0.450, 1.91049508739, 597.35901666110],
[0.438, 6.01178917646, 3178.14579056760],
[0.494, 0.53844942275, 1354.43315884340],
[0.501, 5.51752195462, 2435.15573003500],
[0.432, 3.64903264921, 313.21047591890],
[0.435, 3.02449828967, 533.88375078860],
[0.426, 5.07945534339, 2524.02141025200],
[0.491, 3.59286364200, 230.56457082540],
[0.547, 0.34432090949, 1251.34038462480],
[0.503, 1.57454509207, 454.90936652730],
[0.486, 4.39351469958, 462.02291352810],
[0.524, 2.03003740296, 1279.79457262800],
[0.388, 5.58318013074, 731.94436026870],
[0.449, 1.11025492739, 56.62235130260],
[0.398, 5.19943284273, 3267.01147078460],
[0.416, 1.70821917336, 245.54242435240],
[0.379, 1.80234948769, 2655.56837247380],
[0.355, 1.65214516751, 78.71375183040],
[0.404, 1.72647262603, 1141.13406340540],
[0.335, 6.01254286794, 960.22130923370],
[0.331, 1.74086938716, 490.33408917940],
[0.401, 0.30034336462, 2332.06295581640],
[0.336, 2.64385574909, 1021.24889455140],
[0.389, 0.31259289221, 2413.81508903260],
[0.314, 5.73833529708, 1158.54255114470],
[0.313, 4.74363791106, 938.12990870590],
[0.333, 0.80112437148, 1585.14074202070],
[0.323, 3.52656245280, 3274.12501778540],
[0.395, 1.73181407631, 1593.00504854690],
[0.302, 4.64184749164, 1261.63532536330],
[0.325, 0.54991590409, 43.28902917830],
[0.293, 0.97977818746, 1585.89150154610],
[0.341, 2.80833606944, 1514.29129671650],
[0.304, 6.12522825214, 1262.38608488870],
[0.286, 2.89800423081, 530.21222995640],
[0.387, 0.46648572639, 1592.25428902150],
[0.285, 4.56394598052, 1268.74887236410],
[0.310, 4.69102289591, 76.26607127560],
[0.278, 5.49867187248, 280.96714700450],
[0.358, 5.45926487831, 113.38771495710],
[0.283, 1.09230506350, 1061.82961074400],
[0.326, 0.60265259639, 827.92358748650],
[0.284, 5.36580034539, 1165.65609814550],
[0.281, 5.54635461050, 3370.10424500320],
[0.269, 3.92616563946, 42.53826965290],
[0.275, 2.58465453365, 373.01422095920],
[0.357, 1.39391983207, 1493.09366806600],
[0.258, 5.96670694140, 1269.49963188950],
[0.259, 2.56026216784, 9146.79006902100],
[0.281, 2.74823090198, 4694.00295470760],
[0.281, 3.01324655940, 320.32402291970],
[0.272, 4.18504958920, 8624.21265092720],
[0.245, 1.24462798353, 252.65597135320],
[0.244, 2.02892764690, 3377.21779200400],
[0.324, 1.84851618413, 1289.94650101460],
[0.221, 6.22167997496, 3281.23856478620],
[0.238, 3.93371505401, 3171.03224356680],
[0.226, 5.94296271326, 224.34479570190],
[0.213, 3.68264234750, 1048.33622992530],
[0.216, 5.82941334164, 1567.73225428140],
[0.295, 4.70194747095, 3067.93946934820],
[0.206, 4.98184230959, 1357.61455258110],
[0.202, 1.32439444045, 4326.39340097380],
[0.227, 0.78540105705, 59.80374504030],
[0.237, 5.56926897693, 2943.50605412720],
[0.207, 0.07907015398, 5223.69391980220],
[0.199, 3.30501818656, 4120.20785253660],
[0.194, 5.95526916809, 84.93352695390],
[0.266, 1.58032565718, 983.11585891360],
[0.198, 4.31078641704, 4017.11507831800],
[0.198, 0.30166351366, 1166.40685767090],
[0.188, 0.90738705875, 135.33610313300],
[0.186, 0.69289672485, 92.79783348010],
[0.182, 1.18931462257, 1512.80682400820],
[0.191, 1.04146023518, 1884.12412393800],
[0.174, 6.13734594396, 3597.63043444280],
[0.189, 0.35191512844, 1372.59240610810],
[0.172, 4.35250972697, 1578.02719501990],
[0.173, 2.30241719278, 1176.70179840940],
[0.220, 1.06991056825, 2200.51599359460],
[0.186, 4.90511103807, 3583.40334044120],
[0.189, 0.24160744024, 1670.82502850000],
[0.206, 0.01485146863, 2730.20695868920],
[0.174, 1.83997277029, 746.92221379570],
[0.225, 3.13108099660, 630.33605875840],
[0.206, 5.22730929781, 3995.77443731560],
[0.169, 2.57956682688, 9161.01716302260],
[0.165, 1.51795928301, 4010.00153131720],
[0.181, 2.05055200822, 842.90144101350],
[0.181, 5.96554625357, 1578.77795454530],
[0.166, 1.55114863100, 1070.42763045310],
[0.157, 5.87839958880, 3914.02230409940],
[0.160, 0.43729819176, 2545.36205125440],
[0.168, 5.73975661792, 2847.52682690940],
[0.157, 2.25764581068, 850.01498801430],
[0.187, 0.64918748618, 842.15068148810],
[0.180, 1.88055488803, 685.47393735270],
[0.153, 4.15259684562, 4333.50694797460],
[0.154, 3.65536637158, 77734.01845962799],
[0.151, 3.17795437121, 3590.51688744200],
[0.155, 3.87623547990, 327.43756992050],
[0.171, 3.33647878498, 1912.57831194120],
[0.188, 4.53005359421, 1041.22268292450],
[0.134, 4.09921613445, 530.44172462000],
[0.123, 4.79543460218, 1098.73880610440],
[0.161, 2.02006564218, 860.30992875280],
[0.143, 2.40197278329, 529.16970023280],
[0.115, 1.55831212007, 9153.90361602180],
[0.106, 5.94313244357, 1057.89745748090],
[0.119, 5.10578428676, 1056.93424963440],
[0.100, 5.74974781049, 501.23677709140],
[0.094, 1.40134175492, 1059.33374607940],
[0.098, 3.79115318281, 497.44763618020],
[0.090, 4.09610113044, 1064.04779663520],
[0.102, 1.10442899544, 1969.20066324380],
[0.087, 0.58218477838, 1173.52040467170],
[0.109, 3.83745968299, 525.49817940060],
[0.094, 4.59915291355, 1059.43011429900],
[0.118, 6.11701561559, 1069.67687092770],
[0.107, 5.40509332689, 679.25416222920],
[0.089, 5.90037690244, 757.21715453420],
[0.078, 6.06217863109, 970.51624997220],
[0.080, 5.45470236239, 3163.91869656600],
[0.072, 5.65789862232, 1151.42900414390],
[0.080, 0.04539720100, 1080.72257119160],
[0.075, 4.26526686574, 1058.41872234270],
],
# L2
[
[47233.598, 4.32148323554, 7.11354700080],
[30629.053, 2.93021440216, 529.69096509460],
[38965.550, 0.00000000000, 0.00000000000],
[3189.317, 1.05504615595, 522.57741809380],
[2723.358, 3.41411526638, 1059.38193018920],
[2729.292, 4.84545481351, 536.80451209540],
[1721.069, 4.18734385158, 14.22709400160],
[383.258, 5.76790714387, 419.48464387520],
[367.498, 6.05509120409, 103.09277421860],
[377.524, 0.76048964872, 515.46387109300],
[337.386, 3.78644384244, 3.18139373770],
[308.200, 0.69356654052, 206.18554843720],
[218.408, 3.81389191353, 1589.07289528380],
[198.883, 5.33996443444, 1066.49547719000],
[197.445, 2.48356402053, 3.93215326310],
[146.230, 3.81373196838, 639.89728631400],
[155.862, 1.40642426467, 1052.26838318840],
[129.570, 5.83738872525, 412.37109687440],
[141.932, 1.63435169016, 426.59819087600],
[117.327, 1.41435462588, 625.67019231240],
[96.733, 4.03383427887, 110.20632121940],
[90.823, 1.10630629042, 95.97922721780],
[78.769, 4.63726131329, 543.91805909620],
[72.392, 2.21716670026, 735.87651353180],
[87.292, 2.52235174825, 632.78373931320],
[56.910, 3.12292059854, 213.29909543800],
[48.622, 1.67283791618, 309.27832265580],
[58.475, 0.83216317444, 199.07200143640],
[40.150, 4.02485444740, 21.34064100240],
[39.784, 0.62416945827, 323.50541665740],
[35.718, 2.32581247002, 728.76296653100],
[25.620, 2.51240623862, 1162.47470440780],
[29.255, 3.60838327799, 10.29494073850],
[23.591, 3.00532139306, 956.28915597060],
[27.814, 3.23992013743, 838.96928775040],
[25.993, 4.50118298290, 742.99006053260],
[25.194, 1.21868110687, 1045.15483618760],
[19.458, 4.29028644674, 532.87235883230],
[17.660, 0.80953941560, 508.35032409220],
[15.355, 5.81037986941, 1596.18644228460],
[17.058, 4.20001977723, 2118.76386037840],
[17.040, 1.83402146640, 526.50957135690],
[14.661, 3.99989622586, 117.31986822020],
[13.639, 1.80336677963, 302.16477565500],
[13.230, 2.51856643603, 88.86568021700],
[12.756, 4.36856232414, 1169.58825140860],
[15.292, 0.68174165476, 942.06206196900],
[10.986, 4.43586634639, 525.75881183150],
[13.920, 5.95169568482, 316.39186965660],
[9.437, 2.17684563456, 1155.36115740700],
[8.812, 3.29452783338, 220.41264243880],
[7.823, 5.75672228354, 846.08283475120],
[7.549, 2.70955516779, 533.62311835770],
[9.681, 1.71563161051, 1581.95934828300],
[8.690, 3.31924493607, 831.85574074960],
[6.285, 0.49939863541, 949.17560896980],
[6.685, 2.17560093281, 1265.56747862640],
[5.381, 6.00510875948, 405.25754987360],
[4.676, 1.40846192799, 1258.45393162560],
[4.421, 3.02360159274, 1692.16566950240],
[4.403, 5.47737266160, 433.71173787680],
[4.286, 5.07139951645, 1073.60902419080],
[4.201, 5.28560721767, 18.15924726470],
[3.933, 1.26665387164, 853.19638175200],
[5.351, 3.65320121089, 1272.68102562720],
[4.392, 2.27325303667, 1368.66025284500],
[3.482, 1.53983001273, 519.39602435610],
[2.745, 2.09685315627, 1478.86657406440],
[2.737, 1.06017230524, 1574.84580128220],
[2.897, 2.05128453665, 1361.54670584420],
[3.075, 0.99085727534, 191.95845443560],
[2.462, 2.37173605635, 1471.75302706360],
[2.203, 2.47960567714, 721.64941953020],
[2.096, 3.71482580504, 1485.98012106520],
[1.984, 1.88475229557, 1685.05212250160],
[2.274, 3.03360234351, 1148.24761040620],
[2.041, 6.17114556019, 330.61896365820],
[1.451, 4.72055072637, 32.24332891440],
[1.454, 5.14703918585, 1375.77379984580],
[1.447, 3.18833439444, 635.96513305090],
[1.403, 4.26712075104, 551.03160609700],
[1.420, 1.99288040133, 629.60234557550],
[1.269, 0.03300387779, 2125.87740737920],
[1.276, 2.26356919237, 1788.14489672020],
[1.189, 1.70223550488, 1677.93857550080],
[1.182, 2.18142313946, 1795.25844372100],
[1.366, 1.27629917215, 1038.04128918680],
[1.306, 4.76302079847, 1062.56332392690],
[1.109, 2.97787130235, 81.75213321620],
[1.027, 1.99236027398, 295.05122865420],
[1.349, 4.01621534182, 539.98590583310],
[1.025, 3.75336759986, 28.45418800320],
[0.977, 3.01355125761, 124.43341522100],
[1.290, 4.62594234857, 2648.45482547300],
[1.065, 5.06153058155, 1699.27921650320],
[0.965, 1.17716405513, 99.91138048090],
[1.021, 1.90712102660, 750.10360753340],
[0.923, 3.53450109212, 227.52618943960],
[1.059, 0.13532061468, 416.30325013750],
[0.836, 2.07492422755, 1056.20053645150],
[0.889, 1.75177808106, 1898.35121793960],
[0.772, 2.89217715561, 2008.55753915900],
[1.014, 2.80847772922, 1464.63948006280],
[0.820, 1.99735697577, 2111.65031337760],
[0.787, 4.91912237671, 1055.44977692610],
[0.743, 2.65209650690, 106.27416795630],
[0.705, 0.08006443278, 963.40270297140],
[0.724, 3.29664246938, 628.85158605010],
[0.791, 1.64655202110, 2001.44399215820],
[0.822, 2.74067639972, 618.55664531160],
[0.761, 1.26393500358, 1382.88734684660],
[0.650, 1.19590511216, 422.66603761290],
[0.677, 1.88476058357, 2104.53676637680],
[0.681, 5.47481665606, 5760.49843189760],
[0.681, 3.11621209674, 5746.27133789600],
[0.644, 4.68385640894, 611.44309831080],
[0.752, 3.03497138894, 2221.85663459700],
[0.641, 1.86274530783, 636.71589257630],
[0.614, 3.07677356670, 380.12776796000],
[0.635, 4.53916684689, 9676.48103411560],
[0.635, 0.61458805483, 9690.70812811720],
[0.822, 6.25170365084, 423.41679713830],
[0.762, 4.32362906505, 1802.37199072180],
[0.582, 0.84137872868, 1891.23767093880],
[0.558, 3.96171840325, 440.82528487760],
[0.624, 2.83657771014, 1905.46476494040],
[0.711, 3.43538032357, 824.74219374880],
[0.517, 1.10660016329, 107.02492748170],
[0.535, 1.55761050176, 1994.33044515740],
[0.501, 4.44389802599, 647.01083331480],
[0.414, 5.37130370397, 2228.97018159780],
[0.533, 2.54756313371, 1781.03134971940],
[0.393, 1.26351262287, 210.11770170030],
[0.433, 2.90103969634, 1063.31408345230],
[0.384, 1.36194621083, 203.00415469950],
[0.440, 1.46934545869, 2214.74308759620],
[0.424, 4.98974282486, 3178.14579056760],
[0.338, 2.72210106345, 2324.94940881560],
[0.332, 0.37505564414, 2655.56837247380],
[0.318, 6.11024720065, 934.94851496820],
[0.405, 3.51005860013, 2751.54759969160],
[0.388, 5.00609647265, 2015.67108615980],
[0.424, 4.29668654117, 5753.38488489680],
[0.328, 2.35571531981, 1251.34038462480],
[0.316, 0.16949503062, 1279.79457262800],
[0.345, 2.89328206121, 2957.73314812880],
[0.303, 1.63964826684, 2428.04218303420],
[0.328, 3.36132375845, 1141.13406340540],
[0.294, 2.48947693371, 2641.34127847220],
[0.350, 1.50537240918, 2317.83586181480],
[0.287, 1.69638214958, 2420.92863603340],
[0.272, 0.27466529753, 319.57326339430],
[0.303, 2.43034117616, 70.84944530420],
[0.251, 0.43544711316, 3259.89792378380],
[0.224, 4.49752269293, 5223.69391980220],
[0.272, 2.98590404673, 1457.52593306200],
[0.228, 5.47896916415, 1603.29998928540],
[0.288, 2.30146999217, 2854.64037391020],
[0.207, 5.94297320087, 9153.90361602180],
[0.243, 1.58604251447, 2744.43405269080],
[0.228, 1.28182702946, 2310.72231481400],
[0.224, 1.28623905132, 3060.82592234740],
[0.222, 0.63265553397, 3163.91869656600],
[0.242, 2.52382905368, 3274.12501778540],
[0.188, 6.00513627145, 92.04707395470],
[0.239, 1.93897157244, 2413.81508903260],
[0.214, 1.14529237568, 2531.13495725280],
[0.200, 3.42280996072, 99.16062095550],
[0.179, 0.53892926207, 2207.62954059540],
[0.177, 5.56545270243, 2332.06295581640],
[0.172, 1.38604067808, 945.99421523210],
[0.203, 0.41899069603, 2840.41327990860],
[0.231, 2.26353330460, 2097.42321937600],
[0.228, 3.82701076821, 113.38771495710],
[0.165, 4.08776703733, 6283.07584999140],
[0.202, 3.30429764992, 3067.93946934820],
[0.224, 3.69285208525, 2435.15573003500],
[0.214, 2.55756944911, 2538.24850425360],
[0.203, 2.24205059922, 67.66805156650],
[0.152, 5.48122906518, 10213.28554621100],
[0.191, 2.68685722531, 1773.91780271860],
[0.189, 2.95184620359, 732.69511979410],
[0.149, 1.98737542735, 1049.08698945070],
[0.163, 1.24084734609, 3053.71237534660],
[0.171, 2.34210749987, 1354.43315884340],
[0.112, 5.77407285790, 547.85021235930],
[0.124, 0.14001204498, 860.30992875280],
[0.086, 1.26924601636, 511.53171782990],
[0.114, 5.15982838070, 1592.25428902150],
[0.091, 1.48896790758, 1567.73225428140],
[0.086, 4.34444949905, 1069.67687092770],
],
# L3
[
[6501.665, 2.59862880482, 7.11354700080],
[1356.524, 1.34635886411, 529.69096509460],
[470.716, 2.47503977883, 14.22709400160],
[416.960, 3.24451243214, 536.80451209540],
[352.851, 2.97360159003, 522.57741809380],
[154.880, 2.07565585817, 1059.38193018920],
[86.771, 2.51431584316, 515.46387109300],
[33.538, 3.82633794497, 1066.49547719000],
[44.378, 0.00000000000, 0.00000000000],
[22.644, 2.98231326774, 543.91805909620],
[23.737, 1.27667172313, 412.37109687440],
[28.457, 2.44754756058, 206.18554843720],
[19.798, 2.10099934005, 639.89728631400],
[19.740, 1.40255938973, 419.48464387520],
[18.768, 1.59368403500, 103.09277421860],
[17.033, 2.30214681202, 21.34064100240],
[16.774, 2.59821460673, 1589.07289528380],
[16.214, 3.14521117299, 625.67019231240],
[16.055, 3.36030126297, 1052.26838318840],
[13.392, 2.75973892202, 95.97922721780],
[13.234, 2.53862244340, 199.07200143640],
[12.611, 6.26578110400, 426.59819087600],
[8.637, 2.26563256289, 110.20632121940],
[6.725, 3.42566433316, 309.27832265580],
[8.701, 1.76334960737, 10.29494073850],
[6.527, 4.03869562907, 728.76296653100],
[5.368, 5.25196153539, 323.50541665740],
[5.675, 2.52096417685, 508.35032409220],
[5.399, 2.91184687105, 1045.15483618760],
[3.996, 4.30290261177, 88.86568021700],
[3.857, 3.52381361552, 302.16477565500],
[3.774, 4.09125315146, 735.87651353180],
[3.269, 1.43175991274, 956.28915597060],
[2.783, 4.35817507670, 1596.18644228460],
[2.661, 1.25276590759, 213.29909543800],
[2.553, 2.23785673285, 117.31986822020],
[2.371, 2.89662409244, 742.99006053260],
[2.656, 5.01505839848, 838.96928775040],
[1.948, 2.77248294666, 1169.58825140860],
[2.279, 2.35581871230, 942.06206196900],
[1.474, 1.61011468581, 220.41264243880],
[1.457, 3.09381959396, 2118.76386037840],
[1.937, 5.01388256693, 831.85574074960],
[1.585, 1.40097680805, 405.25754987360],
[1.257, 3.97811260358, 1155.36115740700],
[1.227, 3.45959919972, 1073.60902419080],
[0.986, 3.39209446167, 532.87235883230],
[0.942, 2.70200385825, 191.95845443560],
[0.828, 1.48348768286, 632.78373931320],
[0.797, 1.10706688850, 1162.47470440780],
[0.822, 3.30295824153, 1258.45393162560],
[0.710, 5.89798771980, 853.19638175200],
[0.766, 3.66351539483, 1581.95934828300],
[0.722, 3.74673245797, 433.71173787680],
[0.663, 2.93063953915, 1574.84580128220],
[0.658, 3.52797311863, 525.75881183150],
[0.609, 4.14881313523, 721.64941953020],
[0.598, 4.69454609357, 81.75213321620],
[0.668, 1.96442971289, 1272.68102562720],
[0.515, 1.57251270902, 949.17560896980],
[0.658, 2.02329201466, 526.50957135690],
[0.517, 4.35827478516, 1368.66025284500],
[0.510, 4.95846155301, 1148.24761040620],
[0.507, 4.31396370095, 330.61896365820],
[0.567, 2.27813343743, 551.03160609700],
[0.480, 3.86758235988, 1361.54670584420],
[0.383, 0.24287136454, 611.44309831080],
[0.434, 2.95461755540, 1038.04128918680],
[0.377, 1.42957648215, 124.43341522100],
[0.391, 4.07770324592, 1471.75302706360],
[0.385, 4.70295179800, 519.39602435610],
[0.428, 2.22472522305, 539.98590583310],
[0.343, 4.83463725823, 2125.87740737920],
[0.394, 4.52891996323, 1464.63948006280],
[0.305, 2.02797683648, 1485.98012106520],
[0.283, 0.97461612169, 1905.46476494040],
[0.276, 3.83552772064, 1062.56332392690],
[0.351, 2.06334334462, 533.62311835770],
[0.304, 3.93228052293, 1685.05212250160],
[0.322, 3.54763044791, 846.08283475120],
[0.345, 4.18332148409, 1788.14489672020],
[0.253, 3.12703531516, 1994.33044515740],
[0.257, 1.05361498985, 1478.86657406440],
[0.232, 1.69999081817, 1692.16566950240],
[0.225, 2.51624149780, 1891.23767093880],
[0.217, 4.58512911216, 963.40270297140],
[0.277, 3.63353707701, 1677.93857550080],
[0.242, 2.90163762388, 2310.72231481400],
[0.211, 3.96419403991, 295.05122865420],
[0.199, 5.17046500750, 618.55664531160],
[0.256, 4.19052619061, 1781.03134971940],
[0.192, 0.81556540966, 2221.85663459700],
[0.187, 3.49895198981, 2648.45482547300],
[0.208, 4.11838429822, 2097.42321937600],
[0.183, 3.30680692414, 1699.27921650320],
[0.231, 2.54516792766, 1375.77379984580],
[0.189, 5.74277274755, 2627.11418447060],
[0.214, 5.48031974537, 1354.43315884340],
[0.220, 3.87471989410, 2104.53676637680],
[0.171, 6.10827209399, 1382.88734684660],
[0.184, 5.98415847544, 750.10360753340],
[0.171, 5.25744961028, 824.74219374880],
[0.151, 4.30799091626, 2001.44399215820],
[0.140, 4.27089466070, 1265.56747862640],
[0.097, 4.67188056608, 647.01083331480],
[0.088, 2.43775210355, 440.82528487760],
[0.075, 3.93105183253, 1055.44977692610],
[0.079, 1.88533153220, 934.94851496820],
[0.077, 3.80503143236, 1603.29998928540],
],
# L4
[
[669.483, 0.85282421090, 7.11354700080],
[99.961, 0.74258947751, 14.22709400160],
[114.019, 3.14159265359, 0.00000000000],
[50.024, 1.65346208248, 536.80451209540],
[43.585, 5.82026386621, 529.69096509460],
[31.813, 4.85829986650, 522.57741809380],
[14.742, 4.29061635784, 515.46387109300],
[8.899, 0.71478520741, 1059.38193018920],
[4.957, 1.29502259434, 543.91805909620],
[4.484, 2.31715516627, 1066.49547719000],
[4.251, 0.48326797501, 21.34064100240],
[3.100, 3.00245542678, 412.37109687440],
[2.055, 0.39858940218, 639.89728631400],
[1.762, 4.90536207307, 625.67019231240],
[1.902, 4.25925620271, 199.07200143640],
[1.695, 4.26147580803, 206.18554843720],
[1.375, 5.25546955667, 1052.26838318840],
[1.203, 4.71614633845, 95.97922721780],
[1.086, 1.28604571172, 1589.07289528380],
[0.982, 4.77990073662, 1045.15483618760],
[0.935, 6.05847062188, 88.86568021700],
[0.916, 5.77537499431, 728.76296653100],
[0.890, 4.55299189579, 426.59819087600],
[0.784, 3.40161567950, 419.48464387520],
[0.768, 3.54672049322, 103.09277421860],
[0.670, 0.52223307700, 110.20632121940],
[0.415, 5.22809480633, 302.16477565500],
[0.393, 6.24184621807, 956.28915597060],
[0.381, 5.25466966040, 309.27832265580],
[0.421, 0.59561318533, 117.31986822020],
[0.346, 4.78348312106, 508.35032409220],
[0.319, 3.47979828725, 323.50541665740],
[0.331, 2.95893485883, 1596.18644228460],
[0.295, 4.32713459459, 942.06206196900],
[0.319, 0.47990052824, 831.85574074960],
[0.251, 1.79898001222, 1073.60902419080],
[0.212, 0.43917684084, 220.41264243880],
[0.188, 1.12654974776, 1169.58825140860],
[0.188, 2.16135407548, 1361.54670584420],
[0.180, 3.43266428069, 1148.24761040620],
[0.164, 1.92864127211, 2118.76386037840],
[0.157, 3.02963907392, 1272.68102562720],
[0.093, 5.60436000012, 1581.95934828300],
[0.085, 5.02317256200, 1155.36115740700],
[0.075, 3.13198879608, 632.78373931320],
],
# L5
[
[49.577, 5.25658966184, 7.11354700080],
[15.761, 5.25126837478, 14.22709400160],
[4.343, 0.01461869263, 536.80451209540],
[1.526, 1.09739911439, 522.57741809380],
[0.728, 5.85949047619, 543.91805909620],
[0.694, 0.87382487754, 515.46387109300],
[0.845, 3.14159265359, 0.00000000000],
[0.456, 0.81521692852, 1066.49547719000],
[0.293, 5.62909357048, 1059.38193018920],
[0.090, 0.21178119710, 529.69096509460],
],
]
"""This table contains Jupiter'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 426-430."""
VSOP87_B = [
# B0
[
[2268615.703, 3.55852606718, 529.69096509460],
[109971.634, 3.90809347389, 1059.38193018920],
[110090.358, 0.00000000000, 0.00000000000],
[8101.427, 3.60509573368, 522.57741809380],
[6043.996, 4.25883108794, 1589.07289528380],
[6437.782, 0.30627121409, 536.80451209540],
[1106.880, 2.98534421928, 1162.47470440780],
[941.651, 2.93619072405, 1052.26838318840],
[894.088, 1.75447429921, 7.11354700080],
[767.280, 2.15473594060, 632.78373931320],
[944.328, 1.67522288396, 426.59819087600],
[684.220, 3.67808770098, 213.29909543800],
[629.223, 0.64343282328, 1066.49547719000],
[835.861, 5.17881973234, 103.09277421860],
[531.670, 2.70305954352, 110.20632121940],
[558.524, 0.01354830508, 846.08283475120],
[464.449, 1.17337249185, 949.17560896980],
[431.072, 2.60825000494, 419.48464387520],
[351.433, 4.61062990714, 2118.76386037840],
[123.148, 3.34968181384, 1692.16566950240],
[115.038, 5.04892295442, 316.39186965660],
[132.160, 4.77816990670, 742.99006053260],
[103.402, 2.31878999565, 1478.86657406440],
[116.379, 1.38688232033, 323.50541665740],
[102.420, 3.15293785436, 1581.95934828300],
[103.762, 3.70103838110, 515.46387109300],
[78.650, 3.98318653238, 1265.56747862640],
[69.935, 2.56006216424, 956.28915597060],
[55.597, 0.37500753017, 1375.77379984580],
[51.986, 0.99007119033, 1596.18644228460],
[55.194, 0.40176412035, 525.75881183150],
[63.456, 4.50073574333, 735.87651353180],
[49.691, 0.18649893085, 543.91805909620],
[48.831, 3.57260550671, 533.62311835770],
[28.353, 1.53532744749, 625.67019231240],
[29.209, 5.43145863011, 206.18554843720],
[23.255, 5.95197992848, 838.96928775040],
[22.841, 6.19262787685, 532.87235883230],
[23.202, 4.06473368575, 526.50957135690],
[24.436, 6.10947656959, 1169.58825140860],
[21.116, 4.96322972735, 2648.45482547300],
[17.879, 3.08704395969, 1795.25844372100],
[16.234, 4.83515727869, 1368.66025284500],
[21.314, 2.69476951059, 1045.15483618760],
[15.740, 1.15130330106, 942.06206196900],
[17.325, 1.61550009206, 14.22709400160],
[13.396, 2.30539585502, 853.19638175200],
[11.904, 3.09811974536, 2111.65031337760],
[11.734, 2.83006431723, 2008.55753915900],
[11.291, 0.98957560201, 433.71173787680],
[11.830, 4.76527836803, 309.27832265580],
[10.702, 3.70181397065, 2221.85663459700],
[10.815, 5.81958878617, 1272.68102562720],
[13.505, 3.28126975760, 1155.36115740700],
[10.179, 2.58691128827, 117.31986822020],
[10.632, 5.23487936086, 95.97922721780],
[8.771, 0.40456546655, 220.41264243880],
[7.439, 2.94638292086, 412.37109687440],
[6.151, 2.69100382247, 380.12776796000],
[5.028, 0.72750312028, 1055.44977692610],
[4.939, 0.73756716762, 1905.46476494040],
[5.421, 4.08612438558, 1685.05212250160],
[5.936, 4.32059910537, 1063.31408345230],
[4.737, 4.09303016850, 527.24328453980],
[4.010, 0.51530008355, 1073.60902419080],
[4.709, 1.84067645204, 984.60033162190],
[3.974, 1.33608029246, 2125.87740737920],
[3.762, 3.58647039394, 529.73914920440],
[4.731, 6.16377350841, 532.13864564940],
[4.666, 5.88762905802, 639.89728631400],
[3.763, 0.38865925413, 529.64278098480],
[3.409, 4.05398247269, 1898.35121793960],
[3.457, 3.43865563497, 1485.98012106520],
[4.229, 2.23767157901, 74.78159856730],
[3.091, 0.16470256025, 1699.27921650320],
[2.975, 0.72268908074, 530.65417294110],
[3.162, 1.25048416420, 330.61896365820],
[2.727, 4.37679213321, 149.56319713460],
[2.837, 0.05987107395, 1439.50969814920],
[2.983, 3.25251207220, 528.72775724810],
[2.232, 0.26149880534, 1062.56332392690],
[2.464, 1.16913304420, 453.42489381900],
[2.596, 3.30510149086, 2324.94940881560],
[1.988, 2.85269577619, 1574.84580128220],
[2.527, 5.94458202950, 909.81873305460],
[2.269, 1.30379329597, 3.93215326310],
[1.742, 4.49909767044, 1258.45393162560],
[1.714, 4.12945878208, 2001.44399215820],
[2.029, 3.97938086639, 1056.20053645150],
[1.667, 0.36037092553, 10213.28554621100],
[1.579, 6.11640144795, 1802.37199072180],
[1.393, 3.69324470827, 2214.74308759620],
[1.604, 1.98841031703, 38.13303563780],
[1.325, 1.74025919863, 529.16970023280],
[1.451, 2.39804501178, 2428.04218303420],
[1.594, 2.07556780757, 1021.24889455140],
[1.320, 1.33770977126, 618.55664531160],
[1.346, 3.27591492540, 2641.34127847220],
[1.230, 0.19552728220, 305.34616939270],
[1.223, 2.86681556337, 1382.88734684660],
[1.324, 2.23549334986, 530.21222995640],
[1.056, 3.80579750957, 76.26607127560],
[1.050, 4.68011652614, 1788.14489672020],
[1.226, 5.34003255221, 3178.14579056760],
[1.009, 3.19608028376, 2538.24850425360],
[1.266, 3.04704446731, 604.47256366190],
[0.954, 3.86932544808, 728.76296653100],
[1.124, 1.59560367480, 3.18139373770],
[0.978, 0.25223689838, 983.11585891360],
[0.948, 0.21552742733, 750.10360753340],
[0.946, 3.93927748120, 508.35032409220],
[0.920, 1.14672086939, 963.40270297140],
[0.817, 5.93809619876, 831.85574074960],
[0.770, 2.96062737592, 526.77020378780],
[1.017, 5.55711112145, 199.07200143640],
[0.761, 1.38163787157, 532.61172640140],
[0.726, 3.98337964395, 2317.83586181480],
[0.862, 0.87975657414, 490.33408917940],
[0.868, 3.44331872364, 569.04784100980],
[0.711, 4.11107052823, 2751.54759969160],
[0.708, 0.33555577415, 528.94020556920],
[0.708, 4.00539820601, 530.44172462000],
[0.656, 4.39568451439, 519.39602435610],
[0.801, 4.03984430862, 1364.72809958190],
[0.679, 1.18645749024, 525.49817940060],
[0.645, 5.10510349996, 1361.54670584420],
[0.668, 3.15607509055, 533.88375078860],
[0.663, 0.73722024843, 5223.69391980220],
[0.663, 1.57092786811, 6283.07584999140],
[0.543, 0.26376529935, 227.52618943960],
[0.525, 6.22318693939, 539.98590583310],
[0.513, 4.98337900151, 302.16477565500],
[0.544, 2.22227019273, 2744.43405269080],
[0.532, 2.62425372687, 99.16062095550],
[0.602, 1.56074089013, 454.90936652730],
[0.518, 0.26343805959, 551.03160609700],
[0.516, 1.09376390349, 934.94851496820],
[0.659, 0.62560671589, 1512.80682400820],
[0.524, 0.64710955846, 524.06189080210],
[0.516, 3.69478866795, 535.32003938710],
[0.491, 3.63039940597, 2531.13495725280],
[0.570, 0.61976758791, 540.73666535850],
[0.496, 2.19398015038, 1514.29129671650],
[0.532, 0.20040217534, 525.02509864860],
[0.493, 0.39160693598, 224.34479570190],
[0.449, 0.62392433691, 529.53090640020],
[0.449, 3.71676131146, 529.85102378900],
[0.450, 5.02467015031, 1048.33622992530],
[0.428, 5.44804660290, 11.04570026390],
[0.499, 4.13924061941, 534.35683154060],
[0.528, 1.76471074936, 524.27433912320],
[0.454, 4.53321742354, 1056.93424963440],
[0.520, 2.57406093768, 535.10759106600],
[0.398, 1.40345870113, 960.22130923370],
[0.457, 4.17708652827, 2104.53676637680],
[0.505, 5.36536256321, 1057.89745748090],
[0.535, 4.80455380313, 1593.00504854690],
[0.415, 0.96548127237, 2435.15573003500],
[0.519, 0.54543519483, 1061.82961074400],
[0.359, 4.02704454075, 1059.43011429900],
[0.356, 2.66818105522, 835.03713448730],
[0.443, 5.27513700376, 1.48447270830],
[0.358, 5.94423960514, 440.82528487760],
[0.471, 6.05791940453, 1471.75302706360],
[0.386, 2.15984900214, 9153.90361602180],
[0.424, 2.70929670030, 1038.04128918680],
[0.359, 0.82922836987, 1059.33374607940],
[0.310, 0.88102053266, 529.90341341570],
[0.310, 3.45966511571, 529.47851677350],
[0.300, 3.70331799503, 2634.22773147140],
[0.292, 2.63594456361, 415.55249061210],
[0.279, 1.60669121578, 643.82943957710],
[0.291, 5.83134071820, 1148.24761040620],
[0.370, 5.71572992274, 531.17543780290],
[0.268, 5.39275891813, 1891.23767093880],
[0.275, 3.34108666036, 518.64526483070],
[0.269, 1.06051406954, 1585.14074202070],
[0.306, 2.50289017370, 511.53171782990],
[0.295, 1.84394223501, 547.85021235930],
[0.254, 2.98312992496, 1134.16352875650],
[0.289, 1.86070918711, 21.34064100240],
[0.265, 4.93075479744, 679.25416222920],
[0.250, 0.42860925124, 1969.20066324380],
[0.308, 2.67237933272, 2957.73314812880],
[0.313, 4.88085697819, 528.20649238630],
[0.222, 4.78828764413, 514.71311156760],
[0.221, 4.32763468981, 1677.93857550080],
[0.217, 3.46278526461, 2950.61960112800],
[0.216, 0.52207667980, 2228.97018159780],
[0.214, 5.83569926578, 544.66881862160],
[0.283, 2.88709716090, 35.42472265210],
[0.272, 1.65708415457, 3060.82592234740],
[0.234, 1.68821537711, 2655.56837247380],
[0.205, 3.36186888290, 2847.52682690940],
[0.264, 3.62722625694, 2420.92863603340],
[0.191, 4.26821147044, 430.53034413910],
[0.179, 3.91470663005, 3340.61242669980],
[0.180, 0.04531671003, 387.24131496080],
[0.241, 4.03927631611, 494.26624244250],
[0.176, 4.26298906325, 672.14061522840],
[0.187, 2.72587420586, 299.12639426920],
[0.234, 1.34474827450, 173.94221952280],
[0.171, 0.85473611718, 1603.29998928540],
[0.224, 0.33130232434, 565.11568774670],
[0.200, 1.27632489123, 39.35687591520],
[0.170, 4.96479470273, 1464.63948006280],
[0.211, 1.00937080256, 523.54062594030],
[0.210, 3.75793720248, 2854.64037391020],
[0.162, 5.87784787295, 3480.31056622260],
[0.163, 4.62850343495, 2015.67108615980],
[0.191, 3.33159283750, 535.84130424890],
[0.151, 1.17096741034, 1060.34513803570],
[0.160, 1.81852636004, 312.45971639350],
[0.158, 2.59595816107, 529.43033266370],
[0.158, 1.74472748730, 529.95159752550],
[0.173, 3.62399350412, 230.56457082540],
[0.142, 0.70435921398, 522.52923398400],
[0.144, 5.35763122430, 107.02492748170],
[0.144, 6.13954848857, 1158.54255114470],
[0.178, 0.27566275049, 3906.90875709860],
[0.126, 5.14832919826, 2207.62954059540],
[0.126, 3.41994798109, 2.44768055480],
[0.127, 0.39825164051, 70.84944530420],
[0.123, 4.77865550523, 2524.02141025200],
[0.123, 0.46184813516, 647.01083331480],
[0.144, 3.60261852727, 1058.41872234270],
[0.158, 3.76231915252, 92.04707395470],
[0.119, 4.08266911415, 1585.89150154610],
[0.125, 2.35496721797, 3163.91869656600],
[0.122, 3.21027426317, 3377.21779200400],
[0.121, 3.39770381916, 18.15924726470],
[0.131, 1.67926417552, 1289.94650101460],
[0.115, 2.35735471566, 1550.93985964600],
[0.126, 2.40833814513, 106.27416795630],
[0.131, 1.37610474529, 1023.95720753710],
[0.121, 1.60252617273, 10.29494073850],
[0.121, 0.61420823557, 1592.25428902150],
[0.135, 3.60177675518, 124.43341522100],
[0.137, 2.41724947062, 3274.12501778540],
[0.129, 0.09702914345, 2332.06295581640],
[0.093, 4.88949890397, 1098.73880610440],
[0.106, 5.18592950792, 2281.23049651060],
[0.114, 2.96523316419, 1166.40685767090],
[0.092, 1.65166124027, 860.30992875280],
[0.102, 3.64093193142, 3171.03224356680],
[0.103, 1.63066232967, 1894.41906467650],
[0.080, 0.38766601876, 4694.00295470760],
[0.074, 3.86865238736, 3067.93946934820],
[0.095, 1.66362447044, 1151.42900414390],
],
# B1
[
[177351.787, 5.70166488486, 529.69096509460],
[3230.171, 5.77941619340, 1059.38193018920],
[3081.364, 5.47464296527, 522.57741809380],
[2211.914, 4.73477480209, 536.80451209540],
[1694.232, 3.14159265359, 0.00000000000],
[346.445, 4.74595174109, 1052.26838318840],
[234.264, 5.18856099929, 1066.49547719000],
[196.154, 6.18554286642, 7.11354700080],
[150.468, 3.92721226087, 1589.07289528380],
[114.128, 3.43897271830, 632.78373931320],
[96.667, 2.91426304090, 949.17560896980],
[76.599, 2.50522188662, 103.09277421860],
[81.671, 5.07666097497, 1162.47470440780],
[76.572, 0.61288981445, 419.48464387520],
[73.875, 5.49958292155, 515.46387109300],
[49.915, 3.94799616572, 735.87651353180],
[60.544, 5.44740084359, 213.29909543800],
[36.561, 4.69828392839, 543.91805909620],
[46.032, 0.53850360901, 110.20632121940],
[45.123, 1.89516645239, 846.08283475120],
[36.019, 6.10952578764, 316.39186965660],
[31.975, 4.92452714629, 1581.95934828300],
[21.015, 5.62957731410, 1596.18644228460],
[23.156, 5.84829490183, 323.50541665740],
[24.719, 3.94107395247, 2118.76386037840],
[17.274, 5.65310656429, 533.62311835770],
[16.521, 5.89840100621, 526.50957135690],
[16.698, 5.66663034948, 1265.56747862640],
[15.815, 4.43314786393, 1045.15483618760],
[13.398, 4.30179033605, 532.87235883230],
[11.744, 1.80990486955, 956.28915597060],
[11.925, 4.30094564154, 525.75881183150],
[9.514, 2.02589667166, 206.18554843720],
[10.542, 6.15533910933, 14.22709400160],
[8.414, 3.92910450340, 1478.86657406440],
[8.099, 4.20152809071, 1169.58825140860],
[7.712, 2.99160389601, 942.06206196900],
[8.825, 1.55897920307, 426.59819087600],
[8.884, 4.87430124264, 1155.36115740700],
[7.793, 3.84684930196, 625.67019231240],
[5.646, 3.40915964493, 639.89728631400],
[4.615, 0.83374662294, 117.31986822020],
[4.020, 5.50502127885, 433.71173787680],
[3.704, 0.90226777963, 95.97922721780],
[3.859, 0.69640284662, 853.19638175200],
[3.091, 5.09115860882, 1073.60902419080],
[3.360, 5.10133284081, 1692.16566950240],
[2.892, 4.90418916660, 220.41264243880],
[2.772, 5.09066125724, 2111.65031337760],
[2.425, 3.74438653232, 742.99006053260],
[2.558, 5.46955948791, 1795.25844372100],
[2.466, 4.22278355430, 2648.45482547300],
[1.968, 0.57192251841, 309.27832265580],
[1.794, 4.60765219417, 1272.68102562720],
[1.822, 1.98842964323, 1375.77379984580],
[1.703, 6.12660562937, 2125.87740737920],
[2.011, 5.00936865256, 412.37109687440],
[1.645, 0.08830372958, 1063.31408345230],
[1.875, 5.81006158403, 330.61896365820],
[1.741, 4.58650290431, 1574.84580128220],
[1.529, 5.81660291389, 1258.45393162560],
[1.916, 0.85150399517, 1368.66025284500],
[1.614, 4.36839107221, 728.76296653100],
[1.510, 2.79374165455, 1485.98012106520],
[1.333, 4.84260898693, 1062.56332392690],
[1.359, 5.16511980864, 838.96928775040],
[1.165, 5.66275740881, 508.35032409220],
[1.092, 4.68797557406, 1699.27921650320],
[1.438, 5.78105679279, 1056.20053645150],
[1.083, 3.99886917926, 1471.75302706360],
[1.002, 4.79949608524, 1055.44977692610],
[0.749, 6.14400862030, 519.39602435610],
[0.657, 5.63765568876, 1898.35121793960],
[0.702, 5.04126574492, 1685.05212250160],
[0.607, 3.15707515246, 618.55664531160],
[0.587, 1.37658820775, 199.07200143640],
[0.552, 4.80657729450, 551.03160609700],
[0.494, 4.43417307482, 539.98590583310],
[0.517, 0.05161181997, 3.18139373770],
[0.469, 3.81715950042, 2008.55753915900],
[0.415, 1.34693184108, 1382.88734684660],
[0.382, 4.86764073919, 227.52618943960],
[0.473, 1.72405831407, 532.13864564940],
[0.458, 4.44604993015, 1038.04128918680],
[0.376, 2.23190744786, 529.64278098480],
[0.451, 3.75869883836, 984.60033162190],
[0.376, 5.42971857629, 529.73914920440],
[0.389, 1.92698506631, 525.02509864860],
[0.364, 3.35456685746, 2221.85663459700],
[0.476, 5.93625415892, 527.24328453980],
[0.383, 6.12255867339, 149.56319713460],
[0.301, 4.09378934049, 440.82528487760],
[0.310, 5.58150418981, 2428.04218303420],
[0.282, 4.85996662231, 1788.14489672020],
[0.298, 5.09589374634, 528.72775724810],
[0.340, 4.56537070220, 750.10360753340],
[0.272, 2.35346960340, 534.35683154060],
[0.360, 3.91050161665, 74.78159856730],
[0.299, 1.43093538841, 909.81873305460],
[0.297, 2.56584512211, 530.65417294110],
[0.235, 4.81644489422, 535.10759106600],
[0.306, 0.68420442848, 380.12776796000],
[0.236, 4.63162956792, 526.77020378780],
[0.270, 0.18549916939, 21.34064100240],
[0.288, 4.26655874393, 1802.37199072180],
[0.196, 5.35950443033, 2214.74308759620],
[0.190, 4.54615193260, 2104.53676637680],
[0.193, 4.35426216497, 511.53171782990],
[0.178, 4.51895208036, 3178.14579056760],
[0.194, 0.57050756837, 1361.54670584420],
[0.200, 1.48040474749, 302.16477565500],
[0.168, 5.40141749419, 524.27433912320],
[0.152, 0.68077486546, 1905.46476494040],
[0.149, 1.06678990744, 831.85574074960],
[0.182, 3.62401009613, 38.13303563780],
[0.176, 5.64331384323, 963.40270297140],
[0.184, 4.48850356629, 604.47256366190],
[0.133, 5.45026366125, 2641.34127847220],
[0.143, 2.21577268292, 1439.50969814920],
[0.130, 4.88155705493, 2531.13495725280],
[0.129, 6.15206333598, 547.85021235930],
[0.133, 5.43193972385, 1603.29998928540],
[0.133, 3.49297492409, 529.16970023280],
[0.132, 3.98820790955, 530.21222995640],
[0.118, 5.38352943814, 1891.23767093880],
[0.133, 5.65694269884, 76.26607127560],
[0.145, 2.94976686191, 454.90936652730],
[0.115, 3.29206553804, 3.93215326310],
[0.102, 4.48856749557, 2001.44399215820],
[0.106, 6.08434275898, 10.29494073850],
[0.093, 5.84737771840, 2324.94940881560],
[0.101, 0.15815934254, 2655.56837247380],
[0.115, 3.59221021604, 2015.67108615980],
[0.103, 4.70399583323, 305.34616939270],
[0.084, 0.44180206332, 1593.00504854690],
[0.092, 2.44863388631, 490.33408917940],
[0.087, 6.23817512863, 6283.07584999140],
[0.095, 3.30154605532, 2317.83586181480],
[0.072, 1.90578907085, 528.94020556920],
[0.072, 5.57619428876, 530.44172462000],
[0.078, 5.97323507836, 1585.89150154610],
],
# B2
[
[8094.051, 1.46322843658, 529.69096509460],
[742.415, 0.95691639003, 522.57741809380],
[813.244, 3.14159265359, 0.00000000000],
[398.951, 2.89888666447, 536.80451209540],
[342.226, 1.44683789727, 1059.38193018920],
[73.948, 0.40724675866, 1052.26838318840],
[46.151, 3.48036895772, 1066.49547719000],
[29.314, 0.99088831805, 515.46387109300],
[29.717, 1.92504171329, 1589.07289528380],
[22.753, 4.27124052435, 7.11354700080],
[13.916, 2.92242387338, 543.91805909620],
[12.067, 5.22168932482, 632.78373931320],
[10.703, 4.88024222475, 949.17560896980],
[6.078, 6.21089108431, 1045.15483618760],
[5.935, 0.52977760072, 1581.95934828300],
[5.037, 1.43444929374, 526.50957135690],
[4.564, 0.91811732585, 1162.47470440780],
[4.547, 4.01953745202, 1596.18644228460],
[5.098, 6.03169795231, 735.87651353180],
[3.593, 4.54080164408, 110.20632121940],
[3.443, 1.38618954572, 533.62311835770],
[3.277, 4.39650286553, 14.22709400160],
[3.407, 0.42275631534, 419.48464387520],
[2.904, 2.06041641723, 316.39186965660],
[2.541, 3.98323842017, 323.50541665740],
[3.113, 2.48079280193, 2118.76386037840],
[3.061, 2.39880866911, 532.87235883230],
[2.155, 4.77990637140, 942.06206196900],
[2.143, 3.88727338786, 426.59819087600],
[2.252, 0.37196434120, 1155.36115740700],
[2.019, 3.89985000464, 846.08283475120],
[1.857, 1.19658907851, 103.09277421860],
[1.683, 1.42264195434, 1265.56747862640],
[2.313, 0.87671613055, 213.29909543800],
[1.443, 2.38565505909, 1169.58825140860],
[1.823, 5.80106463776, 625.67019231240],
[1.728, 2.24114678267, 525.75881183150],
[1.198, 0.03252059731, 956.28915597060],
[1.138, 3.46420904745, 1073.60902419080],
[1.086, 5.35279146700, 117.31986822020],
[0.840, 2.89946334223, 95.97922721780],
[0.746, 5.53017890231, 1478.86657406440],
[0.944, 4.05587053500, 206.18554843720],
[0.758, 3.74770617289, 433.71173787680],
[0.673, 1.26396626349, 508.35032409220],
[0.889, 6.07878453176, 728.76296653100],
[0.600, 1.82954494089, 639.89728631400],
[0.589, 1.23625943417, 1258.45393162560],
[0.619, 0.67923057477, 838.96928775040],
[0.566, 5.36336098734, 742.99006053260],
[0.648, 5.32990375008, 853.19638175200],
[0.553, 3.15511946637, 220.41264243880],
[0.432, 1.03719283016, 1692.16566950240],
[0.435, 1.65056479007, 519.39602435610],
[0.430, 1.41830384501, 412.37109687440],
[0.431, 2.20986254651, 1368.66025284500],
[0.415, 4.35372561905, 330.61896365820],
[0.438, 0.16552277290, 1574.84580128220],
[0.312, 4.50639455819, 2125.87740737920],
[0.280, 3.01441283033, 551.03160609700],
[0.309, 0.67399908949, 2111.65031337760],
[0.301, 3.06868080871, 1062.56332392690],
[0.236, 1.94696842200, 1485.98012106520],
[0.235, 3.41850395941, 199.07200143640],
[0.246, 2.61803442505, 309.27832265580],
[0.238, 2.56643737684, 539.98590583310],
[0.248, 2.96997778167, 2648.45482547300],
[0.209, 5.82481690851, 1471.75302706360],
[0.205, 1.20202002469, 1056.20053645150],
[0.188, 0.97113663101, 1685.05212250160],
[0.137, 2.91203499563, 1699.27921650320],
[0.131, 1.79274504072, 1063.31408345230],
[0.161, 1.05926568614, 1795.25844372100],
[0.112, 2.62660288825, 440.82528487760],
[0.110, 3.56263668146, 227.52618943960],
[0.114, 6.13907482464, 1038.04128918680],
[0.103, 4.64287101040, 3.18139373770],
[0.123, 4.81268110532, 21.34064100240],
[0.102, 4.27603827970, 1375.77379984580],
[0.089, 1.22926014128, 1898.35121793960],
[0.080, 0.62129648755, 831.85574074960],
],
# B3
[
[251.624, 3.38087923084, 529.69096509460],
[121.738, 2.73311837200, 522.57741809380],
[48.694, 1.03689996685, 536.80451209540],
[10.988, 2.31463561347, 1052.26838318840],
[8.067, 2.76729757621, 515.46387109300],
[6.205, 1.78115827370, 1066.49547719000],
[7.287, 4.25268318975, 1059.38193018920],
[3.627, 1.13028917221, 543.91805909620],
[2.798, 3.14159265359, 0.00000000000],
[1.898, 2.28934054087, 7.11354700080],
[1.643, 1.77507208483, 1045.15483618760],
[0.945, 0.45261136388, 632.78373931320],
[0.758, 0.30577920142, 949.17560896980],
[0.731, 2.63748223583, 14.22709400160],
[0.876, 0.32927768725, 1589.07289528380],
[0.678, 2.36909615348, 1581.95934828300],
[0.623, 2.48056213600, 1596.18644228460],
[0.736, 1.52532370632, 735.87651353180],
[0.499, 3.67985494258, 419.48464387520],
[0.454, 0.26977404624, 942.06206196900],
[0.453, 3.18232334886, 526.50957135690],
[0.409, 2.88147337106, 110.20632121940],
[0.347, 5.76244285870, 103.09277421860],
[0.310, 2.98017326384, 508.35032409220],
[0.321, 4.40642025933, 532.87235883230],
[0.300, 1.66936571536, 625.67019231240],
[0.295, 1.75924202728, 1073.60902419080],
[0.282, 3.11087801399, 533.62311835770],
[0.263, 0.55255030187, 426.59819087600],
[0.208, 2.17540496886, 1155.36115740700],
[0.183, 4.34670868038, 525.75881183150],
[0.180, 6.07777744541, 639.89728631400],
[0.159, 2.60843864402, 1162.47470440780],
[0.117, 4.70141431381, 95.97922721780],
[0.107, 5.48942805114, 433.71173787680],
[0.105, 3.75192101775, 316.39186965660],
[0.130, 1.37897716939, 323.50541665740],
[0.094, 3.05797832024, 1265.56747862640],
[0.114, 3.75170981478, 117.31986822020],
[0.095, 0.54905691533, 1169.58825140860],
[0.088, 3.26874502411, 213.29909543800],
[0.098, 2.00704668688, 1574.84580128220],
],
# B4
[
[15.050, 4.52956999637, 522.57741809380],
[5.370, 4.47427159142, 529.69096509460],
[4.456, 5.43908581047, 536.80451209540],
[3.422, 0.00000000000, 0.00000000000],
[1.833, 4.51807036227, 515.46387109300],
[1.322, 4.20117611581, 1052.26838318840],
[0.755, 5.59451554966, 543.91805909620],
[0.512, 0.05803177475, 1066.49547719000],
[0.282, 3.66807771223, 1059.38193018920],
[0.147, 3.56490986181, 1045.15483618760],
[0.142, 5.69936472988, 7.11354700080],
[0.112, 1.16718383135, 14.22709400160],
],
# B5
[
[1.445, 0.09198554072, 522.57741809380],
[0.368, 0.00874408003, 515.46387109300],
[0.304, 3.27902945138, 536.80451209540],
[0.129, 0.33959775247, 529.69096509460],
[0.095, 1.29305954542, 543.91805909620],
],
]
"""This table contains Jupiter'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 430-432."""
VSOP87_R = [
# R0
[
[520887429.471, 0.00000000000, 0.00000000000],
[25209327.020, 3.49108640015, 529.69096509460],
[610599.902, 3.84115365602, 1059.38193018920],
[282029.465, 2.57419879933, 632.78373931320],
[187647.391, 2.07590380082, 522.57741809380],
[86792.941, 0.71001090609, 419.48464387520],
[72062.869, 0.21465694745, 536.80451209540],
[65517.227, 5.97995850843, 316.39186965660],
[29134.620, 1.67759243710, 103.09277421860],
[30135.275, 2.16132058449, 949.17560896980],
[23453.209, 3.54023147303, 735.87651353180],
[22283.710, 4.19362773546, 1589.07289528380],
[23947.340, 0.27457854894, 7.11354700080],
[13032.600, 2.96043055741, 1162.47470440780],
[9703.346, 1.90669572402, 206.18554843720],
[12749.004, 2.71550102862, 1052.26838318840],
[9161.431, 4.41352618935, 213.29909543800],
[7894.539, 2.47907551404, 426.59819087600],
[7057.978, 2.18184753111, 1265.56747862640],
[6137.755, 6.26417542514, 846.08283475120],
[5477.093, 5.65729325169, 639.89728631400],
[3502.519, 0.56531297394, 1066.49547719000],
[4136.890, 2.72219979684, 625.67019231240],
[4170.012, 2.01605033912, 515.46387109300],
[2499.966, 4.55182055941, 838.96928775040],
[2616.955, 2.00993967129, 1581.95934828300],
[1911.876, 0.85621927419, 412.37109687440],
[2127.644, 6.12751461750, 742.99006053260],
[1610.549, 3.08867789275, 1368.66025284500],
[1479.484, 2.68026191372, 1478.86657406440],
[1230.708, 1.89042979701, 323.50541665740],
[1216.810, 1.80171561024, 110.20632121940],
[961.072, 4.54876989805, 2118.76386037840],
[885.708, 4.14785948471, 533.62311835770],
[776.700, 3.67696954690, 728.76296653100],
[998.579, 2.87208940110, 309.27832265580],
[1014.959, 1.38673237666, 454.90936652730],
[727.162, 3.98824686402, 1155.36115740700],
[655.289, 2.79065604219, 1685.05212250160],
[821.465, 1.59342534396, 1898.35121793960],
[620.798, 4.82284338962, 956.28915597060],
[653.981, 3.38150775269, 1692.16566950240],
[812.036, 5.94091899141, 909.81873305460],
[562.120, 0.08095987241, 543.91805909620],
[542.221, 0.28360266386, 525.75881183150],
[457.859, 0.12722694510, 1375.77379984580],
[614.784, 2.27624915604, 942.06206196900],
[435.805, 2.60272129748, 95.97922721780],
[496.066, 5.53005947761, 380.12776796000],
[469.965, 2.81896276101, 1795.25844372100],
[445.003, 0.14623567024, 14.22709400160],
[290.869, 3.89339143564, 1471.75302706360],
[276.627, 2.52238450687, 2001.44399215820],
[275.084, 2.98863518924, 526.50957135690],
[293.875, 2.04938438861, 199.07200143640],
[290.985, 6.03131226226, 1169.58825140860],
[338.342, 2.79873192583, 1045.15483618760],
[257.482, 6.13395478303, 532.87235883230],
[319.013, 1.34803130803, 2214.74308759620],
[309.352, 5.36855804945, 1272.68102562720],
[345.804, 1.56404293688, 491.55792945680],
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[1.839, 4.24616044210, 981.63138620530],
[1.567, 3.32429870195, 532.39927808030],
[1.340, 1.94668282270, 528.41894070740],
[1.422, 1.83191577465, 4002.88798431640],
[1.745, 5.76913240451, 490.07345674850],
[1.437, 4.19470227783, 420.44785172170],
[1.419, 0.74849005330, 632.26247445140],
[1.447, 5.65611888743, 373.01422095920],
[1.578, 3.90273683089, 602.98809095360],
[1.385, 3.88479835656, 419.43645976540],
[1.352, 0.81697905853, 1585.14074202070],
[1.399, 1.24785452243, 633.30500417500],
[1.297, 5.57914023189, 1276.61317889030],
[1.491, 1.66541781223, 2655.56837247380],
[1.252, 0.72155670765, 173.94221952280],
[1.658, 5.60924662850, 362.86229257260],
[1.606, 3.95301396173, 2274.54683263650],
[1.213, 4.55264289565, 366.79444583570],
[1.521, 0.55773831071, 1592.25428902150],
[1.220, 3.63029788040, 497.44763618020],
[1.215, 4.42854185903, 531.38788612400],
[1.549, 5.73765962068, 320.32402291970],
[1.480, 4.29779032931, 303.86169668440],
[1.507, 2.27998567874, 758.77106321170],
[1.212, 3.38335836048, 536.85269620520],
[1.245, 4.21639959154, 4.66586644600],
[1.507, 3.52136655355, 774.00954916960],
[1.481, 3.06156044618, 1585.89150154610],
[1.462, 2.30628702634, 1363.24362687360],
[1.180, 3.52708055024, 1064.79855616060],
[1.193, 5.88284733845, 1060.86640289750],
[1.398, 4.99456521692, 842.90144101350],
[1.406, 1.53799746944, 1020.02505427400],
[1.367, 4.10254739443, 799.61241183520],
[1.336, 1.89387272380, 530.96298948180],
[1.238, 3.62226383331, 3487.42411322340],
[1.306, 3.39985119727, 539.25219265020],
[1.156, 0.77127511567, 1603.29998928540],
[1.482, 0.48451915093, 493.04240216510],
[1.247, 5.64344659992, 479.28838891550],
[1.195, 2.39909893341, 561.18353448360],
[1.106, 0.89453807282, 2.92076130680],
[1.227, 2.76231244946, 299.12639426920],
[1.128, 4.72319873338, 124.43341522100],
[1.086, 5.66180289525, 1053.75285589670],
[1.329, 0.16664094530, 536.75632798560],
[1.082, 4.51407359350, 528.25467649610],
[1.105, 1.93890691771, 244.31858407500],
[1.446, 0.65096230619, 1091.62525910360],
[1.071, 4.67974963103, 521.82665856840],
[1.413, 4.72936311016, 1141.13406340540],
[1.086, 2.88721124443, 1262.38608488870],
[1.254, 5.74156595137, 527.99404406520],
[1.082, 5.60975006771, 531.12725369310],
[1.148, 3.27410230525, 1035.00290780100],
[1.224, 3.68807537150, 81.75213321620],
[1.072, 0.48068438564, 1058.63117066380],
[1.036, 1.68789163831, 1070.42763045310],
[1.052, 4.72763208332, 913.75088631770],
[1.166, 4.97812626679, 450.97721326420],
[1.042, 2.90894542321, 3906.90875709860],
[0.997, 1.65967703856, 3259.89792378380],
[1.113, 3.06502453809, 1482.79872732750],
[0.991, 0.91568114148, 576.16138801060],
[0.987, 0.91349590742, 2332.06295581640],
[1.003, 6.17381204883, 391.17346822390],
[1.087, 3.19260020877, 151.04766984290],
[0.987, 2.48065918834, 1912.57831194120],
[0.975, 1.55458771092, 536.28324723360],
[1.193, 2.19383228000, 523.09868295560],
[0.979, 3.28693620660, 1379.70595310890],
[0.963, 2.29845109892, 1467.82087380050],
[1.279, 4.73978455573, 600.54041039880],
[1.269, 1.77171706595, 5120.60114558360],
[0.938, 3.13636271584, 1372.59240610810],
[0.956, 0.94045126791, 429.77958461370],
[1.130, 4.87259620358, 874.39401040250],
[1.044, 3.52819283674, 530.58473697190],
[1.244, 0.80634178279, 419.53282798500],
[0.914, 4.34324212455, 1127.04998175570],
[1.095, 3.17513475763, 6681.22485339960],
[0.926, 5.53099018797, 537.55527162080],
[1.025, 6.08315999637, 469.88722005430],
[0.928, 2.64064849636, 31.01948863700],
[0.887, 5.53922649066, 498.67147645760],
[1.153, 5.20213407651, 554.06998748280],
[0.976, 4.26047885490, 806.72595883600],
[0.871, 5.79751110150, 594.65070367540],
[1.044, 0.31244551729, 528.79719321730],
[0.911, 0.94039205468, 337.73251065900],
[1.197, 3.12884590029, 1966.23171782720],
[0.930, 2.88178471518, 1056.46116888240],
[1.052, 1.69484089706, 484.44438245600],
[0.862, 0.67309397482, 20426.57109242200],
[1.152, 1.16751621652, 1489.91227432830],
[0.847, 3.25831322825, 1063.57471588320],
[0.884, 0.71487680084, 2042.49778910280],
[0.888, 5.38714907441, 5621.84292321040],
[1.137, 4.02029739425, 1670.07426897460],
[0.844, 3.31846798590, 812.14258480740],
[0.860, 4.78175008217, 530.91480537200],
[0.835, 3.63117401608, 451.72797278960],
[0.931, 2.27352189963, 100.64509366380],
[0.939, 3.51238251326, 523.47118997110],
[0.860, 5.34207357904, 528.46712481720],
[0.875, 0.87775537110, 4326.39340097380],
[0.961, 5.69327275886, 498.19839570560],
[0.966, 6.25512226434, 700.45179087970],
[0.842, 3.20535945596, 1670.82502850000],
[0.808, 1.09148925587, 683.18631549230],
[0.810, 5.47935192896, 525.54636351040],
[0.855, 6.06969867736, 446.31134681820],
[0.989, 1.55623875216, 1493.09366806600],
[0.837, 1.49510080792, 1025.44168024540],
[0.974, 3.67667471757, 25565.32572348040],
[0.788, 0.51622458293, 526.98265210890],
[0.820, 1.86002542644, 629.86297800640],
[0.813, 0.45441968195, 4694.00295470760],
[0.953, 0.58786779132, 627.36711334180],
[0.908, 2.82093327912, 3046.59882834580],
[0.912, 2.69124310451, 946.72792841500],
[0.820, 4.14947931572, 1884.12412393800],
[0.948, 0.77931728039, 25551.09862947879],
[0.844, 0.00976249584, 628.59095361920],
[0.910, 0.99542530366, 5760.49843189760],
[0.844, 0.22630964490, 1123.11782849260],
[0.924, 4.41952345708, 5746.27133789600],
[0.967, 3.20618313117, 9050.81084180320],
[0.800, 0.10663079153, 4532.57894941100],
[0.748, 3.01376405927, 5481.75455838080],
[0.752, 5.82360472890, 701.93626358800],
[0.771, 0.12101982692, 635.70450062000],
[0.725, 2.81220410314, 3597.63043444280],
[0.944, 0.40327408174, 1140.38330388000],
[0.726, 5.28930472464, 1304.92435454160],
[0.994, 5.16391370100, 10316.37832042960],
[0.890, 4.10819809692, 1060.13268971460],
[0.962, 1.48376004549, 1062.30269149600],
[0.883, 5.26813169286, 1542.60247236780],
[0.916, 6.02908368648, 7.86430652620],
[0.725, 2.18773773010, 1176.70179840940],
[0.808, 5.81725174908, 1087.69310584050],
[0.757, 0.77440414330, 977.48678462110],
[0.838, 3.81585420192, 986.08480433020],
[0.888, 1.89634795578, 707.56533788050],
[0.854, 5.47701506544, 2818.03500860600],
[0.796, 1.08794807212, 987.30864460760],
[0.856, 2.58042139486, 2803.80791460440],
[0.708, 1.09492310353, 248.72381809010],
[0.811, 3.23726191865, 121.25202148330],
[0.727, 1.56150632966, 4319.27985397300],
[0.687, 2.65457835371, 1567.73225428140],
[0.675, 1.78690909614, 103.14095832840],
[0.853, 4.74476428852, 951.62328952460],
[0.832, 5.14362789810, 1054.71606374320],
[0.846, 1.47557828604, 898.77303279070],
[0.701, 1.72139817505, 5230.80746680300],
[0.863, 3.98700238575, 686.95841006100],
[0.703, 2.89202252444, 63.73589830340],
[0.673, 6.11618580510, 738.32419408660],
[0.806, 4.64475158248, 533.83556667880],
[0.670, 2.67625974048, 1012.91150727320],
[0.668, 4.93815253692, 5172.47623572500],
[0.818, 1.41973280302, 580.09354127370],
[0.652, 3.41422919445, 650.94298657790],
[0.643, 2.46566726278, 1049.82070263360],
[0.859, 2.50530106631, 782.34693644780],
[0.662, 4.13533996643, 733.42883297700],
[0.812, 1.30325352179, 1055.18914449520],
[0.638, 4.21760246824, 1064.04779663520],
[0.637, 6.13121700151, 4752.99159184980],
[0.636, 0.83411828974, 711.49749114360],
[0.642, 1.86741704507, 1053.96530421780],
[0.795, 4.54081089118, 1457.52593306200],
[0.783, 4.37652961667, 105.54045477340],
[0.640, 5.44039474349, 632.03297978780],
[0.651, 5.02431301146, 528.04643369190],
[0.686, 0.27079898498, 11.77941344680],
[0.644, 5.36935176134, 835.78789401270],
[0.639, 1.86699974431, 6172.86952877200],
[0.630, 2.86895754523, 633.53449883860],
[0.826, 1.46026926041, 2199.76523406920],
[0.687, 3.81221717134, 73.29712585900],
[0.697, 4.18082589322, 1.69692102940],
[0.788, 0.21278801649, 313.94418910180],
[0.686, 2.51807576494, 638.41281360570],
[0.847, 5.56263749391, 4429.48617519240],
[0.673, 4.87494072856, 103.04459010880],
[0.663, 4.80713895807, 991.71387862270],
[0.614, 3.87231597482, 767.36908292080],
[0.666, 5.71697262323, 661.09491496450],
[0.681, 2.33844767741, 501.23677709140],
[0.597, 3.03921014345, 6.95348830640],
[0.777, 3.08786050361, 441.57604440300],
[0.588, 0.08236113246, 4164.31198961300],
[0.693, 4.66190836234, 3384.33133900480],
[0.810, 1.97701084490, 860.30992875280],
[0.602, 5.56403449542, 1587.58842257550],
[0.622, 6.11554348965, 7.06536289100],
[0.592, 3.29013906024, 10103.07922499160],
[0.692, 6.10931942233, 12.74262129330],
[0.597, 6.13204711801, 7.27360569520],
[0.594, 2.58839673551, 849.26422848890],
[0.728, 2.73732195088, 6.15033915430],
[0.602, 5.28816527514, 949.12742486000],
[0.568, 1.75508433865, 1077.54117745390],
[0.575, 4.50676079721, 1230.14275597430],
[0.588, 0.65827893998, 4642.78527063040],
[0.561, 3.87565914360, 135.33610313300],
[0.558, 3.36094471852, 24498.83024629040],
[0.557, 3.45629457197, 19896.88012732740],
[0.558, 1.17103892689, 3576.28979344040],
[0.574, 5.19235074140, 104.05598206510],
[0.560, 3.57141429379, 5333.90024102160],
[0.555, 0.18349908409, 512.42548970720],
[0.571, 0.83070148820, 1570.91364801910],
[0.632, 3.67893818442, 1065.01100448170],
[0.744, 2.33083237537, 620.25356634100],
[0.540, 5.15775909675, 1751.53953141600],
[0.592, 3.07238123875, 1446.62324515000],
[0.537, 1.52803865425, 8094.52168583260],
[0.550, 5.50701003577, 1432.39615114840],
[0.546, 2.34388967045, 949.22379307960],
[0.534, 3.04076654796, 7.16173111060],
[0.619, 6.07865159203, 46.47042291600],
[0.562, 0.96641974928, 1438.02522544090],
[0.531, 1.06695547390, 100.17201291180],
[0.599, 3.59295739143, 1144.31545714310],
[0.526, 3.51641923371, 0.75075952540],
[0.564, 0.72677136494, 1059.22187149480],
[0.537, 5.72603965787, 513.22863885930],
[0.630, 2.31183143900, 2729.45619916380],
[0.530, 4.99510636441, 9264.10993724120],
[0.649, 0.95666735852, 920.86443331850],
[0.547, 1.18801926149, 11506.76976979360],
[0.516, 3.28562070858, 734.91330568530],
[0.567, 5.13926871155, 288.08069400530],
[0.538, 0.28159637680, 153.49535039770],
[0.718, 0.48326672359, 842.15068148810],
[0.526, 4.39778401928, 546.15329132990],
[0.695, 2.44235086902, 657.16276170140],
[0.697, 4.99042365686, 12.53017297220],
[0.519, 6.27847163164, 59.80374504030],
[0.504, 2.58550284000, 5378.66178416220],
[0.496, 2.43659402827, 990.22940591440],
[0.617, 5.73284985700, 745.43774108740],
[0.519, 3.10157097770, 9161.01716302260],
[0.654, 1.31181453784, 878.32616366560],
[0.619, 3.71554817226, 2090.30967237520],
[0.500, 4.28937439066, 5216.58037280140],
[0.621, 3.98893673383, 409.92341631960],
[0.685, 1.95310431695, 3156.80514956520],
[0.552, 2.81774132958, 344.70304530790],
[0.551, 1.91969778405, 113.38771495710],
[0.682, 0.87321578326, 6069.77675455340],
[0.651, 5.09951064975, 531.33549649730],
[0.537, 3.67357440226, 605.95703637020],
[0.525, 0.74584814988, 736.83972137830],
[0.505, 3.12494814307, 1475.68518032670],
[0.622, 3.00013939606, 2349.32843120380],
[0.644, 3.00156986335, 298.23262239190],
[0.564, 3.81960833949, 1059.54198888360],
[0.468, 3.50348554992, 4841.85727206680],
[0.491, 1.28535573072, 247.23934538180],
[0.458, 0.45056377876, 1065.60170531270],
[0.543, 2.39704308320, 9690.70812811720],
[0.459, 5.29870259698, 1474.93442080130],
[0.483, 3.63649121244, 131.40394986990],
[0.632, 2.75028345792, 334.55111692130],
[0.483, 0.42979609421, 735.82832942200],
[0.540, 0.54791737146, 51646.11531805379],
[0.531, 0.30026207053, 912.78767847120],
[0.449, 3.02583472996, 5901.23920225600],
[0.544, 2.98747240952, 4223.30062675520],
[0.557, 5.83542572008, 9676.48103411560],
[0.501, 0.03408180117, 1080.72257119160],
[0.517, 4.40400852026, 2545.36205125440],
[0.481, 3.63292807076, 5584.84733259940],
[0.557, 6.11443978190, 976.00231191280],
[0.481, 3.41035583659, 3803.81598288000],
[0.622, 2.29597570837, 9999.98645077300],
[0.454, 2.88584538455, 1987.21689815660],
[0.439, 4.83198101064, 50.40257617910],
[0.475, 2.69994471394, 491.81856188770],
[0.618, 0.72471290082, 1291.43097372290],
[0.503, 0.13449993622, 2015.67108615980],
[0.551, 2.13418546604, 1440.99417085750],
[0.595, 3.78181802545, 6386.16862421000],
[0.434, 2.64411689486, 748.40668650400],
[0.592, 0.32587740408, 737.36098624010],
[0.490, 2.37988828800, 2225.78878786010],
[0.439, 1.33582802018, 995.64603188580],
[0.543, 2.05067702505, 906.84978763800],
[0.466, 2.43707405011, 3362.99069800240],
[0.481, 2.32223226419, 1357.61455258110],
[0.566, 0.59740900184, 350.33211960040],
[0.429, 2.46287580628, 3914.02230409940],
[0.429, 1.01299906509, 4333.50694797460],
[0.425, 1.67255823369, 148.07872442630],
[0.412, 3.29630633921, 7.32599532190],
[0.508, 1.16158524676, 9.56122755560],
[0.524, 5.02562926120, 1090.40141882620],
[0.409, 5.80053072411, 9146.79006902100],
[0.497, 0.01579913593, 1069.67687092770],
[0.548, 6.03429743373, 9367.20271145980],
[0.433, 5.93688350840, 1688.23351623930],
[0.424, 4.18150111530, 550.13783421970],
[0.401, 0.11519846139, 970.51624997220],
[0.503, 5.28212300854, 668.20846196530],
[0.555, 1.00328633255, 141.22580985640],
[0.404, 2.48633976473, 519.65665678700],
[0.441, 6.06185501734, 25.12978191360],
[0.412, 5.87495245826, 6.90109867970],
[0.478, 0.71264950607, 1094.80665284130],
[0.446, 2.71248183031, 31.49256938900],
[0.404, 5.49462012486, 447.93883187840],
[0.391, 1.26105612700, 8.07675484730],
[0.463, 1.93535321271, 6275.96230299060],
[0.507, 3.61089992782, 546.95644048200],
[0.402, 5.86200127054, 927.83496796740],
[0.481, 6.21043578332, 683.98946464440],
[0.483, 5.02142924458, 857.12853501510],
[0.444, 0.84873092377, 1371.84164658270],
[0.391, 2.81753436573, 5798.14642803740],
[0.395, 0.22367886581, 51116.42435295920],
[0.378, 6.03765733432, 1268.74887236410],
[0.471, 6.24506463249, 946.46729598410],
[0.405, 0.57785207581, 107.28555991260],
[0.371, 6.15750793727, 509.24409596950],
[0.370, 4.90330687618, 1436.54075273260],
[0.448, 4.76565111029, 284.14854074220],
[0.474, 0.71146352197, 2108.46891963990],
[0.509, 5.53328407404, 1128.53445446400],
],
# R1
[
[1271801.596, 2.64937511122, 529.69096509460],
[61661.771, 3.00076251018, 1059.38193018920],
[53443.592, 3.89717644226, 522.57741809380],
[31185.167, 4.88276663526, 536.80451209540],
[41390.257, 0.00000000000, 0.00000000000],
[11847.190, 2.41329588176, 419.48464387520],
[9166.360, 4.75979408587, 7.11354700080],
[3175.763, 2.79297987071, 103.09277421860],
[3203.446, 5.21083285476, 735.87651353180],
[3403.605, 3.34688537997, 1589.07289528380],
[2600.003, 3.63435101622, 206.18554843720],
[2412.207, 1.46947308304, 426.59819087600],
[2806.064, 3.74223693580, 515.46387109300],
[2676.575, 4.33052878699, 1052.26838318840],
[2100.507, 3.92762682306, 639.89728631400],
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[0.403, 0.34381388674, 32.24332891440],
[0.402, 5.88926765351, 1570.91364801910],
[0.505, 1.49028912471, 3782.47534187760],
[0.447, 0.03952029309, 245.54242435240],
[0.453, 3.09458004153, 1059.43011429900],
[0.411, 3.21727542472, 1475.68518032670],
[0.426, 3.12237794195, 12566.15169998280],
[0.434, 3.59362426939, 3259.89792378380],
[0.398, 4.91510709622, 4120.20785253660],
[0.399, 4.67075122011, 234.63973644040],
[0.386, 4.81320787761, 970.51624997220],
[0.427, 3.21176085113, 977.48678462110],
[0.411, 4.31566962034, 757.21715453420],
[0.392, 1.86527946688, 885.43971066640],
[0.416, 3.81408093105, 3156.80514956520],
],
# R2
[
[79644.833, 1.35865896596, 529.69096509460],
[8251.618, 5.77773935444, 522.57741809380],
[7029.864, 3.27476965833, 536.80451209540],
[5314.006, 1.83835109712, 1059.38193018920],
[1860.833, 2.97682139367, 7.11354700080],
[836.267, 4.19889881718, 419.48464387520],
[964.466, 5.48031822015, 515.46387109300],
[406.453, 3.78250730354, 1066.49547719000],
[426.570, 2.22753101795, 639.89728631400],
[377.316, 2.24248352873, 1589.07289528380],
[497.920, 3.14159265359, 0.00000000000],
[339.043, 6.12690864038, 625.67019231240],
[362.943, 5.36761847267, 206.18554843720],
[342.048, 6.09922969324, 1052.26838318840],
[279.920, 4.26162555827, 412.37109687440],
[332.578, 0.00328961161, 426.59819087600],
[229.777, 0.70530766213, 735.87651353180],
[200.783, 3.06850623368, 543.91805909620],
[199.807, 4.42884165317, 103.09277421860],
[257.290, 0.96295364983, 632.78373931320],
[138.606, 2.93235671606, 14.22709400160],
[113.535, 0.78713911289, 728.76296653100],
[86.025, 5.14434751994, 323.50541665740],
[94.565, 1.70498041073, 838.96928775040],
[83.469, 0.05834873484, 309.27832265580],
[75.198, 1.60495195911, 956.28915597060],
[70.451, 1.50988357484, 213.29909543800],
[80.328, 2.98122361797, 742.99006053260],
[56.203, 0.95534810533, 1162.47470440780],
[61.649, 6.10137889854, 1045.15483618760],
[66.572, 5.47307178077, 199.07200143640],
[50.057, 2.72063162317, 532.87235883230],
[51.904, 5.58435625607, 942.06206196900],
[39.833, 5.94566506227, 95.97922721780],
[44.548, 5.52445621411, 508.35032409220],
[44.282, 0.27118152557, 526.50957135690],
[29.944, 0.93641735919, 1155.36115740700],
[28.412, 2.87835720211, 525.75881183150],
[26.330, 4.26891877269, 1596.18644228460],
[27.039, 2.80607741398, 1169.58825140860],
[27.477, 2.64841266238, 2118.76386037840],
[22.705, 0.17830004133, 302.16477565500],
[29.347, 1.78589692350, 831.85574074960],
[19.991, 0.04328951895, 949.17560896980],
[19.906, 1.16072627347, 533.62311835770],
[21.714, 1.88820231818, 1272.68102562720],
[17.581, 4.14974757919, 846.08283475120],
[17.085, 5.89188996975, 1258.45393162560],
[21.407, 4.35468497204, 316.39186965660],
[21.295, 0.54429472455, 1265.56747862640],
[19.859, 0.06453825800, 1581.95934828300],
[17.025, 0.53383755278, 1368.66025284500],
[12.804, 3.90044242142, 433.71173787680],
[13.072, 0.79468040717, 110.20632121940],
[11.945, 0.40671403646, 1361.54670584420],
[11.695, 4.44394618065, 405.25754987360],
[11.979, 2.22872778682, 220.41264243880],
[9.633, 6.01002272123, 853.19638175200],
[10.163, 0.99504635158, 1471.75302706360],
[8.977, 1.60328709409, 1692.16566950240],
[8.701, 3.52167876799, 1073.60902419080],
[8.314, 5.60169732564, 1574.84580128220],
[8.958, 6.26708748901, 519.39602435610],
[7.828, 0.65241611799, 1478.86657406440],
[7.833, 0.17920601344, 1685.05212250160],
[7.451, 0.88421084942, 88.86568021700],
[7.320, 0.89341249264, 721.64941953020],
[9.135, 1.51210840939, 1148.24761040620],
[6.110, 2.50080005128, 3.18139373770],
[7.037, 4.44127496638, 330.61896365820],
[5.163, 2.79219166952, 21.34064100240],
[5.079, 2.97991736844, 1375.77379984580],
[4.930, 0.04683167622, 1677.93857550080],
[4.664, 2.28007273876, 1485.98012106520],
[4.692, 0.86220230505, 3.93215326310],
[5.307, 0.85008578245, 1788.14489672020],
[4.239, 0.40758287124, 629.60234557550],
[4.230, 1.61046658091, 635.96513305090],
[3.627, 2.71151441113, 551.03160609700],
[3.314, 0.55067236587, 1795.25844372100],
[4.409, 1.28127751050, 1464.63948006280],
[3.270, 1.18744032691, 1905.46476494040],
[3.226, 6.18716071251, 1038.04128918680],
[3.103, 6.22971614425, 2001.44399215820],
[3.410, 2.44624067925, 539.98590583310],
[3.174, 5.54870592599, 191.95845443560],
[2.590, 3.24430559059, 1062.56332392690],
[2.614, 0.55149554149, 2104.53676637680],
[2.174, 5.32613824409, 1891.23767093880],
[2.659, 4.82459974220, 416.30325013750],
[2.187, 1.71707514653, 628.85158605010],
[2.263, 6.19233486371, 1994.33044515740],
[2.328, 4.28236795066, 963.40270297140],
[2.579, 0.03256542251, 1898.35121793960],
[2.077, 3.32602157426, 1699.27921650320],
[2.529, 2.39697505835, 227.52618943960],
[2.468, 0.06551346218, 750.10360753340],
[1.989, 0.29206371261, 636.71589257630],
[1.927, 0.32286661566, 295.05122865420],
[1.904, 3.43534792123, 647.01083331480],
[1.940, 0.29170673525, 2111.65031337760],
[1.880, 3.14403615586, 611.44309831080],
[2.324, 1.94960720763, 824.74219374880],
[1.854, 4.71794950485, 2125.87740737920],
[2.547, 1.23908353090, 2221.85663459700],
[1.814, 1.60250861074, 2008.55753915900],
[1.611, 5.83466560322, 422.66603761290],
[1.667, 2.32455940876, 440.82528487760],
[1.622, 0.36650974375, 1056.20053645150],
[1.624, 2.42139677881, 10.29494073850],
[1.622, 3.51892791175, 1055.44977692610],
[1.606, 5.76205763975, 117.31986822020],
[1.646, 5.88662636573, 2317.83586181480],
[2.026, 4.61781314145, 423.41679713830],
[2.098, 1.04559231028, 1781.03134971940],
[1.868, 1.12487729469, 618.55664531160],
[1.885, 2.78775930564, 1802.37199072180],
[1.445, 0.08308050305, 1382.88734684660],
[1.797, 3.00776822706, 2648.45482547300],
[1.422, 0.17649746278, 2420.92863603340],
[1.129, 1.59030291320, 380.12776796000],
[1.126, 4.19989673600, 547.85021235930],
[1.186, 5.98943062173, 2310.72231481400],
[1.108, 4.22655117757, 934.94851496820],
[1.259, 1.19687222266, 1063.31408345230],
[1.072, 3.86169004168, 1603.29998928540],
[0.946, 5.59968097387, 99.91138048090],
[0.937, 1.03083276760, 81.75213321620],
[0.938, 6.18136092771, 945.99421523210],
[0.908, 2.54355964041, 6283.07584999140],
[0.874, 5.21903196047, 2207.62954059540],
[0.874, 6.01240284465, 511.53171782990],
[1.188, 0.75698357968, 2097.42321937600],
[0.789, 3.91035208173, 10213.28554621100],
[1.000, 1.34667100304, 732.69511979410],
[0.952, 1.55355777420, 2324.94940881560],
[0.811, 5.00475553271, 319.57326339430],
[0.763, 3.98527559630, 337.73251065900],
[0.880, 1.14789972199, 952.35700270750],
[0.780, 4.69463316930, 5746.27133789600],
[0.910, 0.08774541571, 2737.32050569000],
[0.773, 0.77131695762, 5760.49843189760],
[0.764, 6.11686539353, 9676.48103411560],
[0.758, 2.19350719860, 9690.70812811720],
[0.671, 1.19532387143, 124.43341522100],
[0.661, 5.99578306627, 501.23677709140],
[0.729, 0.65312263578, 2538.24850425360],
[0.825, 2.70770030205, 3370.10424500320],
[0.670, 5.44169923277, 107.02492748170],
[0.739, 1.14609907817, 2641.34127847220],
[0.866, 3.02831268213, 3046.59882834580],
[0.718, 4.83684196454, 860.30992875280],
[0.813, 6.01229270247, 2214.74308759620],
[0.746, 1.12371143332, 739.80866679490],
[0.741, 5.93171662010, 2634.22773147140],
[0.667, 0.89885058003, 106.27416795630],
[0.573, 2.42701822581, 739.05790726950],
[0.734, 0.72837704619, 1354.43315884340],
[0.662, 2.21768976390, 2015.67108615980],
[0.782, 2.52401202862, 3679.38256765900],
[0.779, 2.38608991574, 3267.01147078460],
[0.553, 1.85211127676, 453.42489381900],
[0.701, 4.23431087374, 9683.59458111640],
[0.571, 2.98435419019, 1262.38608488870],
[0.621, 1.24462887440, 3803.81598288000],
[0.563, 5.99845316446, 1049.08698945070],
[0.538, 4.92334194042, 447.79581952650],
[0.534, 0.99911551571, 462.02291352810],
[0.541, 6.19275150397, 1987.21689815660],
[0.511, 3.28553278370, 4.66586644600],
[0.539, 5.33214565622, 2751.54759969160],
[0.651, 5.12199308959, 3156.80514956520],
[0.483, 3.03782387056, 3281.23856478620],
[0.476, 2.17592053936, 149.56319713460],
[0.510, 5.35664230912, 9.56122755560],
[0.490, 1.57324553106, 1251.34038462480],
[0.467, 5.92343423840, 203.00415469950],
[0.528, 5.81786945766, 2627.11418447060],
[0.447, 3.51498961805, 18.15924726470],
[0.429, 0.16627197188, 74.78159856730],
[0.497, 0.30985248432, 2428.04218303420],
[0.516, 3.89424540015, 2516.90786325120],
[0.519, 2.43126348834, 3686.49611465980],
[0.404, 2.77840802846, 7.16173111060],
[0.533, 4.77083438961, 3473.19701922180],
[0.515, 3.54549816613, 3178.14579056760],
[0.533, 5.61415688189, 2524.02141025200],
[0.458, 4.91616403047, 3067.93946934820],
[0.400, 3.13887720912, 540.73666535850],
[0.378, 0.86122450940, 525.02509864860],
],
# R3
[
[3519.257, 6.05800633846, 529.69096509460],
[1073.239, 1.67321345760, 536.80451209540],
[915.666, 1.41329676116, 522.57741809380],
[341.593, 0.52296542656, 1059.38193018920],
[254.893, 1.19625473533, 7.11354700080],
[221.512, 0.95225226237, 515.46387109300],
[69.078, 2.26885282314, 1066.49547719000],
[89.729, 3.14159265359, 0.00000000000],
[57.827, 1.41389745339, 543.91805909620],
[57.653, 0.52580117593, 639.89728631400],
[51.079, 5.98016364677, 412.37109687440],
[46.935, 1.57864237959, 625.67019231240],
[42.824, 6.11689609099, 419.48464387520],
[37.477, 1.18262762330, 14.22709400160],
[33.816, 1.66671706951, 1052.26838318840],
[31.195, 1.04290245896, 1589.07289528380],
[30.023, 4.63236245032, 426.59819087600],
[33.531, 0.84784977903, 206.18554843720],
[20.804, 2.50071243814, 728.76296653100],
[14.466, 0.96040197071, 508.35032409220],
[12.969, 1.50233788550, 1045.15483618760],
[11.654, 3.55513510121, 323.50541665740],
[12.319, 2.60952614503, 735.87651353180],
[15.023, 0.89136998434, 199.07200143640],
[11.160, 1.79041437555, 309.27832265580],
[10.554, 6.27845112678, 956.28915597060],
[9.812, 6.26016859519, 103.09277421860],
[9.301, 3.45126812476, 838.96928775040],
[6.672, 1.87004905364, 302.16477565500],
[7.442, 1.28047007623, 742.99006053260],
[7.178, 0.92022189637, 942.06206196900],
[5.577, 1.37980792905, 95.97922721780],
[6.834, 3.45228722967, 831.85574074960],
[4.632, 2.82934545414, 1596.18644228460],
[3.969, 1.21290005054, 1169.58825140860],
[3.869, 5.99495313698, 213.29909543800],
[3.551, 6.10714791535, 405.25754987360],
[2.943, 2.32831075458, 1155.36115740700],
[2.442, 1.86965213405, 532.87235883230],
[2.410, 0.42627205128, 220.41264243880],
[2.289, 1.94941487274, 1073.60902419080],
[2.274, 0.09211517505, 632.78373931320],
[2.189, 1.58907745204, 2118.76386037840],
[2.387, 5.97080671477, 1162.47470440780],
[2.104, 1.06751462671, 21.34064100240],
[2.128, 1.51119399925, 1258.45393162560],
[2.491, 0.35125020737, 1272.68102562720],
[2.006, 5.94487388360, 110.20632121940],
[1.980, 2.54989377864, 88.86568021700],
[2.040, 2.16463966964, 433.71173787680],
[1.955, 2.70341589777, 721.64941953020],
[1.670, 4.46255717328, 853.19638175200],
[1.910, 2.25964760758, 1361.54670584420],
[1.710, 1.98372066321, 525.75881183150],
[1.520, 0.11641358425, 949.17560896980],
[2.003, 3.16520599208, 1148.24761040620],
[1.710, 2.70850417287, 330.61896365820],
[1.629, 0.47376028854, 526.50957135690],
[1.229, 3.01987279595, 963.40270297140],
[1.671, 0.44352103086, 533.62311835770],
[1.207, 1.15774089269, 1574.84580128220],
[1.146, 2.54505851138, 846.08283475120],
[1.355, 1.17462112647, 1038.04128918680],
[1.001, 2.70272799283, 519.39602435610],
[1.372, 0.67467128629, 551.03160609700],
[0.983, 4.17198081351, 2627.11418447060],
[1.084, 1.07011164067, 227.52618943960],
[0.892, 2.92543286761, 1368.66025284500],
[0.823, 4.86559196955, 611.44309831080],
[1.136, 1.78981738432, 1581.95934828300],
[0.897, 4.91073630270, 1670.82502850000],
[0.908, 3.68804047330, 824.74219374880],
[0.789, 3.23380893250, 2125.87740737920],
[0.771, 2.39070707004, 2317.83586181480],
[0.891, 0.59692950778, 539.98590583310],
[0.876, 4.52127091462, 750.10360753340],
[0.802, 0.20759322884, 1141.13406340540],
[0.850, 0.94145487094, 191.95845443560],
[0.762, 2.25149516048, 2538.24850425360],
[0.694, 0.67080348659, 440.82528487760],
[0.741, 5.79934203525, 1485.98012106520],
[0.643, 2.48127580335, 1265.56747862640],
[0.575, 6.13756590872, 1279.79457262800],
[0.636, 5.51001645505, 2413.81508903260],
[0.636, 4.40777238491, 1382.88734684660],
[0.555, 2.18233983981, 1062.56332392690],
[0.564, 1.92775967119, 2634.22773147140],
[0.531, 2.04824376019, 295.05122865420],
[0.541, 2.32424368689, 1471.75302706360],
[0.697, 2.27179476322, 1699.27921650320],
[0.546, 1.95774905730, 1677.93857550080],
[0.465, 4.35550844067, 1692.16566950240],
[0.508, 2.50298248836, 2207.62954059540],
[0.496, 5.77087043616, 1478.86657406440],
[0.440, 5.98661963879, 934.94851496820],
[0.424, 2.80194129521, 81.75213321620],
[0.406, 3.93940190897, 316.39186965660],
[0.506, 0.18719982992, 10.29494073850],
],
# R4
[
[128.628, 0.08419309557, 536.80451209540],
[113.458, 4.24858855779, 529.69096509460],
[82.650, 3.29754909408, 522.57741809380],
[37.883, 2.73326611144, 515.46387109300],
[26.694, 5.69142588558, 7.11354700080],
[17.650, 5.40012536918, 1059.38193018920],
[12.612, 6.01560416057, 543.91805909620],
[9.287, 0.76813946494, 1066.49547719000],
[8.107, 5.68228065707, 14.22709400160],
[6.271, 5.12286932534, 639.89728631400],
[6.978, 1.42751292055, 412.37109687440],
[5.377, 3.33501947275, 625.67019231240],
[2.911, 3.40334805052, 1052.26838318840],
[2.593, 4.16090412984, 728.76296653100],
[2.562, 2.89802035072, 426.59819087600],
[2.268, 6.22195938856, 1589.07289528380],
[2.114, 3.11758855774, 1045.15483618760],
[1.673, 2.81399290364, 206.18554843720],
[1.805, 2.60030006919, 199.07200143640],
[1.823, 1.89432426038, 419.48464387520],
[1.522, 1.33432648232, 1596.18644228460],
[1.697, 0.00000000000, 0.00000000000],
[1.039, 4.41904942302, 956.28915597060],
[1.161, 5.16181311538, 831.85574074960],
[0.916, 3.17245716108, 508.35032409220],
[0.870, 5.79387813500, 1169.58825140860],
[0.916, 1.87129662931, 1148.24761040620],
[0.955, 0.66801367802, 1361.54670584420],
[0.788, 1.47515450553, 1272.68102562720],
[0.966, 5.47457968043, 220.41264243880],
[0.788, 2.42252866885, 117.31986822020],
[0.712, 0.49655897030, 1073.60902419080],
[0.656, 3.53022740783, 302.16477565500],
[0.681, 2.84507174340, 191.95845443560],
[0.771, 2.19893222018, 942.06206196900],
[0.765, 5.31147257700, 551.03160609700],
[0.667, 3.72432305249, 88.86568021700],
[0.534, 1.83172084748, 647.01083331480],
[0.553, 0.85896003802, 330.61896365820],
[0.543, 5.26057584439, 21.34064100240],
[0.584, 3.82243061802, 618.55664531160],
[0.512, 4.44485521707, 110.20632121940],
[0.612, 1.59320941864, 3.18139373770],
[0.631, 1.83863158533, 10.29494073850],
[0.491, 1.52912023181, 405.25754987360],
[0.521, 0.24011424451, 433.71173787680],
],
# R5
[
[11.188, 4.75249399945, 536.80451209540],
[4.255, 5.91516229170, 522.57741809380],
[2.079, 5.56781555864, 515.46387109300],
[1.908, 4.29659647286, 543.91805909620],
[1.875, 3.69357495838, 7.11354700080],
[1.590, 5.49312796166, 1066.49547719000],
[1.612, 4.13222808529, 1059.38193018920],
[1.240, 3.77981722506, 14.22709400160],
[1.033, 4.50671820436, 529.69096509460],
],
]
"""This table contains Jupiter'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 432-434."""
ORBITAL_ELEM = [
[34.351519, 3036.3027748, 0.0002233, 0.000000037], # L
[5.202603209, 0.0000001913, 0.0, 0.0], # a
[0.04849793, 0.000163225, -0.0000004714, -0.00000000201], # e
[1.303267, -0.0054965, 0.00000466, -0.000000002], # i
[100.464407, 1.0209774, 0.00040315, 0.000000404], # Omega
[14.331207, 1.6126352, 0.00103042, -0.000004464] # pie
]
"""This table contains the parameters to compute Jupiter's orbital elements for
the mean equinox of date. Based in Table 31.A, page 213"""
ORBITAL_ELEM_J2000 = [
[34.351519, 3034.9056606, -0.00008501, 0.000000016], # L
[1.303267, -0.0019877, 0.0000332, 0.000000097], # i
[100.464407, 0.1767232, 0.000907, -0.000007272], # Omega
[14.331207, 0.2155209, 0.00072211, -0.000004485] # pie
]
"""This table contains the parameters to compute Jupiter's orbital elements for
the standard equinox J2000.0. Based on Table 31.B, page 215"""
[docs]class Jupiter(object):
"""
Class Jupiter models that planet.
"""
[docs] @staticmethod
def geometric_heliocentric_position(epoch, tofk5=True):
"""This method computes the geometric heliocentric position of planet
Jupiter for a given epoch, using the VSOP87 theory.
:param epoch: Epoch to compute Jupiter 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 = Jupiter.geometric_heliocentric_position(epoch)
>>> print(round(l.to_positive(), 4))
241.5873
>>> print(round(b, 4))
0.8216
>>> print(round(r, 5))
5.36848
"""
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
Jupiter for a given epoch, using the VSOP87 theory.
:param epoch: Epoch to compute Jupiter 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 Jupiter 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 = Jupiter.orbital_elements_mean_equinox(epoch)
>>> print(round(l, 6))
222.433723
>>> print(round(a, 8))
5.20260333
>>> print(round(e, 7))
0.0486046
>>> print(round(i, 6))
1.29967
>>> print(round(ome, 5))
101.13309
>>> print(round(arg, 6))
-85.745532
"""
return orbital_elements(epoch, ORBITAL_ELEM, ORBITAL_ELEM)
[docs] @staticmethod
def orbital_elements_j2000(epoch):
"""This method computes the orbital elements of Jupiter 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 = Jupiter.orbital_elements_j2000(epoch)
>>> print(round(l, 6))
221.518802
>>> print(round(a, 8))
5.20260333
>>> print(round(e, 7))
0.0486046
>>> print(round(i, 6))
1.30198
>>> print(round(ome, 5))
100.58051
>>> print(round(arg, 6))
-86.107875
"""
return orbital_elements(epoch, ORBITAL_ELEM, ORBITAL_ELEM_J2000)
[docs] @staticmethod
def geocentric_position(epoch):
"""This method computes the geocentric position of Jupiter (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 = Jupiter.geocentric_position(epoch)
>>> print(ra.ra_str(n_dec=1))
12h 47' 9.6''
>>> print(dec.dms_str(n_dec=1))
-3d 41' 55.3''
>>> print(elon.dms_str(n_dec=1))
76d 2' 26.0''
"""
# First check that input value is of correct types
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input type")
# Compute the heliocentric position of Jupiter
l, b, r = Jupiter.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 Jupiter coordinates with this correction
l, b, r = Jupiter.geometric_heliocentric_position(epoch, tofk5=False)
# Compute second iteration
lr = l.rad()
br = b.rad()
x = r * cos(br) * cos(lr) - r0 * cos(b0r) * cos(l0r)
y = r * cos(br) * sin(lr) - r0 * cos(b0r) * sin(l0r)
z = r * sin(br) - r0 * sin(b0r)
# Compute longitude and latitude
lamb = atan2(y, x)
beta = atan2(z, sqrt(x * x + y * y))
# Now, let's compute the aberration effect
t = (epoch - JDE2000) / 36525
e = 0.016708634 + t * (-0.000042037 - t * 0.0000001267)
pie = 102.93735 + t * (1.71946 + t * 0.00046)
pie = radians(pie)
lon = l0 + 180.0
lon = lon.rad()
k = 20.49552 # The constant of aberration
deltal1 = k * (-cos(lon - lamb) + e * cos(pie - lamb)) / cos(beta)
deltab1 = -k * sin(beta) * (sin(lon - lamb) - e * sin(pie - lamb))
deltal1 = Angle(0, 0, deltal1)
deltab1 = Angle(0, 0, deltab1)
# Correction to FK5 system
lamb = Angle(lamb, radians=True)
lamb = lamb.to_positive()
beta = Angle(beta, radians=True)
l_prime = lamb - t * (1.397 + t * 0.00031)
deltal2 = Angle(0, 0, -0.09033)
a = 0.03916 * (cos(l_prime.rad()) + sin(l_prime.rad()))
a = a * tan(b.rad())
deltal2 += Angle(0, 0, a)
deltab2 = 0.03916 * (cos(l_prime.rad()) - sin(l_prime.rad()))
deltab2 = Angle(0, 0, deltab2)
# Apply the corrections
lamb = lamb + deltal1 + deltal2
beta = beta + deltab1 + deltab2
# Correction for nutation
dpsi = nutation_longitude(epoch)
lamb += dpsi
e = true_obliquity(epoch)
ra, dec = ecliptical2equatorial(lamb, beta, e)
# Let's compute the elongation angle
lons, lats, rs = Sun.apparent_geocentric_position(epoch)
lambr = lamb.rad()
lsr = lons.rad()
betar = beta.rad()
elon = acos(cos(betar) * cos(lambr - lsr))
elon = Angle(elon, radians=True)
return ra, dec, elon
[docs] @staticmethod
def conjunction(epoch):
"""This method computes the time of the conjunction closest to the
given epoch.
:param epoch: Epoch close to the desired conjunction
:type epoch: :py:class:`Epoch`
:returns: The time when the conjunction happens, as an Epoch
:rtype: :py:class:`Epoch`
:raises: TypeError if input value is of wrong type.
:raises: ValueError if input epoch outside the -2000/4000 range.
>>> epoch = Epoch(1993, 10, 1.0)
>>> conj = Jupiter.conjunction(epoch)
>>> y, m, d = conj.get_date()
>>> print(y)
1993
>>> print(m)
10
>>> print(round(d, 4))
18.3341
"""
# 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 Jupiter's conjunction
a = 2451671.186
b = 398.884046
m0 = 121.898
m1 = 33.140229
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
aa = Angle(aa).rad() # Convert to radians
corr = (0.1027 + t * (0.0002 - t * 0.00009)
+ sin(m) * (-2.2637 + t * (0.0163 - t * 0.00003))
+ cos(m) * (-6.154 + t * (-0.021 + t * 0.00008))
+ sin(2.0 * m) * (-0.2021 + t * (-0.0017 + t * 0.00001))
+ cos(2.0 * m) * (0.131 - t * 0.0008)
+ sin(3.0 * m) * (0.0086)
+ cos(3.0 * m) * (0.0087 + t * 0.0002)
+ sin(aa) * (0.0 + t * (0.0144 - t * 0.00008))
+ cos(aa) * (0.3642 + t * (-0.0019 - t * 0.00029)))
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 = Jupiter.opposition(epoch)
>>> y, m, d = oppo.get_date()
>>> print(y)
-6
>>> print(m)
9
>>> print(round(d, 4))
15.2865
"""
# 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 Jupiter's opposition
a = 2451870.628
b = 398.884046
m0 = 318.4681
m1 = 33.140229
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
aa = Angle(aa).rad() # Convert to radians
corr = (-0.1029 - t * t * 0.00009
+ sin(m) * (-1.9658 + t * (-0.0056 + t * 0.00007))
+ cos(m) * (6.1537 + t * (0.021 - t * 0.00006))
+ sin(2.0 * m) * (-0.2081 - t * 0.0013)
+ cos(2.0 * m) * (-0.1116 - t * 0.001)
+ sin(3.0 * m) * (0.0074 + t * 0.0001)
+ cos(3.0 * m) * (-0.0097 - t * 0.0001)
+ sin(aa) * (0.0 + t * (0.0144 - t * 0.00008))
+ cos(aa) * (0.3642 + t * (-0.0019 - t * 0.00029)))
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 = Jupiter.station_longitude_1(epoch)
>>> y, m, d = sta1.get_date()
>>> print(y)
2018
>>> print(m)
3
>>> print(round(d, 4))
9.1288
"""
# 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 Jupiter's opposition
a = 2451870.628
b = 398.884046
m0 = 318.4681
m1 = 33.140229
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
aa = Angle(aa).rad() # Convert to radians
corr = (-60.367 + t * (-0.0001 - t * 0.00009)
+ sin(m) * (-2.3144 + t * (-0.0124 + t * 0.00007))
+ cos(m) * (6.7439 + t * (0.0166 - t * 0.00006))
+ sin(2.0 * m) * (-0.2259 - t * 0.001)
+ cos(2.0 * m) * (-0.1497 - t * 0.0014)
+ sin(3.0 * m) * (0.0105 + t * 0.0001)
+ cos(3.0 * m) * (-0.0098)
+ sin(aa) * (0.0 + t * (0.0144 - t * 0.00008))
+ cos(aa) * (0.3642 + t * (-0.0019 - t * 0.00029)))
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 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)
>>> sta2 = Jupiter.station_longitude_2(epoch)
>>> y, m, d = sta2.get_date()
>>> print(y)
2018
>>> print(m)
7
>>> print(round(d, 4))
10.6679
"""
# 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 Jupiter's opposition
a = 2451870.628
b = 398.884046
m0 = 318.4681
m1 = 33.140229
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
aa = Angle(aa).rad() # Convert to radians
corr = (60.3023 + t * (0.0002 - t * 0.00009)
+ sin(m) * (0.3506 + t * (-0.0034 + t * 0.00004))
+ cos(m) * (5.3635 + t * (0.0247 - t * 0.00007))
+ sin(2.0 * m) * (-0.1872 - t * 0.0016)
+ cos(2.0 * m) * (-0.0037 - t * 0.0005)
+ sin(3.0 * m) * (0.0012 + t * 0.0001)
+ cos(3.0 * m) * (-0.0096 - t * 0.0001)
+ sin(aa) * (0.0 + t * (0.0144 - t * 0.00008))
+ cos(aa) * (0.3642 + t * (-0.0019 - t * 0.00029)))
to_return = jde0 + corr
return Epoch(to_return)
[docs] @staticmethod
def perihelion_aphelion(epoch, perihelion=True):
"""This method computes the time of Perihelion (or Aphelion) closer to
a given epoch.
:param epoch: Epoch close to the desired Perihelion (or Aphelion)
:type epoch: :py:class:`Epoch`
:param peihelion: If True, the epoch of the closest Perihelion is
computed, if False, the epoch of the closest Aphelion is found.
:type bool:
:returns: The epoch of the desired Perihelion (or Aphelion)
:rtype: :py:class:`Epoch`
:raises: TypeError if input values are of wrong type.
>>> epoch = Epoch(2019, 2, 23.0)
>>> e = Jupiter.perihelion_aphelion(epoch)
>>> y, m, d, h, mi, s = e.get_full_date()
>>> print(y)
2023
>>> print(m)
1
>>> print(d)
20
>>> print(h)
11
>>> epoch = Epoch(1981, 6, 1.0)
>>> e = Jupiter.perihelion_aphelion(epoch, perihelion=False)
>>> y, m, d, h, mi, s = e.get_full_date()
>>> print(y)
1981
>>> print(m)
7
>>> print(d)
28
>>> print(h)
6
"""
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input value")
# First approximation
k = 0.0843 * (epoch.year() - 2011.2)
if perihelion:
k = round(k)
else:
k = round(k + 0.5) - 0.5
jde = 2455636.936 + k * (4332.897065 - k * 0.0001367)
# Compute the epochs a month before and after
jde_before = jde - 30.0
jde_after = jde + 30.0
# Compute the Sun-Jupiter distance for each epoch
l, b, r_b = Jupiter.geometric_heliocentric_position(Epoch(jde_before))
l, b, r = Jupiter.geometric_heliocentric_position(Epoch(jde))
l, b, r_a = Jupiter.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 Jupiter, 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 = Jupiter.passage_nodes(epoch)
>>> year, month, day = time.get_date()
>>> print(year)
2025
>>> print(month)
9
>>> print(round(day, 1))
15.6
>>> print(round(r, 4))
5.1729
"""
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input types")
# Get the orbital parameters
l, a, e, i, ome, arg = Jupiter.orbital_elements_mean_equinox(epoch)
# Compute the time of passage through perihelion
t = Jupiter.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):
"""This function computes the approximate magnitude of Jupiter.
:param sun_dist: Distance from Jupiter to Sun, in Astronomical Units
:type sun_dist: float
:param earth_dist: Distance Jupiter to Earth, in Astronomical Units
:type earth_dist: float
:returns: Jupiter's magnitude
:rtype: float
:raises: TypeError if input values are of wrong type.
"""
if not (isinstance(sun_dist, float) and isinstance(earth_dist, float)):
raise TypeError("Invalid input types")
m = -8.93 + 5.0 * log10(sun_dist * earth_dist)
return round(m, 1)
def main():
# Let's define a small helper function
def print_me(msg, val):
print("{}: {}".format(msg, val))
# Let's show some uses of Jupiter class
print("\n" + 35 * "*")
print("*** Use of Jupiter class")
print(35 * "*" + "\n")
# Let's now compute the heliocentric position for a given epoch
epoch = Epoch(2018, 10, 27.0)
lon, lat, r = Jupiter.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 = Jupiter.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 Jupiter at 2065.6.24
epoch = Epoch(2065, 6, 24.0)
l, a, e, i, ome, arg = Jupiter.orbital_elements_mean_equinox(epoch)
print_me("Mean longitude of the planet", round(l, 6)) # 222.433723
print_me("Semimajor axis of the orbit (UA)", round(a, 8)) # 5.20260333
print_me("Eccentricity of the orbit", round(e, 7)) # 0.0486046
print_me("Inclination on plane of the ecliptic", round(i, 6)) # 1.29967
print_me("Longitude of the ascending node", round(ome, 5)) # 101.13309
print_me("Argument of the perihelion", round(arg, 6)) # -85.745532
print("")
# Compute the time of the conjunction close to 1993/10/1
epoch = Epoch(1993, 10, 1.0)
conj = Jupiter.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 = Jupiter.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 = Jupiter.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 = Jupiter.station_longitude_2(epoch)
y, m, d = sta2.get_date()
d = round(d, 4)
date = "{}/{}/{}".format(y, m, d)
print_me("Date of station in longitude #2", date)
print("")
# Find the epoch of the Aphelion closer to 1981/6/1
epoch = Epoch(1981, 6, 1.0)
e = Jupiter.perihelion_aphelion(epoch, perihelion=False)
y, m, d, h, mi, s = e.get_full_date()
peri = str(y) + '/' + str(m) + '/' + str(d) + ' at ' + str(h) + ' hours'
print_me("The Aphelion closest to 1981/6/1 will happen on", peri)
print("")
# Compute the time of passage through an ascending node
epoch = Epoch(2019, 1, 1)
time, r = Jupiter.passage_nodes(epoch)
y, m, d = time.get_date()
d = round(d, 1)
print("Time of passage through ascending node: {}/{}/{}".format(y, m, d))
# 2025/9/15.6
print("Radius vector at ascending node: {}".format(round(r, 4))) # 5.1729
if __name__ == "__main__":
main()