# -*- 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 Epoch import Epoch
from Coordinates import geometric_vsop_pos, apparent_vsop_pos
"""
.. module:: Venus
:synopsis: Class to model Venus planet
:license: GNU Lesser General Public License v3 (LGPLv3)
.. moduleauthor:: Dagoberto Salazar
"""
VSOP87_L = [
# L0
[
[317614666.774, 0.00000000000, 0.00000000000],
[1353968.419, 5.59313319619, 10213.28554621100],
[89891.645, 5.30650048468, 20426.57109242200],
[5477.201, 4.41630652531, 7860.41939243920],
[3455.732, 2.69964470778, 11790.62908865880],
[2372.061, 2.99377539568, 3930.20969621960],
[1317.108, 5.18668219093, 26.29831979980],
[1664.069, 4.25018935030, 1577.34354244780],
[1438.322, 4.15745043958, 9683.59458111640],
[1200.521, 6.15357115319, 30639.85663863300],
[761.380, 1.95014702120, 529.69096509460],
[707.676, 1.06466707214, 775.52261132400],
[584.836, 3.99839884762, 191.44826611160],
[769.314, 0.81629615911, 9437.76293488700],
[499.915, 4.12340210074, 15720.83878487840],
[326.221, 4.59056473097, 10404.73381232260],
[429.498, 3.58642859752, 19367.18916223280],
[326.967, 5.67736583705, 5507.55323866740],
[231.937, 3.16251057072, 9153.90361602180],
[179.695, 4.65337915578, 1109.37855209340],
[128.263, 4.22604493736, 20.77539549240],
[155.464, 5.57043888948, 19651.04848109800],
[127.907, 0.96209822685, 5661.33204915220],
[105.547, 1.53721191253, 801.82093112380],
[85.722, 0.35589249966, 3154.68708489560],
[99.121, 0.83288185132, 213.29909543800],
[98.804, 5.39389655503, 13367.97263110660],
[82.094, 3.21596990826, 18837.49819713819],
[88.031, 3.88868860307, 9999.98645077300],
[71.577, 0.11145739345, 11015.10647733480],
[56.122, 4.24039855475, 7.11354700080],
[70.239, 0.67458813282, 23581.25817731760],
[50.796, 0.24531603049, 11322.66409830440],
[46.111, 5.31576465717, 18073.70493865020],
[44.574, 6.06282201966, 40853.14218484400],
[42.594, 5.32873337210, 2352.86615377180],
[42.635, 1.79955421680, 7084.89678111520],
[41.177, 0.36240972161, 382.89653222320],
[35.749, 2.70448479296, 10206.17199921020],
[33.893, 2.02347322198, 6283.07584999140],
[29.138, 3.59230925768, 22003.91463486980],
[28.479, 2.22375414002, 1059.38193018920],
[29.850, 4.02176977477, 10239.58386601080],
[33.252, 2.10025596509, 27511.46787353720],
[30.172, 4.94191919890, 13745.34623902240],
[29.252, 3.51392387787, 283.85931886520],
[24.424, 2.70177493852, 8624.21265092720],
[20.274, 3.79493637509, 14143.49524243060],
[24.322, 4.27814493315, 5.52292430740],
[26.260, 0.54067587552, 17298.18232732620],
[20.492, 0.58547075036, 38.02767263580],
[18.988, 4.13811500642, 4551.95349705880],
[23.739, 4.82870797552, 6872.67311951120],
[15.885, 1.50067222283, 8635.94200376320],
[19.069, 6.12025580313, 29050.78374334920],
[18.269, 3.04740408477, 19999.97290154599],
[13.656, 4.41336292334, 3532.06069281140],
[17.094, 3.52161526430, 31441.67756975680],
[10.955, 2.84562790076, 18307.80723204360],
[11.048, 2.58361219075, 9786.68735533500],
[9.904, 1.08737710389, 7064.12138562280],
[10.576, 0.85419784436, 10596.18207843420],
[9.231, 5.52471655579, 12566.15169998280],
[11.599, 5.81007422699, 19896.88012732740],
[11.807, 1.91250672543, 21228.39202354580],
[10.105, 2.34270786693, 10742.97651130560],
[8.154, 1.92331359797, 15.25247118500],
[8.893, 1.97291388515, 10186.98722641120],
[9.352, 4.94508904764, 35371.88726597640],
[6.821, 4.39733188968, 8662.24032356300],
[6.688, 1.55310437864, 14945.31617355440],
[6.413, 2.17677652923, 10988.80815753500],
[5.802, 1.93462125906, 3340.61242669980],
[5.950, 2.96578175391, 4732.03062734340],
[5.275, 5.01877102496, 28286.99048486120],
[7.047, 1.00111452053, 632.78373931320],
[5.048, 4.27886209626, 29580.47470844380],
[6.305, 0.35506331180, 103.09277421860],
[5.959, 5.04792949464, 245.83164622940],
[4.651, 0.85218058876, 6770.71060124560],
[5.580, 0.48723384809, 522.57741809380],
[5.327, 3.03115417024, 10021.83728009940],
[5.010, 5.77375166500, 28521.09277825460],
[4.608, 1.93302108394, 4705.73230754360],
[5.526, 3.36797048901, 25158.60171976540],
[3.863, 4.89351531412, 25934.12433108940],
[5.303, 0.08161426841, 39302.09696219600],
[4.254, 5.36046113295, 21535.94964451540],
[3.763, 1.05304597315, 19.66976089979],
[4.407, 4.02575374517, 74.78159856730],
[4.145, 1.14356412295, 9676.48103411560],
[4.318, 4.38289970585, 316.39186965660],
[3.642, 6.11733529325, 3128.38876509580],
[3.238, 5.39551036769, 419.48464387520],
[3.909, 4.05263635330, 9690.70812811720],
[3.152, 0.72553551731, 16496.36139620240],
[3.496, 0.72414615705, 3723.50895892300],
[3.755, 3.80208713127, 19786.67380610799],
[2.891, 3.33782737770, 32217.20018108080],
[3.016, 1.57249112496, 17277.40693183380],
[3.825, 0.19612312903, 426.59819087600],
[3.798, 0.45524571743, 10316.37832042960],
[2.570, 1.20813474107, 13936.79450513400],
[2.796, 3.65128969074, 206.18554843720],
[2.466, 3.61988676373, 1551.04522264800],
[3.108, 1.50325806664, 43232.30665841560],
[2.976, 4.79415001304, 29088.81141598500],
[2.217, 3.59623681714, 24356.78078864160],
[2.227, 4.96059221940, 536.80451209540],
[2.397, 3.45249688427, 19374.30270923360],
[2.462, 0.53295178258, 19360.07561523199],
[2.205, 2.70399309963, 12592.45001978260],
[2.230, 3.01413465913, 18875.52586977400],
[1.858, 4.06129152783, 2379.16447357160],
[1.807, 3.15086214479, 9573.38825989700],
[2.238, 5.52216925076, 10138.50394764370],
[2.195, 2.32046770554, 8094.52168583260],
[2.101, 2.90421302975, 9967.45389998160],
[1.916, 4.56513949099, 2218.75710418680],
[1.467, 2.42640162465, 10234.06094170340],
[1.726, 5.59790693845, 20452.86941222180],
[1.455, 2.44757248737, 1589.07289528380],
[1.991, 4.04623390359, 31749.23519072640],
[1.406, 2.71736996917, 16983.99614745660],
[1.658, 0.11252373292, 153.77881048480],
[1.851, 2.92898027939, 47162.51635463520],
[1.492, 1.07513892753, 9103.90699411760],
[1.247, 2.48433565896, 17778.11626694899],
[1.549, 4.20553654300, 3442.57494496540],
[1.243, 3.95452438599, 170.67287061920],
[1.694, 6.20694480406, 33019.02111220460],
[1.221, 4.77931820602, 30110.16567353840],
[1.206, 0.30531303095, 29864.33402730900],
[1.238, 5.05581820608, 20213.27199698400],
[1.152, 3.26229919481, 11.72935283600],
[1.179, 1.69491074791, 20400.27277262220],
[1.165, 2.88995128147, 574.34479833480],
[1.306, 0.14519588607, 9146.79006902100],
[1.113, 1.52598846804, 10426.58464164900],
[1.104, 2.58791423813, 18849.22754997420],
[1.045, 0.57539216420, 15874.61759536320],
[1.360, 2.41976595457, 38734.37832446560],
[0.981, 4.37930727798, 110.20632121940],
[1.095, 0.49492867814, 51066.42773105500],
[1.146, 4.54241454215, 10220.39909321180],
[0.981, 1.65915064733, 10103.07922499160],
[1.270, 4.69374306132, 9050.81084180320],
[1.065, 4.41645258887, 22805.73556599360],
[0.854, 2.34437926957, 6681.22485339960],
[1.104, 0.49781459714, 1.48447270830],
[1.075, 1.09857593161, 377.37360791580],
[1.114, 4.35024775806, 51092.72605085480],
[0.829, 5.41196274578, 27991.40181316000],
[0.900, 2.74195379617, 41962.52073693740],
[1.010, 2.96092073452, 135.62532501000],
[0.768, 3.98260860494, 18844.61174413899],
[1.018, 1.36891050752, 36949.23080842420],
[0.726, 1.67728773965, 21202.09370374600],
[0.727, 0.89048212541, 467.96499035440],
[0.869, 2.93767679827, 10192.51015071860],
[0.696, 5.35698039414, 10063.72234907640],
[0.920, 4.17128923588, 18734.40542291960],
[0.691, 1.50594097883, 27197.28169366760],
[0.835, 0.48050621092, 20618.01935853360],
[0.711, 0.19750098222, 18830.38465013739],
[0.811, 0.16685071959, 12432.04265039780],
[0.756, 3.79022623226, 9161.01716302260],
[0.622, 5.33659507738, 9411.46461508720],
[0.862, 5.72705356405, 10175.15251057320],
[0.853, 0.10404188453, 2107.03450754240],
[0.742, 3.96365892051, 813.55028395980],
[0.705, 0.71229660616, 220.41264243880],
[0.584, 1.71900692700, 36.02786667740],
[0.612, 0.36418385449, 949.17560896980],
[0.587, 1.58648949290, 6.62855890001],
[0.581, 5.49288908804, 6309.37416979120],
[0.581, 4.80353237853, 24150.08005134500],
[0.516, 6.07328802561, 38.13303563780],
[0.627, 5.47281424954, 9580.50180689780],
[0.601, 1.40500080774, 1162.47470440780],
[0.620, 4.00681042667, 9992.87290377220],
[0.611, 3.62010998629, 7255.56965173440],
[0.697, 2.22359630727, 348.92442044800],
[0.693, 5.77432072851, 55022.93574707440],
[0.494, 0.29761886866, 7058.59846131540],
[0.563, 0.24172140474, 37410.56723987860],
[0.487, 5.86917216517, 10137.01947493540],
[0.493, 2.04534833854, 735.87651353180],
[0.636, 2.79707392326, 40879.44050464380],
[0.519, 4.13945657630, 16522.65971600220],
[0.535, 4.60569597820, 19573.37471066999],
[0.555, 5.88120421263, 26735.94526221320],
[0.440, 5.61490649795, 23958.63178523340],
[0.541, 0.62494922735, 10007.09999777380],
[0.427, 4.02335620501, 14.22709400160],
[0.434, 0.29028429049, 9264.10993724120],
[0.451, 1.66320363626, 26087.90314157420],
[0.422, 3.38413582674, 10787.63034454580],
[0.569, 5.14001758731, 27490.69247804480],
[0.421, 4.23407313457, 39793.76025465480],
[0.458, 5.28786368820, 49.75702547180],
[0.418, 5.69097790790, 14765.23904326980],
[0.475, 0.97544690438, 1052.26838318840],
[0.387, 4.41665162999, 21.85082932640],
[0.523, 2.90512426870, 20235.12282631040],
[0.506, 5.26999314618, 29999.95935231900],
[0.438, 2.49457071132, 20956.26205751660],
[0.530, 0.71368442157, 33794.54372352860],
[0.382, 1.92119365480, 3.93215326310],
[0.365, 3.81715328784, 20419.45754542119],
[0.426, 2.06384083608, 38204.68735937100],
[0.496, 0.44077356179, 9835.91193829520],
[0.410, 4.93346326003, 19264.09638801420],
[0.380, 3.79573358631, 8521.11987670860],
[0.334, 5.51158557799, 10251.31321884680],
[0.412, 2.56129670728, 77.67377042800],
[0.418, 2.37865963521, 32.53255079140],
[0.325, 6.03020523465, 18947.70451835760],
[0.400, 0.91999360201, 227.47613278900],
[0.437, 0.91420135162, 58953.14544329400],
[0.360, 0.82477639126, 22.77520145080],
[0.413, 4.22381905655, 44809.65020086340],
[0.375, 3.15657291896, 19992.85935454519],
[0.371, 6.05370874275, 20007.08644854680],
[0.361, 5.44371227904, 19470.28193645139],
[0.386, 5.28120540405, 47623.85278608960],
[0.389, 0.73216672240, 19050.79729257620],
[0.320, 2.84811591194, 10199.05845220940],
[0.386, 3.88754165531, 1975.49254585600],
[0.276, 4.33979180814, 20809.46762464520],
[0.276, 0.50647429773, 9830.38901398780],
[0.309, 3.79299100668, 18204.71445782499],
[0.377, 0.73768791281, 11506.76976979360],
[0.322, 0.96138442100, 30666.15495843280],
[0.363, 1.30472406690, 9367.20271145980],
[0.366, 2.79972786028, 11272.66747640020],
[0.271, 4.66141338193, 846.08283475120],
[0.259, 0.42031175750, 39264.06928956020],
[0.285, 0.40546033634, 30.91412563500],
[0.247, 4.80676426942, 36147.40987730040],
[0.264, 2.71608177583, 11.04570026390],
[0.233, 2.76423842887, 187.92514776260],
[0.248, 1.60765612338, 10497.14486507620],
[0.271, 0.82348919630, 19793.78735310880],
[0.225, 3.80080957016, 8631.32619792800],
[0.263, 1.92311689852, 37724.75341974820],
[0.214, 5.01663795092, 639.89728631400],
[0.289, 0.12342601246, 20277.00789528740],
[0.210, 0.12771800254, 29.82143814880],
[0.227, 4.18036609801, 17468.85519794540],
[0.274, 2.34929343000, 62883.35513951360],
[0.260, 5.65254501655, 48739.85989708300],
[0.271, 4.95325404028, 4214.06901508480],
[0.219, 2.08775228014, 194.97138446060],
[0.191, 2.49267248333, 568.82187402740],
[0.250, 1.52909737354, 6037.24420376200],
[0.231, 5.23674429498, 491.66329245880],
[0.182, 4.98046042571, 18418.01355326299],
[0.188, 2.82273639603, 1385.89527633620],
[0.204, 4.09939796199, 14919.01785375460],
[0.176, 3.82400982460, 9360.08916445900],
[0.198, 2.76491873243, 10217.21769947410],
[0.168, 5.19268384202, 1066.49547719000],
[0.199, 1.95301487982, 7564.83072073800],
[0.171, 2.59623459612, 20405.79569692960],
[0.172, 5.29332132623, 11764.33076885900],
[0.165, 2.88557908025, 10207.76262190360],
[0.164, 3.25435371801, 3914.95722503460],
[0.200, 3.82443218090, 18314.92077904440],
[0.169, 1.78341902878, 31022.75317085620],
[0.179, 0.90840065587, 7880.08915333899],
[0.163, 2.79665037814, 41.55079098480],
[0.154, 3.90796293476, 30213.25844775700],
[0.153, 0.07463240782, 28528.20632525540],
[0.194, 5.95838706838, 8617.09910392640],
[0.171, 4.58206324409, 20447.34648791440],
[0.150, 2.11647586229, 17248.42530185440],
[0.149, 2.17259986320, 9929.42622734580],
[0.191, 0.82310353823, 52670.06959330260],
[0.148, 2.94315921485, 41654.96311596780],
[0.149, 4.49798039726, 30831.30490474460],
[0.184, 2.46923348701, 34596.36465465240],
[0.146, 2.69452930300, 43071.89928903080],
[0.159, 2.11137713570, 19317.19254032860],
[0.154, 2.76536164654, 28513.97923125379],
[0.140, 4.94595038686, 9256.99639024040],
[0.141, 2.57248458154, 13553.89797291080],
[0.137, 1.66482327575, 2636.72547263700],
[0.140, 5.23039605990, 22645.32819660879],
[0.132, 5.35690599728, 19624.75016129820],
[0.140, 2.90637712614, 48947.66387067660],
[0.129, 3.95303623681, 32858.61374281979],
[0.156, 6.01143316387, 29057.89729034999],
[0.134, 5.75241675118, 68050.42387851159],
[0.154, 3.66827363753, 276.74577186440],
[0.176, 3.77298381177, 66813.56483573320],
[0.126, 5.00217740223, 27461.71084806540],
[0.135, 1.34807013920, 53285.18483524180],
[0.150, 0.25029475344, 290.97286586600],
[0.152, 3.13035670092, 29043.67019634839],
[0.169, 5.04348109430, 73.29712585900],
[0.166, 5.39219948035, 41236.03871706720],
[0.163, 5.59796070987, 7576.56007357400],
[0.126, 0.77391784606, 49.99662190420],
[0.163, 0.44241846674, 20350.30502114640],
[0.136, 3.09066368912, 418.92439890060],
[0.154, 0.47086190960, 28418.00000403600],
[0.120, 0.88536981986, 29573.36116144300],
[0.132, 1.48009769040, 17085.95866572220],
[0.126, 1.39497760964, 966.97087743560],
[0.143, 3.84026797958, 14128.24277124560],
[0.147, 2.11627427804, 34363.36559755600],
[0.106, 2.04696932293, 37674.99639427640],
[0.106, 1.43873202489, 27682.14074415640],
[0.149, 0.09286508794, 8144.27871130440],
[0.103, 0.01992041470, 18300.69368504279],
[0.121, 3.57602835443, 45.14121963660],
[0.125, 0.11630302078, 149.56319713460],
[0.102, 4.17947097730, 2333.19639287200],
[0.099, 1.51324741657, 10419.47109464820],
[0.133, 3.02183293676, 76251.32777062019],
[0.136, 4.17517197268, 3646.35037735440],
[0.123, 0.44045588682, 515.46387109300],
[0.113, 5.69261397718, 10110.19277199240],
[0.098, 6.23797900467, 202.25339517410],
[0.099, 3.75627530197, 59728.66805461800],
[0.101, 4.62832557536, 65236.22129328540],
[0.111, 1.25947267588, 10846.06928552420],
[0.110, 5.87455577536, 38500.27603107220],
[0.128, 6.01024562160, 90394.82301305079],
[0.091, 1.77665981007, 1539.31586981200],
[0.092, 0.99804571578, 95.97922721780],
[0.120, 3.93060866244, 38526.57435087200],
[0.117, 2.24143299549, 56600.27928952220],
[0.118, 6.09121325940, 29786.66025688100],
[0.098, 4.60938156207, 11787.10597030980],
[0.097, 3.92727733144, 11794.15220700780],
[0.093, 5.23395435043, 14169.79356223040],
[0.096, 5.27525709038, 8734.41897214660],
[0.094, 0.18166654805, 67589.08744705719],
[0.110, 4.96279287076, 48417.97290558199],
[0.086, 0.39533409505, 3956.50801601940],
[0.085, 5.69642646462, 37703.97802425580],
[0.114, 5.19676285428, 70743.77453195279],
[0.081, 5.51324815184, 412.37109687440],
[0.089, 2.13409771828, 44768.09940987860],
[0.084, 6.02475904578, 10632.77019008620],
[0.085, 4.60912614442, 45585.17281218740],
[0.078, 4.47358603432, 114.43928868521],
[0.097, 4.02223363535, 10218.80847051840],
[0.081, 1.03870237004, 9793.80090233580],
[0.092, 0.80301220092, 24383.07910844140],
[0.087, 2.15124790938, 28313.28880466100],
[0.075, 5.17868679355, 63658.87775083760],
[0.078, 5.81927313665, 567.71863773040],
[0.075, 1.72618192481, 19580.48825767080],
[0.071, 0.10259261764, 90695.75207512038],
[0.077, 6.16012067704, 1573.82042409880],
[0.076, 5.12884307551, 49515.38250840700],
[0.069, 0.29569499484, 10175.25787357520],
[0.061, 4.80385549281, 19889.76658032659],
[0.060, 4.56685040226, 30426.55754319500],
[0.062, 4.16222812699, 42430.48572729180],
[0.050, 6.17899839001, 22779.43724619380],
[0.048, 1.52546758016, 20639.87018786000],
[0.046, 4.41738494249, 34570.06633485260],
[0.037, 4.69675087759, 44007.82926973960],
],
# L1
[
[1021352943052.898, 0.00000000000, 0.00000000000],
[95707.712, 2.46424448979, 10213.28554621100],
[14444.977, 0.51624564679, 20426.57109242200],
[213.374, 1.79547929368, 30639.85663863300],
[151.669, 6.10635282369, 1577.34354244780],
[173.904, 2.65535879443, 26.29831979980],
[82.233, 5.70234133730, 191.44826611160],
[69.734, 2.68136034979, 9437.76293488700],
[52.408, 3.60013087656, 775.52261132400],
[38.318, 1.03379038025, 529.69096509460],
[29.633, 1.25056322354, 5507.55323866740],
[25.056, 6.10664792855, 10404.73381232260],
[17.772, 6.19369798901, 1109.37855209340],
[16.510, 2.64330452640, 7.11354700080],
[14.230, 5.45138233941, 9153.90361602180],
[12.607, 1.24464400689, 40853.14218484400],
[11.627, 4.97604495371, 213.29909543800],
[12.563, 1.88122199199, 382.89653222320],
[8.869, 0.95282732248, 13367.97263110660],
[7.374, 4.39476760580, 10206.17199921020],
[6.552, 2.28168808058, 2352.86615377180],
[6.255, 4.08056644034, 3154.68708489560],
[6.697, 5.05673427795, 801.82093112380],
[4.084, 4.12103826030, 18837.49819713819],
[4.882, 3.44515199115, 11015.10647733480],
[3.549, 6.19934345402, 5.52292430740],
[3.448, 1.77405651704, 11322.66409830440],
[4.290, 0.08154809210, 6283.07584999140],
[3.694, 2.48453945256, 5661.33204915220],
[3.555, 1.48036949420, 1059.38193018920],
[3.023, 2.24092938317, 18073.70493865020],
[3.000, 0.39169917698, 15.25247118500],
[2.563, 0.35147506973, 22003.91463486980],
[2.774, 1.45683830639, 10239.58386601080],
[2.951, 5.34618097429, 7084.89678111520],
[2.344, 2.36652432105, 17298.18232732620],
[2.405, 2.36085282088, 10596.18207843420],
[1.720, 4.72129626061, 10186.98722641120],
[2.209, 2.07730338665, 8635.94200376320],
[2.122, 4.47091605309, 8624.21265092720],
[1.527, 0.67146857292, 14143.49524243060],
[1.473, 2.59350470099, 7064.12138562280],
[1.311, 0.90408820221, 12566.15169998280],
[1.474, 5.92236241437, 9786.68735533500],
[1.237, 2.59740787132, 4551.95349705880],
[1.219, 2.83617320088, 9676.48103411560],
[1.116, 3.83715584719, 21228.39202354580],
[1.006, 4.26200749078, 426.59819087600],
[1.150, 2.35531987378, 9690.70812811720],
[1.219, 2.27324315182, 522.57741809380],
[1.150, 0.81088598778, 10742.97651130560],
[1.101, 3.74248783564, 18307.80723204360],
[1.031, 2.03889374176, 38.02767263580],
[0.971, 6.10590045414, 3532.06069281140],
[0.844, 4.75124127613, 10988.80815753500],
[0.908, 1.06613723738, 10021.83728009940],
[0.824, 0.23090829723, 28286.99048486120],
[0.821, 2.60456032773, 19.66976089979],
[0.728, 0.10716917942, 4705.73230754360],
[0.744, 3.33129778857, 536.80451209540],
[0.816, 1.27303930175, 19896.88012732740],
[0.929, 1.08024621325, 11790.62908865880],
[0.797, 2.23891816523, 3723.50895892300],
[0.704, 5.95307260017, 20.77539549240],
[0.665, 0.21346689192, 7860.41939243920],
[0.733, 2.22147883292, 19360.07561523199],
[0.702, 1.76206343944, 19374.30270923360],
[0.575, 2.38792087791, 6770.71060124560],
[0.538, 1.52023264138, 25934.12433108940],
[0.690, 4.01873754171, 19651.04848109800],
[0.532, 4.41576130890, 574.34479833480],
[0.540, 2.15936134728, 16496.36139620240],
[0.576, 5.41170044566, 206.18554843720],
[0.482, 0.40815793538, 3340.61242669980],
[0.501, 3.08578363577, 245.83164622940],
[0.488, 5.22311611589, 25158.60171976540],
[0.450, 0.21279844600, 11.72935283600],
[0.432, 1.32004964493, 103.09277421860],
[0.434, 5.91094755233, 19786.67380610799],
[0.564, 0.38776462529, 19367.18916223280],
[0.421, 2.71057839701, 13936.79450513400],
[0.549, 6.08792865644, 3930.20969621960],
[0.478, 4.70234715828, 14945.31617355440],
[0.408, 4.80890663927, 32217.20018108080],
[0.404, 2.85003595942, 29864.33402730900],
[0.407, 2.94002049006, 10220.39909321180],
[0.359, 0.72354778897, 419.48464387520],
[0.449, 1.44520508753, 8662.24032356300],
[0.353, 2.22195492336, 51066.42773105500],
[0.324, 1.40308439067, 29580.47470844380],
[0.443, 1.93864353398, 9146.79006902100],
[0.314, 0.96837035284, 20618.01935853360],
[0.324, 5.10759068171, 24356.78078864160],
[0.324, 1.80146948625, 18830.38465013739],
[0.370, 6.16895004656, 2218.75710418680],
[0.278, 2.20429108375, 18844.61174413899],
[0.286, 3.08459438435, 17277.40693183380],
[0.383, 0.13890934755, 4732.03062734340],
[0.292, 0.43528982259, 29088.81141598500],
[0.273, 5.84415407168, 9573.38825989700],
[0.324, 2.14144542781, 9999.98645077300],
[0.264, 5.20407029554, 220.41264243880],
[0.254, 0.34411959301, 28521.09277825460],
[0.300, 3.76014360906, 8094.52168583260],
[0.301, 3.64457981649, 20400.27277262220],
[0.287, 1.84003536598, 1589.07289528380],
[0.206, 0.97167234723, 10234.06094170340],
[0.212, 0.24173677600, 36.02786667740],
[0.216, 5.88618923030, 18875.52586977400],
[0.198, 1.89506914939, 20452.86941222180],
[0.258, 6.27611355094, 1551.04522264800],
[0.197, 2.09222675324, 9683.59458111640],
[0.217, 5.79472589364, 9103.90699411760],
[0.188, 0.39123199129, 19573.37471066999],
[0.195, 6.23142464829, 30110.16567353840],
[0.187, 5.49670351645, 170.67287061920],
[0.178, 4.90042854659, 10787.63034454580],
[0.188, 1.62614804098, 9161.01716302260],
[0.211, 2.71884568392, 15720.83878487840],
[0.177, 1.88170417337, 33019.02111220460],
[0.209, 2.66033422116, 3442.57494496540],
[0.164, 4.92240093026, 10426.58464164900],
[0.186, 5.13678812068, 7255.56965173440],
[0.177, 5.70206821967, 9992.87290377220],
[0.214, 2.70027196648, 3128.38876509580],
[0.208, 3.38876526854, 17778.11626694899],
[0.147, 4.25008782855, 16983.99614745660],
[0.148, 3.46404418130, 21202.09370374600],
[0.189, 1.43553862242, 2379.16447357160],
[0.139, 2.99154379541, 110.20632121940],
[0.159, 5.23851679605, 10007.09999777380],
[0.136, 0.88942869764, 22805.73556599360],
[0.155, 5.90500835975, 12592.45001978260],
[0.151, 0.03422618975, 27991.40181316000],
[0.153, 4.01743770323, 33794.54372352860],
[0.121, 0.51392111799, 21535.94964451540],
[0.109, 2.25388616761, 26735.94526221320],
[0.109, 0.78612823474, 6681.22485339960],
[0.122, 4.84805105466, 19992.85935454519],
[0.112, 3.31796669604, 36949.23080842420],
[0.106, 3.34507236765, 10103.07922499160],
[0.114, 4.36384000196, 20007.08644854680],
[0.098, 5.07711736751, 135.62532501000],
[0.120, 5.41870615047, 37724.75341974820],
[0.103, 2.62610244425, 20213.27199698400],
[0.085, 5.04808202087, 9830.38901398780],
[0.103, 2.01549383816, 45585.17281218740],
[0.088, 2.62613816931, 21.85082932640],
[0.084, 3.50355880173, 639.89728631400],
[0.099, 0.61079620895, 41654.96311596780],
[0.088, 3.63836700262, 49515.38250840700],
[0.098, 2.42401801881, 23581.25817731760],
[0.081, 0.46468679835, 77.67377042800],
[0.092, 4.82530051729, 29043.67019634839],
[0.102, 4.27051236894, 15874.61759536320],
[0.090, 4.34075776744, 29057.89729034999],
[0.081, 0.01896422336, 24150.08005134500],
[0.093, 1.79250830018, 12432.04265039780],
[0.087, 5.25157021446, 14128.24277124560],
[0.089, 5.65756996753, 377.37360791580],
[0.097, 5.67942873241, 227.47613278900],
[0.076, 2.93363913259, 38204.68735937100],
[0.091, 2.60544242067, 1052.26838318840],
[0.087, 3.82284200928, 27511.46787353720],
[0.073, 4.75280755154, 40879.44050464380],
[0.067, 3.54815262526, 30666.15495843280],
[0.067, 5.81350818057, 20809.46762464520],
[0.064, 4.24772678145, 153.77881048480],
[0.064, 2.99454749109, 27197.28169366760],
[0.070, 4.03868009742, 56600.27928952220],
[0.071, 4.33628806850, 39264.06928956020],
[0.069, 1.73648747605, 37410.56723987860],
[0.065, 1.08206062736, 68050.42387851159],
[0.062, 4.77698454650, 3914.95722503460],
[0.061, 4.96121014691, 34596.36465465240],
[0.063, 5.04865067599, 53445.59220462660],
[0.058, 3.74010494151, 1066.49547719000],
[0.057, 5.39355890141, 20419.45754542119],
[0.057, 3.59399518494, 735.87651353180],
[0.065, 2.10322000074, 74.78159856730],
[0.073, 1.31083648835, 11272.66747640020],
[0.055, 1.33161298098, 18300.69368504279],
[0.065, 4.21150522641, 49.75702547180],
[0.061, 5.66161679402, 17468.85519794540],
[0.053, 4.30231233835, 18849.22754997420],
[0.055, 2.63906959481, 52670.06959330260],
[0.050, 5.69803054279, 39793.76025465480],
[0.049, 0.77345264124, 35371.88726597640],
[0.048, 6.00565977593, 283.85931886520],
[0.047, 2.63299859494, 51868.24866217880],
[0.046, 0.05105081843, 38526.57435087200],
[0.050, 4.37549274002, 28513.97923125379],
[0.046, 2.93422086586, 27682.14074415640],
[0.051, 5.45979584751, 60530.48898574180],
[0.045, 5.59492908223, 467.96499035440],
[0.045, 2.34680401001, 9411.46461508720],
[0.045, 0.02999265111, 44809.65020086340],
[0.043, 5.62725673544, 14.22709400160],
[0.047, 3.73567275749, 64460.69868196140],
[0.046, 0.12586526756, 57375.80190084620],
[0.044, 2.03114426076, 18314.92077904440],
[0.039, 0.99375127466, 94138.32702008578],
[0.053, 0.41974404621, 30831.30490474460],
[0.055, 1.38351566741, 38500.27603107220],
[0.041, 4.47012768909, 40077.61957352000],
[0.041, 0.36665992484, 19999.97290154599],
[0.040, 3.06358586355, 813.55028395980],
[0.040, 2.16802870803, 59728.66805461800],
[0.037, 1.08739100421, 17085.95866572220],
[0.039, 1.31040309875, 48739.85989708300],
[0.036, 1.43280677914, 42456.78404709160],
[0.037, 0.14190533464, 29050.78374334920],
[0.037, 3.66792179278, 20956.26205751660],
[0.025, 3.38876180652, 7058.59846131540],
[0.031, 6.16829805337, 10192.51015071860],
],
# L2
[
[54127.076, 0.00000000000, 0.00000000000],
[3891.460, 0.34514360047, 10213.28554621100],
[1337.880, 2.02011286082, 20426.57109242200],
[23.836, 2.04592119012, 26.29831979980],
[19.331, 3.53527371458, 30639.85663863300],
[9.984, 3.97130221102, 775.52261132400],
[7.046, 1.51962593409, 1577.34354244780],
[6.014, 0.99926757893, 191.44826611160],
[3.163, 4.36095475762, 9437.76293488700],
[2.125, 2.65810625752, 40853.14218484400],
[1.934, 3.39287946981, 382.89653222320],
[1.460, 6.04899046273, 529.69096509460],
[1.346, 2.94633106219, 5507.55323866740],
[1.025, 1.40598904981, 10404.73381232260],
[1.221, 3.73339139385, 3154.68708489560],
[1.033, 3.52858472904, 11015.10647733480],
[0.955, 5.11133878923, 801.82093112380],
[0.742, 1.49198584483, 1109.37855209340],
[0.525, 3.32087042103, 213.29909543800],
[0.578, 0.92614279843, 10239.58386601080],
[0.602, 5.19220099775, 7084.89678111520],
[0.431, 2.67159914364, 13367.97263110660],
[0.389, 4.14116341739, 8635.94200376320],
[0.355, 1.12061570874, 9153.90361602180],
[0.301, 3.90047984197, 10596.18207843420],
[0.212, 5.32697688872, 18837.49819713819],
[0.260, 0.22761369281, 2352.86615377180],
[0.243, 4.70747902991, 6283.07584999140],
[0.196, 4.10467294392, 11790.62908865880],
[0.194, 6.01197759470, 7860.41939243920],
[0.140, 4.97015671653, 14143.49524243060],
[0.134, 4.10529011674, 17298.18232732620],
[0.119, 3.39375528828, 11322.66409830440],
[0.126, 0.09854516140, 18073.70493865020],
[0.122, 5.92478855457, 574.34479833480],
[0.107, 0.35660030184, 1059.38193018920],
[0.108, 2.25352052666, 12566.15169998280],
[0.093, 5.48716819776, 10021.83728009940],
[0.084, 4.89744332968, 18307.80723204360],
[0.074, 2.35354025573, 426.59819087600],
[0.093, 4.99316908815, 14945.31617355440],
[0.069, 3.86409065860, 51066.42773105500],
[0.082, 5.36280178643, 10186.98722641120],
[0.077, 3.75728548372, 3723.50895892300],
[0.063, 5.39882267787, 21228.39202354580],
[0.056, 4.11564786973, 7064.12138562280],
[0.056, 6.26920407723, 32217.20018108080],
[0.060, 5.02186497542, 19367.18916223280],
[0.058, 5.13263709670, 20400.27277262220],
[0.051, 4.52870390511, 22003.91463486980],
[0.041, 3.83822107919, 16496.36139620240],
[0.041, 3.36020411807, 4705.73230754360],
[0.043, 5.98371820588, 15720.83878487840],
[0.047, 0.18498155367, 18875.52586977400],
[0.038, 0.52232581277, 1551.04522264800],
[0.039, 5.05391675878, 10742.97651130560],
[0.036, 3.16242472203, 20452.86941222180],
[0.035, 5.17462577483, 29088.81141598500],
[0.035, 3.47325394141, 24356.78078864160],
[0.031, 4.74511706231, 28521.09277825460],
[0.029, 0.19383091192, 19896.88012732740],
[0.033, 1.80059867635, 20618.01935853360],
[0.024, 0.14022912457, 21202.09370374600],
[0.022, 4.73565067573, 10988.80815753500],
[0.018, 0.74039763161, 25158.60171976540],
[0.019, 1.53770232218, 28286.99048486120],
[0.014, 1.49084059765, 30110.16567353840],
[0.013, 4.72171283479, 29864.33402730900],
[0.013, 5.79700427846, 29580.47470844380],
[0.014, 3.69205225010, 27511.46787353720],
],
# L3
[
[135.742, 4.80389020993, 10213.28554621100],
[77.846, 3.66876371591, 20426.57109242200],
[26.023, 0.00000000000, 0.00000000000],
[1.214, 5.31970006917, 30639.85663863300],
[0.254, 4.15021671822, 40853.14218484400],
[0.008, 5.55523563261, 51066.42773105500],
[0.008, 1.40501229148, 1577.34354244780],
[0.006, 1.27791479726, 10404.73381232260],
[0.006, 5.76447068962, 10239.58386601080],
],
# L4
[
[114.016, 3.14159265359, 0.00000000000],
[3.209, 5.20514170164, 20426.57109242200],
[1.714, 2.51099591706, 10213.28554621100],
[0.050, 0.71356059861, 30639.85663863300],
[0.023, 5.68127607034, 40853.14218484400],
],
# L5
[
[0.874, 3.14159265359, 0.00000000000],
[0.117, 0.54643013000, 20426.57109242200],
[0.118, 1.90548541922, 10213.28554621100],
[0.002, 1.07734277826, 40853.14218484400],
[0.002, 1.89460223529, 30639.85663863300],
],
]
"""This table contains Venus'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 418-420."""
VSOP87_B = [
# B0
[
[5923638.472, 0.26702775813, 10213.28554621100],
[40107.978, 1.14737178106, 20426.57109242200],
[32814.918, 3.14159265359, 0.00000000000],
[1011.392, 1.08946123021, 30639.85663863300],
[149.458, 6.25390296069, 18073.70493865020],
[137.788, 0.86020146523, 1577.34354244780],
[129.973, 3.67152483651, 9437.76293488700],
[119.507, 3.70468812804, 2352.86615377180],
[107.971, 4.53903677647, 22003.91463486980],
[92.029, 1.53954562706, 9153.90361602180],
[52.982, 2.28138172277, 5507.55323866740],
[45.617, 0.72319641722, 10239.58386601080],
[38.855, 2.93437865147, 10186.98722641120],
[43.491, 6.14015776699, 11790.62908865880],
[41.700, 5.99126845246, 19896.88012732740],
[39.644, 3.86842095901, 8635.94200376320],
[39.175, 3.94960351174, 529.69096509460],
[33.320, 4.83194909595, 14143.49524243060],
[23.711, 2.90646621218, 10988.80815753500],
[23.500, 2.00770618322, 13367.97263110660],
[21.809, 2.69701424951, 19651.04848109800],
[20.653, 0.98666685459, 775.52261132400],
[16.976, 4.13711782135, 10021.83728009940],
[17.835, 5.96268643102, 25934.12433108940],
[14.949, 5.61075168206, 10404.73381232260],
[18.579, 1.80529277514, 40853.14218484400],
[15.407, 3.29563855296, 11015.10647733480],
[12.936, 5.42651448496, 29580.47470844380],
[11.962, 3.57604253827, 10742.97651130560],
[11.827, 1.19070919600, 8624.21265092720],
[11.466, 5.12780364967, 6283.07584999140],
[9.484, 2.75167834335, 191.44826611160],
[13.129, 5.70735942511, 9683.59458111640],
[8.583, 0.43182249199, 9786.68735533500],
[9.763, 0.14614896296, 20618.01935853360],
[8.148, 1.30548515603, 15720.83878487840],
[6.050, 6.26541665966, 11322.66409830440],
[5.955, 4.92235372433, 1059.38193018920],
[6.983, 3.44920932146, 17298.18232732620],
[6.228, 1.13312070908, 29864.33402730900],
[6.186, 4.92498052443, 19367.18916223280],
[6.155, 2.42413946900, 4705.73230754360],
[5.204, 3.42528906628, 9103.90699411760],
[6.000, 3.57639095526, 3154.68708489560],
[4.796, 3.86676184909, 7860.41939243920],
[5.289, 4.99182712443, 7084.89678111520],
[4.070, 5.58798144740, 12566.15169998280],
[3.942, 5.68758787835, 10206.17199921020],
[3.797, 3.89520601076, 10192.51015071860],
[3.798, 6.06410995916, 10234.06094170340],
[3.579, 0.73789669235, 4551.95349705880],
[3.641, 2.61501257205, 15874.61759536320],
[3.266, 0.97517223854, 23581.25817731760],
[2.813, 0.29951755546, 9411.46461508720],
[3.048, 2.51085146990, 33794.54372352860],
[2.559, 4.58043833032, 801.82093112380],
[2.462, 5.05790874754, 29050.78374334920],
[2.593, 5.73113176751, 20213.27199698400],
[2.625, 4.24272906574, 213.29909543800],
[2.246, 0.82112963936, 28286.99048486120],
[2.229, 2.22457598233, 10426.58464164900],
[1.742, 1.48394229233, 7058.59846131540],
[1.660, 5.42775825275, 32217.20018108080],
[1.491, 4.64883377941, 1109.37855209340],
[2.010, 0.75702888128, 9999.98645077300],
[1.562, 3.93962080463, 37724.75341974820],
[1.538, 2.17309577080, 21535.94964451540],
[1.546, 4.70759186462, 14945.31617355440],
[1.200, 1.48282382657, 9830.38901398780],
[1.224, 5.55090394449, 5661.33204915220],
[1.111, 1.20276209213, 9573.38825989700],
[1.064, 1.98891375536, 26.29831979980],
[1.041, 5.38535116069, 7.11354700080],
[1.036, 1.16719443387, 8662.24032356300],
[1.143, 3.20596958337, 3532.06069281140],
[1.201, 0.81913312536, 8094.52168583260],
[1.005, 2.38429892132, 27511.46787353720],
[1.047, 4.56525030769, 20419.45754542119],
[0.968, 6.18496721871, 25158.60171976540],
[1.044, 1.98055689074, 10596.18207843420],
[0.962, 0.48573513747, 23958.63178523340],
[0.846, 0.01566400887, 3128.38876509580],
[0.792, 5.39686899735, 24356.78078864160],
[0.858, 5.34692750735, 41654.96311596780],
[0.757, 6.25904553773, 20452.86941222180],
[0.801, 4.62406152514, 9929.42622734580],
[0.802, 5.37234892520, 10497.14486507620],
[0.750, 3.85219782842, 21228.39202354580],
[0.700, 1.98097957188, 3930.20969621960],
[0.719, 6.11596800207, 10218.80847051840],
[0.672, 6.23429601219, 14765.23904326980],
[0.639, 5.37566437358, 1589.07289528380],
[0.605, 2.42330391120, 10251.31321884680],
[0.726, 6.16683781802, 18875.52586977400],
[0.613, 5.99731180690, 4732.03062734340],
[0.720, 3.84286345199, 10207.76262190360],
[0.637, 6.17053891156, 10220.39909321180],
[0.515, 1.03001478293, 22779.43724619380],
[0.574, 0.43813688572, 17085.95866572220],
[0.510, 1.41065159851, 9161.01716302260],
[0.569, 3.34601425125, 3340.61242669980],
[0.608, 1.25236241968, 10175.25787357520],
[0.524, 2.39794248670, 26087.90314157420],
[0.542, 1.34665646732, 29088.81141598500],
[0.527, 4.01994270827, 18849.22754997420],
[0.569, 1.65498800378, 39264.06928956020],
[0.518, 4.96996115446, 30213.25844775700],
[0.514, 5.78413007838, 12592.45001978260],
[0.538, 4.56198493922, 10063.72234907640],
[0.484, 4.18538027381, 14919.01785375460],
[0.493, 4.79939382739, 9146.79006902100],
[0.427, 3.76876868949, 11272.66747640020],
[0.495, 0.49175293655, 45585.17281218740],
[0.494, 3.74345863918, 31441.67756975680],
[0.524, 0.97991794166, 30110.16567353840],
[0.483, 1.87898057316, 51066.42773105500],
[0.505, 3.70047474212, 20400.27277262220],
[0.351, 4.34026574490, 10137.01947493540],
[0.355, 5.56672554631, 18837.49819713819],
[0.328, 3.78427378910, 6681.22485339960],
[0.349, 4.20550749672, 20956.26205751660],
[0.333, 4.44969281739, 28521.09277825460],
[0.296, 2.83205515646, 17277.40693183380],
[0.311, 2.57334132897, 20809.46762464520],
[0.294, 0.75089224483, 3149.16416058820],
[0.377, 3.98143308775, 21202.09370374600],
[0.272, 5.56183082489, 16496.36139620240],
[0.314, 0.02584607093, 13745.34623902240],
[0.263, 0.55328410985, 36147.40987730040],
[0.286, 5.16408902215, 426.59819087600],
[0.279, 4.29871615943, 19999.97290154599],
[0.280, 1.92925047377, 49515.38250840700],
[0.265, 4.81168402147, 20235.12282631040],
[0.273, 5.12740051559, 35371.88726597640],
[0.306, 5.28903794869, 382.89653222320],
[0.223, 2.50591724074, 26709.64694241340],
[0.235, 5.96522395118, 10198.03307502600],
[0.234, 3.52866583267, 10228.53801739600],
[0.224, 6.24561979789, 7064.12138562280],
[0.251, 2.84739274245, 33019.02111220460],
[0.196, 1.50610393790, 31749.23519072640],
[0.192, 1.69321442572, 13341.67431130680],
[0.180, 6.19353087076, 39793.76025465480],
[0.199, 1.16433321880, 22805.73556599360],
[0.180, 3.72646417141, 1551.04522264800],
[0.173, 3.35235705827, 53445.59220462660],
[0.195, 1.51901264131, 43232.30665841560],
[0.174, 2.84049662693, 9967.45389998160],
[0.163, 4.29160537719, 36949.23080842420],
[0.169, 0.37000676558, 10459.11719244040],
[0.137, 5.61149803116, 10529.67741586760],
[0.139, 0.87847805052, 16522.65971600220],
[0.139, 4.12576475427, 36301.18868778519],
[0.127, 5.14447758616, 5481.25491886760],
[0.131, 3.11317801589, 9896.89367655440],
[0.131, 0.89697384735, 3442.57494496540],
[0.121, 1.32802112907, 38734.37832446560],
[0.122, 1.59017183044, 10110.19277199240],
[0.123, 2.33714216061, 10316.37832042960],
[0.133, 2.90682399304, 9793.80090233580],
[0.111, 2.52077634760, 13936.79450513400],
[0.120, 0.36076947165, 536.80451209540],
[0.115, 2.53355582059, 26735.94526221320],
[0.108, 2.65839634325, 10232.95530711079],
[0.108, 0.55230439694, 10193.61578531121],
[0.138, 1.06919239240, 65236.22129328540],
[0.101, 3.17012502017, 19317.19254032860],
[0.127, 5.63110477712, 10288.06714477830],
[0.127, 3.86278127025, 10138.50394764370],
[0.137, 2.93350659460, 47162.51635463520],
[0.095, 5.03917884334, 52175.80628314840],
[0.094, 0.71308489207, 38500.27603107220],
[0.092, 5.46204624886, 11764.33076885900],
[0.096, 1.52914774412, 9690.70812811720],
[0.101, 0.83318284426, 6489.77658728800],
[0.115, 3.76443612245, 522.57741809380],
[0.089, 2.53312656681, 10735.86296430480],
[0.082, 0.85628515615, 2379.16447357160],
[0.103, 5.22683237620, 103.09277421860],
[0.090, 2.12423586627, 28313.28880466100],
[0.090, 0.39668501735, 9580.50180689780],
[0.074, 6.02680095550, 3723.50895892300],
[0.081, 5.25045057985, 10419.47109464820],
[0.080, 4.23724598221, 10007.09999777380],
[0.091, 2.48874147947, 10846.06928552420],
[0.085, 3.82784790321, 51868.24866217880],
[0.081, 2.26235214191, 3903.91137641980],
[0.097, 0.77295091600, 18307.80723204360],
[0.094, 0.17063414792, 6872.67311951120],
[0.080, 5.62254102739, 29999.95935231900],
[0.068, 2.71762936670, 16983.99614745660],
[0.066, 0.76731351736, 20.77539549240],
[0.075, 0.36155638007, 39302.09696219600],
[0.075, 2.27327165974, 8521.11987670860],
[0.058, 2.14482855875, 8631.32619792800],
[0.064, 5.83569051301, 2118.76386037840],
[0.058, 2.98524209824, 19889.76658032659],
[0.054, 1.78260668333, 40077.61957352000],
[0.055, 4.70485939861, 639.89728631400],
[0.060, 5.89661892920, 41962.52073693740],
[0.066, 2.24746237999, 74.78159856730],
[0.061, 3.40726181591, 27490.69247804480],
[0.051, 3.07811180039, 24150.08005134500],
[0.057, 2.30081371235, 20529.66386664059],
[0.052, 2.37192464233, 29573.36116144300],
[0.052, 4.76610409132, 57375.80190084620],
[0.047, 1.61630288856, 30831.30490474460],
[0.054, 5.89684197257, 19903.99367432819],
[0.040, 5.32101847424, 42430.48572729180],
[0.051, 5.29186795569, 29587.58825544460],
],
# B1
[
[513347.602, 1.80364310797, 10213.28554621100],
[4380.100, 3.38615711591, 20426.57109242200],
[196.586, 2.53001197486, 30639.85663863300],
[199.162, 0.00000000000, 0.00000000000],
[14.031, 2.27087044687, 9437.76293488700],
[12.958, 1.50735622957, 18073.70493865020],
[11.941, 5.60462450426, 1577.34354244780],
[10.324, 5.24224313355, 2352.86615377180],
[9.294, 6.07545631303, 22003.91463486980],
[7.441, 1.50257909439, 11790.62908865880],
[8.031, 0.29371105198, 9153.90361602180],
[7.514, 5.08081885990, 10186.98722641120],
[4.669, 3.87801635015, 10239.58386601080],
[4.399, 3.58872736593, 40853.14218484400],
[3.975, 1.28397121206, 10404.73381232260],
[4.657, 0.75073886819, 5507.55323866740],
[3.783, 4.33004753984, 19651.04848109800],
[3.390, 4.88976070903, 10988.80815753500],
[3.555, 1.25927550356, 19896.88012732740],
[3.479, 5.50797002160, 529.69096509460],
[2.884, 0.08549582037, 14143.49524243060],
[1.786, 0.37134513186, 13367.97263110660],
[1.600, 1.68378002982, 20618.01935853360],
[1.539, 1.21683853657, 25934.12433108940],
[1.341, 2.90077139758, 15720.83878487840],
[0.993, 1.74681248965, 11322.66409830440],
[1.165, 6.13437155401, 7860.41939243920],
[1.115, 0.66743690380, 29580.47470844380],
[0.923, 2.25384969096, 10021.83728009940],
[0.965, 1.36425494833, 9683.59458111640],
[0.973, 0.39071758442, 6283.07584999140],
[0.805, 0.53331923557, 8624.21265092720],
[0.913, 0.76046003719, 8635.94200376320],
[0.991, 0.55319879330, 19367.18916223280],
[0.609, 2.62364470139, 23581.25817731760],
[0.532, 5.10925676528, 9786.68735533500],
[0.476, 6.17672999981, 11015.10647733480],
[0.472, 1.69672629200, 17298.18232732620],
[0.503, 2.65840772485, 29864.33402730900],
[0.456, 5.01205315518, 10742.97651130560],
[0.478, 3.94100005156, 775.52261132400],
[0.477, 3.71554345922, 10596.18207843420],
[0.347, 2.34551062680, 9411.46461508720],
[0.458, 2.31894399069, 9999.98645077300],
[0.374, 3.76878356974, 21228.39202354580],
[0.440, 4.33400244581, 15874.61759536320],
[0.349, 1.31468836511, 10234.06094170340],
[0.310, 5.45422332781, 10192.51015071860],
[0.346, 0.94242286364, 1059.38193018920],
[0.308, 4.90145899142, 3930.20969621960],
[0.331, 4.89498986674, 10206.17199921020],
[0.269, 2.39650266204, 801.82093112380],
[0.269, 0.00589873499, 9830.38901398780],
[0.261, 3.48196147279, 7058.59846131540],
[0.290, 0.10953964861, 29050.78374334920],
[0.283, 6.12133736787, 20419.45754542119],
[0.232, 3.07845850030, 12566.15169998280],
[0.265, 4.02431894973, 33794.54372352860],
[0.220, 2.37315851889, 4551.95349705880],
[0.247, 3.07626728158, 28286.99048486120],
[0.202, 3.56872121409, 21535.94964451540],
[0.225, 5.76888896320, 213.29909543800],
[0.217, 0.88382111135, 20213.27199698400],
[0.172, 6.12653050186, 9161.01716302260],
[0.195, 5.47240855400, 37724.75341974820],
[0.153, 4.07656151671, 27511.46787353720],
[0.174, 1.33676849359, 32217.20018108080],
[0.157, 5.98474214437, 26.29831979980],
[0.163, 5.45519134760, 10426.58464164900],
[0.129, 2.08748660996, 3128.38876509580],
[0.131, 1.51959002513, 10218.80847051840],
[0.139, 4.42330401713, 10220.39909321180],
[0.126, 2.62296638037, 22779.43724619380],
[0.146, 4.69869606856, 25158.60171976540],
[0.172, 6.13435208788, 18837.49819713819],
[0.157, 5.44507403858, 4705.73230754360],
[0.117, 6.18296175153, 20400.27277262220],
[0.164, 3.30849473132, 51066.42773105500],
[0.113, 3.64412860654, 7.11354700080],
[0.109, 5.21220660788, 8662.24032356300],
[0.133, 1.78047296245, 191.44826611160],
[0.117, 0.14681677884, 9146.79006902100],
[0.116, 0.61940521198, 41654.96311596780],
[0.096, 1.49631428731, 7084.89678111520],
[0.096, 1.21744230443, 10198.03307502600],
[0.082, 1.45863866349, 10207.76262190360],
[0.085, 6.04057728058, 21202.09370374600],
[0.083, 0.19985600927, 14919.01785375460],
[0.077, 5.50132310610, 5661.33204915220],
[0.077, 2.00173927326, 10228.53801739600],
[0.093, 1.85466268819, 45585.17281218740],
[0.066, 3.25826124156, 1109.37855209340],
[0.089, 0.64100435648, 3154.68708489560],
[0.061, 3.80043027736, 11272.66747640020],
[0.077, 1.85516358950, 3532.06069281140],
[0.062, 0.81341290651, 382.89653222320],
[0.072, 2.35312965005, 9103.90699411760],
[0.053, 3.21969389511, 20452.86941222180],
[0.067, 1.42090542131, 24356.78078864160],
[0.056, 2.97733070198, 30110.16567353840],
[0.051, 4.22406663447, 20809.46762464520],
[0.058, 6.20761936031, 29088.81141598500],
[0.061, 3.27309494322, 49515.38250840700],
[0.046, 5.49443476235, 31441.67756975680],
[0.050, 4.16651052942, 13341.67431130680],
[0.047, 1.25473247769, 33019.02111220460],
[0.047, 2.03402044389, 23958.63178523340],
[0.036, 5.24409311105, 3149.16416058820],
[0.038, 4.15337829669, 18849.22754997420],
[0.042, 0.43005959574, 1589.07289528380],
[0.041, 1.21289342964, 12592.45001978260],
[0.038, 5.91928287144, 28521.09277825460],
[0.033, 3.98241699279, 4732.03062734340],
[0.035, 2.24417218267, 16496.36139620240],
[0.040, 6.13293942728, 26087.90314157420],
[0.044, 1.78123294860, 426.59819087600],
[0.041, 3.16744909855, 39264.06928956020],
[0.033, 4.96183427323, 536.80451209540],
[0.034, 0.12963030501, 30213.25844775700],
[0.036, 5.41167321573, 522.57741809380],
[0.027, 4.44250239485, 17277.40693183380],
[0.034, 5.94541303751, 9929.42622734580],
[0.033, 0.40689057274, 10497.14486507620],
[0.023, 2.59067946967, 10175.25787357520],
[0.022, 0.69625017371, 19999.97290154599],
[0.023, 3.76162101633, 10251.31321884680],
[0.023, 0.62711494266, 35371.88726597640],
[0.022, 4.64142978776, 19889.76658032659],
[0.020, 4.01315480107, 26709.64694241340],
[0.020, 4.03344400680, 29573.36116144300],
[0.023, 0.90416640595, 8094.52168583260],
[0.022, 1.92092469688, 17085.95866572220],
[0.019, 5.04938942644, 6681.22485339960],
],
# B2
[
[22377.665, 3.38509143877, 10213.28554621100],
[281.739, 0.00000000000, 0.00000000000],
[173.164, 5.25563766915, 20426.57109242200],
[26.945, 3.87040891568, 30639.85663863300],
[1.174, 0.09768632072, 10186.98722641120],
[0.685, 3.19139067811, 11790.62908865880],
[0.788, 4.36515965295, 10239.58386601080],
[0.592, 5.22270440328, 40853.14218484400],
[0.515, 6.12821215207, 10988.80815753500],
[0.538, 0.57550272342, 2352.86615377180],
[0.540, 3.11657836329, 18073.70493865020],
[0.454, 2.79306867629, 10404.73381232260],
[0.374, 6.10468482446, 9437.76293488700],
[0.431, 4.00778431184, 1577.34354244780],
[0.360, 6.01747842320, 19651.04848109800],
[0.375, 1.31319959789, 22003.91463486980],
[0.354, 5.12509281266, 9153.90361602180],
[0.150, 4.58623687118, 15720.83878487840],
[0.164, 5.41790158607, 5507.55323866740],
[0.159, 2.78191550878, 19896.88012732740],
[0.157, 0.65774905071, 529.69096509460],
[0.155, 2.54824315372, 9683.59458111640],
[0.109, 2.01866665583, 14143.49524243060],
[0.106, 2.28289033017, 6283.07584999140],
[0.115, 3.23636374193, 20618.01935853360],
[0.128, 5.32400510939, 13367.97263110660],
[0.087, 3.28265082435, 11322.66409830440],
[0.090, 5.23585072275, 10596.18207843420],
[0.055, 4.82369879741, 7058.59846131540],
[0.044, 0.58444963462, 10206.17199921020],
[0.044, 2.34401612969, 19367.18916223280],
[0.038, 4.55053233088, 9999.98645077300],
[0.039, 5.84340580032, 10220.39909321180],
[0.036, 4.41006216127, 51066.42773105500],
[0.039, 3.14348236386, 9411.46461508720],
[0.033, 4.55748660340, 10742.97651130560],
[0.037, 2.79630938717, 25934.12433108940],
[0.034, 0.55287110072, 11015.10647733480],
[0.034, 2.25809144959, 29580.47470844380],
[0.038, 1.88638747393, 801.82093112380],
[0.034, 1.22706917271, 10021.83728009940],
[0.027, 4.83867137637, 9830.38901398780],
[0.027, 4.31140179350, 23581.25817731760],
[0.027, 2.17187621336, 8635.94200376320],
[0.020, 5.66581696952, 21228.39202354580],
[0.024, 2.17208107850, 18849.22754997420],
[0.020, 5.29318634138, 775.52261132400],
[0.019, 2.73486845601, 3128.38876509580],
[0.013, 3.40362915274, 1059.38193018920],
[0.014, 0.05074160195, 7860.41939243920],
[0.014, 5.43035907265, 26.29831979980],
[0.012, 3.24834347355, 9103.90699411760],
[0.013, 5.04826725887, 7.11354700080],
[0.015, 1.42027402522, 29050.78374334920],
[0.010, 4.98138067490, 10426.58464164900],
[0.011, 0.85773045784, 17298.18232732620],
[0.011, 4.23048200054, 29864.33402730900],
[0.010, 0.26447399758, 3930.20969621960],
[0.011, 1.46728576671, 20419.45754542119],
],
# B3
[
[646.671, 4.99166565277, 10213.28554621100],
[19.952, 3.14159265359, 0.00000000000],
[5.540, 0.77376923951, 20426.57109242200],
[2.526, 5.44493763020, 30639.85663863300],
[0.079, 1.51447613604, 10186.98722641120],
[0.056, 0.63647808442, 40853.14218484400],
[0.058, 5.70731176550, 10239.58386601080],
[0.031, 4.72523061067, 11790.62908865880],
[0.026, 1.02068113372, 10988.80815753500],
[0.025, 5.60599130442, 9437.76293488700],
[0.017, 2.05293621864, 2352.86615377180],
[0.011, 4.33056892256, 10404.73381232260],
[0.009, 1.36283915068, 19651.04848109800],
[0.007, 4.69592781899, 18073.70493865020],
[0.006, 2.97926526705, 22003.91463486980],
],
# B4
[
[14.102, 0.31537190181, 10213.28554621100],
[0.190, 2.35466404492, 20426.57109242200],
[0.164, 0.74476215141, 30639.85663863300],
[0.214, 3.14159265359, 0.00000000000],
[0.004, 2.34190883009, 40853.14218484400],
],
# B5
[
[0.239, 2.05201727566, 10213.28554621100],
[0.039, 0.00000000000, 0.00000000000],
[0.011, 3.82500275251, 20426.57109242200],
[0.009, 2.32953116868, 30639.85663863300],
],
]
"""This table contains Venus'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
page 420."""
VSOP87_R = [
# R0
[
[72334820.905, 0.00000000000, 0.00000000000],
[489824.185, 4.02151832268, 10213.28554621100],
[1658.058, 4.90206728012, 20426.57109242200],
[1632.093, 2.84548851892, 7860.41939243920],
[1378.048, 1.12846590600, 11790.62908865880],
[498.399, 2.58682187717, 9683.59458111640],
[373.958, 1.42314837063, 3930.20969621960],
[263.616, 5.52938185920, 9437.76293488700],
[237.455, 2.55135903978, 15720.83878487840],
[221.983, 2.01346776772, 19367.18916223280],
[119.467, 3.01975365264, 10404.73381232260],
[125.896, 2.72769833559, 1577.34354244780],
[76.178, 1.59577224486, 9153.90361602180],
[85.336, 3.98607953754, 19651.04848109800],
[74.347, 4.11957854039, 5507.55323866740],
[41.904, 1.64273363458, 18837.49819713819],
[42.493, 3.81864530735, 13367.97263110660],
[39.430, 5.39019422358, 23581.25817731760],
[29.042, 5.67739528728, 5661.33204915220],
[27.555, 5.72392407794, 775.52261132400],
[27.283, 4.82151812709, 11015.10647733480],
[31.274, 2.31806719544, 9999.98645077300],
[19.700, 4.96157560245, 11322.66409830440],
[19.809, 0.53189326492, 27511.46787353720],
[13.567, 3.75530870628, 18073.70493865020],
[12.921, 1.13381083556, 10206.17199921020],
[16.215, 0.56453834290, 529.69096509460],
[11.821, 5.09025877427, 3154.68708489560],
[11.728, 0.23432298744, 7084.89678111520],
[13.079, 5.24353197586, 17298.18232732620],
[13.180, 3.37207825651, 13745.34623902240],
[9.097, 3.07004895769, 1109.37855209340],
[10.818, 2.45024712908, 10239.58386601080],
[11.438, 4.56838894696, 29050.78374334920],
[8.377, 5.78327612352, 30639.85663863300],
[8.193, 1.95023111860, 22003.91463486980],
[9.308, 1.61615909286, 2352.86615377180],
[10.652, 1.95528396140, 31441.67756975680],
[10.357, 1.20234990061, 15874.61759536320],
[9.585, 1.46639856228, 19999.97290154599],
[6.506, 2.17390732263, 14143.49524243060],
[7.562, 1.13789564977, 8624.21265092720],
[6.434, 0.84419623033, 6283.07584999140],
[5.898, 0.01093731110, 8635.94200376320],
[5.632, 3.94956548631, 12566.15169998280],
[5.523, 1.27394296557, 18307.80723204360],
[4.488, 2.47835729057, 191.44826611160],
[4.529, 4.73027770400, 19896.88012732740],
[6.193, 3.25881250939, 6872.67311951120],
[6.070, 0.35337419942, 21228.39202354580],
[4.315, 2.59737099519, 4551.95349705880],
[6.005, 3.37874723475, 35371.88726597640],
[3.852, 1.01162850357, 9786.68735533500],
[4.033, 0.00050855580, 801.82093112380],
[3.920, 5.56542869407, 10596.18207843420],
[2.709, 5.80195530112, 7064.12138562280],
[3.216, 0.39767254848, 10186.98722641120],
[3.089, 6.26174762876, 14945.31617355440],
[2.982, 4.21196716354, 28521.09277825460],
[3.284, 0.70709821006, 10742.97651130560],
[3.484, 4.79878191875, 39302.09696219600],
[3.172, 1.80518954174, 25158.60171976540],
[2.463, 0.68708153678, 10988.80815753500],
[2.374, 3.77948685343, 21535.94964451540],
[2.198, 2.82996372521, 8662.24032356300],
[1.958, 5.41763804167, 16496.36139620240],
[1.876, 2.63426768393, 29580.47470844380],
[1.902, 2.85782199133, 3532.06069281140],
[1.706, 3.67573010379, 26.29831979980],
[1.817, 0.41611036449, 4705.73230754360],
[1.858, 1.50368318296, 10021.83728009940],
[2.087, 6.22112874639, 43232.30665841560],
[1.950, 2.21447019683, 19786.67380610799],
[1.497, 0.00134773824, 17277.40693183380],
[1.819, 3.23144993268, 29088.81141598500],
[1.423, 5.85979618707, 9676.48103411560],
[1.223, 5.55818994329, 6770.71060124560],
[1.140, 5.92088900094, 13936.79450513400],
[1.484, 2.47665429253, 31749.23519072640],
[1.185, 1.42087628351, 4732.03062734340],
[1.323, 2.48821075422, 9690.70812811720],
[1.249, 1.88323673734, 19374.30270923360],
[1.270, 5.24647873116, 19360.07561523199],
[1.402, 5.17536780118, 10316.37832042960],
[1.042, 3.05454698508, 25934.12433108940],
[1.174, 1.42913732999, 18875.52586977400],
[1.278, 1.35747287297, 47162.51635463520],
[0.917, 6.26337648765, 20618.01935853360],
[0.905, 1.12740203561, 12592.45001978260],
[1.093, 4.64451720605, 33019.02111220460],
[1.014, 1.09259406433, 1059.38193018920],
[0.783, 2.02118183873, 24356.78078864160],
[0.779, 0.41585274010, 3340.61242669980],
[0.700, 1.14936815714, 16983.99614745660],
[0.878, 0.87852464964, 38734.37832446560],
[0.623, 0.89976912165, 17778.11626694899],
[0.608, 1.58476225197, 9573.38825989700],
[0.800, 3.94213003073, 10138.50394764370],
[0.760, 1.31851313748, 9967.45389998160],
[0.802, 2.78173370208, 51092.72605085480],
[0.664, 4.45864682400, 3128.38876509580],
[0.674, 5.11214939998, 382.89653222320],
[0.530, 0.85392938403, 10234.06094170340],
[0.509, 3.56809374595, 28286.99048486120],
[0.600, 4.25927726907, 41962.52073693740],
[0.601, 5.78144137895, 213.29909543800],
[0.595, 2.83045104588, 22805.73556599360],
[0.673, 6.06079908421, 36949.23080842420],
[0.535, 5.85422519711, 9103.90699411760],
[0.544, 5.44806074800, 3723.50895892300],
[0.492, 3.83802404893, 27991.40181316000],
[0.635, 0.76494024849, 8094.52168583260],
[0.434, 6.22214487735, 27197.28169366760],
[0.459, 3.55062885479, 20213.27199698400],
[0.398, 6.16269975784, 10426.58464164900],
[0.378, 2.41665947591, 18844.61174413899],
[0.421, 4.86552697954, 9146.79006902100],
[0.500, 4.20351458644, 55022.93574707440],
[0.404, 4.95834410782, 37410.56723987860],
[0.402, 2.97963246945, 10220.39909321180],
[0.464, 2.59869499733, 18734.40542291960],
[0.352, 0.08963076359, 10103.07922499160],
[0.348, 4.90260339364, 18830.38465013739],
[0.338, 3.22520096478, 24150.08005134500],
[0.375, 6.17532088136, 26087.90314157420],
[0.425, 1.20052578280, 40879.44050464380],
[0.408, 3.12833060705, 9050.81084180320],
[0.385, 1.94284690176, 283.85931886520],
[0.337, 4.87838699272, 12432.04265039780],
[0.326, 4.27369741426, 26735.94526221320],
[0.309, 0.50597475053, 38204.68735937100],
[0.329, 3.88430599153, 29864.33402730900],
[0.313, 1.36138752543, 10192.51015071860],
[0.347, 3.58439807209, 27490.69247804480],
[0.251, 3.78618457047, 10063.72234907640],
[0.244, 3.83523342668, 9411.46461508720],
[0.281, 4.50895206233, 32217.20018108080],
[0.237, 0.87748812245, 6681.22485339960],
[0.315, 5.62657778233, 58953.14544329400],
[0.311, 4.15626121491, 10175.15251057320],
[0.247, 2.53637594113, 16522.65971600220],
[0.219, 5.08729383251, 7058.59846131540],
[0.291, 3.72567217056, 29999.95935231900],
[0.267, 2.97685503991, 19573.37471066999],
[0.280, 3.70200084294, 47623.85278608960],
[0.239, 3.94545782067, 9580.50180689780],
[0.246, 2.18244883930, 9161.01716302260],
[0.253, 2.69506547016, 3442.57494496540],
[0.265, 2.62811801237, 44809.65020086340],
[0.194, 4.78926136175, 33794.54372352860],
[0.187, 3.65620881095, 20452.86941222180],
[0.224, 2.43601863127, 9992.87290377220],
[0.193, 2.55112161845, 2379.16447357160],
[0.201, 1.90356905733, 1551.04522264800],
[0.176, 4.29837616553, 10137.01947493540],
[0.184, 6.16061560223, 36147.40987730040],
[0.175, 2.71984797040, 20809.46762464520],
[0.186, 2.55098927966, 14919.01785375460],
[0.161, 4.13272567123, 23958.63178523340],
[0.221, 4.83552377614, 20277.00789528740],
[0.160, 1.81472642729, 10787.63034454580],
[0.199, 5.74259798330, 30666.15495843280],
[0.160, 4.46270605493, 18947.70451835760],
[0.187, 2.98688597588, 2218.75710418680],
[0.189, 5.34607810282, 10007.09999777380],
[0.198, 0.77846666692, 62883.35513951360],
[0.144, 5.00261963924, 9264.10993724120],
[0.171, 2.05212624568, 7255.56965173440],
[0.188, 4.08173534559, 48739.85989708300],
[0.146, 3.94191715702, 6309.37416979120],
[0.146, 5.06313558118, 39264.06928956020],
[0.135, 5.93689169614, 37724.75341974820],
[0.139, 2.81266025896, 20.77539549240],
[0.177, 5.16224804657, 9835.91193829520],
[0.119, 1.37254262864, 40077.61957352000],
[0.120, 0.21443767468, 31022.75317085620],
[0.128, 2.92458887798, 7.11354700080],
[0.150, 5.73646272556, 632.78373931320],
[0.106, 0.62224833817, 11272.66747640020],
[0.114, 2.63301326520, 17468.85519794540],
[0.123, 6.22518843711, 53285.18483524180],
[0.107, 1.17258978900, 43071.89928903080],
[0.103, 1.09613781581, 41654.96311596780],
[0.109, 2.01412667085, 20419.45754542119],
[0.102, 4.23406964348, 10251.31321884680],
[0.116, 1.27731728606, 10199.05845220940],
[0.103, 5.25887538465, 9830.38901398780],
[0.112, 2.24436894064, 18204.71445782499],
[0.111, 2.23547857955, 8521.11987670860],
[0.118, 0.23754207200, 10497.14486507620],
[0.123, 0.88054816668, 34596.36465465240],
[0.102, 4.39438646620, 18300.69368504279],
[0.131, 6.01711652115, 9367.20271145980],
[0.100, 5.00532389609, 10175.25787357520],
[0.107, 0.41270197502, 40853.14218484400],
[0.132, 5.45008342761, 11506.76976979360],
[0.098, 1.07722950958, 13553.89797291080],
[0.094, 2.91720097590, 44007.82926973960],
[0.097, 1.04004223634, 68050.42387851159],
[0.127, 2.20215372683, 66813.56483573320],
[0.111, 1.57823839032, 29043.67019634839],
[0.118, 2.33268176890, 18314.92077904440],
[0.090, 2.42353056125, 32858.61374281979],
[0.109, 3.82796787296, 19470.28193645139],
[0.111, 4.47666957576, 29057.89729034999],
[0.101, 3.41528493660, 19264.09638801420],
[0.092, 3.66289799512, 22645.32819660879],
[0.094, 6.07530805791, 10846.06928552420],
[0.114, 4.02718653431, 7576.56007357400],
[0.087, 6.01842459303, 17085.95866572220],
[0.109, 5.46886607309, 52670.06959330260],
[0.107, 0.54805946713, 34363.36559755600],
[0.108, 5.44460610707, 19050.79729257620],
[0.076, 6.15177368654, 27682.14074415640],
[0.107, 4.80525404063, 8144.27871130440],
[0.073, 1.60549217847, 20956.26205751660],
[0.097, 5.13542051130, 22779.43724619380],
[0.068, 2.31300447144, 8631.32619792800],
[0.091, 4.28652743953, 10110.19277199240],
[0.093, 5.27290609264, 522.57741809380],
[0.071, 3.65565961690, 11764.33076885900],
[0.089, 1.79712963206, 45585.17281218740],
[0.067, 2.25900071584, 9360.08916445900],
[0.085, 0.67062144972, 56600.27928952220],
[0.080, 1.58278081077, 19992.85935454519],
[0.065, 6.23472325597, 10419.47109464820],
[0.064, 0.53356325917, 17248.42530185440],
[0.085, 4.52011215904, 29786.66025688100],
[0.068, 4.48235266554, 10632.77019008620],
[0.064, 4.33495700921, 47938.03896595920],
[0.071, 3.03858484137, 11787.10597030980],
[0.087, 4.81823063172, 2107.03450754240],
[0.070, 2.35648061034, 11794.15220700780],
[0.080, 2.33248094128, 38526.57435087200],
[0.070, 3.70454061100, 8734.41897214660],
[0.077, 4.49569185467, 20007.08644854680],
[0.072, 1.19410424468, 10217.21769947410],
[0.068, 2.01841060183, 14128.24277124560],
[0.064, 5.39293951654, 7880.08915333899],
[0.066, 3.20467071127, 14765.23904326980],
[0.080, 3.41620457770, 48417.97290558199],
[0.080, 3.39651161571, 245.83164622940],
[0.066, 5.85414440204, 9793.80090233580],
[0.082, 3.62592908644, 70743.77453195279],
[0.058, 4.95174942212, 30110.16567353840],
[0.079, 6.24161471033, 6037.24420376200],
[0.069, 5.50183658445, 19793.78735310880],
[0.056, 1.24148350566, 10207.76262190360],
[0.070, 2.45123308846, 10218.80847051840],
[0.064, 5.53983104501, 10735.86296430480],
[0.054, 3.62259713240, 27461.71084806540],
[0.073, 1.75882480924, 1589.07289528380],
[0.075, 3.38244819846, 4214.06901508480],
[0.054, 0.64971567468, 9929.42622734580],
[0.054, 3.40959637230, 18418.01355326299],
[0.056, 3.65815006538, 14169.79356223040],
[0.056, 0.71243223808, 9896.89367655440],
[0.052, 1.33348131940, 20400.27277262220],
[0.067, 3.12806595400, 5481.25491886760],
[0.058, 0.54482893546, 28313.28880466100],
[0.054, 0.15603935681, 19580.48825767080],
[0.051, 3.37515473510, 9256.99639024040],
[0.063, 3.38848970950, 49515.38250840700],
[0.069, 4.90917651401, 63498.47038145279],
[0.057, 5.07437742030, 18521.10632748160],
[0.050, 1.59156823654, 18631.31264870099],
[0.054, 6.25816208666, 37674.99639427640],
[0.057, 5.48065460919, 24383.07910844140],
[0.045, 1.10466490660, 10408.25693067160],
[0.051, 3.61196470313, 426.59819087600],
[0.057, 2.09567711267, 60530.48898574180],
[0.060, 5.94659889997, 13897.66359620120],
[0.051, 5.47238517720, 57837.13833230060],
[0.051, 2.32438478428, 19779.56025910719],
[0.052, 3.23766328818, 18940.59097135679],
[0.043, 5.74921510909, 51868.24866217880],
[0.048, 1.12206254877, 9779.57380833420],
[0.058, 3.08646083897, 12074.48840752400],
[0.046, 4.07536026888, 7863.94251078820],
[0.045, 4.75746520642, 7856.89627409019],
[0.054, 4.43528236634, 8617.09910392640],
[0.050, 3.70569982975, 42456.78404709160],
[0.044, 1.29248911155, 69166.43098950500],
[0.046, 0.41229872114, 7564.83072073800],
[0.044, 6.17937388307, 13341.67431130680],
[0.053, 4.71388531889, 53445.59220462660],
[0.041, 3.48003037828, 37895.42629036740],
[0.040, 1.23305546260, 10228.53801739600],
[0.053, 5.04979874661, 74673.98422817240],
[0.039, 1.36646013032, 21202.09370374600],
[0.039, 2.15376025201, 8947.71806758460],
[0.041, 6.17532984460, 65236.22129328540],
[0.052, 1.29052331493, 90394.82301305079],
[0.039, 0.70253732683, 18093.37469954999],
[0.052, 1.18164377451, 10211.80107350270],
[0.047, 1.78672260794, 10401.21069397360],
[0.040, 3.66961416802, 10198.03307502600],
[0.051, 2.71698589018, 94325.03270927040],
[0.036, 1.25091711620, 10323.49186743040],
[0.049, 1.21335959420, 9721.62225375220],
[0.042, 6.05968230173, 105460.99111839019],
[0.046, 5.06978748275, 20350.30502114640],
[0.040, 1.97645050921, 32243.49850088060],
[0.036, 4.96702216961, 36301.18868778519],
[0.037, 5.29642935562, 38.02767263580],
[0.039, 0.52064327313, 26709.64694241340],
[0.035, 2.34112124655, 58946.51688439399],
[0.034, 1.82989750626, 17675.02349273040],
[0.034, 0.76493664110, 55798.45835839840],
[0.035, 1.09353675147, 69159.80243060499],
[0.031, 5.59148330297, 10639.88373708700],
[0.032, 3.32960781870, 71519.29714327680],
[0.031, 5.98191446392, 24341.52831745660],
[0.031, 0.68615213145, 10202.23984594710],
[0.030, 4.42039942947, 10459.11719244040],
[0.029, 1.30367701539, 20103.06567576459],
[0.031, 4.51793347997, 2957.71589447660],
[0.035, 4.05634321290, 19903.99367432819],
[0.030, 1.32113757427, 574.34479833480],
[0.029, 3.36506645849, 10288.06714477830],
[0.029, 1.40019042576, 9988.94075050910],
[0.032, 0.21932095318, 24978.52458948080],
[0.034, 5.22945947227, 8673.96967639900],
[0.039, 4.50883171158, 16004.69810374360],
[0.028, 2.32945945641, 11392.48008525060],
[0.034, 3.92498967835, 536.80451209540],
[0.032, 5.46972716255, 64607.84893354619],
[0.028, 2.38858990128, 20235.12282631040],
[0.030, 3.34585843979, 39793.76025465480],
[0.026, 5.36096904409, 1478.86657406440],
],
# R1
[
[34551.039, 0.89198710598, 10213.28554621100],
[234.203, 1.77224942714, 20426.57109242200],
[233.998, 3.14159265359, 0.00000000000],
[23.864, 1.11274502648, 9437.76293488700],
[10.568, 4.59168210921, 1577.34354244780],
[9.124, 4.53540907003, 10404.73381232260],
[6.599, 5.97703999838, 5507.55323866740],
[4.667, 3.87683960551, 9153.90361602180],
[3.840, 5.66196924375, 13367.97263110660],
[2.666, 2.82413291285, 10206.17199921020],
[2.194, 2.05314419626, 775.52261132400],
[2.094, 2.55137285015, 18837.49819713819],
[1.782, 2.64808558644, 30639.85663863300],
[1.845, 1.87612936641, 11015.10647733480],
[1.303, 0.20613045603, 11322.66409830440],
[1.169, 0.79431893441, 17298.18232732620],
[1.001, 6.16555101536, 10239.58386601080],
[0.915, 4.59854496966, 1109.37855209340],
[0.884, 0.66706834422, 18073.70493865020],
[0.849, 5.58641571940, 12566.15169998280],
[1.071, 4.94792017474, 6283.07584999140],
[0.887, 2.47785193216, 3154.68708489560],
[0.904, 0.81413053841, 10596.18207843420],
[0.818, 0.90016838097, 5661.33204915220],
[0.845, 5.48504338112, 529.69096509460],
[0.824, 3.74837629121, 7084.89678111520],
[0.652, 5.07444932607, 22003.91463486980],
[0.847, 0.44119876869, 8635.94200376320],
[0.638, 4.10125791268, 191.44826611160],
[0.615, 3.14417599741, 10186.98722641120],
[0.527, 5.86792949279, 2352.86615377180],
[0.520, 5.33201358267, 14143.49524243060],
[0.576, 2.25212731258, 21228.39202354580],
[0.662, 2.86880467345, 8624.21265092720],
[0.554, 2.17186191243, 18307.80723204360],
[0.515, 4.34331395104, 9786.68735533500],
[0.501, 5.56479589366, 10742.97651130560],
[0.426, 1.02161443120, 7064.12138562280],
[0.418, 1.26803034691, 9676.48103411560],
[0.391, 0.78974645621, 9690.70812811720],
[0.334, 3.18175822557, 10988.80815753500],
[0.375, 0.66142254036, 19360.07561523199],
[0.364, 0.19369831864, 19374.30270923360],
[0.313, 1.09734397626, 4551.95349705880],
[0.330, 0.58817502306, 16496.36139620240],
[0.339, 5.76768761396, 10021.83728009940],
[0.291, 3.65846764668, 25158.60171976540],
[0.223, 4.33581625553, 19786.67380610799],
[0.266, 3.57408827667, 801.82093112380],
[0.274, 5.73346687248, 11790.62908865880],
[0.275, 5.65814317085, 19896.88012732740],
[0.212, 4.27038489878, 4705.73230754360],
[0.230, 6.13406345590, 1059.38193018920],
[0.204, 4.87348390351, 7860.41939243920],
[0.241, 1.13551531894, 26.29831979980],
[0.206, 0.31907973682, 382.89653222320],
[0.216, 2.54741101724, 19651.04848109800],
[0.212, 3.15264941106, 14945.31617355440],
[0.163, 1.13604744392, 13936.79450513400],
[0.151, 5.11341268743, 28521.09277825460],
[0.151, 0.81278755582, 6770.71060124560],
[0.150, 5.02227334847, 29088.81141598500],
[0.146, 1.37568138685, 10220.39909321180],
[0.127, 4.49298610074, 3532.06069281140],
[0.121, 6.26589208179, 29580.47470844380],
[0.147, 6.16092774714, 8662.24032356300],
[0.114, 0.00114012635, 25934.12433108940],
[0.115, 3.56897715344, 24356.78078864160],
[0.124, 0.67547060274, 3723.50895892300],
[0.145, 0.36415036222, 9146.79006902100],
[0.104, 4.27865011376, 9573.38825989700],
[0.136, 5.09581116181, 19367.18916223280],
[0.102, 1.53637788668, 17277.40693183380],
[0.117, 0.57543238496, 9999.98645077300],
[0.092, 0.22936081655, 18830.38465013739],
[0.112, 4.04771058036, 9103.90699411760],
[0.098, 3.78447692407, 213.29909543800],
[0.085, 5.84471458481, 10234.06094170340],
[0.079, 0.64440357793, 18844.61174413899],
[0.084, 0.56950139213, 9683.59458111640],
[0.107, 1.77067111589, 17778.11626694899],
[0.081, 6.19048382717, 20618.01935853360],
[0.087, 0.15771136594, 33019.02111220460],
[0.082, 4.80683817059, 3930.20969621960],
[0.086, 2.21505615071, 8094.52168583260],
[0.064, 2.69215119482, 16983.99614745660],
[0.069, 0.83385751986, 3128.38876509580],
[0.081, 4.88025042367, 4732.03062734340],
[0.059, 3.34348033725, 10787.63034454580],
[0.061, 0.04044699966, 9161.01716302260],
[0.064, 4.13127333938, 9992.87290377220],
[0.060, 6.24603986632, 32217.20018108080],
[0.054, 3.38449893196, 10426.58464164900],
[0.054, 5.15939119644, 28286.99048486120],
[0.063, 4.32339245083, 12592.45001978260],
[0.060, 4.48753846170, 18875.52586977400],
[0.057, 3.64912085313, 10007.09999777380],
[0.049, 5.10267262491, 19573.37471066999],
[0.047, 5.79444960738, 68050.42387851159],
[0.052, 3.56658420552, 7255.56965173440],
[0.050, 1.61783309819, 36949.23080842420],
[0.053, 2.64370544855, 15874.61759536320],
[0.040, 3.93466530964, 20419.45754542119],
[0.051, 0.79154899901, 23581.25817731760],
[0.038, 1.77428239418, 10103.07922499160],
[0.049, 1.12423644455, 3442.57494496540],
[0.040, 5.22874487975, 21535.94964451540],
[0.038, 1.12473430132, 7.11354700080],
[0.038, 0.11510547453, 11272.66747640020],
[0.036, 2.02476324983, 7058.59846131540],
[0.047, 0.05589432390, 12432.04265039780],
[0.034, 3.45481114998, 9830.38901398780],
[0.045, 4.59817214088, 10192.51015071860],
[0.037, 4.93959675364, 3340.61242669980],
[0.044, 0.70533027806, 20213.27199698400],
[0.034, 2.16487642765, 64460.69868196140],
[0.031, 1.57612397319, 36147.40987730040],
[0.028, 2.56454760402, 94138.32702008578],
[0.033, 1.08907268562, 29864.33402730900],
[0.029, 0.59718407064, 59728.66805461800],
[0.031, 3.04423979263, 40879.44050464380],
[0.035, 0.32247158762, 1589.07289528380],
[0.031, 3.27727318906, 19992.85935454519],
[0.027, 5.83705748551, 17085.95866572220],
[0.032, 2.64260788260, 41962.52073693740],
[0.028, 4.90613317287, 29050.78374334920],
[0.025, 4.55050389739, 14919.01785375460],
[0.028, 3.58851614957, 40853.14218484400],
[0.029, 2.79705093386, 20007.08644854680],
[0.033, 0.93862065616, 15720.83878487840],
[0.024, 2.74970637101, 18947.70451835760],
[0.024, 4.38966861409, 46386.99374331120],
[0.024, 0.73361964525, 9411.46461508720],
[0.028, 4.19559784013, 37674.99639427640],
[0.023, 1.00023735538, 22779.43724619380],
[0.026, 0.46990555736, 13745.34623902240],
[0.028, 4.65181292126, 1551.04522264800],
[0.025, 4.18690270765, 44007.82926973960],
[0.022, 0.98102807789, 426.59819087600],
[0.030, 1.24986033487, 27461.71084806540],
[0.027, 3.94986823486, 17468.85519794540],
[0.021, 6.09897508157, 18300.69368504279],
[0.025, 4.75875623888, 27991.40181316000],
[0.022, 2.95281481673, 40077.61957352000],
[0.028, 6.12038264955, 38500.27603107220],
[0.022, 4.11184201321, 19779.56025910719],
[0.027, 3.72446446080, 19793.78735310880],
[0.020, 4.27086627368, 31441.67756975680],
[0.022, 4.99040169444, 31022.75317085620],
[0.023, 1.33505132122, 65236.22129328540],
[0.021, 4.46897353468, 53285.18483524180],
[0.020, 4.15140915983, 2218.75710418680],
[0.025, 2.18447182965, 27511.46787353720],
[0.019, 1.43653410349, 27197.28169366760],
[0.027, 1.22555218015, 42430.48572729180],
[0.019, 3.65054338893, 49515.38250840700],
[0.022, 5.88380811711, 10218.80847051840],
[0.018, 2.29853355765, 19264.09638801420],
[0.017, 5.44429906531, 6681.22485339960],
[0.020, 3.68116637773, 14128.24277124560],
[0.021, 4.30316190532, 44809.65020086340],
[0.020, 2.48583613985, 33794.54372352860],
[0.017, 3.02735393984, 28528.20632525540],
[0.019, 5.92656850674, 22805.73556599360],
[0.022, 5.30827572791, 10207.76262190360],
[0.020, 0.75829381378, 18314.92077904440],
[0.017, 5.63315744126, 16522.65971600220],
[0.016, 1.71021408448, 536.80451209540],
[0.015, 5.27016880041, 53445.59220462660],
[0.017, 5.61443395877, 47938.03896595920],
[0.015, 5.81110284451, 43071.89928903080],
[0.015, 4.96237667003, 19999.97290154599],
[0.018, 0.55618686515, 14765.23904326980],
[0.014, 3.48144272414, 29786.66025688100],
[0.015, 5.84132627836, 10228.53801739600],
[0.016, 1.05720065324, 26735.94526221320],
[0.014, 6.08462030302, 35371.88726597640],
[0.014, 2.84532871890, 574.34479833480],
[0.015, 5.34517715140, 10198.03307502600],
[0.013, 0.45004137509, 20452.86941222180],
],
# R2
[
[1406.587, 5.06366395190, 10213.28554621100],
[15.529, 5.47321687981, 20426.57109242200],
[13.059, 0.00000000000, 0.00000000000],
[1.099, 2.78883988292, 9437.76293488700],
[0.488, 6.27806914496, 1577.34354244780],
[0.361, 6.11914188253, 10404.73381232260],
[0.310, 1.38984998403, 5507.55323866740],
[0.389, 1.95017779915, 11015.10647733480],
[0.372, 2.33222828423, 775.52261132400],
[0.207, 5.63406721595, 10239.58386601080],
[0.168, 1.10765197296, 13367.97263110660],
[0.175, 6.16674652950, 30639.85663863300],
[0.168, 3.64495311632, 7084.89678111520],
[0.120, 5.85815843789, 9153.90361602180],
[0.160, 2.21564938463, 3154.68708489560],
[0.118, 2.62358866565, 8635.94200376320],
[0.112, 2.36235956804, 10596.18207843420],
[0.092, 0.72664449269, 12566.15169998280],
[0.067, 3.76089669118, 18837.49819713819],
[0.065, 2.47983709990, 11790.62908865880],
[0.048, 4.26620187144, 2352.86615377180],
[0.048, 5.50898189550, 191.44826611160],
[0.048, 2.54730918293, 17298.18232732620],
[0.046, 3.40293459332, 14143.49524243060],
[0.041, 1.83997113019, 11322.66409830440],
[0.037, 6.17871126027, 1109.37855209340],
[0.039, 4.77190210316, 18073.70493865020],
[0.035, 3.10133256432, 4705.73230754360],
[0.046, 3.30090415967, 6283.07584999140],
[0.034, 3.91721765773, 10021.83728009940],
[0.034, 3.24663787383, 22003.91463486980],
[0.042, 3.39360926939, 14945.31617355440],
[0.044, 4.42979374073, 7860.41939243920],
[0.034, 2.16381407025, 16496.36139620240],
[0.031, 0.45714618479, 26.29831979980],
[0.035, 3.62868651241, 801.82093112380],
[0.032, 1.84138997078, 382.89653222320],
[0.025, 3.32908650295, 18307.80723204360],
[0.026, 3.64313769818, 29088.81141598500],
[0.029, 3.82967178810, 10186.98722641120],
[0.022, 3.17741520378, 28521.09277825460],
[0.021, 2.52643834111, 529.69096509460],
[0.025, 5.71401244457, 21202.09370374600],
[0.021, 3.77813434325, 21228.39202354580],
[0.019, 5.24505118517, 19896.88012732740],
[0.018, 4.62463651925, 19651.04848109800],
[0.016, 3.35893297896, 28286.99048486120],
[0.015, 5.05571633205, 33019.02111220460],
[0.014, 2.83786355803, 19786.67380610799],
[0.014, 1.79922718553, 9830.38901398780],
[0.014, 3.14801263138, 19367.18916223280],
[0.014, 3.57896195191, 10988.80815753500],
[0.013, 3.06303088617, 10742.97651130560],
[0.013, 5.43981998532, 25158.60171976540],
[0.015, 4.83166312889, 18875.52586977400],
[0.012, 2.54141086214, 7064.12138562280],
[0.012, 4.45255110769, 15720.83878487840],
[0.010, 1.87933121728, 24356.78078864160],
[0.011, 2.58708635685, 9103.90699411760],
[0.010, 2.17901309900, 3723.50895892300],
[0.008, 3.63520673832, 1059.38193018920],
[0.008, 4.67523115598, 25934.12433108940],
[0.009, 5.97856553283, 9683.59458111640],
],
# R3
[
[49.582, 3.22263554520, 10213.28554621100],
[0.831, 3.21219077104, 20426.57109242200],
[0.112, 3.14159265359, 0.00000000000],
[0.013, 3.77448689585, 30639.85663863300],
[0.009, 4.19802043629, 10239.58386601080],
[0.006, 0.20714935358, 10186.98722641120],
[0.005, 0.68781956122, 8635.94200376320],
],
# R4
[
[0.573, 0.92229697820, 10213.28554621100],
[0.040, 0.95468912157, 20426.57109242200],
[0.006, 3.14159265359, 0.00000000000],
],
# R5
[
[0.045, 0.30032866722, 10213.28554621100],
[0.002, 5.29627718483, 20426.57109242200],
],
]
"""This table contains Venus'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 420-421."""
[docs]class Venus(object):
"""
Class Venus models that planet.
"""
[docs] @staticmethod
def geometric_heliocentric_position(epoch, toFK5=True):
""""This method computes the geometric heliocentric position of planet
Venus for a given epoch, using the VSOP87 theory.
:param epoch: Epoch to compute Venus 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(1992, 12, 20.0)
>>> l, b, r = Venus.geometric_heliocentric_position(epoch, toFK5=False)
>>> print(round(l.to_positive(), 5))
26.11412
>>> print(round(b, 4))
-2.6206
>>> print(round(r, 6))
0.724602
"""
# First check that input values are of correct types
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input types")
# Second, call auxiliary function in charge of computations
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
Venus for a given epoch, using the VSOP87 theory.
:param epoch: Epoch to compute Venus 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.
"""
# First check that input values are of correct types
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input types")
# Second, call auxiliary function in charge of computations
return apparent_vsop_pos(epoch, VSOP87_L, VSOP87_B, VSOP87_R)
def main():
# Let's define a small helper function
def print_me(msg, val):
print("{}: {}".format(msg, val))
# Let's show some uses of Venus class
print("\n" + 35 * "*")
print("*** Use of Venus class")
print(35 * "*" + "\n")
# Let's now compute the heliocentric position for a given epoch
epoch = Epoch(1992, 12, 20.0)
lon, lat, r = Venus.geometric_heliocentric_position(epoch)
print_me("Geometric Heliocentric Longitude", lon.to_positive())
print_me("Geometric Heliocentric Latitude", lat)
print_me("Radius vector", r)
if __name__ == "__main__":
main()