Venus

Class to model Venus planet.

pymeeus.Venus.ORBITAL_ELEM = [[181.979801, 58519.2130302, 0.00031014, 1.5e-08], [0.72332982, 0.0, 0.0, 0.0], [0.00677192, -4.7765e-05, 9.81e-08, 4.6e-10], [3.394662, 0.0010037, -8.8e-07, -7e-09], [76.67992, 0.9011206, 0.00040618, -9.3e-08], [131.563703, 1.4022288, -0.00107618, -5.678e-06]]

This table contains the parameters to compute Venus’ orbital elements for the mean equinox of date. Based in Table 31.A, page 212

pymeeus.Venus.ORBITAL_ELEM_J2000 = [[181.979801, 58517.815676, 1.65e-06, -2e-09], [3.394662, -0.0008568, -3.244e-05, 9e-09], [76.67992, -0.2780134, -0.00014257, -1.64e-07], [131.563703, 0.0048746, -0.00138467, -5.695e-06]]

This table contains the parameters to compute Venus’ orbital elements for the standard equinox J2000.0. Based on Table 31.B, page 214

pymeeus.Venus.VSOP87_B = [[[5923638.472, 0.26702775813, 10213.285546211], [40107.978, 1.14737178106, 20426.571092422], [32814.918, 3.14159265359, 0.0], [1011.392, 1.08946123021, 30639.856638633], [149.458, 6.25390296069, 18073.7049386502], [137.788, 0.86020146523, 1577.3435424478], [129.973, 3.67152483651, 9437.762934887], [119.507, 3.70468812804, 2352.8661537718], [107.971, 4.53903677647, 22003.9146348698], [92.029, 1.53954562706, 9153.9036160218], [52.982, 2.28138172277, 5507.5532386674], [45.617, 0.72319641722, 10239.5838660108], [38.855, 2.93437865147, 10186.9872264112], [43.491, 6.14015776699, 11790.6290886588], [41.7, 5.99126845246, 19896.8801273274], [39.644, 3.86842095901, 8635.9420037632], [39.175, 3.94960351174, 529.6909650946], [33.32, 4.83194909595, 14143.4952424306], [23.711, 2.90646621218, 10988.808157535], [23.5, 2.00770618322, 13367.9726311066], [21.809, 2.69701424951, 19651.048481098], [20.653, 0.98666685459, 775.522611324], [16.976, 4.13711782135, 10021.8372800994], [17.835, 5.96268643102, 25934.1243310894], [14.949, 5.61075168206, 10404.7338123226], [18.579, 1.80529277514, 40853.142184844], [15.407, 3.29563855296, 11015.1064773348], [12.936, 5.42651448496, 29580.4747084438], [11.962, 3.57604253827, 10742.9765113056], [11.827, 1.190709196, 8624.2126509272], [11.466, 5.12780364967, 6283.0758499914], [9.484, 2.75167834335, 191.4482661116], [13.129, 5.70735942511, 9683.5945811164], [8.583, 0.43182249199, 9786.687355335], [9.763, 0.14614896296, 20618.0193585336], [8.148, 1.30548515603, 15720.8387848784], [6.05, 6.26541665966, 11322.6640983044], [5.955, 4.92235372433, 1059.3819301892], [6.983, 3.44920932146, 17298.1823273262], [6.228, 1.13312070908, 29864.334027309], [6.186, 4.92498052443, 19367.1891622328], [6.155, 2.424139469, 4705.7323075436], [5.204, 3.42528906628, 9103.9069941176], [6.0, 3.57639095526, 3154.6870848956], [4.796, 3.86676184909, 7860.4193924392], [5.289, 4.99182712443, 7084.8967811152], [4.07, 5.5879814474, 12566.1516999828], [3.942, 5.68758787835, 10206.1719992102], [3.797, 3.89520601076, 10192.5101507186], [3.798, 6.06410995916, 10234.0609417034], [3.579, 0.73789669235, 4551.9534970588], [3.641, 2.61501257205, 15874.6175953632], [3.266, 0.97517223854, 23581.2581773176], [2.813, 0.29951755546, 9411.4646150872], [3.048, 2.5108514699, 33794.5437235286], [2.559, 4.58043833032, 801.8209311238], [2.462, 5.05790874754, 29050.7837433492], [2.593, 5.73113176751, 20213.271996984], [2.625, 4.24272906574, 213.299095438], [2.246, 0.82112963936, 28286.9904848612], [2.229, 2.22457598233, 10426.584641649], [1.742, 1.48394229233, 7058.5984613154], [1.66, 5.42775825275, 32217.2001810808], [1.491, 4.64883377941, 1109.3785520934], [2.01, 0.75702888128, 9999.986450773], [1.562, 3.93962080463, 37724.7534197482], [1.538, 2.1730957708, 21535.9496445154], [1.546, 4.70759186462, 14945.3161735544], [1.2, 1.48282382657, 9830.3890139878], [1.224, 5.55090394449, 5661.3320491522], [1.111, 1.20276209213, 9573.388259897], [1.064, 1.98891375536, 26.2983197998], [1.041, 5.38535116069, 7.1135470008], [1.036, 1.16719443387, 8662.240323563], [1.143, 3.20596958337, 3532.0606928114], [1.201, 0.81913312536, 8094.5216858326], [1.005, 2.38429892132, 27511.4678735372], [1.047, 4.56525030769, 20419.45754542119], [0.968, 6.18496721871, 25158.6017197654], [1.044, 1.98055689074, 10596.1820784342], [0.962, 0.48573513747, 23958.6317852334], [0.846, 0.01566400887, 3128.3887650958], [0.792, 5.39686899735, 24356.7807886416], [0.858, 5.34692750735, 41654.9631159678], [0.757, 6.25904553773, 20452.8694122218], [0.801, 4.62406152514, 9929.4262273458], [0.802, 5.3723489252, 10497.1448650762], [0.75, 3.85219782842, 21228.3920235458], [0.7, 1.98097957188, 3930.2096962196], [0.719, 6.11596800207, 10218.8084705184], [0.672, 6.23429601219, 14765.2390432698], [0.639, 5.37566437358, 1589.0728952838], [0.605, 2.4233039112, 10251.3132188468], [0.726, 6.16683781802, 18875.525869774], [0.613, 5.9973118069, 4732.0306273434], [0.72, 3.84286345199, 10207.7626219036], [0.637, 6.17053891156, 10220.3990932118], [0.515, 1.03001478293, 22779.4372461938], [0.574, 0.43813688572, 17085.9586657222], [0.51, 1.41065159851, 9161.0171630226], [0.569, 3.34601425125, 3340.6124266998], [0.608, 1.25236241968, 10175.2578735752], [0.524, 2.3979424867, 26087.9031415742], [0.542, 1.34665646732, 29088.811415985], [0.527, 4.01994270827, 18849.2275499742], [0.569, 1.65498800378, 39264.0692895602], [0.518, 4.96996115446, 30213.258447757], [0.514, 5.78413007838, 12592.4500197826], [0.538, 4.56198493922, 10063.7223490764], [0.484, 4.18538027381, 14919.0178537546], [0.493, 4.79939382739, 9146.790069021], [0.427, 3.76876868949, 11272.6674764002], [0.495, 0.49175293655, 45585.1728121874], [0.494, 3.74345863918, 31441.6775697568], [0.524, 0.97991794166, 30110.1656735384], [0.483, 1.87898057316, 51066.427731055], [0.505, 3.70047474212, 20400.2727726222], [0.351, 4.3402657449, 10137.0194749354], [0.355, 5.56672554631, 18837.49819713819], [0.328, 3.7842737891, 6681.2248533996], [0.349, 4.20550749672, 20956.2620575166], [0.333, 4.44969281739, 28521.0927782546], [0.296, 2.83205515646, 17277.4069318338], [0.311, 2.57334132897, 20809.4676246452], [0.294, 0.75089224483, 3149.1641605882], [0.377, 3.98143308775, 21202.093703746], [0.272, 5.56183082489, 16496.3613962024], [0.314, 0.02584607093, 13745.3462390224], [0.263, 0.55328410985, 36147.4098773004], [0.286, 5.16408902215, 426.598190876], [0.279, 4.29871615943, 19999.97290154599], [0.28, 1.92925047377, 49515.382508407], [0.265, 4.81168402147, 20235.1228263104], [0.273, 5.12740051559, 35371.8872659764], [0.306, 5.28903794869, 382.8965322232], [0.223, 2.50591724074, 26709.6469424134], [0.235, 5.96522395118, 10198.033075026], [0.234, 3.52866583267, 10228.538017396], [0.224, 6.24561979789, 7064.1213856228], [0.251, 2.84739274245, 33019.0211122046], [0.196, 1.5061039379, 31749.2351907264], [0.192, 1.69321442572, 13341.6743113068], [0.18, 6.19353087076, 39793.7602546548], [0.199, 1.1643332188, 22805.7355659936], [0.18, 3.72646417141, 1551.045222648], [0.173, 3.35235705827, 53445.5922046266], [0.195, 1.51901264131, 43232.3066584156], [0.174, 2.84049662693, 9967.4538999816], [0.163, 4.29160537719, 36949.2308084242], [0.169, 0.37000676558, 10459.1171924404], [0.137, 5.61149803116, 10529.6774158676], [0.139, 0.87847805052, 16522.6597160022], [0.139, 4.12576475427, 36301.18868778519], [0.127, 5.14447758616, 5481.2549188676], [0.131, 3.11317801589, 9896.8936765544], [0.131, 0.89697384735, 3442.5749449654], [0.121, 1.32802112907, 38734.3783244656], [0.122, 1.59017183044, 10110.1927719924], [0.123, 2.33714216061, 10316.3783204296], [0.133, 2.90682399304, 9793.8009023358], [0.111, 2.5207763476, 13936.794505134], [0.12, 0.36076947165, 536.8045120954], [0.115, 2.53355582059, 26735.9452622132], [0.108, 2.65839634325, 10232.95530711079], [0.108, 0.55230439694, 10193.61578531121], [0.138, 1.0691923924, 65236.2212932854], [0.101, 3.17012502017, 19317.1925403286], [0.127, 5.63110477712, 10288.0671447783], [0.127, 3.86278127025, 10138.5039476437], [0.137, 2.9335065946, 47162.5163546352], [0.095, 5.03917884334, 52175.8062831484], [0.094, 0.71308489207, 38500.2760310722], [0.092, 5.46204624886, 11764.330768859], [0.096, 1.52914774412, 9690.7081281172], [0.101, 0.83318284426, 6489.776587288], [0.115, 3.76443612245, 522.5774180938], [0.089, 2.53312656681, 10735.8629643048], [0.082, 0.85628515615, 2379.1644735716], [0.103, 5.2268323762, 103.0927742186], [0.09, 2.12423586627, 28313.288804661], [0.09, 0.39668501735, 9580.5018068978], [0.074, 6.0268009555, 3723.508958923], [0.081, 5.25045057985, 10419.4710946482], [0.08, 4.23724598221, 10007.0999977738], [0.091, 2.48874147947, 10846.0692855242], [0.085, 3.82784790321, 51868.2486621788], [0.081, 2.26235214191, 3903.9113764198], [0.097, 0.772950916, 18307.8072320436], [0.094, 0.17063414792, 6872.6731195112], [0.08, 5.62254102739, 29999.959352319], [0.068, 2.7176293667, 16983.9961474566], [0.066, 0.76731351736, 20.7753954924], [0.075, 0.36155638007, 39302.096962196], [0.075, 2.27327165974, 8521.1198767086], [0.058, 2.14482855875, 8631.326197928], [0.064, 5.83569051301, 2118.7638603784], [0.058, 2.98524209824, 19889.76658032659], [0.054, 1.78260668333, 40077.61957352], [0.055, 4.70485939861, 639.897286314], [0.06, 5.8966189292, 41962.5207369374], [0.066, 2.24746237999, 74.7815985673], [0.061, 3.40726181591, 27490.6924780448], [0.051, 3.07811180039, 24150.080051345], [0.057, 2.30081371235, 20529.66386664059], [0.052, 2.37192464233, 29573.361161443], [0.052, 4.76610409132, 57375.8019008462], [0.047, 1.61630288856, 30831.3049047446], [0.054, 5.89684197257, 19903.99367432819], [0.04, 5.32101847424, 42430.4857272918], [0.051, 5.29186795569, 29587.5882554446]], [[513347.602, 1.80364310797, 10213.285546211], [4380.1, 3.38615711591, 20426.571092422], [196.586, 2.53001197486, 30639.856638633], [199.162, 0.0, 0.0], [14.031, 2.27087044687, 9437.762934887], [12.958, 1.50735622957, 18073.7049386502], [11.941, 5.60462450426, 1577.3435424478], [10.324, 5.24224313355, 2352.8661537718], [9.294, 6.07545631303, 22003.9146348698], [7.441, 1.50257909439, 11790.6290886588], [8.031, 0.29371105198, 9153.9036160218], [7.514, 5.0808188599, 10186.9872264112], [4.669, 3.87801635015, 10239.5838660108], [4.399, 3.58872736593, 40853.142184844], [3.975, 1.28397121206, 10404.7338123226], [4.657, 0.75073886819, 5507.5532386674], [3.783, 4.33004753984, 19651.048481098], [3.39, 4.88976070903, 10988.808157535], [3.555, 1.25927550356, 19896.8801273274], [3.479, 5.5079700216, 529.6909650946], [2.884, 0.08549582037, 14143.4952424306], [1.786, 0.37134513186, 13367.9726311066], [1.6, 1.68378002982, 20618.0193585336], [1.539, 1.21683853657, 25934.1243310894], [1.341, 2.90077139758, 15720.8387848784], [0.993, 1.74681248965, 11322.6640983044], [1.165, 6.13437155401, 7860.4193924392], [1.115, 0.6674369038, 29580.4747084438], [0.923, 2.25384969096, 10021.8372800994], [0.965, 1.36425494833, 9683.5945811164], [0.973, 0.39071758442, 6283.0758499914], [0.805, 0.53331923557, 8624.2126509272], [0.913, 0.76046003719, 8635.9420037632], [0.991, 0.5531987933, 19367.1891622328], [0.609, 2.62364470139, 23581.2581773176], [0.532, 5.10925676528, 9786.687355335], [0.476, 6.17672999981, 11015.1064773348], [0.472, 1.696726292, 17298.1823273262], [0.503, 2.65840772485, 29864.334027309], [0.456, 5.01205315518, 10742.9765113056], [0.478, 3.94100005156, 775.522611324], [0.477, 3.71554345922, 10596.1820784342], [0.347, 2.3455106268, 9411.4646150872], [0.458, 2.31894399069, 9999.986450773], [0.374, 3.76878356974, 21228.3920235458], [0.44, 4.33400244581, 15874.6175953632], [0.349, 1.31468836511, 10234.0609417034], [0.31, 5.45422332781, 10192.5101507186], [0.346, 0.94242286364, 1059.3819301892], [0.308, 4.90145899142, 3930.2096962196], [0.331, 4.89498986674, 10206.1719992102], [0.269, 2.39650266204, 801.8209311238], [0.269, 0.00589873499, 9830.3890139878], [0.261, 3.48196147279, 7058.5984613154], [0.29, 0.10953964861, 29050.7837433492], [0.283, 6.12133736787, 20419.45754542119], [0.232, 3.0784585003, 12566.1516999828], [0.265, 4.02431894973, 33794.5437235286], [0.22, 2.37315851889, 4551.9534970588], [0.247, 3.07626728158, 28286.9904848612], [0.202, 3.56872121409, 21535.9496445154], [0.225, 5.7688889632, 213.299095438], [0.217, 0.88382111135, 20213.271996984], [0.172, 6.12653050186, 9161.0171630226], [0.195, 5.472408554, 37724.7534197482], [0.153, 4.07656151671, 27511.4678735372], [0.174, 1.33676849359, 32217.2001810808], [0.157, 5.98474214437, 26.2983197998], [0.163, 5.4551913476, 10426.584641649], [0.129, 2.08748660996, 3128.3887650958], [0.131, 1.51959002513, 10218.8084705184], [0.139, 4.42330401713, 10220.3990932118], [0.126, 2.62296638037, 22779.4372461938], [0.146, 4.69869606856, 25158.6017197654], [0.172, 6.13435208788, 18837.49819713819], [0.157, 5.44507403858, 4705.7323075436], [0.117, 6.18296175153, 20400.2727726222], [0.164, 3.30849473132, 51066.427731055], [0.113, 3.64412860654, 7.1135470008], [0.109, 5.21220660788, 8662.240323563], [0.133, 1.78047296245, 191.4482661116], [0.117, 0.14681677884, 9146.790069021], [0.116, 0.61940521198, 41654.9631159678], [0.096, 1.49631428731, 7084.8967811152], [0.096, 1.21744230443, 10198.033075026], [0.082, 1.45863866349, 10207.7626219036], [0.085, 6.04057728058, 21202.093703746], [0.083, 0.19985600927, 14919.0178537546], [0.077, 5.5013231061, 5661.3320491522], [0.077, 2.00173927326, 10228.538017396], [0.093, 1.85466268819, 45585.1728121874], [0.066, 3.25826124156, 1109.3785520934], [0.089, 0.64100435648, 3154.6870848956], [0.061, 3.80043027736, 11272.6674764002], [0.077, 1.8551635895, 3532.0606928114], [0.062, 0.81341290651, 382.8965322232], [0.072, 2.35312965005, 9103.9069941176], [0.053, 3.21969389511, 20452.8694122218], [0.067, 1.42090542131, 24356.7807886416], [0.056, 2.97733070198, 30110.1656735384], [0.051, 4.22406663447, 20809.4676246452], [0.058, 6.20761936031, 29088.811415985], [0.061, 3.27309494322, 49515.382508407], [0.046, 5.49443476235, 31441.6775697568], [0.05, 4.16651052942, 13341.6743113068], [0.047, 1.25473247769, 33019.0211122046], [0.047, 2.03402044389, 23958.6317852334], [0.036, 5.24409311105, 3149.1641605882], [0.038, 4.15337829669, 18849.2275499742], [0.042, 0.43005959574, 1589.0728952838], [0.041, 1.21289342964, 12592.4500197826], [0.038, 5.91928287144, 28521.0927782546], [0.033, 3.98241699279, 4732.0306273434], [0.035, 2.24417218267, 16496.3613962024], [0.04, 6.13293942728, 26087.9031415742], [0.044, 1.7812329486, 426.598190876], [0.041, 3.16744909855, 39264.0692895602], [0.033, 4.96183427323, 536.8045120954], [0.034, 0.12963030501, 30213.258447757], [0.036, 5.41167321573, 522.5774180938], [0.027, 4.44250239485, 17277.4069318338], [0.034, 5.94541303751, 9929.4262273458], [0.033, 0.40689057274, 10497.1448650762], [0.023, 2.59067946967, 10175.2578735752], [0.022, 0.69625017371, 19999.97290154599], [0.023, 3.76162101633, 10251.3132188468], [0.023, 0.62711494266, 35371.8872659764], [0.022, 4.64142978776, 19889.76658032659], [0.02, 4.01315480107, 26709.6469424134], [0.02, 4.0334440068, 29573.361161443], [0.023, 0.90416640595, 8094.5216858326], [0.022, 1.92092469688, 17085.9586657222], [0.019, 5.04938942644, 6681.2248533996]], [[22377.665, 3.38509143877, 10213.285546211], [281.739, 0.0, 0.0], [173.164, 5.25563766915, 20426.571092422], [26.945, 3.87040891568, 30639.856638633], [1.174, 0.09768632072, 10186.9872264112], [0.685, 3.19139067811, 11790.6290886588], [0.788, 4.36515965295, 10239.5838660108], [0.592, 5.22270440328, 40853.142184844], [0.515, 6.12821215207, 10988.808157535], [0.538, 0.57550272342, 2352.8661537718], [0.54, 3.11657836329, 18073.7049386502], [0.454, 2.79306867629, 10404.7338123226], [0.374, 6.10468482446, 9437.762934887], [0.431, 4.00778431184, 1577.3435424478], [0.36, 6.0174784232, 19651.048481098], [0.375, 1.31319959789, 22003.9146348698], [0.354, 5.12509281266, 9153.9036160218], [0.15, 4.58623687118, 15720.8387848784], [0.164, 5.41790158607, 5507.5532386674], [0.159, 2.78191550878, 19896.8801273274], [0.157, 0.65774905071, 529.6909650946], [0.155, 2.54824315372, 9683.5945811164], [0.109, 2.01866665583, 14143.4952424306], [0.106, 2.28289033017, 6283.0758499914], [0.115, 3.23636374193, 20618.0193585336], [0.128, 5.32400510939, 13367.9726311066], [0.087, 3.28265082435, 11322.6640983044], [0.09, 5.23585072275, 10596.1820784342], [0.055, 4.82369879741, 7058.5984613154], [0.044, 0.58444963462, 10206.1719992102], [0.044, 2.34401612969, 19367.1891622328], [0.038, 4.55053233088, 9999.986450773], [0.039, 5.84340580032, 10220.3990932118], [0.036, 4.41006216127, 51066.427731055], [0.039, 3.14348236386, 9411.4646150872], [0.033, 4.5574866034, 10742.9765113056], [0.037, 2.79630938717, 25934.1243310894], [0.034, 0.55287110072, 11015.1064773348], [0.034, 2.25809144959, 29580.4747084438], [0.038, 1.88638747393, 801.8209311238], [0.034, 1.22706917271, 10021.8372800994], [0.027, 4.83867137637, 9830.3890139878], [0.027, 4.3114017935, 23581.2581773176], [0.027, 2.17187621336, 8635.9420037632], [0.02, 5.66581696952, 21228.3920235458], [0.024, 2.1720810785, 18849.2275499742], [0.02, 5.29318634138, 775.522611324], [0.019, 2.73486845601, 3128.3887650958], [0.013, 3.40362915274, 1059.3819301892], [0.014, 0.05074160195, 7860.4193924392], [0.014, 5.43035907265, 26.2983197998], [0.012, 3.24834347355, 9103.9069941176], [0.013, 5.04826725887, 7.1135470008], [0.015, 1.42027402522, 29050.7837433492], [0.01, 4.9813806749, 10426.584641649], [0.011, 0.85773045784, 17298.1823273262], [0.011, 4.23048200054, 29864.334027309], [0.01, 0.26447399758, 3930.2096962196], [0.011, 1.46728576671, 20419.45754542119]], [[646.671, 4.99166565277, 10213.285546211], [19.952, 3.14159265359, 0.0], [5.54, 0.77376923951, 20426.571092422], [2.526, 5.4449376302, 30639.856638633], [0.079, 1.51447613604, 10186.9872264112], [0.056, 0.63647808442, 40853.142184844], [0.058, 5.7073117655, 10239.5838660108], [0.031, 4.72523061067, 11790.6290886588], [0.026, 1.02068113372, 10988.808157535], [0.025, 5.60599130442, 9437.762934887], [0.017, 2.05293621864, 2352.8661537718], [0.011, 4.33056892256, 10404.7338123226], [0.009, 1.36283915068, 19651.048481098], [0.007, 4.69592781899, 18073.7049386502], [0.006, 2.97926526705, 22003.9146348698]], [[14.102, 0.31537190181, 10213.285546211], [0.19, 2.35466404492, 20426.571092422], [0.164, 0.74476215141, 30639.856638633], [0.214, 3.14159265359, 0.0], [0.004, 2.34190883009, 40853.142184844]], [[0.239, 2.05201727566, 10213.285546211], [0.039, 0.0, 0.0], [0.011, 3.82500275251, 20426.571092422], [0.009, 2.32953116868, 30639.856638633]]]

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.

pymeeus.Venus.VSOP87_L = [[[317614666.774, 0.0, 0.0], [1353968.419, 5.59313319619, 10213.285546211], [89891.645, 5.30650048468, 20426.571092422], [5477.201, 4.41630652531, 7860.4193924392], [3455.732, 2.69964470778, 11790.6290886588], [2372.061, 2.99377539568, 3930.2096962196], [1317.108, 5.18668219093, 26.2983197998], [1664.069, 4.2501893503, 1577.3435424478], [1438.322, 4.15745043958, 9683.5945811164], [1200.521, 6.15357115319, 30639.856638633], [761.38, 1.9501470212, 529.6909650946], [707.676, 1.06466707214, 775.522611324], [584.836, 3.99839884762, 191.4482661116], [769.314, 0.81629615911, 9437.762934887], [499.915, 4.12340210074, 15720.8387848784], [326.221, 4.59056473097, 10404.7338123226], [429.498, 3.58642859752, 19367.1891622328], [326.967, 5.67736583705, 5507.5532386674], [231.937, 3.16251057072, 9153.9036160218], [179.695, 4.65337915578, 1109.3785520934], [128.263, 4.22604493736, 20.7753954924], [155.464, 5.57043888948, 19651.048481098], [127.907, 0.96209822685, 5661.3320491522], [105.547, 1.53721191253, 801.8209311238], [85.722, 0.35589249966, 3154.6870848956], [99.121, 0.83288185132, 213.299095438], [98.804, 5.39389655503, 13367.9726311066], [82.094, 3.21596990826, 18837.49819713819], [88.031, 3.88868860307, 9999.986450773], [71.577, 0.11145739345, 11015.1064773348], [56.122, 4.24039855475, 7.1135470008], [70.239, 0.67458813282, 23581.2581773176], [50.796, 0.24531603049, 11322.6640983044], [46.111, 5.31576465717, 18073.7049386502], [44.574, 6.06282201966, 40853.142184844], [42.594, 5.3287333721, 2352.8661537718], [42.635, 1.7995542168, 7084.8967811152], [41.177, 0.36240972161, 382.8965322232], [35.749, 2.70448479296, 10206.1719992102], [33.893, 2.02347322198, 6283.0758499914], [29.138, 3.59230925768, 22003.9146348698], [28.479, 2.22375414002, 1059.3819301892], [29.85, 4.02176977477, 10239.5838660108], [33.252, 2.10025596509, 27511.4678735372], [30.172, 4.9419191989, 13745.3462390224], [29.252, 3.51392387787, 283.8593188652], [24.424, 2.70177493852, 8624.2126509272], [20.274, 3.79493637509, 14143.4952424306], [24.322, 4.27814493315, 5.5229243074], [26.26, 0.54067587552, 17298.1823273262], [20.492, 0.58547075036, 38.0276726358], [18.988, 4.13811500642, 4551.9534970588], [23.739, 4.82870797552, 6872.6731195112], [15.885, 1.50067222283, 8635.9420037632], [19.069, 6.12025580313, 29050.7837433492], [18.269, 3.04740408477, 19999.97290154599], [13.656, 4.41336292334, 3532.0606928114], [17.094, 3.5216152643, 31441.6775697568], [10.955, 2.84562790076, 18307.8072320436], [11.048, 2.58361219075, 9786.687355335], [9.904, 1.08737710389, 7064.1213856228], [10.576, 0.85419784436, 10596.1820784342], [9.231, 5.52471655579, 12566.1516999828], [11.599, 5.81007422699, 19896.8801273274], [11.807, 1.91250672543, 21228.3920235458], [10.105, 2.34270786693, 10742.9765113056], [8.154, 1.92331359797, 15.252471185], [8.893, 1.97291388515, 10186.9872264112], [9.352, 4.94508904764, 35371.8872659764], [6.821, 4.39733188968, 8662.240323563], [6.688, 1.55310437864, 14945.3161735544], [6.413, 2.17677652923, 10988.808157535], [5.802, 1.93462125906, 3340.6124266998], [5.95, 2.96578175391, 4732.0306273434], [5.275, 5.01877102496, 28286.9904848612], [7.047, 1.00111452053, 632.7837393132], [5.048, 4.27886209626, 29580.4747084438], [6.305, 0.3550633118, 103.0927742186], [5.959, 5.04792949464, 245.8316462294], [4.651, 0.85218058876, 6770.7106012456], [5.58, 0.48723384809, 522.5774180938], [5.327, 3.03115417024, 10021.8372800994], [5.01, 5.773751665, 28521.0927782546], [4.608, 1.93302108394, 4705.7323075436], [5.526, 3.36797048901, 25158.6017197654], [3.863, 4.89351531412, 25934.1243310894], [5.303, 0.08161426841, 39302.096962196], [4.254, 5.36046113295, 21535.9496445154], [3.763, 1.05304597315, 19.66976089979], [4.407, 4.02575374517, 74.7815985673], [4.145, 1.14356412295, 9676.4810341156], [4.318, 4.38289970585, 316.3918696566], [3.642, 6.11733529325, 3128.3887650958], [3.238, 5.39551036769, 419.4846438752], [3.909, 4.0526363533, 9690.7081281172], [3.152, 0.72553551731, 16496.3613962024], [3.496, 0.72414615705, 3723.508958923], [3.755, 3.80208713127, 19786.67380610799], [2.891, 3.3378273777, 32217.2001810808], [3.016, 1.57249112496, 17277.4069318338], [3.825, 0.19612312903, 426.598190876], [3.798, 0.45524571743, 10316.3783204296], [2.57, 1.20813474107, 13936.794505134], [2.796, 3.65128969074, 206.1855484372], [2.466, 3.61988676373, 1551.045222648], [3.108, 1.50325806664, 43232.3066584156], [2.976, 4.79415001304, 29088.811415985], [2.217, 3.59623681714, 24356.7807886416], [2.227, 4.9605922194, 536.8045120954], [2.397, 3.45249688427, 19374.3027092336], [2.462, 0.53295178258, 19360.07561523199], [2.205, 2.70399309963, 12592.4500197826], [2.23, 3.01413465913, 18875.525869774], [1.858, 4.06129152783, 2379.1644735716], [1.807, 3.15086214479, 9573.388259897], [2.238, 5.52216925076, 10138.5039476437], [2.195, 2.32046770554, 8094.5216858326], [2.101, 2.90421302975, 9967.4538999816], [1.916, 4.56513949099, 2218.7571041868], [1.467, 2.42640162465, 10234.0609417034], [1.726, 5.59790693845, 20452.8694122218], [1.455, 2.44757248737, 1589.0728952838], [1.991, 4.04623390359, 31749.2351907264], [1.406, 2.71736996917, 16983.9961474566], [1.658, 0.11252373292, 153.7788104848], [1.851, 2.92898027939, 47162.5163546352], [1.492, 1.07513892753, 9103.9069941176], [1.247, 2.48433565896, 17778.11626694899], [1.549, 4.205536543, 3442.5749449654], [1.243, 3.95452438599, 170.6728706192], [1.694, 6.20694480406, 33019.0211122046], [1.221, 4.77931820602, 30110.1656735384], [1.206, 0.30531303095, 29864.334027309], [1.238, 5.05581820608, 20213.271996984], [1.152, 3.26229919481, 11.729352836], [1.179, 1.69491074791, 20400.2727726222], [1.165, 2.88995128147, 574.3447983348], [1.306, 0.14519588607, 9146.790069021], [1.113, 1.52598846804, 10426.584641649], [1.104, 2.58791423813, 18849.2275499742], [1.045, 0.5753921642, 15874.6175953632], [1.36, 2.41976595457, 38734.3783244656], [0.981, 4.37930727798, 110.2063212194], [1.095, 0.49492867814, 51066.427731055], [1.146, 4.54241454215, 10220.3990932118], [0.981, 1.65915064733, 10103.0792249916], [1.27, 4.69374306132, 9050.8108418032], [1.065, 4.41645258887, 22805.7355659936], [0.854, 2.34437926957, 6681.2248533996], [1.104, 0.49781459714, 1.4844727083], [1.075, 1.09857593161, 377.3736079158], [1.114, 4.35024775806, 51092.7260508548], [0.829, 5.41196274578, 27991.40181316], [0.9, 2.74195379617, 41962.5207369374], [1.01, 2.96092073452, 135.62532501], [0.768, 3.98260860494, 18844.61174413899], [1.018, 1.36891050752, 36949.2308084242], [0.726, 1.67728773965, 21202.093703746], [0.727, 0.89048212541, 467.9649903544], [0.869, 2.93767679827, 10192.5101507186], [0.696, 5.35698039414, 10063.7223490764], [0.92, 4.17128923588, 18734.4054229196], [0.691, 1.50594097883, 27197.2816936676], [0.835, 0.48050621092, 20618.0193585336], [0.711, 0.19750098222, 18830.38465013739], [0.811, 0.16685071959, 12432.0426503978], [0.756, 3.79022623226, 9161.0171630226], [0.622, 5.33659507738, 9411.4646150872], [0.862, 5.72705356405, 10175.1525105732], [0.853, 0.10404188453, 2107.0345075424], [0.742, 3.96365892051, 813.5502839598], [0.705, 0.71229660616, 220.4126424388], [0.584, 1.719006927, 36.0278666774], [0.612, 0.36418385449, 949.1756089698], [0.587, 1.5864894929, 6.62855890001], [0.581, 5.49288908804, 6309.3741697912], [0.581, 4.80353237853, 24150.080051345], [0.516, 6.07328802561, 38.1330356378], [0.627, 5.47281424954, 9580.5018068978], [0.601, 1.40500080774, 1162.4747044078], [0.62, 4.00681042667, 9992.8729037722], [0.611, 3.62010998629, 7255.5696517344], [0.697, 2.22359630727, 348.924420448], [0.693, 5.77432072851, 55022.9357470744], [0.494, 0.29761886866, 7058.5984613154], [0.563, 0.24172140474, 37410.5672398786], [0.487, 5.86917216517, 10137.0194749354], [0.493, 2.04534833854, 735.8765135318], [0.636, 2.79707392326, 40879.4405046438], [0.519, 4.1394565763, 16522.6597160022], [0.535, 4.6056959782, 19573.37471066999], [0.555, 5.88120421263, 26735.9452622132], [0.44, 5.61490649795, 23958.6317852334], [0.541, 0.62494922735, 10007.0999977738], [0.427, 4.02335620501, 14.2270940016], [0.434, 0.29028429049, 9264.1099372412], [0.451, 1.66320363626, 26087.9031415742], [0.422, 3.38413582674, 10787.6303445458], [0.569, 5.14001758731, 27490.6924780448], [0.421, 4.23407313457, 39793.7602546548], [0.458, 5.2878636882, 49.7570254718], [0.418, 5.6909779079, 14765.2390432698], [0.475, 0.97544690438, 1052.2683831884], [0.387, 4.41665162999, 21.8508293264], [0.523, 2.9051242687, 20235.1228263104], [0.506, 5.26999314618, 29999.959352319], [0.438, 2.49457071132, 20956.2620575166], [0.53, 0.71368442157, 33794.5437235286], [0.382, 1.9211936548, 3.9321532631], [0.365, 3.81715328784, 20419.45754542119], [0.426, 2.06384083608, 38204.687359371], [0.496, 0.44077356179, 9835.9119382952], [0.41, 4.93346326003, 19264.0963880142], [0.38, 3.79573358631, 8521.1198767086], [0.334, 5.51158557799, 10251.3132188468], [0.412, 2.56129670728, 77.673770428], [0.418, 2.37865963521, 32.5325507914], [0.325, 6.03020523465, 18947.7045183576], [0.4, 0.91999360201, 227.476132789], [0.437, 0.91420135162, 58953.145443294], [0.36, 0.82477639126, 22.7752014508], [0.413, 4.22381905655, 44809.6502008634], [0.375, 3.15657291896, 19992.85935454519], [0.371, 6.05370874275, 20007.0864485468], [0.361, 5.44371227904, 19470.28193645139], [0.386, 5.28120540405, 47623.8527860896], [0.389, 0.7321667224, 19050.7972925762], [0.32, 2.84811591194, 10199.0584522094], [0.386, 3.88754165531, 1975.492545856], [0.276, 4.33979180814, 20809.4676246452], [0.276, 0.50647429773, 9830.3890139878], [0.309, 3.79299100668, 18204.71445782499], [0.377, 0.73768791281, 11506.7697697936], [0.322, 0.961384421, 30666.1549584328], [0.363, 1.3047240669, 9367.2027114598], [0.366, 2.79972786028, 11272.6674764002], [0.271, 4.66141338193, 846.0828347512], [0.259, 0.4203117575, 39264.0692895602], [0.285, 0.40546033634, 30.914125635], [0.247, 4.80676426942, 36147.4098773004], [0.264, 2.71608177583, 11.0457002639], [0.233, 2.76423842887, 187.9251477626], [0.248, 1.60765612338, 10497.1448650762], [0.271, 0.8234891963, 19793.7873531088], [0.225, 3.80080957016, 8631.326197928], [0.263, 1.92311689852, 37724.7534197482], [0.214, 5.01663795092, 639.897286314], [0.289, 0.12342601246, 20277.0078952874], [0.21, 0.12771800254, 29.8214381488], [0.227, 4.18036609801, 17468.8551979454], [0.274, 2.34929343, 62883.3551395136], [0.26, 5.65254501655, 48739.859897083], [0.271, 4.95325404028, 4214.0690150848], [0.219, 2.08775228014, 194.9713844606], [0.191, 2.49267248333, 568.8218740274], [0.25, 1.52909737354, 6037.244203762], [0.231, 5.23674429498, 491.6632924588], [0.182, 4.98046042571, 18418.01355326299], [0.188, 2.82273639603, 1385.8952763362], [0.204, 4.09939796199, 14919.0178537546], [0.176, 3.8240098246, 9360.089164459], [0.198, 2.76491873243, 10217.2176994741], [0.168, 5.19268384202, 1066.49547719], [0.199, 1.95301487982, 7564.830720738], [0.171, 2.59623459612, 20405.7956969296], [0.172, 5.29332132623, 11764.330768859], [0.165, 2.88557908025, 10207.7626219036], [0.164, 3.25435371801, 3914.9572250346], [0.2, 3.8244321809, 18314.9207790444], [0.169, 1.78341902878, 31022.7531708562], [0.179, 0.90840065587, 7880.08915333899], [0.163, 2.79665037814, 41.5507909848], [0.154, 3.90796293476, 30213.258447757], [0.153, 0.07463240782, 28528.2063252554], [0.194, 5.95838706838, 8617.0991039264], [0.171, 4.58206324409, 20447.3464879144], [0.15, 2.11647586229, 17248.4253018544], [0.149, 2.1725998632, 9929.4262273458], [0.191, 0.82310353823, 52670.0695933026], [0.148, 2.94315921485, 41654.9631159678], [0.149, 4.49798039726, 30831.3049047446], [0.184, 2.46923348701, 34596.3646546524], [0.146, 2.694529303, 43071.8992890308], [0.159, 2.1113771357, 19317.1925403286], [0.154, 2.76536164654, 28513.97923125379], [0.14, 4.94595038686, 9256.9963902404], [0.141, 2.57248458154, 13553.8979729108], [0.137, 1.66482327575, 2636.725472637], [0.14, 5.2303960599, 22645.32819660879], [0.132, 5.35690599728, 19624.7501612982], [0.14, 2.90637712614, 48947.6638706766], [0.129, 3.95303623681, 32858.61374281979], [0.156, 6.01143316387, 29057.89729034999], [0.134, 5.75241675118, 68050.42387851159], [0.154, 3.66827363753, 276.7457718644], [0.176, 3.77298381177, 66813.5648357332], [0.126, 5.00217740223, 27461.7108480654], [0.135, 1.3480701392, 53285.1848352418], [0.15, 0.25029475344, 290.972865866], [0.152, 3.13035670092, 29043.67019634839], [0.169, 5.0434810943, 73.297125859], [0.166, 5.39219948035, 41236.0387170672], [0.163, 5.59796070987, 7576.560073574], [0.126, 0.77391784606, 49.9966219042], [0.163, 0.44241846674, 20350.3050211464], [0.136, 3.09066368912, 418.9243989006], [0.154, 0.4708619096, 28418.000004036], [0.12, 0.88536981986, 29573.361161443], [0.132, 1.4800976904, 17085.9586657222], [0.126, 1.39497760964, 966.9708774356], [0.143, 3.84026797958, 14128.2427712456], [0.147, 2.11627427804, 34363.365597556], [0.106, 2.04696932293, 37674.9963942764], [0.106, 1.43873202489, 27682.1407441564], [0.149, 0.09286508794, 8144.2787113044], [0.103, 0.0199204147, 18300.69368504279], [0.121, 3.57602835443, 45.1412196366], [0.125, 0.11630302078, 149.5631971346], [0.102, 4.1794709773, 2333.196392872], [0.099, 1.51324741657, 10419.4710946482], [0.133, 3.02183293676, 76251.32777062019], [0.136, 4.17517197268, 3646.3503773544], [0.123, 0.44045588682, 515.463871093], [0.113, 5.69261397718, 10110.1927719924], [0.098, 6.23797900467, 202.2533951741], [0.099, 3.75627530197, 59728.668054618], [0.101, 4.62832557536, 65236.2212932854], [0.111, 1.25947267588, 10846.0692855242], [0.11, 5.87455577536, 38500.2760310722], [0.128, 6.0102456216, 90394.82301305079], [0.091, 1.77665981007, 1539.315869812], [0.092, 0.99804571578, 95.9792272178], [0.12, 3.93060866244, 38526.574350872], [0.117, 2.24143299549, 56600.2792895222], [0.118, 6.0912132594, 29786.660256881], [0.098, 4.60938156207, 11787.1059703098], [0.097, 3.92727733144, 11794.1522070078], [0.093, 5.23395435043, 14169.7935622304], [0.096, 5.27525709038, 8734.4189721466], [0.094, 0.18166654805, 67589.08744705719], [0.11, 4.96279287076, 48417.97290558199], [0.086, 0.39533409505, 3956.5080160194], [0.085, 5.69642646462, 37703.9780242558], [0.114, 5.19676285428, 70743.77453195279], [0.081, 5.51324815184, 412.3710968744], [0.089, 2.13409771828, 44768.0994098786], [0.084, 6.02475904578, 10632.7701900862], [0.085, 4.60912614442, 45585.1728121874], [0.078, 4.47358603432, 114.43928868521], [0.097, 4.02223363535, 10218.8084705184], [0.081, 1.03870237004, 9793.8009023358], [0.092, 0.80301220092, 24383.0791084414], [0.087, 2.15124790938, 28313.288804661], [0.075, 5.17868679355, 63658.8777508376], [0.078, 5.81927313665, 567.7186377304], [0.075, 1.72618192481, 19580.4882576708], [0.071, 0.10259261764, 90695.75207512038], [0.077, 6.16012067704, 1573.8204240988], [0.076, 5.12884307551, 49515.382508407], [0.069, 0.29569499484, 10175.2578735752], [0.061, 4.80385549281, 19889.76658032659], [0.06, 4.56685040226, 30426.557543195], [0.062, 4.16222812699, 42430.4857272918], [0.05, 6.17899839001, 22779.4372461938], [0.048, 1.52546758016, 20639.87018786], [0.046, 4.41738494249, 34570.0663348526], [0.037, 4.69675087759, 44007.8292697396]], [[1021352943052.898, 0.0, 0.0], [95707.712, 2.46424448979, 10213.285546211], [14444.977, 0.51624564679, 20426.571092422], [213.374, 1.79547929368, 30639.856638633], [151.669, 6.10635282369, 1577.3435424478], [173.904, 2.65535879443, 26.2983197998], [82.233, 5.7023413373, 191.4482661116], [69.734, 2.68136034979, 9437.762934887], [52.408, 3.60013087656, 775.522611324], [38.318, 1.03379038025, 529.6909650946], [29.633, 1.25056322354, 5507.5532386674], [25.056, 6.10664792855, 10404.7338123226], [17.772, 6.19369798901, 1109.3785520934], [16.51, 2.6433045264, 7.1135470008], [14.23, 5.45138233941, 9153.9036160218], [12.607, 1.24464400689, 40853.142184844], [11.627, 4.97604495371, 213.299095438], [12.563, 1.88122199199, 382.8965322232], [8.869, 0.95282732248, 13367.9726311066], [7.374, 4.3947676058, 10206.1719992102], [6.552, 2.28168808058, 2352.8661537718], [6.255, 4.08056644034, 3154.6870848956], [6.697, 5.05673427795, 801.8209311238], [4.084, 4.1210382603, 18837.49819713819], [4.882, 3.44515199115, 11015.1064773348], [3.549, 6.19934345402, 5.5229243074], [3.448, 1.77405651704, 11322.6640983044], [4.29, 0.0815480921, 6283.0758499914], [3.694, 2.48453945256, 5661.3320491522], [3.555, 1.4803694942, 1059.3819301892], [3.023, 2.24092938317, 18073.7049386502], [3.0, 0.39169917698, 15.252471185], [2.563, 0.35147506973, 22003.9146348698], [2.774, 1.45683830639, 10239.5838660108], [2.951, 5.34618097429, 7084.8967811152], [2.344, 2.36652432105, 17298.1823273262], [2.405, 2.36085282088, 10596.1820784342], [1.72, 4.72129626061, 10186.9872264112], [2.209, 2.07730338665, 8635.9420037632], [2.122, 4.47091605309, 8624.2126509272], [1.527, 0.67146857292, 14143.4952424306], [1.473, 2.59350470099, 7064.1213856228], [1.311, 0.90408820221, 12566.1516999828], [1.474, 5.92236241437, 9786.687355335], [1.237, 2.59740787132, 4551.9534970588], [1.219, 2.83617320088, 9676.4810341156], [1.116, 3.83715584719, 21228.3920235458], [1.006, 4.26200749078, 426.598190876], [1.15, 2.35531987378, 9690.7081281172], [1.219, 2.27324315182, 522.5774180938], [1.15, 0.81088598778, 10742.9765113056], [1.101, 3.74248783564, 18307.8072320436], [1.031, 2.03889374176, 38.0276726358], [0.971, 6.10590045414, 3532.0606928114], [0.844, 4.75124127613, 10988.808157535], [0.908, 1.06613723738, 10021.8372800994], [0.824, 0.23090829723, 28286.9904848612], [0.821, 2.60456032773, 19.66976089979], [0.728, 0.10716917942, 4705.7323075436], [0.744, 3.33129778857, 536.8045120954], [0.816, 1.27303930175, 19896.8801273274], [0.929, 1.08024621325, 11790.6290886588], [0.797, 2.23891816523, 3723.508958923], [0.704, 5.95307260017, 20.7753954924], [0.665, 0.21346689192, 7860.4193924392], [0.733, 2.22147883292, 19360.07561523199], [0.702, 1.76206343944, 19374.3027092336], [0.575, 2.38792087791, 6770.7106012456], [0.538, 1.52023264138, 25934.1243310894], [0.69, 4.01873754171, 19651.048481098], [0.532, 4.4157613089, 574.3447983348], [0.54, 2.15936134728, 16496.3613962024], [0.576, 5.41170044566, 206.1855484372], [0.482, 0.40815793538, 3340.6124266998], [0.501, 3.08578363577, 245.8316462294], [0.488, 5.22311611589, 25158.6017197654], [0.45, 0.212798446, 11.729352836], [0.432, 1.32004964493, 103.0927742186], [0.434, 5.91094755233, 19786.67380610799], [0.564, 0.38776462529, 19367.1891622328], [0.421, 2.71057839701, 13936.794505134], [0.549, 6.08792865644, 3930.2096962196], [0.478, 4.70234715828, 14945.3161735544], [0.408, 4.80890663927, 32217.2001810808], [0.404, 2.85003595942, 29864.334027309], [0.407, 2.94002049006, 10220.3990932118], [0.359, 0.72354778897, 419.4846438752], [0.449, 1.44520508753, 8662.240323563], [0.353, 2.22195492336, 51066.427731055], [0.324, 1.40308439067, 29580.4747084438], [0.443, 1.93864353398, 9146.790069021], [0.314, 0.96837035284, 20618.0193585336], [0.324, 5.10759068171, 24356.7807886416], [0.324, 1.80146948625, 18830.38465013739], [0.37, 6.16895004656, 2218.7571041868], [0.278, 2.20429108375, 18844.61174413899], [0.286, 3.08459438435, 17277.4069318338], [0.383, 0.13890934755, 4732.0306273434], [0.292, 0.43528982259, 29088.811415985], [0.273, 5.84415407168, 9573.388259897], [0.324, 2.14144542781, 9999.986450773], [0.264, 5.20407029554, 220.4126424388], [0.254, 0.34411959301, 28521.0927782546], [0.3, 3.76014360906, 8094.5216858326], [0.301, 3.64457981649, 20400.2727726222], [0.287, 1.84003536598, 1589.0728952838], [0.206, 0.97167234723, 10234.0609417034], [0.212, 0.241736776, 36.0278666774], [0.216, 5.8861892303, 18875.525869774], [0.198, 1.89506914939, 20452.8694122218], [0.258, 6.27611355094, 1551.045222648], [0.197, 2.09222675324, 9683.5945811164], [0.217, 5.79472589364, 9103.9069941176], [0.188, 0.39123199129, 19573.37471066999], [0.195, 6.23142464829, 30110.1656735384], [0.187, 5.49670351645, 170.6728706192], [0.178, 4.90042854659, 10787.6303445458], [0.188, 1.62614804098, 9161.0171630226], [0.211, 2.71884568392, 15720.8387848784], [0.177, 1.88170417337, 33019.0211122046], [0.209, 2.66033422116, 3442.5749449654], [0.164, 4.92240093026, 10426.584641649], [0.186, 5.13678812068, 7255.5696517344], [0.177, 5.70206821967, 9992.8729037722], [0.214, 2.70027196648, 3128.3887650958], [0.208, 3.38876526854, 17778.11626694899], [0.147, 4.25008782855, 16983.9961474566], [0.148, 3.4640441813, 21202.093703746], [0.189, 1.43553862242, 2379.1644735716], [0.139, 2.99154379541, 110.2063212194], [0.159, 5.23851679605, 10007.0999977738], [0.136, 0.88942869764, 22805.7355659936], [0.155, 5.90500835975, 12592.4500197826], [0.151, 0.03422618975, 27991.40181316], [0.153, 4.01743770323, 33794.5437235286], [0.121, 0.51392111799, 21535.9496445154], [0.109, 2.25388616761, 26735.9452622132], [0.109, 0.78612823474, 6681.2248533996], [0.122, 4.84805105466, 19992.85935454519], [0.112, 3.31796669604, 36949.2308084242], [0.106, 3.34507236765, 10103.0792249916], [0.114, 4.36384000196, 20007.0864485468], [0.098, 5.07711736751, 135.62532501], [0.12, 5.41870615047, 37724.7534197482], [0.103, 2.62610244425, 20213.271996984], [0.085, 5.04808202087, 9830.3890139878], [0.103, 2.01549383816, 45585.1728121874], [0.088, 2.62613816931, 21.8508293264], [0.084, 3.50355880173, 639.897286314], [0.099, 0.61079620895, 41654.9631159678], [0.088, 3.63836700262, 49515.382508407], [0.098, 2.42401801881, 23581.2581773176], [0.081, 0.46468679835, 77.673770428], [0.092, 4.82530051729, 29043.67019634839], [0.102, 4.27051236894, 15874.6175953632], [0.09, 4.34075776744, 29057.89729034999], [0.081, 0.01896422336, 24150.080051345], [0.093, 1.79250830018, 12432.0426503978], [0.087, 5.25157021446, 14128.2427712456], [0.089, 5.65756996753, 377.3736079158], [0.097, 5.67942873241, 227.476132789], [0.076, 2.93363913259, 38204.687359371], [0.091, 2.60544242067, 1052.2683831884], [0.087, 3.82284200928, 27511.4678735372], [0.073, 4.75280755154, 40879.4405046438], [0.067, 3.54815262526, 30666.1549584328], [0.067, 5.81350818057, 20809.4676246452], [0.064, 4.24772678145, 153.7788104848], [0.064, 2.99454749109, 27197.2816936676], [0.07, 4.03868009742, 56600.2792895222], [0.071, 4.3362880685, 39264.0692895602], [0.069, 1.73648747605, 37410.5672398786], [0.065, 1.08206062736, 68050.42387851159], [0.062, 4.7769845465, 3914.9572250346], [0.061, 4.96121014691, 34596.3646546524], [0.063, 5.04865067599, 53445.5922046266], [0.058, 3.74010494151, 1066.49547719], [0.057, 5.39355890141, 20419.45754542119], [0.057, 3.59399518494, 735.8765135318], [0.065, 2.10322000074, 74.7815985673], [0.073, 1.31083648835, 11272.6674764002], [0.055, 1.33161298098, 18300.69368504279], [0.065, 4.21150522641, 49.7570254718], [0.061, 5.66161679402, 17468.8551979454], [0.053, 4.30231233835, 18849.2275499742], [0.055, 2.63906959481, 52670.0695933026], [0.05, 5.69803054279, 39793.7602546548], [0.049, 0.77345264124, 35371.8872659764], [0.048, 6.00565977593, 283.8593188652], [0.047, 2.63299859494, 51868.2486621788], [0.046, 0.05105081843, 38526.574350872], [0.05, 4.37549274002, 28513.97923125379], [0.046, 2.93422086586, 27682.1407441564], [0.051, 5.45979584751, 60530.4889857418], [0.045, 5.59492908223, 467.9649903544], [0.045, 2.34680401001, 9411.4646150872], [0.045, 0.02999265111, 44809.6502008634], [0.043, 5.62725673544, 14.2270940016], [0.047, 3.73567275749, 64460.6986819614], [0.046, 0.12586526756, 57375.8019008462], [0.044, 2.03114426076, 18314.9207790444], [0.039, 0.99375127466, 94138.32702008578], [0.053, 0.41974404621, 30831.3049047446], [0.055, 1.38351566741, 38500.2760310722], [0.041, 4.47012768909, 40077.61957352], [0.041, 0.36665992484, 19999.97290154599], [0.04, 3.06358586355, 813.5502839598], [0.04, 2.16802870803, 59728.668054618], [0.037, 1.08739100421, 17085.9586657222], [0.039, 1.31040309875, 48739.859897083], [0.036, 1.43280677914, 42456.7840470916], [0.037, 0.14190533464, 29050.7837433492], [0.037, 3.66792179278, 20956.2620575166], [0.025, 3.38876180652, 7058.5984613154], [0.031, 6.16829805337, 10192.5101507186]], [[54127.076, 0.0, 0.0], [3891.46, 0.34514360047, 10213.285546211], [1337.88, 2.02011286082, 20426.571092422], [23.836, 2.04592119012, 26.2983197998], [19.331, 3.53527371458, 30639.856638633], [9.984, 3.97130221102, 775.522611324], [7.046, 1.51962593409, 1577.3435424478], [6.014, 0.99926757893, 191.4482661116], [3.163, 4.36095475762, 9437.762934887], [2.125, 2.65810625752, 40853.142184844], [1.934, 3.39287946981, 382.8965322232], [1.46, 6.04899046273, 529.6909650946], [1.346, 2.94633106219, 5507.5532386674], [1.025, 1.40598904981, 10404.7338123226], [1.221, 3.73339139385, 3154.6870848956], [1.033, 3.52858472904, 11015.1064773348], [0.955, 5.11133878923, 801.8209311238], [0.742, 1.49198584483, 1109.3785520934], [0.525, 3.32087042103, 213.299095438], [0.578, 0.92614279843, 10239.5838660108], [0.602, 5.19220099775, 7084.8967811152], [0.431, 2.67159914364, 13367.9726311066], [0.389, 4.14116341739, 8635.9420037632], [0.355, 1.12061570874, 9153.9036160218], [0.301, 3.90047984197, 10596.1820784342], [0.212, 5.32697688872, 18837.49819713819], [0.26, 0.22761369281, 2352.8661537718], [0.243, 4.70747902991, 6283.0758499914], [0.196, 4.10467294392, 11790.6290886588], [0.194, 6.0119775947, 7860.4193924392], [0.14, 4.97015671653, 14143.4952424306], [0.134, 4.10529011674, 17298.1823273262], [0.119, 3.39375528828, 11322.6640983044], [0.126, 0.0985451614, 18073.7049386502], [0.122, 5.92478855457, 574.3447983348], [0.107, 0.35660030184, 1059.3819301892], [0.108, 2.25352052666, 12566.1516999828], [0.093, 5.48716819776, 10021.8372800994], [0.084, 4.89744332968, 18307.8072320436], [0.074, 2.35354025573, 426.598190876], [0.093, 4.99316908815, 14945.3161735544], [0.069, 3.8640906586, 51066.427731055], [0.082, 5.36280178643, 10186.9872264112], [0.077, 3.75728548372, 3723.508958923], [0.063, 5.39882267787, 21228.3920235458], [0.056, 4.11564786973, 7064.1213856228], [0.056, 6.26920407723, 32217.2001810808], [0.06, 5.02186497542, 19367.1891622328], [0.058, 5.1326370967, 20400.2727726222], [0.051, 4.52870390511, 22003.9146348698], [0.041, 3.83822107919, 16496.3613962024], [0.041, 3.36020411807, 4705.7323075436], [0.043, 5.98371820588, 15720.8387848784], [0.047, 0.18498155367, 18875.525869774], [0.038, 0.52232581277, 1551.045222648], [0.039, 5.05391675878, 10742.9765113056], [0.036, 3.16242472203, 20452.8694122218], [0.035, 5.17462577483, 29088.811415985], [0.035, 3.47325394141, 24356.7807886416], [0.031, 4.74511706231, 28521.0927782546], [0.029, 0.19383091192, 19896.8801273274], [0.033, 1.80059867635, 20618.0193585336], [0.024, 0.14022912457, 21202.093703746], [0.022, 4.73565067573, 10988.808157535], [0.018, 0.74039763161, 25158.6017197654], [0.019, 1.53770232218, 28286.9904848612], [0.014, 1.49084059765, 30110.1656735384], [0.013, 4.72171283479, 29864.334027309], [0.013, 5.79700427846, 29580.4747084438], [0.014, 3.6920522501, 27511.4678735372]], [[135.742, 4.80389020993, 10213.285546211], [77.846, 3.66876371591, 20426.571092422], [26.023, 0.0, 0.0], [1.214, 5.31970006917, 30639.856638633], [0.254, 4.15021671822, 40853.142184844], [0.008, 5.55523563261, 51066.427731055], [0.008, 1.40501229148, 1577.3435424478], [0.006, 1.27791479726, 10404.7338123226], [0.006, 5.76447068962, 10239.5838660108]], [[114.016, 3.14159265359, 0.0], [3.209, 5.20514170164, 20426.571092422], [1.714, 2.51099591706, 10213.285546211], [0.05, 0.71356059861, 30639.856638633], [0.023, 5.68127607034, 40853.142184844]], [[0.874, 3.14159265359, 0.0], [0.117, 0.54643013, 20426.571092422], [0.118, 1.90548541922, 10213.285546211], [0.002, 1.07734277826, 40853.142184844], [0.002, 1.89460223529, 30639.856638633]]]

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.

pymeeus.Venus.VSOP87_R = [[[72334820.905, 0.0, 0.0], [489824.185, 4.02151832268, 10213.285546211], [1658.058, 4.90206728012, 20426.571092422], [1632.093, 2.84548851892, 7860.4193924392], [1378.048, 1.128465906, 11790.6290886588], [498.399, 2.58682187717, 9683.5945811164], [373.958, 1.42314837063, 3930.2096962196], [263.616, 5.5293818592, 9437.762934887], [237.455, 2.55135903978, 15720.8387848784], [221.983, 2.01346776772, 19367.1891622328], [119.467, 3.01975365264, 10404.7338123226], [125.896, 2.72769833559, 1577.3435424478], [76.178, 1.59577224486, 9153.9036160218], [85.336, 3.98607953754, 19651.048481098], [74.347, 4.11957854039, 5507.5532386674], [41.904, 1.64273363458, 18837.49819713819], [42.493, 3.81864530735, 13367.9726311066], [39.43, 5.39019422358, 23581.2581773176], [29.042, 5.67739528728, 5661.3320491522], [27.555, 5.72392407794, 775.522611324], [27.283, 4.82151812709, 11015.1064773348], [31.274, 2.31806719544, 9999.986450773], [19.7, 4.96157560245, 11322.6640983044], [19.809, 0.53189326492, 27511.4678735372], [13.567, 3.75530870628, 18073.7049386502], [12.921, 1.13381083556, 10206.1719992102], [16.215, 0.5645383429, 529.6909650946], [11.821, 5.09025877427, 3154.6870848956], [11.728, 0.23432298744, 7084.8967811152], [13.079, 5.24353197586, 17298.1823273262], [13.18, 3.37207825651, 13745.3462390224], [9.097, 3.07004895769, 1109.3785520934], [10.818, 2.45024712908, 10239.5838660108], [11.438, 4.56838894696, 29050.7837433492], [8.377, 5.78327612352, 30639.856638633], [8.193, 1.9502311186, 22003.9146348698], [9.308, 1.61615909286, 2352.8661537718], [10.652, 1.9552839614, 31441.6775697568], [10.357, 1.20234990061, 15874.6175953632], [9.585, 1.46639856228, 19999.97290154599], [6.506, 2.17390732263, 14143.4952424306], [7.562, 1.13789564977, 8624.2126509272], [6.434, 0.84419623033, 6283.0758499914], [5.898, 0.0109373111, 8635.9420037632], [5.632, 3.94956548631, 12566.1516999828], [5.523, 1.27394296557, 18307.8072320436], [4.488, 2.47835729057, 191.4482661116], [4.529, 4.730277704, 19896.8801273274], [6.193, 3.25881250939, 6872.6731195112], [6.07, 0.35337419942, 21228.3920235458], [4.315, 2.59737099519, 4551.9534970588], [6.005, 3.37874723475, 35371.8872659764], [3.852, 1.01162850357, 9786.687355335], [4.033, 0.0005085558, 801.8209311238], [3.92, 5.56542869407, 10596.1820784342], [2.709, 5.80195530112, 7064.1213856228], [3.216, 0.39767254848, 10186.9872264112], [3.089, 6.26174762876, 14945.3161735544], [2.982, 4.21196716354, 28521.0927782546], [3.284, 0.70709821006, 10742.9765113056], [3.484, 4.79878191875, 39302.096962196], [3.172, 1.80518954174, 25158.6017197654], [2.463, 0.68708153678, 10988.808157535], [2.374, 3.77948685343, 21535.9496445154], [2.198, 2.82996372521, 8662.240323563], [1.958, 5.41763804167, 16496.3613962024], [1.876, 2.63426768393, 29580.4747084438], [1.902, 2.85782199133, 3532.0606928114], [1.706, 3.67573010379, 26.2983197998], [1.817, 0.41611036449, 4705.7323075436], [1.858, 1.50368318296, 10021.8372800994], [2.087, 6.22112874639, 43232.3066584156], [1.95, 2.21447019683, 19786.67380610799], [1.497, 0.00134773824, 17277.4069318338], [1.819, 3.23144993268, 29088.811415985], [1.423, 5.85979618707, 9676.4810341156], [1.223, 5.55818994329, 6770.7106012456], [1.14, 5.92088900094, 13936.794505134], [1.484, 2.47665429253, 31749.2351907264], [1.185, 1.42087628351, 4732.0306273434], [1.323, 2.48821075422, 9690.7081281172], [1.249, 1.88323673734, 19374.3027092336], [1.27, 5.24647873116, 19360.07561523199], [1.402, 5.17536780118, 10316.3783204296], [1.042, 3.05454698508, 25934.1243310894], [1.174, 1.42913732999, 18875.525869774], [1.278, 1.35747287297, 47162.5163546352], [0.917, 6.26337648765, 20618.0193585336], [0.905, 1.12740203561, 12592.4500197826], [1.093, 4.64451720605, 33019.0211122046], [1.014, 1.09259406433, 1059.3819301892], [0.783, 2.02118183873, 24356.7807886416], [0.779, 0.4158527401, 3340.6124266998], [0.7, 1.14936815714, 16983.9961474566], [0.878, 0.87852464964, 38734.3783244656], [0.623, 0.89976912165, 17778.11626694899], [0.608, 1.58476225197, 9573.388259897], [0.8, 3.94213003073, 10138.5039476437], [0.76, 1.31851313748, 9967.4538999816], [0.802, 2.78173370208, 51092.7260508548], [0.664, 4.458646824, 3128.3887650958], [0.674, 5.11214939998, 382.8965322232], [0.53, 0.85392938403, 10234.0609417034], [0.509, 3.56809374595, 28286.9904848612], [0.6, 4.25927726907, 41962.5207369374], [0.601, 5.78144137895, 213.299095438], [0.595, 2.83045104588, 22805.7355659936], [0.673, 6.06079908421, 36949.2308084242], [0.535, 5.85422519711, 9103.9069941176], [0.544, 5.448060748, 3723.508958923], [0.492, 3.83802404893, 27991.40181316], [0.635, 0.76494024849, 8094.5216858326], [0.434, 6.22214487735, 27197.2816936676], [0.459, 3.55062885479, 20213.271996984], [0.398, 6.16269975784, 10426.584641649], [0.378, 2.41665947591, 18844.61174413899], [0.421, 4.86552697954, 9146.790069021], [0.5, 4.20351458644, 55022.9357470744], [0.404, 4.95834410782, 37410.5672398786], [0.402, 2.97963246945, 10220.3990932118], [0.464, 2.59869499733, 18734.4054229196], [0.352, 0.08963076359, 10103.0792249916], [0.348, 4.90260339364, 18830.38465013739], [0.338, 3.22520096478, 24150.080051345], [0.375, 6.17532088136, 26087.9031415742], [0.425, 1.2005257828, 40879.4405046438], [0.408, 3.12833060705, 9050.8108418032], [0.385, 1.94284690176, 283.8593188652], [0.337, 4.87838699272, 12432.0426503978], [0.326, 4.27369741426, 26735.9452622132], [0.309, 0.50597475053, 38204.687359371], [0.329, 3.88430599153, 29864.334027309], [0.313, 1.36138752543, 10192.5101507186], [0.347, 3.58439807209, 27490.6924780448], [0.251, 3.78618457047, 10063.7223490764], [0.244, 3.83523342668, 9411.4646150872], [0.281, 4.50895206233, 32217.2001810808], [0.237, 0.87748812245, 6681.2248533996], [0.315, 5.62657778233, 58953.145443294], [0.311, 4.15626121491, 10175.1525105732], [0.247, 2.53637594113, 16522.6597160022], [0.219, 5.08729383251, 7058.5984613154], [0.291, 3.72567217056, 29999.959352319], [0.267, 2.97685503991, 19573.37471066999], [0.28, 3.70200084294, 47623.8527860896], [0.239, 3.94545782067, 9580.5018068978], [0.246, 2.1824488393, 9161.0171630226], [0.253, 2.69506547016, 3442.5749449654], [0.265, 2.62811801237, 44809.6502008634], [0.194, 4.78926136175, 33794.5437235286], [0.187, 3.65620881095, 20452.8694122218], [0.224, 2.43601863127, 9992.8729037722], [0.193, 2.55112161845, 2379.1644735716], [0.201, 1.90356905733, 1551.045222648], [0.176, 4.29837616553, 10137.0194749354], [0.184, 6.16061560223, 36147.4098773004], [0.175, 2.7198479704, 20809.4676246452], [0.186, 2.55098927966, 14919.0178537546], [0.161, 4.13272567123, 23958.6317852334], [0.221, 4.83552377614, 20277.0078952874], [0.16, 1.81472642729, 10787.6303445458], [0.199, 5.7425979833, 30666.1549584328], [0.16, 4.46270605493, 18947.7045183576], [0.187, 2.98688597588, 2218.7571041868], [0.189, 5.34607810282, 10007.0999977738], [0.198, 0.77846666692, 62883.3551395136], [0.144, 5.00261963924, 9264.1099372412], [0.171, 2.05212624568, 7255.5696517344], [0.188, 4.08173534559, 48739.859897083], [0.146, 3.94191715702, 6309.3741697912], [0.146, 5.06313558118, 39264.0692895602], [0.135, 5.93689169614, 37724.7534197482], [0.139, 2.81266025896, 20.7753954924], [0.177, 5.16224804657, 9835.9119382952], [0.119, 1.37254262864, 40077.61957352], [0.12, 0.21443767468, 31022.7531708562], [0.128, 2.92458887798, 7.1135470008], [0.15, 5.73646272556, 632.7837393132], [0.106, 0.62224833817, 11272.6674764002], [0.114, 2.6330132652, 17468.8551979454], [0.123, 6.22518843711, 53285.1848352418], [0.107, 1.172589789, 43071.8992890308], [0.103, 1.09613781581, 41654.9631159678], [0.109, 2.01412667085, 20419.45754542119], [0.102, 4.23406964348, 10251.3132188468], [0.116, 1.27731728606, 10199.0584522094], [0.103, 5.25887538465, 9830.3890139878], [0.112, 2.24436894064, 18204.71445782499], [0.111, 2.23547857955, 8521.1198767086], [0.118, 0.237542072, 10497.1448650762], [0.123, 0.88054816668, 34596.3646546524], [0.102, 4.3943864662, 18300.69368504279], [0.131, 6.01711652115, 9367.2027114598], [0.1, 5.00532389609, 10175.2578735752], [0.107, 0.41270197502, 40853.142184844], [0.132, 5.45008342761, 11506.7697697936], [0.098, 1.07722950958, 13553.8979729108], [0.094, 2.9172009759, 44007.8292697396], [0.097, 1.04004223634, 68050.42387851159], [0.127, 2.20215372683, 66813.5648357332], [0.111, 1.57823839032, 29043.67019634839], [0.118, 2.3326817689, 18314.9207790444], [0.09, 2.42353056125, 32858.61374281979], [0.109, 3.82796787296, 19470.28193645139], [0.111, 4.47666957576, 29057.89729034999], [0.101, 3.4152849366, 19264.0963880142], [0.092, 3.66289799512, 22645.32819660879], [0.094, 6.07530805791, 10846.0692855242], [0.114, 4.02718653431, 7576.560073574], [0.087, 6.01842459303, 17085.9586657222], [0.109, 5.46886607309, 52670.0695933026], [0.107, 0.54805946713, 34363.365597556], [0.108, 5.44460610707, 19050.7972925762], [0.076, 6.15177368654, 27682.1407441564], [0.107, 4.80525404063, 8144.2787113044], [0.073, 1.60549217847, 20956.2620575166], [0.097, 5.1354205113, 22779.4372461938], [0.068, 2.31300447144, 8631.326197928], [0.091, 4.28652743953, 10110.1927719924], [0.093, 5.27290609264, 522.5774180938], [0.071, 3.6556596169, 11764.330768859], [0.089, 1.79712963206, 45585.1728121874], [0.067, 2.25900071584, 9360.089164459], [0.085, 0.67062144972, 56600.2792895222], [0.08, 1.58278081077, 19992.85935454519], [0.065, 6.23472325597, 10419.4710946482], [0.064, 0.53356325917, 17248.4253018544], [0.085, 4.52011215904, 29786.660256881], [0.068, 4.48235266554, 10632.7701900862], [0.064, 4.33495700921, 47938.0389659592], [0.071, 3.03858484137, 11787.1059703098], [0.087, 4.81823063172, 2107.0345075424], [0.07, 2.35648061034, 11794.1522070078], [0.08, 2.33248094128, 38526.574350872], [0.07, 3.704540611, 8734.4189721466], [0.077, 4.49569185467, 20007.0864485468], [0.072, 1.19410424468, 10217.2176994741], [0.068, 2.01841060183, 14128.2427712456], [0.064, 5.39293951654, 7880.08915333899], [0.066, 3.20467071127, 14765.2390432698], [0.08, 3.4162045777, 48417.97290558199], [0.08, 3.39651161571, 245.8316462294], [0.066, 5.85414440204, 9793.8009023358], [0.082, 3.62592908644, 70743.77453195279], [0.058, 4.95174942212, 30110.1656735384], [0.079, 6.24161471033, 6037.244203762], [0.069, 5.50183658445, 19793.7873531088], [0.056, 1.24148350566, 10207.7626219036], [0.07, 2.45123308846, 10218.8084705184], [0.064, 5.53983104501, 10735.8629643048], [0.054, 3.6225971324, 27461.7108480654], [0.073, 1.75882480924, 1589.0728952838], [0.075, 3.38244819846, 4214.0690150848], [0.054, 0.64971567468, 9929.4262273458], [0.054, 3.4095963723, 18418.01355326299], [0.056, 3.65815006538, 14169.7935622304], [0.056, 0.71243223808, 9896.8936765544], [0.052, 1.3334813194, 20400.2727726222], [0.067, 3.128065954, 5481.2549188676], [0.058, 0.54482893546, 28313.288804661], [0.054, 0.15603935681, 19580.4882576708], [0.051, 3.3751547351, 9256.9963902404], [0.063, 3.3884897095, 49515.382508407], [0.069, 4.90917651401, 63498.47038145279], [0.057, 5.0743774203, 18521.1063274816], [0.05, 1.59156823654, 18631.31264870099], [0.054, 6.25816208666, 37674.9963942764], [0.057, 5.48065460919, 24383.0791084414], [0.045, 1.1046649066, 10408.2569306716], [0.051, 3.61196470313, 426.598190876], [0.057, 2.09567711267, 60530.4889857418], [0.06, 5.94659889997, 13897.6635962012], [0.051, 5.4723851772, 57837.1383323006], [0.051, 2.32438478428, 19779.56025910719], [0.052, 3.23766328818, 18940.59097135679], [0.043, 5.74921510909, 51868.2486621788], [0.048, 1.12206254877, 9779.5738083342], [0.058, 3.08646083897, 12074.488407524], [0.046, 4.07536026888, 7863.9425107882], [0.045, 4.75746520642, 7856.89627409019], [0.054, 4.43528236634, 8617.0991039264], [0.05, 3.70569982975, 42456.7840470916], [0.044, 1.29248911155, 69166.430989505], [0.046, 0.41229872114, 7564.830720738], [0.044, 6.17937388307, 13341.6743113068], [0.053, 4.71388531889, 53445.5922046266], [0.041, 3.48003037828, 37895.4262903674], [0.04, 1.2330554626, 10228.538017396], [0.053, 5.04979874661, 74673.9842281724], [0.039, 1.36646013032, 21202.093703746], [0.039, 2.15376025201, 8947.7180675846], [0.041, 6.1753298446, 65236.2212932854], [0.052, 1.29052331493, 90394.82301305079], [0.039, 0.70253732683, 18093.37469954999], [0.052, 1.18164377451, 10211.8010735027], [0.047, 1.78672260794, 10401.2106939736], [0.04, 3.66961416802, 10198.033075026], [0.051, 2.71698589018, 94325.0327092704], [0.036, 1.2509171162, 10323.4918674304], [0.049, 1.2133595942, 9721.6222537522], [0.042, 6.05968230173, 105460.99111839019], [0.046, 5.06978748275, 20350.3050211464], [0.04, 1.97645050921, 32243.4985008806], [0.036, 4.96702216961, 36301.18868778519], [0.037, 5.29642935562, 38.0276726358], [0.039, 0.52064327313, 26709.6469424134], [0.035, 2.34112124655, 58946.51688439399], [0.034, 1.82989750626, 17675.0234927304], [0.034, 0.7649366411, 55798.4583583984], [0.035, 1.09353675147, 69159.80243060499], [0.031, 5.59148330297, 10639.883737087], [0.032, 3.3296078187, 71519.2971432768], [0.031, 5.98191446392, 24341.5283174566], [0.031, 0.68615213145, 10202.2398459471], [0.03, 4.42039942947, 10459.1171924404], [0.029, 1.30367701539, 20103.06567576459], [0.031, 4.51793347997, 2957.7158944766], [0.035, 4.0563432129, 19903.99367432819], [0.03, 1.32113757427, 574.3447983348], [0.029, 3.36506645849, 10288.0671447783], [0.029, 1.40019042576, 9988.9407505091], [0.032, 0.21932095318, 24978.5245894808], [0.034, 5.22945947227, 8673.969676399], [0.039, 4.50883171158, 16004.6981037436], [0.028, 2.32945945641, 11392.4800852506], [0.034, 3.92498967835, 536.8045120954], [0.032, 5.46972716255, 64607.84893354619], [0.028, 2.38858990128, 20235.1228263104], [0.03, 3.34585843979, 39793.7602546548], [0.026, 5.36096904409, 1478.8665740644]], [[34551.039, 0.89198710598, 10213.285546211], [234.203, 1.77224942714, 20426.571092422], [233.998, 3.14159265359, 0.0], [23.864, 1.11274502648, 9437.762934887], [10.568, 4.59168210921, 1577.3435424478], [9.124, 4.53540907003, 10404.7338123226], [6.599, 5.97703999838, 5507.5532386674], [4.667, 3.87683960551, 9153.9036160218], [3.84, 5.66196924375, 13367.9726311066], [2.666, 2.82413291285, 10206.1719992102], [2.194, 2.05314419626, 775.522611324], [2.094, 2.55137285015, 18837.49819713819], [1.782, 2.64808558644, 30639.856638633], [1.845, 1.87612936641, 11015.1064773348], [1.303, 0.20613045603, 11322.6640983044], [1.169, 0.79431893441, 17298.1823273262], [1.001, 6.16555101536, 10239.5838660108], [0.915, 4.59854496966, 1109.3785520934], [0.884, 0.66706834422, 18073.7049386502], [0.849, 5.5864157194, 12566.1516999828], [1.071, 4.94792017474, 6283.0758499914], [0.887, 2.47785193216, 3154.6870848956], [0.904, 0.81413053841, 10596.1820784342], [0.818, 0.90016838097, 5661.3320491522], [0.845, 5.48504338112, 529.6909650946], [0.824, 3.74837629121, 7084.8967811152], [0.652, 5.07444932607, 22003.9146348698], [0.847, 0.44119876869, 8635.9420037632], [0.638, 4.10125791268, 191.4482661116], [0.615, 3.14417599741, 10186.9872264112], [0.527, 5.86792949279, 2352.8661537718], [0.52, 5.33201358267, 14143.4952424306], [0.576, 2.25212731258, 21228.3920235458], [0.662, 2.86880467345, 8624.2126509272], [0.554, 2.17186191243, 18307.8072320436], [0.515, 4.34331395104, 9786.687355335], [0.501, 5.56479589366, 10742.9765113056], [0.426, 1.0216144312, 7064.1213856228], [0.418, 1.26803034691, 9676.4810341156], [0.391, 0.78974645621, 9690.7081281172], [0.334, 3.18175822557, 10988.808157535], [0.375, 0.66142254036, 19360.07561523199], [0.364, 0.19369831864, 19374.3027092336], [0.313, 1.09734397626, 4551.9534970588], [0.33, 0.58817502306, 16496.3613962024], [0.339, 5.76768761396, 10021.8372800994], [0.291, 3.65846764668, 25158.6017197654], [0.223, 4.33581625553, 19786.67380610799], [0.266, 3.57408827667, 801.8209311238], [0.274, 5.73346687248, 11790.6290886588], [0.275, 5.65814317085, 19896.8801273274], [0.212, 4.27038489878, 4705.7323075436], [0.23, 6.1340634559, 1059.3819301892], [0.204, 4.87348390351, 7860.4193924392], [0.241, 1.13551531894, 26.2983197998], [0.206, 0.31907973682, 382.8965322232], [0.216, 2.54741101724, 19651.048481098], [0.212, 3.15264941106, 14945.3161735544], [0.163, 1.13604744392, 13936.794505134], [0.151, 5.11341268743, 28521.0927782546], [0.151, 0.81278755582, 6770.7106012456], [0.15, 5.02227334847, 29088.811415985], [0.146, 1.37568138685, 10220.3990932118], [0.127, 4.49298610074, 3532.0606928114], [0.121, 6.26589208179, 29580.4747084438], [0.147, 6.16092774714, 8662.240323563], [0.114, 0.00114012635, 25934.1243310894], [0.115, 3.56897715344, 24356.7807886416], [0.124, 0.67547060274, 3723.508958923], [0.145, 0.36415036222, 9146.790069021], [0.104, 4.27865011376, 9573.388259897], [0.136, 5.09581116181, 19367.1891622328], [0.102, 1.53637788668, 17277.4069318338], [0.117, 0.57543238496, 9999.986450773], [0.092, 0.22936081655, 18830.38465013739], [0.112, 4.04771058036, 9103.9069941176], [0.098, 3.78447692407, 213.299095438], [0.085, 5.84471458481, 10234.0609417034], [0.079, 0.64440357793, 18844.61174413899], [0.084, 0.56950139213, 9683.5945811164], [0.107, 1.77067111589, 17778.11626694899], [0.081, 6.19048382717, 20618.0193585336], [0.087, 0.15771136594, 33019.0211122046], [0.082, 4.80683817059, 3930.2096962196], [0.086, 2.21505615071, 8094.5216858326], [0.064, 2.69215119482, 16983.9961474566], [0.069, 0.83385751986, 3128.3887650958], [0.081, 4.88025042367, 4732.0306273434], [0.059, 3.34348033725, 10787.6303445458], [0.061, 0.04044699966, 9161.0171630226], [0.064, 4.13127333938, 9992.8729037722], [0.06, 6.24603986632, 32217.2001810808], [0.054, 3.38449893196, 10426.584641649], [0.054, 5.15939119644, 28286.9904848612], [0.063, 4.32339245083, 12592.4500197826], [0.06, 4.4875384617, 18875.525869774], [0.057, 3.64912085313, 10007.0999977738], [0.049, 5.10267262491, 19573.37471066999], [0.047, 5.79444960738, 68050.42387851159], [0.052, 3.56658420552, 7255.5696517344], [0.05, 1.61783309819, 36949.2308084242], [0.053, 2.64370544855, 15874.6175953632], [0.04, 3.93466530964, 20419.45754542119], [0.051, 0.79154899901, 23581.2581773176], [0.038, 1.77428239418, 10103.0792249916], [0.049, 1.12423644455, 3442.5749449654], [0.04, 5.22874487975, 21535.9496445154], [0.038, 1.12473430132, 7.1135470008], [0.038, 0.11510547453, 11272.6674764002], [0.036, 2.02476324983, 7058.5984613154], [0.047, 0.0558943239, 12432.0426503978], [0.034, 3.45481114998, 9830.3890139878], [0.045, 4.59817214088, 10192.5101507186], [0.037, 4.93959675364, 3340.6124266998], [0.044, 0.70533027806, 20213.271996984], [0.034, 2.16487642765, 64460.6986819614], [0.031, 1.57612397319, 36147.4098773004], [0.028, 2.56454760402, 94138.32702008578], [0.033, 1.08907268562, 29864.334027309], [0.029, 0.59718407064, 59728.668054618], [0.031, 3.04423979263, 40879.4405046438], [0.035, 0.32247158762, 1589.0728952838], [0.031, 3.27727318906, 19992.85935454519], [0.027, 5.83705748551, 17085.9586657222], [0.032, 2.6426078826, 41962.5207369374], [0.028, 4.90613317287, 29050.7837433492], [0.025, 4.55050389739, 14919.0178537546], [0.028, 3.58851614957, 40853.142184844], [0.029, 2.79705093386, 20007.0864485468], [0.033, 0.93862065616, 15720.8387848784], [0.024, 2.74970637101, 18947.7045183576], [0.024, 4.38966861409, 46386.9937433112], [0.024, 0.73361964525, 9411.4646150872], [0.028, 4.19559784013, 37674.9963942764], [0.023, 1.00023735538, 22779.4372461938], [0.026, 0.46990555736, 13745.3462390224], [0.028, 4.65181292126, 1551.045222648], [0.025, 4.18690270765, 44007.8292697396], [0.022, 0.98102807789, 426.598190876], [0.03, 1.24986033487, 27461.7108480654], [0.027, 3.94986823486, 17468.8551979454], [0.021, 6.09897508157, 18300.69368504279], [0.025, 4.75875623888, 27991.40181316], [0.022, 2.95281481673, 40077.61957352], [0.028, 6.12038264955, 38500.2760310722], [0.022, 4.11184201321, 19779.56025910719], [0.027, 3.7244644608, 19793.7873531088], [0.02, 4.27086627368, 31441.6775697568], [0.022, 4.99040169444, 31022.7531708562], [0.023, 1.33505132122, 65236.2212932854], [0.021, 4.46897353468, 53285.1848352418], [0.02, 4.15140915983, 2218.7571041868], [0.025, 2.18447182965, 27511.4678735372], [0.019, 1.43653410349, 27197.2816936676], [0.027, 1.22555218015, 42430.4857272918], [0.019, 3.65054338893, 49515.382508407], [0.022, 5.88380811711, 10218.8084705184], [0.018, 2.29853355765, 19264.0963880142], [0.017, 5.44429906531, 6681.2248533996], [0.02, 3.68116637773, 14128.2427712456], [0.021, 4.30316190532, 44809.6502008634], [0.02, 2.48583613985, 33794.5437235286], [0.017, 3.02735393984, 28528.2063252554], [0.019, 5.92656850674, 22805.7355659936], [0.022, 5.30827572791, 10207.7626219036], [0.02, 0.75829381378, 18314.9207790444], [0.017, 5.63315744126, 16522.6597160022], [0.016, 1.71021408448, 536.8045120954], [0.015, 5.27016880041, 53445.5922046266], [0.017, 5.61443395877, 47938.0389659592], [0.015, 5.81110284451, 43071.8992890308], [0.015, 4.96237667003, 19999.97290154599], [0.018, 0.55618686515, 14765.2390432698], [0.014, 3.48144272414, 29786.660256881], [0.015, 5.84132627836, 10228.538017396], [0.016, 1.05720065324, 26735.9452622132], [0.014, 6.08462030302, 35371.8872659764], [0.014, 2.8453287189, 574.3447983348], [0.015, 5.3451771514, 10198.033075026], [0.013, 0.45004137509, 20452.8694122218]], [[1406.587, 5.0636639519, 10213.285546211], [15.529, 5.47321687981, 20426.571092422], [13.059, 0.0, 0.0], [1.099, 2.78883988292, 9437.762934887], [0.488, 6.27806914496, 1577.3435424478], [0.361, 6.11914188253, 10404.7338123226], [0.31, 1.38984998403, 5507.5532386674], [0.389, 1.95017779915, 11015.1064773348], [0.372, 2.33222828423, 775.522611324], [0.207, 5.63406721595, 10239.5838660108], [0.168, 1.10765197296, 13367.9726311066], [0.175, 6.1667465295, 30639.856638633], [0.168, 3.64495311632, 7084.8967811152], [0.12, 5.85815843789, 9153.9036160218], [0.16, 2.21564938463, 3154.6870848956], [0.118, 2.62358866565, 8635.9420037632], [0.112, 2.36235956804, 10596.1820784342], [0.092, 0.72664449269, 12566.1516999828], [0.067, 3.76089669118, 18837.49819713819], [0.065, 2.4798370999, 11790.6290886588], [0.048, 4.26620187144, 2352.8661537718], [0.048, 5.5089818955, 191.4482661116], [0.048, 2.54730918293, 17298.1823273262], [0.046, 3.40293459332, 14143.4952424306], [0.041, 1.83997113019, 11322.6640983044], [0.037, 6.17871126027, 1109.3785520934], [0.039, 4.77190210316, 18073.7049386502], [0.035, 3.10133256432, 4705.7323075436], [0.046, 3.30090415967, 6283.0758499914], [0.034, 3.91721765773, 10021.8372800994], [0.034, 3.24663787383, 22003.9146348698], [0.042, 3.39360926939, 14945.3161735544], [0.044, 4.42979374073, 7860.4193924392], [0.034, 2.16381407025, 16496.3613962024], [0.031, 0.45714618479, 26.2983197998], [0.035, 3.62868651241, 801.8209311238], [0.032, 1.84138997078, 382.8965322232], [0.025, 3.32908650295, 18307.8072320436], [0.026, 3.64313769818, 29088.811415985], [0.029, 3.8296717881, 10186.9872264112], [0.022, 3.17741520378, 28521.0927782546], [0.021, 2.52643834111, 529.6909650946], [0.025, 5.71401244457, 21202.093703746], [0.021, 3.77813434325, 21228.3920235458], [0.019, 5.24505118517, 19896.8801273274], [0.018, 4.62463651925, 19651.048481098], [0.016, 3.35893297896, 28286.9904848612], [0.015, 5.05571633205, 33019.0211122046], [0.014, 2.83786355803, 19786.67380610799], [0.014, 1.79922718553, 9830.3890139878], [0.014, 3.14801263138, 19367.1891622328], [0.014, 3.57896195191, 10988.808157535], [0.013, 3.06303088617, 10742.9765113056], [0.013, 5.43981998532, 25158.6017197654], [0.015, 4.83166312889, 18875.525869774], [0.012, 2.54141086214, 7064.1213856228], [0.012, 4.45255110769, 15720.8387848784], [0.01, 1.87933121728, 24356.7807886416], [0.011, 2.58708635685, 9103.9069941176], [0.01, 2.179013099, 3723.508958923], [0.008, 3.63520673832, 1059.3819301892], [0.008, 4.67523115598, 25934.1243310894], [0.009, 5.97856553283, 9683.5945811164]], [[49.582, 3.2226355452, 10213.285546211], [0.831, 3.21219077104, 20426.571092422], [0.112, 3.14159265359, 0.0], [0.013, 3.77448689585, 30639.856638633], [0.009, 4.19802043629, 10239.5838660108], [0.006, 0.20714935358, 10186.9872264112], [0.005, 0.68781956122, 8635.9420037632]], [[0.573, 0.9222969782, 10213.285546211], [0.04, 0.95468912157, 20426.571092422], [0.006, 3.14159265359, 0.0]], [[0.045, 0.30032866722, 10213.285546211], [0.002, 5.29627718483, 20426.571092422]]]

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.

class pymeeus.Venus.Venus

Class Venus models that planet.

__weakref__

list of weak references to the object (if defined)

static apparent_heliocentric_position(epoch)

This method computes the apparent heliocentric position of planet Venus for a given epoch, using the VSOP87 theory.

Parameters:epoch (Epoch) – Epoch to compute Venus position, as an Epoch object Returns:A tuple with the heliocentric longitude and latitude (as Angle objects), and the radius vector (as a float, in astronomical units), in that order Return type:tuple Raises:TypeError if input value is of wrong type.

static eastern_elongation(epoch)

This method computes the time of the eastern elongation closest to the given epoch, as well as the corresponding maximum elongation angle.

Parameters:epoch (Epoch) – Epoch close to the desired eastern elongation Returns:A tuple with the time when the eastern elongation happens, as an Epoch, and the maximum elongation angle, as an Angle Return type:tuple Raises:TypeError if input value is of wrong type. Raises:ValueError if input epoch outside the -2000/4000 range.

>>> epoch = Epoch(2019, 10, 1.0)
>>> time, elongation = Venus.eastern_elongation(epoch)
>>> y, m, d = time.get_date()
>>> print(y)
2020
>>> print(m)
3
>>> print(round(d, 4))
24.9179
>>> print(round(elongation, 4))
46.078

static geocentric_position(epoch)

This method computes the geocentric position of Venus (right ascension and declination) for the given epoch, as well as the elongation angle.

Parameters:epoch (Epoch) – Epoch to compute geocentric position, as an Epoch object Returns:A tuple containing the right ascension, the declination and the elongation angle as Angle objects Return type:tuple Raises:TypeError if input value is of wrong type.

>>> epoch = Epoch(1992, 12, 20.0)
>>> ra, dec, elon = Venus.geocentric_position(epoch)
>>> print(ra.ra_str(n_dec=1))
21h 4' 41.5''
>>> print(dec.dms_str(n_dec=1))
-18d 53' 16.8''
>>> print(elon.dms_str(n_dec=1))
44d 46' 8.9''

static geometric_heliocentric_position(epoch, tofk5=True)

This method computes the geometric heliocentric position of planet Venus for a given epoch, using the VSOP87 theory.

Parameters:

• epoch (Epoch) – Epoch to compute Venus position, as an Epoch object
• tofk5 (bool) – Whether or not the small correction to convert to the FK5 system will be applied or not

Returns:

A tuple with the heliocentric longitude and latitude (as Angle objects), and the radius vector (as a float, in astronomical units), in that order

Return type:

tuple

Raises:

TypeError if input value is of wrong type.

>>> epoch = Epoch(1992, 12, 20.0)
>>> l, b, r = Venus.geometric_heliocentric_position(epoch, tofk5=False)
>>> print(round(l, 5))
26.11412
>>> print(round(b, 4))
-2.6206
>>> print(round(r, 6))
0.724602

static illuminated_fraction(epoch)

This function computes an approximation of the illuminated fraction of Venus disk, as seen from Earth.

Parameters:epoch (Epoch) – Epoch to compute the illuminated fraction Returns:Illuminated fraction of Venus disk Return type:float Raises:TypeError if input values are of wrong type.

>>> epoch = Epoch(1992, 12, 20)
>>> k = Venus.illuminated_fraction(epoch)
>>> print(round(k, 2))
0.64

static inferior_conjunction(epoch)

This method computes the time of the inferior conjunction closest to the given epoch.

Parameters:epoch (Epoch) – Epoch close to the desired inferior conjunction Returns:The time when the inferior conjunction happens, as an Epoch Return type:Epoch Raises:TypeError if input value is of wrong type. Raises:ValueError if input epoch outside the -2000/4000 range.

>>> epoch = Epoch(1882, 12, 1.0)
>>> conjunction = Venus.inferior_conjunction(epoch)
>>> y, m, d = conjunction.get_date()
>>> print(y)
1882
>>> print(m)
12
>>> print(round(d, 1))
6.7

static magnitude(sun_dist, earth_dist, phase_angle)

This function computes the approximate magnitude of Venus.

Parameters:

• sun_dist (float) – Distance from Venus to the Sun, in Astronomical Units
• earth_dist (float) – Distance from Venus to Earth, in Astronomical Units
• phase_angle (float, Angle) – Venus phase angle

Returns:

Venus’ magnitude

Return type:

float

Raises:

TypeError if input values are of wrong type.

>>> sun_dist = 0.724604
>>> earth_dist = 0.910947
>>> phase_angle = Angle(72.96)
>>> m = Venus.magnitude(sun_dist, earth_dist, phase_angle)
>>> print(m)
-3.8

static orbital_elements_j2000(epoch)

This method computes the orbital elements of Venus for the standard equinox J2000.0 for a given epoch.

Parameters:epoch (Epoch) – Epoch to compute orbital elements, as an Epoch object 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) Return type:tuple Raises:TypeError if input value is of wrong type.

>>> epoch = Epoch(2065, 6, 24.0)
>>> l, a, e, i, ome, arg = Venus.orbital_elements_j2000(epoch)
>>> print(round(l, 6))
337.731227
>>> print(round(a, 8))
0.72332982
>>> print(round(e, 7))
0.0067407
>>> print(round(i, 6))
3.394087
>>> print(round(ome, 5))
76.49782
>>> print(round(arg, 6))
55.068476

static orbital_elements_mean_equinox(epoch)

This method computes the orbital elements of Venus for the mean equinox of the date for a given epoch.

Parameters:epoch (Epoch) – Epoch to compute orbital elements, as an Epoch object 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) Return type:tuple Raises:TypeError if input value is of wrong type.

>>> epoch = Epoch(2065, 6, 24.0)
>>> l, a, e, i, ome, arg = Venus.orbital_elements_mean_equinox(epoch)
>>> print(round(l, 6))
338.646306
>>> print(round(a, 8))
0.72332982
>>> print(round(e, 7))
0.0067407
>>> print(round(i, 6))
3.395319
>>> print(round(ome, 5))
77.27012
>>> print(round(arg, 6))
55.211257

static passage_nodes(epoch, ascending=True)

This function computes the time of passage by the nodes (ascending or descending) of Venus, nearest to the given epoch.

Parameters:

• epoch (Epoch) – Epoch closest to the node passage
• ascending (bool) – Whether the time of passage by the ascending (True) or descending (False) node will be computed

Returns:

Tuple containing: - Time of passage through the node (Epoch) - Radius vector when passing through the node (in AU, float)

Return type:

tuple

Raises:

TypeError if input values are of wrong type.

>>> epoch = Epoch(1979, 1, 1)
>>> time, r = Venus.passage_nodes(epoch)
>>> year, month, day = time.get_date()
>>> print(year)
1978
>>> print(month)
11
>>> print(round(day, 1))
27.4
>>> print(round(r, 4))
0.7205

static perihelion_aphelion(epoch, perihelion=True)

This method computes the time of Perihelion (or Aphelion) closer to a given epoch.

Parameters:

• epoch (Epoch) – Epoch close to the desired Perihelion (or Aphelion)
• peihelion – If True, the epoch of the closest Perihelion is computed, if False, the epoch of the closest Aphelion is found.

Returns:

The epoch of the desired Perihelion (or Aphelion)

Return type:

Epoch

Raises:

TypeError if input values are of wrong type.

>>> epoch = Epoch(1978, 10, 15.0)
>>> e = Venus.perihelion_aphelion(epoch)
>>> y, m, d, h, mi, s = e.get_full_date()
>>> print(y)
1978
>>> print(m)
12
>>> print(d)
31
>>> print(h)
4
>>> epoch = Epoch(1979, 2, 1.0)
>>> e = Venus.perihelion_aphelion(epoch, perihelion=False)
>>> y, m, d, h, mi, s = e.get_full_date()
>>> print(y)
1979
>>> print(m)
4
>>> print(d)
22
>>> print(h)
12

static 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.

Parameters:epoch (Epoch) – Epoch close to the desired inferior conjunction Returns:Time when the 1st station in longitude happens, as an Epoch Return type:Epoch Raises:TypeError if input value is of wrong type. Raises:ValueError if input epoch outside the -2000/4000 range.

>>> epoch = Epoch(2018, 12, 1.0)
>>> sta1 = Venus.station_longitude_1(epoch)
>>> y, m, d = sta1.get_date()
>>> print(y)
2018
>>> print(m)
10
>>> print(round(d, 4))
5.7908

static station_longitude_2(epoch)

This method computes the time of the 1st station in longitude (i.e. when the planet is stationary and begins to move eastward - prograde - among the starts) closest to the given epoch.

Parameters:epoch (Epoch) – Epoch close to the desired inferior conjunction Returns:Time when the 2nd station in longitude happens, as an Epoch Return type:Epoch Raises:TypeError if input value is of wrong type. Raises:ValueError if input epoch outside the -2000/4000 range.

>>> epoch = Epoch(2018, 12, 1.0)
>>> sta2 = Venus.station_longitude_2(epoch)
>>> y, m, d = sta2.get_date()
>>> print(y)
2018
>>> print(m)
11
>>> print(round(d, 4))
16.439

static superior_conjunction(epoch)

This method computes the time of the superior conjunction closest to the given epoch.

Parameters:epoch (Epoch) – Epoch close to the desired superior conjunction Returns:The time when the superior conjunction happens, as an Epoch Return type: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)
>>> conjunction = Venus.superior_conjunction(epoch)
>>> y, m, d = conjunction.get_date()
>>> print(y)
1994
>>> print(m)
1
>>> print(round(d, 2))
17.05

static western_elongation(epoch)

This method computes the time of the western elongation closest to the given epoch, as well as the corresponding maximum elongation angle.

Parameters:epoch (Epoch) – Epoch close to the desired western elongation Returns:A tuple with the time when the western elongation happens, as an Epoch, and the maximum elongation angle, as an Angle Return type:tuple Raises:TypeError if input value is of wrong type. Raises:ValueError if input epoch outside the -2000/4000 range.

>>> epoch = Epoch(2019, 1, 1.0)
>>> time, elongation = Venus.western_elongation(epoch)
>>> y, m, d = time.get_date()
>>> print(y)
2019
>>> print(m)
1
>>> print(round(d, 4))
6.1895
>>> print(round(elongation, 4))
46.9571