# -*- coding: utf-8 -*-
# PyMeeus: Python module implementing astronomical algorithms.
# Copyright (C) 2018 Dagoberto Salazar
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
from math import sin, cos, tan, acos, atan2, sqrt, radians, log10
from pymeeus.Angle import Angle
from pymeeus.Epoch import Epoch, JDE2000
from pymeeus.Coordinates import (
geometric_vsop_pos, apparent_vsop_pos, orbital_elements,
nutation_longitude, true_obliquity, ecliptical2equatorial
)
from pymeeus.Earth import Earth
from pymeeus.Sun import Sun
"""
.. module:: Neptune
:synopsis: Class to model Neptune planet
:license: GNU Lesser General Public License v3 (LGPLv3)
.. moduleauthor:: Dagoberto Salazar
"""
VSOP87_L = [
# L0
[
[531188633.047, 0.00000000000, 0.00000000000],
[1798475.509, 2.90101273050, 38.13303563780],
[1019727.662, 0.48580923660, 1.48447270830],
[124531.845, 4.83008090682, 36.64856292950],
[42064.450, 5.41054991607, 2.96894541660],
[37714.589, 6.09221834946, 35.16409022120],
[33784.734, 1.24488865578, 76.26607127560],
[16482.741, 0.00007729261, 491.55792945680],
[9198.582, 4.93747059924, 39.61750834610],
[8994.249, 0.27462142569, 175.16605980020],
[4216.235, 1.98711914364, 73.29712585900],
[3364.818, 1.03590121818, 33.67961751290],
[2284.800, 4.20606932559, 4.45341812490],
[1433.512, 2.78340432711, 74.78159856730],
[900.240, 2.07606702418, 109.94568878850],
[744.996, 3.19032530145, 71.81265315070],
[506.206, 5.74785370252, 114.39910691340],
[399.552, 0.34972342569, 1021.24889455140],
[345.195, 3.46186210169, 41.10198105440],
[306.338, 0.49684039897, 0.52126486180],
[287.322, 4.50523446022, 0.04818410980],
[323.004, 2.24815188609, 32.19514480460],
[340.323, 3.30369900416, 77.75054398390],
[266.605, 4.88932609483, 0.96320784650],
[227.079, 1.79713054538, 453.42489381900],
[244.722, 1.24693337933, 9.56122755560],
[232.887, 2.50459795017, 137.03302416240],
[282.170, 2.24565579693, 146.59425171800],
[251.941, 5.78166597292, 388.46515523820],
[150.180, 2.99706110414, 5.93789083320],
[170.404, 3.32390630650, 108.46121608020],
[151.401, 2.19153094280, 33.94024994380],
[148.295, 0.85948986145, 111.43016149680],
[118.672, 3.67706204305, 2.44768055480],
[101.821, 5.70539236951, 0.11187458460],
[97.873, 2.80518260528, 8.07675484730],
[103.054, 4.40441222000, 70.32818044240],
[103.305, 0.04078966679, 0.26063243090],
[109.300, 2.41599378049, 183.24281464750],
[73.938, 1.32805041516, 529.69096509460],
[77.725, 4.16446516424, 4.19278569400],
[86.379, 4.22834506045, 490.07345674850],
[81.536, 5.19908046216, 493.04240216510],
[71.503, 5.29530386579, 350.33211960040],
[64.418, 3.54541016050, 168.05251279940],
[62.570, 0.15028731465, 182.27960680100],
[58.488, 3.50106873945, 145.10977900970],
[48.276, 1.11259925628, 112.91463420510],
[47.229, 4.57373229818, 46.20979048510],
[39.124, 1.66569356050, 213.29909543800],
[47.728, 0.12906212461, 484.44438245600],
[46.858, 3.01699530327, 498.67147645760],
[38.659, 2.38685706479, 2.92076130680],
[47.046, 4.49844660400, 173.68158709190],
[47.565, 2.58404814824, 219.89137757700],
[44.714, 5.47302733614, 176.65053250850],
[32.279, 3.45759151220, 30.71067209630],
[28.249, 4.13282446716, 6.59228213900],
[24.433, 4.55736848232, 106.97674337190],
[24.661, 3.67822620786, 181.75834193920],
[24.505, 1.55095867965, 7.11354700080],
[21.848, 1.04366818343, 39.09624348430],
[16.936, 6.10896452834, 44.72531777680],
[22.169, 2.74932970271, 256.53994050650],
[16.614, 4.98188930613, 37.61177077600],
[17.728, 3.55049134167, 1.37259812370],
[17.347, 2.14069234880, 42.58645376270],
[14.953, 3.36405649131, 98.89998852460],
[14.566, 0.69857991985, 1550.93985964600],
[15.676, 6.22010212025, 454.90936652730],
[13.243, 5.61712542227, 68.84370773410],
[14.837, 3.52557245517, 25.60286266560],
[12.757, 0.04509743861, 11.04570026390],
[11.988, 4.81687553351, 24.11838995730],
[11.060, 1.78958277553, 7.42236354150],
[12.108, 1.87022663714, 79.23501669220],
[11.698, 0.49005698002, 1.59634729290],
[10.459, 2.38743199893, 381.35160823740],
[11.681, 3.85151357766, 218.40690486870],
[8.744, 0.14168568610, 148.07872442630],
[9.196, 1.00274090619, 72.07328558160],
[11.343, 0.81432278263, 525.49817940060],
[10.097, 5.03383557061, 601.76425067620],
[8.035, 1.77685723010, 0.21244832110],
[8.382, 3.07534786987, 1.27202438720],
[10.803, 2.92081211459, 293.18850343600],
[7.666, 1.52223325105, 115.88357962170],
[7.531, 5.37537256533, 5.10780943070],
[8.691, 4.74352784364, 143.62530630140],
[10.183, 1.15395455831, 6244.94281435360],
[8.283, 0.35956716764, 138.51749687070],
[9.544, 4.02452832984, 152.53214255120],
[7.274, 4.10937535938, 251.43213107580],
[7.465, 1.72131945843, 31.01948863700],
[6.902, 4.62452068308, 2.70831298570],
[7.094, 5.11528393609, 312.19908396260],
[7.929, 2.10765101655, 27.08733537390],
[6.156, 3.50746507109, 28.57180808220],
[7.134, 2.05292376023, 278.25883401880],
[8.193, 2.58588219154, 141.22580985640],
[5.499, 2.09250039025, 1.69692102940],
[5.279, 4.09390686798, 983.11585891360],
[6.947, 3.48041784595, 415.29185818120],
[5.916, 0.68957324226, 62.25142559510],
[5.925, 4.02504592620, 255.05546779820],
[4.606, 1.17779101436, 43.24084506850],
[5.357, 3.63061058987, 5.41662597140],
[5.918, 2.57693824084, 10175.15251057320],
[5.482, 3.07979737280, 329.83706636550],
[3.956, 5.00418696742, 184.72728735580],
[5.408, 3.31313295602, 528.20649238630],
[4.767, 4.91981150665, 456.39383923560],
[3.770, 1.57277409442, 32.71640966640],
[3.924, 4.92763242635, 180.27386923090],
[3.707, 4.82965453201, 221.37585028530],
[3.802, 4.96279204998, 594.65070367540],
[4.014, 1.63905164030, 40.58071619260],
[3.061, 0.39713858313, 1.43628859850],
[3.261, 4.65478978469, 29.22619938800],
[3.474, 5.65891305944, 395.57870223900],
[2.918, 5.91079083895, 1.22384027740],
[3.649, 3.88114678609, 494.52687487340],
[3.225, 5.57423738665, 1014.13534755060],
[2.845, 0.56009386585, 144.14657116320],
[2.848, 0.55423029727, 567.82400073240],
[3.440, 1.70887250883, 12.53017297220],
[3.267, 5.63287799820, 488.58898404020],
[3.107, 5.79335949207, 105.49227066360],
[2.712, 2.43726364359, 60.76695288680],
[3.202, 2.21483496593, 41.05379694460],
[3.134, 4.69665220513, 82.85835341460],
[3.590, 5.69939670162, 1124.34166877000],
[2.967, 0.54448940101, 135.54855145410],
[3.211, 4.19927605853, 291.70403072770],
[2.899, 5.99669788291, 22.63391724900],
[3.143, 2.93495725805, 31.23193695810],
[2.729, 4.62707721219, 5.62907429250],
[2.513, 5.60391563025, 19.12245511120],
[2.690, 5.32070128202, 2.00573757010],
[2.630, 6.00855841124, 37.16982779130],
[2.296, 6.06934502789, 451.94042111070],
[2.858, 4.88677262419, 258.02441321480],
[2.879, 5.12239168488, 38.65430049960],
[2.270, 2.08634524182, 30.05628079050],
[2.301, 3.35951602914, 1028.36244155220],
[3.001, 3.59143817947, 211.81462272970],
[2.237, 0.38455553470, 3.62333672240],
[2.901, 3.24755614136, 366.48562929500],
[2.592, 1.36262641469, 35.42472265210],
[2.418, 4.93467056526, 47.69426319340],
[2.089, 5.79838063413, 4.66586644600],
[2.586, 2.69392971321, 38.18121974760],
[1.913, 5.53560681085, 149.56319713460],
[1.971, 6.00790964671, 34.20088237470],
[2.586, 6.24984047544, 38.08485152800],
[2.098, 4.57819744766, 1019.76442184310],
[1.869, 3.85907708723, 911.04257333200],
[2.486, 5.21235809332, 140.00196957900],
[1.795, 1.68012868451, 1059.38193018920],
[2.326, 2.82664069146, 807.94979911340],
[1.984, 5.54763522932, 1022.73336725970],
[1.919, 5.10717766499, 216.92243216040],
[2.004, 5.47811228948, 63.73589830340],
[2.021, 4.15631916516, 178.13500521680],
[1.760, 6.00927149342, 172.19711438360],
[2.140, 2.65037925793, 700.66423920080],
[1.988, 3.35850272780, 186.21176006410],
[1.956, 5.01527508588, 294.67297614430],
[1.966, 4.07957525462, 20.60692781950],
[1.637, 0.53823942149, 67.35923502580],
[1.540, 2.62327849119, 41.75637236020],
[1.810, 5.81430038477, 129.91947716160],
[1.776, 4.37047808449, 328.35259365720],
[1.460, 2.63664516309, 2.85707083200],
[1.388, 2.10598045632, 3.93215326310],
[1.352, 0.55618245459, 0.65439130580],
[1.668, 2.77543377384, 16.15350969460],
[1.338, 0.37643611305, 14.01464568050],
[1.218, 0.73456434750, 426.59819087600],
[1.531, 4.54891769768, 526.72201967800],
[1.610, 3.40993944436, 403.13419222450],
[1.361, 4.48227243414, 17.63798240290],
[1.589, 5.59323020112, 3302.47939106200],
[1.132, 5.64520725360, 151.04766984290],
[1.357, 4.06399031430, 26.82670294300],
[1.494, 4.98692049495, 666.72398925700],
[1.077, 4.30911470250, 0.63313944640],
[1.042, 6.02756893581, 106.01353552540],
[1.060, 0.74679491358, 487.36514376280],
[1.310, 3.78526380930, 386.98068252990],
[1.342, 4.52685061062, 563.63121503840],
[0.986, 0.00600924269, 81.37388070630],
[1.232, 5.17443930901, 331.32153907380],
[0.929, 4.51267465978, 38.39366806870],
[0.956, 3.50447791020, 64.95973858080],
[0.929, 4.43109514438, 37.87240320690],
[0.926, 6.09803297747, 4.14460158420],
[0.972, 0.59038366513, 8.90683624980],
[1.246, 4.69840351226, 389.94962794650],
[1.009, 5.98451242784, 142.14083359310],
[1.020, 0.83233892300, 39.35687591520],
[1.013, 0.37845630298, 36.90919536040],
[0.940, 2.42688145966, 343.21857259960],
[0.974, 5.23958752786, 253.57099508990],
[0.964, 5.09748190218, 357.44566660120],
[0.835, 1.45568626670, 35.21227433100],
[1.077, 0.71409061316, 44.07092647100],
[1.083, 2.27578897621, 6.90109867970],
[0.938, 5.03471583911, 69.36497259590],
[1.078, 1.20253141912, 35.68535508300],
[1.027, 0.18243183397, 84.34282612290],
[0.764, 4.62720907712, 0.83008140250],
[1.013, 0.42234855022, 32.45577723550],
[0.939, 4.50445799766, 365.00115658670],
[0.756, 0.82872484717, 17.52610781830],
[0.916, 3.89409205418, 38.24491022240],
[0.736, 4.78125743795, 5.36844186160],
[0.762, 0.01897337130, 189.39315380180],
[0.738, 2.31770478416, 42.32582133180],
[0.860, 4.82440483506, 210.33015002140],
[0.888, 3.20360339895, 348.84764689210],
[0.916, 5.04967792934, 38.02116105320],
[0.638, 0.63267396269, 244.31858407500],
[0.636, 1.02615137352, 2080.63082474060],
[0.774, 5.44432678139, 367.97010200330],
[0.644, 1.94044989547, 446.31134681820],
[0.631, 4.82928491724, 460.53844081980],
[0.855, 3.57592750113, 439.78275515400],
[0.678, 4.48687912809, 351.81659230870],
[0.724, 4.89141609280, 119.50691634410],
[0.594, 0.59315717529, 491.03666459500],
[0.655, 1.99014093000, 19.01058052660],
[0.580, 2.57189536188, 492.07919431860],
[0.694, 0.08328521209, 5.67725840230],
[0.733, 5.81485239057, 29.74746424980],
[0.666, 3.42196897591, 179.09821306330],
[0.678, 0.29428615814, 171.23390653710],
[0.635, 2.13805182663, 164.12035953630],
[0.623, 5.61454940380, 285.37238101960],
[0.529, 1.88063108785, 416.77633088950],
[0.529, 5.13250788030, 697.74347789400],
[0.500, 1.49548514415, 704.85702489480],
[0.487, 4.97772067947, 274.06604832480],
[0.666, 6.26456825266, 1474.67378837040],
[0.532, 0.25784352716, 477.33083545520],
[0.557, 0.71378452161, 80.71948940050],
[0.556, 2.60791360513, 418.26080359780],
[0.584, 4.29064541383, 16.67477455640],
[0.524, 5.42759392280, 290.21955801940],
[0.524, 0.29054995359, 247.23934538180],
[0.541, 4.36400580938, 815.06334611420],
[0.526, 1.66512720297, 97.41551581630],
[0.497, 4.72640318293, 401.64971951620],
[0.432, 2.98481475894, 100.38446123290],
[0.382, 0.28067758468, 8.38557138800],
[0.424, 6.16774845481, 178.78939652260],
[0.484, 0.01535318279, 738.79727483860],
[0.518, 4.48916591410, 875.83029900100],
[0.506, 5.38611121207, 404.61866493280],
[0.396, 4.62747640832, 6.15033915430],
[0.466, 0.23340415764, 120.99138905240],
[0.409, 3.08849480895, 59.28248017850],
[0.470, 5.01853200224, 313.68355667090],
[0.442, 3.68919475089, 457.87831194390],
[0.384, 3.69499925394, 160.93896579860],
[0.364, 0.76192181046, 104.00779795530],
[0.416, 0.26652109651, 103.09277421860],
[0.401, 4.06530055968, 14.66903698630],
[0.454, 3.72767803715, 476.43131808350],
[0.434, 0.33533802200, 984.60033162190],
[0.340, 0.99915726716, 31.54075349880],
[0.420, 3.65147769268, 20.49505323490],
[0.334, 0.35121412008, 1227.43444298860],
[0.323, 5.45836731979, 918.15612033280],
[0.407, 4.19457842203, 309.79958751760],
[0.381, 0.01364856960, 495.49008271990],
[0.334, 4.05924071124, 8.33738727820],
[0.380, 3.17063415023, 487.62577619370],
[0.309, 0.48352303405, 118.02244363580],
[0.380, 2.70238752925, 134.11226285560],
[0.362, 4.88985810610, 438.29828244570],
[0.327, 2.91090790412, 505.78502345840],
[0.308, 0.96082817124, 21.14944454070],
[0.288, 1.48123872077, 220.41264243880],
[0.293, 2.56582281789, 662.53120356300],
[0.331, 4.37715965811, 180.79513409270],
[0.326, 2.46104924164, 169.53698550770],
[0.289, 2.63591886391, 55.77101804070],
[0.288, 5.02487283285, 1440.73353842660],
[0.344, 1.48930997270, 166.56804009110],
[0.266, 0.63672427386, 79.18683258240],
[0.268, 5.02354540478, 377.41945497430],
[0.308, 1.50185265748, 77.22927912210],
[0.324, 5.30240189273, 457.61767951300],
[0.265, 1.08736632800, 450.45594840240],
[0.264, 0.83337660655, 488.37653571910],
[0.290, 1.80003152563, 101.86893394120],
[0.262, 2.30390003360, 494.73932319450],
[0.325, 5.52669889053, 441.26722786230],
[0.254, 0.02963623277, 117.36805233000],
[0.300, 0.17435705540, 252.91660378410],
[0.315, 5.34885013040, 183.76407950930],
[0.313, 5.45945846595, 13.49338081870],
[0.306, 5.23085809622, 45.24658263860],
[0.237, 0.32676889138, 208.84567731310],
[0.263, 2.66670785888, 464.73122651380],
[0.234, 1.82700149824, 52175.80628314840],
[0.275, 5.04385701142, 156.15547927360],
[0.265, 5.64967127743, 326.86812094890],
[0.247, 1.74540930625, 65.87476231750],
[0.269, 6.09827783249, 1654.03263386460],
[0.229, 2.25832077914, 190.66517818900],
[0.294, 5.45249564193, 206.18554843720],
[0.238, 1.55647021369, 79.88940799800],
[0.230, 6.13158632762, 178.34745353790],
[0.274, 4.10829870815, 518.38463239980],
[0.225, 3.86300359251, 171.98466606250],
[0.228, 2.48511565618, 12566.15169998280],
[0.272, 5.61149862463, 148.33935685720],
[0.214, 1.45987216039, 522.57741809380],
[0.211, 4.04791980901, 6205.32530600750],
[0.266, 0.99036038827, 209.10630974400],
[0.230, 0.54049951530, 532.61172640140],
[0.226, 3.84152961620, 283.62727588040],
[0.243, 5.32730346969, 485.92885516430],
[0.209, 4.35051470487, 536.80451209540],
[0.232, 3.01948719112, 10.93382567930],
[0.264, 5.70536379124, 490.33408917940],
[0.280, 3.99993658196, 674.80074410430],
[0.246, 0.37698964335, 157.63995198190],
[0.219, 5.67679857772, 52099.54021187280],
[0.251, 1.52353965506, 6.85291456990],
[0.203, 5.44328656642, 145.63104387150],
[0.238, 0.96169723853, 497.18700374930],
[0.219, 4.52300776062, 1615.89959822680],
[0.275, 2.37619210741, 2118.76386037840],
[0.258, 5.12448148780, 608.87779767700],
[0.260, 3.88543008475, 513.07988101300],
[0.191, 3.72574595369, 65.22037101170],
[0.211, 0.06484535455, 215.43795945210],
[0.236, 3.95835282821, 141.48644228730],
[0.189, 5.28135043909, 377.15882254340],
[0.243, 4.35559878377, 482.95990974770],
[0.243, 6.06808644973, 154.01661525950],
[0.249, 1.57215637373, 14.22709400160],
[0.238, 1.93340192445, 500.15594916590],
[0.209, 5.02893682321, 364.55921360200],
[0.227, 5.72984298540, 1543.82631264520],
[0.217, 2.45036922991, 187.17496791060],
[0.181, 1.65699502247, 1627.20593092160],
[0.214, 1.60213179145, 11.30633269480],
[0.203, 0.74638490279, 14.55716240170],
[0.192, 3.17719161639, 343.47920503050],
[0.177, 1.50027795761, 9.44935297100],
[0.177, 0.03038098292, 165.60483224460],
[0.176, 4.64462444674, 315.16802937920],
[0.208, 2.65835778368, 496.01134758170],
[0.174, 2.76155855705, 49.17873590170],
[0.196, 1.95549714182, 335.77495719870],
[0.200, 4.16839394758, 285.11174858870],
[0.199, 0.06168021293, 73.55775828990],
[0.188, 6.17288913873, 535.32003938710],
[0.215, 1.92414563346, 552.69738935910],
[0.166, 5.49038139690, 10135.53500222710],
[0.192, 0.96973434120, 304.23420369990],
[0.209, 5.34065233845, 13.64213866500],
[0.203, 5.11234865419, 324.72925693480],
[0.177, 3.50680841790, 207.36120460480],
[0.174, 1.95010708561, 319.31263096340],
[0.187, 5.57685931698, 266.10116806210],
[0.181, 1.43525075751, 279.74330672710],
[0.165, 4.00537112057, 493.56366702690],
[0.191, 1.68313683465, 563.37058260750],
[0.173, 3.93200456456, 238.90195810360],
[0.161, 5.96143146317, 36.12729806770],
[0.194, 2.37664231450, 944.98282327580],
[0.165, 0.97421918976, 556.51766803760],
[0.189, 1.11279570541, 1127.26243007680],
[0.172, 0.75085513952, 267.58564077040],
[0.193, 2.12636756833, 20350.30502114640],
[0.181, 2.10814562080, 113.87784205160],
[0.194, 1.13504964219, 57.25549074900],
[0.181, 6.23699820519, 355.96119389290],
[0.198, 5.68125942959, 6280.10690457480],
[0.173, 5.15083799917, 474.94684537520],
[0.151, 1.66981962338, 116.53797092750],
[0.150, 5.42593657173, 526.98265210890],
[0.205, 4.16096717573, 711.44930703380],
[0.177, 3.49360697678, 421.22974901440],
[0.168, 0.52839230204, 487.10451133190],
[0.160, 4.77712663799, 524.01370669230],
[0.145, 2.81448128781, 1512.80682400820],
[0.146, 4.99570112660, 142.66209845490],
[0.188, 0.82104161550, 10210.31660079440],
[0.145, 4.96888131586, 1189.30140735080],
[0.181, 2.99704790590, 75.74480641380],
[0.176, 0.41626373842, 222.86032299360],
[0.137, 2.96534226337, 6206.80977871580],
[0.138, 1.22260849471, 187.69623277240],
[0.128, 2.53394068407, 276.77436131050],
[0.130, 3.04810765699, 310.71461125430],
[0.122, 3.01323006886, 70.84944530420],
[0.111, 0.77449448649, 179.35884549420],
[0.141, 0.18423889807, 131.40394986990],
[0.126, 5.77648809669, 525.23754696970],
[0.124, 2.93225731024, 179.61947792510],
[0.111, 6.18471578216, 981.63138620530],
[0.141, 2.63342951123, 381.61224066830],
[0.110, 5.25053027081, 986.08480433020],
[0.096, 3.86591534559, 240.12579838100],
[0.120, 3.78755085035, 1057.89745748090],
[0.093, 4.54014016637, 36.69674703930],
[0.109, 1.53327585900, 419.74527630610],
[0.094, 4.21870300178, 1024.21783996800],
[0.109, 2.15905156247, 289.56516671360],
[0.104, 0.20665642552, 564.85505531580],
[0.081, 1.89134135215, 36.60037881970],
[0.080, 4.38832594589, 10137.01947493540],
[0.080, 1.73940577376, 39.50563376150],
[0.084, 0.81316746605, 170.71264167530],
[0.090, 0.60145818457, 36.76043751410],
[0.074, 4.92511651321, 1549.45538693770],
[0.072, 5.06852406179, 249.94765836750],
],
# L1
[
[3837687716.731, 0.00000000000, 0.00000000000],
[16604.187, 4.86319129565, 1.48447270830],
[15807.148, 2.27923488532, 38.13303563780],
[3334.701, 3.68199676020, 76.26607127560],
[1305.840, 3.67320813491, 2.96894541660],
[604.832, 1.50477747549, 35.16409022120],
[178.623, 3.45318524147, 39.61750834610],
[106.537, 2.45126138334, 4.45341812490],
[105.747, 2.75479326550, 33.67961751290],
[72.684, 5.48724732699, 36.64856292950],
[57.069, 5.21649804970, 0.52126486180],
[57.355, 1.85767603384, 114.39910691340],
[35.368, 4.51676827545, 74.78159856730],
[32.216, 5.90411489680, 77.75054398390],
[29.871, 3.67043294114, 388.46515523820],
[28.866, 5.16877529164, 9.56122755560],
[28.742, 5.16732589024, 2.44768055480],
[25.507, 5.24526281928, 168.05251279940],
[24.869, 4.73193067810, 182.27960680100],
[20.205, 5.78945415677, 1021.24889455140],
[19.022, 1.82981144269, 484.44438245600],
[18.661, 1.31606255521, 498.67147645760],
[15.063, 4.95003893760, 137.03302416240],
[15.094, 3.98705254940, 32.19514480460],
[10.720, 2.44148149225, 4.19278569400],
[11.725, 4.89255650674, 71.81265315070],
[9.581, 1.23188039594, 5.93789083320],
[9.606, 1.88534821556, 41.10198105440],
[8.968, 0.01758559103, 8.07675484730],
[9.882, 6.08165628679, 7.11354700080],
[7.632, 5.51307048241, 73.29712585900],
[6.992, 0.61688864282, 2.92076130680],
[5.543, 2.24141557794, 46.20979048510],
[4.845, 3.71055823750, 112.91463420510],
[3.700, 5.25713252333, 111.43016149680],
[3.233, 6.10303038418, 70.32818044240],
[2.939, 4.86520586648, 98.89998852460],
[2.403, 2.90637675099, 601.76425067620],
[2.398, 1.04343654629, 6.59228213900],
[2.784, 4.95821114677, 108.46121608020],
[2.894, 4.20148844767, 381.35160823740],
[2.111, 5.93089610785, 25.60286266560],
[2.075, 5.20632201951, 30.71067209630],
[2.126, 0.54976393136, 41.05379694460],
[2.235, 2.38045158073, 453.42489381900],
[1.859, 0.89409373259, 24.11838995730],
[2.018, 3.42245274178, 31.01948863700],
[1.700, 3.91715254287, 11.04570026390],
[1.776, 3.86571077241, 395.57870223900],
[1.644, 0.15855999051, 152.53214255120],
[1.646, 3.34591387314, 44.72531777680],
[1.876, 2.59784179105, 33.94024994380],
[1.614, 0.42137145545, 175.16605980020],
[1.468, 6.12983933526, 1550.93985964600],
[1.408, 6.13722948564, 490.07345674850],
[1.207, 0.59525736062, 312.19908396260],
[1.336, 3.28611928206, 493.04240216510],
[1.176, 5.87266726996, 5.41662597140],
[1.517, 3.12967210501, 491.55792945680],
[1.053, 4.60375516830, 79.23501669220],
[1.037, 4.89007314395, 1.27202438720],
[1.034, 5.93741289103, 32.71640966640],
[1.038, 1.13470380744, 1014.13534755060],
[1.002, 1.85850922283, 5.10780943070],
[0.983, 0.05345050384, 7.42236354150],
[0.998, 1.73689827444, 1028.36244155220],
[1.193, 4.63176675581, 60.76695288680],
[0.940, 3.09103721222, 62.25142559510],
[0.994, 4.11489180313, 4.66586644600],
[0.890, 0.87049255398, 31.23193695810],
[0.852, 5.35508394316, 144.14657116320],
[0.922, 5.12373360511, 145.10977900970],
[0.789, 0.37496785039, 26.82670294300],
[0.828, 4.06035194600, 115.88357962170],
[0.711, 3.14189997439, 278.25883401880],
[0.727, 1.39718382835, 213.29909543800],
[0.781, 0.10946327923, 173.68158709190],
[0.793, 6.13086312116, 567.82400073240],
[0.669, 4.50554989443, 27.08733537390],
[0.825, 1.35568908148, 129.91947716160],
[0.738, 3.56766018960, 176.65053250850],
[0.714, 6.24797992301, 106.97674337190],
[0.654, 1.13177751192, 68.84370773410],
[0.624, 0.01567750666, 28.57180808220],
[0.608, 4.60180625368, 189.39315380180],
[0.595, 0.00857468445, 42.58645376270],
[0.530, 5.61201247153, 12.53017297220],
[0.521, 1.02371768017, 415.29185818120],
[0.639, 0.68930265745, 529.69096509460],
[0.526, 3.02138731705, 5.62907429250],
[0.456, 4.44331571392, 43.24084506850],
[0.524, 3.43316448349, 38.65430049960],
[0.436, 2.41630174435, 82.85835341460],
[0.424, 1.95736011325, 477.33083545520],
[0.443, 3.39350946329, 357.44566660120],
[0.383, 1.90232196422, 22.63391724900],
[0.479, 5.55141744216, 37.61177077600],
[0.462, 3.80436154644, 343.21857259960],
[0.384, 5.60377408953, 594.65070367540],
[0.369, 4.45577410338, 6.90109867970],
[0.358, 3.69126616347, 3.93215326310],
[0.352, 3.10952926034, 135.54855145410],
[0.368, 3.53577440355, 40.58071619260],
[0.424, 5.27159202779, 181.75834193920],
[0.361, 0.29018303419, 72.07328558160],
[0.390, 5.49512204296, 350.33211960040],
[0.378, 2.74122401337, 488.37653571910],
[0.372, 0.39980033572, 494.73932319450],
[0.353, 1.10614174053, 20.60692781950],
[0.296, 0.86351261285, 149.56319713460],
[0.307, 5.39420288683, 160.93896579860],
[0.395, 1.93577214824, 10137.01947493540],
[0.288, 2.28755739359, 47.69426319340],
[0.295, 2.48737537240, 19.12245511120],
[0.290, 0.18636083306, 143.62530630140],
[0.266, 3.09977370364, 69.36497259590],
[0.266, 1.21002824826, 505.78502345840],
[0.252, 3.12745026026, 460.53844081980],
[0.328, 0.50849285663, 6206.80977871580],
[0.257, 3.64119914774, 446.31134681820],
[0.239, 5.54080102299, 911.04257333200],
[0.265, 0.62702473701, 253.57099508990],
[0.287, 2.44403568436, 16.67477455640],
[0.231, 2.47026250085, 454.90936652730],
[0.230, 3.24571542922, 1066.49547719000],
[0.282, 1.48595620175, 983.11585891360],
[0.212, 5.41931177641, 64.95973858080],
[0.213, 1.64175339637, 1089.12939443900],
[0.238, 2.69801319489, 882.94384600180],
[0.210, 4.53976756699, 1093.32218013300],
[0.220, 2.30038816175, 1052.26838318840],
[0.256, 0.42073598460, 23.90594163620],
[0.216, 5.44225918870, 39.09624348430],
[0.201, 2.58746514605, 119.50691634410],
[0.224, 4.43751392203, 639.89728631400],
[0.186, 2.50651218075, 487.36514376280],
[0.189, 4.05785534221, 120.99138905240],
[0.184, 2.24245977278, 815.06334611420],
[0.202, 3.43517732411, 45.24658263860],
[0.175, 4.49165234532, 171.23390653710],
[0.171, 5.50633466316, 179.09821306330],
[0.200, 6.12663205401, 14.22709400160],
[0.173, 2.61090344107, 389.94962794650],
[0.167, 3.94754384833, 77.22927912210],
[0.166, 3.41009128748, 81.37388070630],
[0.163, 3.88198848446, 556.51766803760],
[0.164, 1.49614763046, 63.73589830340],
[0.176, 3.86129425367, 148.33935685720],
[0.161, 2.22215642318, 574.93754773320],
[0.171, 0.66899426684, 179.31066138440],
[0.161, 1.21480182441, 1024.43028828910],
[0.155, 3.25842414799, 10251.41858184880],
[0.183, 5.45168150656, 218.40690486870],
[0.152, 3.35145509017, 285.37238101960],
[0.152, 0.42398786475, 274.06604832480],
[0.146, 5.70714579127, 419.48464387520],
[0.156, 0.64321524870, 1029.84691426050],
[0.147, 4.30958930740, 157.63995198190],
[0.147, 1.80689177510, 377.41945497430],
[0.140, 1.49826604627, 386.98068252990],
[0.137, 2.14480243915, 563.63121503840],
[0.127, 3.98726599710, 84.34282612290],
[0.134, 4.16039455079, 169.53698550770],
[0.121, 0.29300927469, 206.18554843720],
[0.129, 2.67625057010, 180.79513409270],
[0.134, 3.18868986487, 166.56804009110],
[0.135, 5.07517561780, 426.59819087600],
[0.136, 1.81672451740, 151.04766984290],
[0.129, 3.64795525602, 183.76407950930],
[0.116, 6.06435563172, 220.41264243880],
[0.123, 4.46641157829, 1022.73336725970],
[0.112, 4.34485256988, 138.51749687070],
[0.116, 5.58946529961, 35.68535508300],
[0.108, 1.03796693383, 488.58898404020],
[0.108, 2.10378485880, 494.52687487340],
[0.106, 0.87068583107, 1059.38193018920],
[0.097, 0.74486741478, 485.92885516430],
[0.095, 5.54259914856, 497.18700374930],
[0.085, 3.16062141266, 522.57741809380],
[0.097, 6.05634803604, 482.95990974770],
[0.095, 0.23111852730, 500.15594916590],
[0.084, 2.64687252518, 536.80451209540],
[0.074, 3.90678924318, 1019.76442184310],
],
# L2
[
[53892.649, 0.00000000000, 0.00000000000],
[281.251, 1.19084538887, 38.13303563780],
[295.693, 1.85520292248, 1.48447270830],
[270.190, 5.72143228148, 76.26607127560],
[23.023, 1.21035596452, 2.96894541660],
[7.333, 0.54033306830, 2.44768055480],
[9.057, 4.42544992035, 35.16409022120],
[5.223, 0.67427930044, 168.05251279940],
[5.201, 3.02338671812, 182.27960680100],
[4.288, 3.84351844003, 114.39910691340],
[3.925, 3.53214557374, 484.44438245600],
[3.741, 5.90238217874, 498.67147645760],
[2.966, 0.31002477611, 4.45341812490],
[3.415, 0.55971639038, 74.78159856730],
[3.255, 1.84921884906, 175.16605980020],
[2.157, 1.89135758747, 388.46515523820],
[2.211, 4.37997092240, 7.11354700080],
[1.847, 3.48574435762, 9.56122755560],
[2.451, 4.68586840176, 491.55792945680],
[1.844, 5.12281562096, 33.67961751290],
[2.204, 1.69321574906, 77.75054398390],
[1.652, 2.55859494053, 36.64856292950],
[1.309, 4.52400192922, 1021.24889455140],
[1.124, 0.38710602242, 137.03302416240],
[0.664, 0.88101734307, 4.19278569400],
[0.497, 2.24615784762, 395.57870223900],
[0.512, 6.22609200672, 381.35160823740],
[0.582, 5.25716719826, 31.01948863700],
[0.446, 0.36647221351, 98.89998852460],
[0.383, 5.48585528762, 5.93789083320],
[0.375, 4.61250246774, 8.07675484730],
[0.354, 1.30783918287, 601.76425067620],
[0.259, 5.66033623678, 112.91463420510],
[0.247, 2.89695614593, 189.39315380180],
[0.245, 4.26572913391, 220.41264243880],
[0.200, 0.52604535784, 64.95973858080],
[0.191, 4.88786653062, 39.61750834610],
[0.233, 3.16423779113, 41.10198105440],
[0.248, 5.85877831382, 1059.38193018920],
[0.194, 2.37949641473, 73.29712585900],
[0.227, 0.20028518978, 60.76695288680],
[0.184, 3.01962045713, 1014.13534755060],
[0.190, 5.57500985081, 343.21857259960],
[0.172, 3.66036463613, 477.33083545520],
[0.172, 0.59550457102, 46.20979048510],
[0.182, 1.92429384025, 183.76407950930],
[0.171, 1.61368476689, 357.44566660120],
[0.173, 6.23717119485, 493.04240216510],
[0.217, 1.46218158211, 71.81265315070],
[0.178, 0.34928799031, 1028.36244155220],
[0.169, 4.91086673212, 166.56804009110],
[0.157, 5.89200571154, 169.53698550770],
[0.182, 2.33457064554, 152.53214255120],
[0.151, 3.81621340568, 146.59425171800],
[0.136, 2.75150881988, 144.14657116320],
[0.104, 6.03262825314, 529.69096509460],
[0.076, 0.20932812381, 453.42489381900],
],
# L3
[
[31.254, 0.00000000000, 0.00000000000],
[12.461, 6.04431418812, 1.48447270830],
[14.541, 1.35337075856, 76.26607127560],
[11.547, 6.11257808366, 38.13303563780],
[1.351, 4.93951495175, 2.96894541660],
[0.741, 2.35936954597, 168.05251279940],
[0.715, 1.27409542804, 182.27960680100],
[0.537, 5.23632185196, 484.44438245600],
[0.523, 4.16769839601, 498.67147645760],
[0.664, 0.55871435877, 31.01948863700],
[0.301, 2.69253200796, 7.11354700080],
[0.194, 2.05904114139, 137.03302416240],
[0.206, 2.51012178002, 74.78159856730],
[0.160, 5.63111039032, 114.39910691340],
[0.149, 3.09327713923, 35.16409022120],
],
# L4
[
[113.998, 3.14159265359, 0.00000000000],
[0.605, 3.18211885677, 76.26607127560]
],
# L5
[
[0.874, 3.14159265359, 0.00000000000]
],
]
"""This table contains Neptune'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 452-453."""
VSOP87_B = [
# B0
[
[3088622.933, 1.44104372626, 38.13303563780],
[27780.087, 5.91271882843, 76.26607127560],
[27623.609, 0.00000000000, 0.00000000000],
[15355.490, 2.52123799481, 36.64856292950],
[15448.133, 3.50877080888, 39.61750834610],
[1999.919, 1.50998669505, 74.78159856730],
[1967.540, 4.37778195768, 1.48447270830],
[1015.137, 3.21561035875, 35.16409022120],
[605.767, 2.80246601405, 73.29712585900],
[594.878, 2.12892708114, 41.10198105440],
[588.805, 3.18655882497, 2.96894541660],
[401.830, 4.16883287237, 114.39910691340],
[254.333, 3.27120499438, 453.42489381900],
[261.647, 3.76722704749, 213.29909543800],
[279.964, 1.68165309699, 77.75054398390],
[205.590, 4.25652348864, 529.69096509460],
[140.455, 3.52969556376, 137.03302416240],
[98.530, 4.16774829927, 33.67961751290],
[51.257, 1.95121181203, 4.45341812490],
[67.971, 4.66970781659, 71.81265315070],
[41.931, 5.41783694467, 111.43016149680],
[41.822, 5.94832001477, 112.91463420510],
[30.637, 0.93620571932, 42.58645376270],
[11.084, 5.88898793049, 108.46121608020],
[9.620, 0.03944255108, 70.32818044240],
[9.664, 0.22455797403, 79.23501669220],
[9.728, 5.30069593532, 32.19514480460],
[7.386, 3.00684933642, 426.59819087600],
[7.087, 0.12535040656, 109.94568878850],
[6.021, 6.20514068152, 115.88357962170],
[6.169, 3.62098109648, 983.11585891360],
[4.777, 0.75210194972, 5.93789083320],
[6.391, 5.84646101060, 148.07872442630],
[6.251, 2.41678769385, 152.53214255120],
[4.539, 5.58182098700, 175.16605980020],
[5.006, 4.60815664851, 1059.38193018920],
[4.289, 4.19647392821, 47.69426319340],
[5.795, 5.07516716087, 415.29185818120],
[4.749, 2.51605725604, 37.61177077600],
[4.119, 1.72779509865, 28.57180808220],
[4.076, 6.00252170354, 145.10977900970],
[4.429, 5.65995321659, 98.89998852460],
[3.950, 2.74104636753, 350.33211960040],
[4.091, 1.61787956945, 39.09624348430],
[4.131, 4.40682554313, 37.16982779130],
[4.710, 3.50929350767, 38.65430049960],
[4.440, 4.78977105547, 38.08485152800],
[4.433, 1.23386935925, 38.18121974760],
[3.762, 4.83940791709, 491.55792945680],
[2.606, 1.20956732792, 451.94042111070],
[2.537, 2.18628045751, 454.90936652730],
[2.328, 5.19779918719, 72.07328558160],
[2.502, 0.85987904350, 106.97674337190],
[2.342, 0.81387240947, 4.19278569400],
[1.981, 0.46617960831, 184.72728735580],
[1.963, 6.01909114576, 44.07092647100],
[2.180, 0.70099749844, 206.18554843720],
[1.811, 0.40456996647, 40.58071619260],
[1.814, 3.64699555185, 220.41264243880],
[1.705, 6.13551142362, 181.75834193920],
[1.855, 5.61635630213, 35.68535508300],
[1.595, 2.97147156093, 37.87240320690],
[1.785, 2.42154818096, 388.46515523820],
[1.595, 3.05266110075, 38.39366806870],
[1.437, 1.48678704605, 135.54855145410],
[1.387, 2.46149266117, 138.51749687070],
[1.366, 1.52026779665, 68.84370773410],
[1.575, 3.58964541604, 38.02116105320],
[1.297, 5.06156596196, 33.94024994380],
[1.487, 0.20211121607, 30.05628079050],
[1.504, 5.80298577327, 46.20979048510],
[1.192, 0.87275514483, 42.32582133180],
[1.569, 2.43405967107, 38.24491022240],
[1.207, 1.84658687853, 251.43213107580],
[1.015, 0.53439848924, 129.91947716160],
[0.999, 2.47463873948, 312.19908396260],
[0.990, 3.41514319052, 144.14657116320],
[0.963, 4.31733242907, 151.04766984290],
[1.020, 0.98226686775, 143.62530630140],
[0.941, 1.02993053785, 221.37585028530],
[0.938, 2.43648356625, 567.82400073240],
[1.111, 0.65175024456, 146.59425171800],
[0.777, 0.00175975222, 218.40690486870],
[0.895, 0.25123869620, 30.71067209630],
[0.795, 5.80519741659, 149.56319713460],
[0.737, 3.40060492866, 446.31134681820],
[0.719, 1.43795191278, 8.07675484730],
[0.720, 0.00651007550, 460.53844081980],
[0.766, 4.03399506246, 522.57741809380],
[0.666, 1.39457824982, 84.34282612290],
[0.584, 1.01405548136, 536.80451209540],
[0.596, 0.62390100715, 35.21227433100],
[0.598, 5.39946724188, 41.05379694460],
[0.475, 5.80072248338, 7.42236354150],
[0.510, 1.34478579740, 258.02441321480],
[0.458, 5.25325523118, 80.71948940050],
[0.421, 3.24496387889, 416.77633088950],
[0.446, 1.19167306357, 180.27386923090],
[0.471, 0.92632922375, 44.72531777680],
[0.387, 1.68488418788, 183.24281464750],
[0.375, 0.15223869165, 255.05546779820],
[0.354, 4.21526988674, 0.96320784650],
[0.379, 2.16947487177, 105.49227066360],
[0.341, 4.79194051680, 110.20632121940],
[0.427, 5.15774894584, 31.54075349880],
[0.302, 3.45706306280, 100.38446123290],
[0.298, 2.26790695187, 639.89728631400],
[0.279, 0.25689162963, 39.50563376150],
[0.320, 3.58085653166, 45.24658263860],
[0.269, 5.72024180826, 36.76043751410],
[0.247, 0.61040148804, 186.21176006410],
[0.245, 0.64173616273, 419.48464387520],
[0.235, 0.73189197665, 10213.28554621100],
[0.232, 0.37399822852, 490.07345674850],
[0.230, 5.76570492457, 12.53017297220],
[0.240, 4.13447692727, 0.52126486180],
[0.279, 1.62614865256, 294.67297614430],
[0.238, 2.18528916550, 219.89137757700],
[0.262, 3.08384135298, 6.59228213900],
[0.217, 2.93214905312, 27.08733537390],
[0.217, 4.69210602828, 406.10313764110],
[0.219, 1.35212712560, 216.92243216040],
[0.200, 2.35215465744, 605.95703637020],
[0.232, 3.92583619589, 1512.80682400820],
[0.223, 5.52392277606, 187.69623277240],
[0.190, 0.29169556516, 291.70403072770],
[0.236, 3.12464145036, 563.63121503840],
[0.193, 0.53675942386, 60.76695288680],
[0.215, 3.78391259001, 103.09277421860],
[0.172, 5.63262770743, 7.11354700080],
[0.164, 4.14700645532, 77.22927912210],
[0.162, 0.72021213236, 11.04570026390],
[0.160, 4.23490438166, 487.36514376280],
[0.191, 0.37651439206, 31.01948863700],
[0.157, 1.02419759383, 6283.07584999140],
[0.157, 4.42530429545, 6206.80977871580],
[0.178, 6.24797160202, 316.39186965660],
[0.161, 5.65988283675, 343.21857259960],
[0.153, 5.58405022784, 252.08652238160],
[0.189, 4.80791039970, 641.12112659140],
[0.166, 5.50438043692, 662.53120356300],
[0.146, 5.08949604858, 286.59622129700],
[0.145, 2.13015521881, 2042.49778910280],
[0.156, 2.19452173251, 274.06604832480],
[0.148, 4.85696640135, 442.75170057060],
[0.187, 4.96121139073, 1589.07289528380],
[0.155, 2.28260574227, 142.14083359310],
[0.134, 1.29277093566, 456.39383923560],
[0.126, 5.59769497652, 179.35884549420],
[0.146, 2.53359213478, 256.53994050650],
[0.140, 1.57962199954, 75.74480641380],
[0.123, 0.05442220184, 944.98282327580],
[0.122, 1.90676379802, 418.26080359780],
[0.154, 1.86865302773, 331.32153907380],
[0.144, 5.52229258454, 14.01464568050],
[0.138, 2.80728175526, 82.85835341460],
[0.107, 0.66995358132, 190.66517818900],
[0.114, 1.48894980280, 253.57099508990],
[0.110, 5.32587573069, 240.12579838100],
[0.105, 0.65548440578, 173.68158709190],
[0.102, 2.58735617801, 450.45594840240],
[0.098, 0.44044795266, 328.35259365720],
[0.101, 4.71267656829, 117.36805233000],
[0.094, 0.54938580474, 293.18850343600],
[0.095, 2.17636214523, 101.86893394120],
[0.093, 0.63687810471, 377.15882254340],
[0.091, 5.84828809934, 10137.01947493540],
[0.089, 1.02830167997, 1021.24889455140],
[0.094, 1.79320597168, 493.04240216510],
[0.080, 1.58140274465, 69.15252427480],
[0.075, 0.23453373368, 63.73589830340],
[0.071, 1.51961989690, 488.58898404020],
],
# B1
[
[227279.214, 3.80793089870, 38.13303563780],
[1803.120, 1.97576485377, 76.26607127560],
[1385.733, 4.82555548018, 36.64856292950],
[1433.300, 3.14159265359, 0.00000000000],
[1073.298, 6.08054240712, 39.61750834610],
[147.903, 3.85766231348, 74.78159856730],
[136.448, 0.47764957338, 1.48447270830],
[70.285, 6.18782052139, 35.16409022120],
[51.899, 5.05221791891, 73.29712585900],
[37.273, 4.89476629246, 41.10198105440],
[42.568, 0.30721737205, 114.39910691340],
[37.104, 5.75999349109, 2.96894541660],
[26.399, 5.21566335936, 213.29909543800],
[16.949, 4.26463671859, 77.75054398390],
[18.747, 0.90426522185, 453.42489381900],
[12.951, 6.17709713139, 529.69096509460],
[10.502, 1.20336443465, 137.03302416240],
[4.416, 1.25478204684, 111.43016149680],
[4.383, 6.14147099615, 71.81265315070],
[3.694, 0.94837702528, 33.67961751290],
[2.957, 4.77532871210, 4.45341812490],
[2.698, 1.92435531119, 112.91463420510],
[1.989, 3.96637567224, 42.58645376270],
[1.150, 4.30568700024, 37.61177077600],
[0.871, 4.81775882249, 152.53214255120],
[0.944, 2.21777772050, 109.94568878850],
[0.936, 1.17054983940, 148.07872442630],
[0.925, 2.40329074000, 206.18554843720],
[0.690, 1.57381082857, 38.65430049960],
[0.624, 2.79466003645, 79.23501669220],
[0.726, 4.13829519132, 28.57180808220],
[0.640, 2.46161252327, 115.88357962170],
[0.531, 2.96991530500, 98.89998852460],
[0.537, 1.95986772922, 220.41264243880],
[0.539, 2.06690307827, 40.58071619260],
[0.716, 0.55781847010, 350.33211960040],
[0.563, 1.84072805158, 983.11585891360],
[0.533, 1.34787677940, 47.69426319340],
[0.566, 1.80111775954, 175.16605980020],
[0.449, 1.62191691011, 144.14657116320],
[0.371, 2.74239666472, 415.29185818120],
[0.381, 6.11910193382, 426.59819087600],
[0.366, 2.39752585360, 129.91947716160],
[0.456, 3.19611413854, 108.46121608020],
[0.327, 3.62341506247, 38.18121974760],
[0.328, 0.89613145346, 38.08485152800],
[0.341, 3.87265469070, 35.68535508300],
[0.331, 4.48858774501, 460.53844081980],
[0.414, 1.03543720726, 70.32818044240],
[0.310, 0.51297445145, 37.16982779130],
[0.287, 2.18351651800, 491.55792945680],
[0.274, 6.11504724934, 522.57741809380],
[0.281, 3.81657117512, 5.93789083320],
[0.298, 4.00532631258, 39.09624348430],
[0.265, 5.26569823181, 446.31134681820],
[0.319, 1.34097217817, 184.72728735580],
[0.203, 6.02944475303, 149.56319713460],
[0.205, 5.53935732020, 536.80451209540],
[0.226, 6.17710997862, 454.90936652730],
[0.186, 3.24302117645, 4.19278569400],
[0.179, 4.91458426239, 451.94042111070],
[0.198, 2.30775852880, 146.59425171800],
[0.166, 1.16793600058, 72.07328558160],
[0.147, 2.10574339673, 44.07092647100],
[0.123, 1.98250467171, 46.20979048510],
[0.159, 3.46955908364, 145.10977900970],
[0.116, 5.88971113590, 38.02116105320],
[0.115, 4.73412534395, 38.24491022240],
[0.125, 3.42713474801, 251.43213107580],
[0.128, 1.51108932026, 221.37585028530],
[0.127, 0.17176461812, 138.51749687070],
[0.124, 5.85160407534, 1059.38193018920],
[0.091, 2.38273591235, 30.05628079050],
[0.118, 5.27114846878, 37.87240320690],
[0.117, 5.35267669439, 38.39366806870],
[0.099, 5.19920708255, 135.54855145410],
[0.114, 4.37452353441, 388.46515523820],
[0.093, 4.64183693718, 106.97674337190],
[0.084, 1.35269684746, 33.94024994380],
[0.111, 3.56226463770, 181.75834193920],
[0.082, 3.18401661435, 42.32582133180],
[0.084, 5.51669920239, 8.07675484730],
],
# B2
[
[9690.766, 5.57123750291, 38.13303563780],
[78.815, 3.62705474219, 76.26607127560],
[71.523, 0.45476688580, 36.64856292950],
[58.646, 3.14159265359, 0.00000000000],
[29.915, 1.60671721861, 39.61750834610],
[6.472, 5.60736756575, 74.78159856730],
[5.800, 2.25341847151, 1.48447270830],
[4.309, 1.68126737666, 35.16409022120],
[3.502, 2.39142672984, 114.39910691340],
[2.649, 0.65061457644, 73.29712585900],
[1.518, 0.37600329684, 213.29909543800],
[1.223, 1.23116043030, 2.96894541660],
[0.766, 5.45279753249, 453.42489381900],
[0.779, 2.07081431472, 529.69096509460],
[0.496, 0.26552533921, 41.10198105440],
[0.469, 5.87866293959, 77.75054398390],
[0.482, 5.63056237954, 137.03302416240],
[0.345, 1.80085651594, 71.81265315070],
[0.274, 2.86650141006, 33.67961751290],
[0.158, 4.63868656467, 206.18554843720],
[0.166, 1.24877330835, 220.41264243880],
[0.153, 2.87376446497, 111.43016149680],
[0.116, 3.63838544843, 112.91463420510],
[0.085, 0.43712705655, 4.45341812490],
[0.104, 6.12597614674, 144.14657116320],
],
# B3
[
[273.423, 1.01688979072, 38.13303563780],
[2.274, 2.36805657126, 36.64856292950],
[2.029, 5.33364321342, 76.26607127560],
[2.393, 0.00000000000, 0.00000000000],
[0.538, 3.21934211365, 39.61750834610],
[0.242, 4.52650721578, 114.39910691340],
[0.185, 1.04913770083, 74.78159856730],
[0.155, 3.62376309338, 35.16409022120],
[0.157, 3.94195369610, 1.48447270830],
],
# B4
[[5.728, 2.66872693322, 38.13303563780]],
# B5
[[0.113, 4.70646877989, 38.13303563780]],
]
"""This table contains Neptune'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 453."""
VSOP87_R = [
# R0
[
[3007013206.102, 0.00000000000, 0.00000000000],
[27062259.490, 1.32999458930, 38.13303563780],
[1691764.281, 3.25186138896, 36.64856292950],
[807830.737, 5.18592836167, 1.48447270830],
[537760.613, 4.52113902845, 35.16409022120],
[495725.642, 1.57105654815, 491.55792945680],
[274571.970, 1.84552256801, 175.16605980020],
[135134.095, 3.37220607384, 39.61750834610],
[121801.825, 5.79754444303, 76.26607127560],
[100895.397, 0.37702748681, 73.29712585900],
[69791.722, 3.79617226928, 2.96894541660],
[46687.838, 5.74937810094, 33.67961751290],
[24593.778, 0.50801728204, 109.94568878850],
[16939.242, 1.59422166991, 71.81265315070],
[14229.686, 1.07786112902, 74.78159856730],
[12011.825, 1.92062131635, 1021.24889455140],
[8394.731, 0.67816895547, 146.59425171800],
[7571.800, 1.07149263431, 388.46515523820],
[5720.852, 2.59059512267, 4.45341812490],
[4839.672, 1.90685991070, 41.10198105440],
[4483.492, 2.90573457534, 529.69096509460],
[4270.202, 3.41343865825, 453.42489381900],
[4353.790, 0.67985662370, 32.19514480460],
[4420.804, 1.74993796503, 108.46121608020],
[2881.063, 1.98600105123, 137.03302416240],
[2635.535, 3.09755943422, 213.29909543800],
[3380.930, 0.84810683275, 183.24281464750],
[2878.942, 3.67415901855, 350.33211960040],
[2306.293, 2.80962935724, 70.32818044240],
[2530.149, 5.79839567009, 490.07345674850],
[2523.132, 0.48630800015, 493.04240216510],
[2087.303, 0.61858378281, 33.94024994380],
[1976.522, 5.11703044560, 168.05251279940],
[1905.254, 1.72186472126, 182.27960680100],
[1654.039, 1.92782545887, 145.10977900970],
[1435.072, 1.70005157785, 484.44438245600],
[1403.029, 4.58914203187, 498.67147645760],
[1499.193, 1.01623299513, 219.89137757700],
[1398.860, 0.76220317620, 176.65053250850],
[1403.377, 6.07659416908, 173.68158709190],
[1128.560, 5.96661179805, 9.56122755560],
[1228.304, 1.59881465324, 77.75054398390],
[835.414, 3.97066884218, 114.39910691340],
[811.186, 3.00258880870, 46.20979048510],
[731.925, 2.10447054189, 181.75834193920],
[615.781, 2.97874625677, 106.97674337190],
[704.778, 1.18738210880, 256.53994050650],
[502.040, 1.38657803368, 5.93789083320],
[530.357, 4.24059166485, 111.43016149680],
[437.096, 2.27029212923, 1550.93985964600],
[400.250, 1.25609325435, 8.07675484730],
[421.011, 1.89084929506, 30.71067209630],
[382.457, 3.29965259685, 983.11585891360],
[422.485, 5.53186169605, 525.49817940060],
[355.389, 2.27847846648, 218.40690486870],
[280.062, 1.54129714238, 98.89998852460],
[314.499, 3.95932948594, 381.35160823740],
[280.556, 4.54238271682, 44.72531777680],
[267.738, 5.13323364247, 112.91463420510],
[333.311, 5.75067616021, 39.09624348430],
[291.625, 4.02398326341, 68.84370773410],
[321.429, 1.50625025822, 454.90936652730],
[309.196, 2.85452752153, 72.07328558160],
[345.094, 1.35905860594, 293.18850343600],
[307.439, 0.31964571332, 601.76425067620],
[251.356, 3.53992782846, 312.19908396260],
[248.152, 3.41078346726, 37.61177077600],
[306.000, 2.72475094464, 6244.94281435360],
[293.532, 4.89079857814, 528.20649238630],
[234.479, 0.59231043427, 42.58645376270],
[239.628, 3.16441455173, 143.62530630140],
[214.523, 3.62480283040, 278.25883401880],
[246.198, 1.01506302015, 141.22580985640],
[174.089, 5.55011789988, 567.82400073240],
[163.934, 2.10166491786, 2.44768055480],
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[3.345, 3.94392179077, 20389.92252949249],
[4.639, 6.24618220184, 821.39499582230],
[3.934, 0.26992234338, 1655.51710657290],
[4.431, 2.48647437800, 549.72844394250],
[4.168, 5.39993754642, 236.50246165860],
[4.020, 0.07393243012, 52136.18877480229],
[4.055, 1.34004288978, 1054.92851206430],
[3.275, 0.98533127454, 1344.75431120880],
[3.213, 2.97105590703, 20386.95358407589],
[4.428, 0.06728869735, 491.29729702590],
[4.063, 0.06192838570, 6168.67674307800],
[3.804, 5.34897033476, 523.75307426140],
[3.917, 5.67905809516, 1131.19458333990],
[3.833, 0.87811168267, 52.69019803950],
[4.020, 2.69209723289, 1439.46151403940],
[4.373, 1.86209663434, 73.55775828990],
[3.159, 1.04693380342, 703.37255218650],
[3.116, 5.20159166840, 449.23210812500],
[3.258, 4.65131076542, 696.25900518570],
[3.427, 0.27003884843, 2389.90914739640],
[4.349, 0.07531141761, 20426.57109242200],
[3.383, 5.61838426864, 699.22795060230],
[3.305, 1.41666877290, 562.14674233010],
[3.297, 5.46677712589, 1442.21801113490],
[3.277, 2.71815883511, 980.14691349700],
[3.171, 4.49510885866, 1439.24906571830],
[4.175, 4.24327707038, 381.61224066830],
[3.155, 3.40776789576, 39.72938293070],
[4.112, 0.90309319273, 1087.69310584050],
[3.350, 5.27474671017, 80.71948940050],
[3.725, 1.52448613082, 1058.10990580200],
[3.650, 3.59798316565, 192.80404220310],
[3.837, 1.48519528444, 10098.88643929760],
[2.959, 1.23012121982, 2500.11546861580],
[3.330, 6.12470287875, 10172.18356515660],
[3.361, 4.31837298696, 492.07919431860],
[3.288, 3.14692435376, 347.36317418380],
[2.992, 5.01304660316, 175.21424391000],
[3.294, 2.52694043155, 1692.16566950240],
[2.984, 1.81780659890, 175.11787569040],
[3.013, 0.92957285991, 1515.77576942480],
[3.863, 5.46044928570, 332.80601178210],
[3.403, 1.10932483984, 987.30864460760],
[3.312, 0.67710158807, 977.48678462110],
[3.030, 1.77996261146, 156489.28581380739],
[3.605, 4.89955108152, 1043.88281180040],
[2.937, 0.60469671230, 990.22940591440],
[3.276, 4.26765608367, 1189.30140735080],
[2.966, 5.29808076929, 31.98269648350],
[2.994, 2.58599359402, 178.08682110700],
[3.905, 1.87748122254, 1158.28191871380],
[3.110, 3.09203517638, 235.93301268700],
[3.313, 2.70308129756, 604.47256366190],
[3.276, 1.24440460327, 874.65464283340],
[3.276, 5.58544609667, 950.92071410900],
[3.746, 0.33859914037, 913.96333463880],
[3.552, 3.07180917863, 240.38643081190],
[2.885, 6.01130634957, 1097.51496582700],
[3.643, 5.11977873355, 452.20105354160],
[2.768, 4.38396269009, 391.43410065480],
[2.776, 5.01821594830, 8.90683624980],
[2.990, 5.62911695857, 140.65636088480],
[2.761, 4.05534163807, 6283.07584999140],
[3.226, 4.76711354367, 6241.97386893700],
[3.748, 4.84009347869, 341.73409989130],
[2.752, 4.53621078796, 6206.80977871580],
[3.847, 2.40982343643, 26086.41866886590],
[2.727, 3.28234198801, 483.48117460950],
[2.884, 4.05452029151, 1.22384027740],
[2.702, 3.72061244391, 946.46729598410],
[2.723, 4.37517047024, 15.19030184810],
[2.847, 5.22951186538, 661.04673085470],
[2.680, 4.19379121323, 13.18456427800],
[3.269, 0.43119778520, 496.97455542820],
[3.489, 3.82213189319, 625.99451521810],
[3.757, 3.88223872147, 495.70253104100],
[2.872, 5.00345974886, 252.08652238160],
[3.742, 2.03372773652, 8.59801970910],
[3.172, 1.11135762382, 260.99335863140],
[3.341, 2.91360557418, 304.23420369990],
[2.915, 2.63627684599, 6681.22485339960],
[2.915, 1.43773625890, 6604.95878212400],
[2.629, 2.09824407450, 2713.41456405380],
[2.901, 3.33924800230, 515.46387109300],
[2.803, 1.23584865903, 6643.09181776180],
[3.045, 3.33515866438, 921.07688163960],
[2.699, 5.42597794650, 925.26966733360],
[2.808, 5.77870303237, 1024.21783996800],
[3.028, 3.75501312393, 511.59540830470],
[3.090, 2.49453093252, 14.66903698630],
[2.913, 4.83296711477, 515.93695184500],
[3.139, 5.99134254710, 570.74476203920],
[2.752, 3.08268180744, 853.19638175200],
[2.779, 3.74527347899, 494.00561001160],
[2.643, 1.99093797444, 470.21728845440],
[2.763, 4.01095972177, 448.97147569410],
[2.643, 5.24970673655, 249.94765836750],
[3.426, 4.73955481174, 1050.99635880120],
[2.573, 2.01267457287, 1514.29129671650],
[2.633, 1.63640090603, 170.71264167530],
[3.034, 4.48979734509, 560.71045373160],
[3.025, 5.51446170055, 369.45457471160],
[3.095, 4.01459691667, 1615.89959822680],
[2.490, 0.15301603966, 78187.44335344699],
[2.589, 0.79196093766, 1228.91891569690],
[3.143, 5.33170343283, 1542.34183993690],
[3.138, 4.50785484172, 461.76228109720],
[2.812, 3.74246594120, 2.00573757010],
[3.062, 4.88018345098, 227.96813242430],
[2.553, 4.85437812287, 488.84961647110],
[2.971, 1.27359129352, 530.91480537200],
[2.646, 3.64828423565, 335.77495719870],
[3.329, 2.71693827722, 171.02145821600],
[2.648, 0.60243117586, 70.58881287330],
[3.061, 5.05044834864, 378.64329525170],
[2.738, 4.75405645015, 151.26011816400],
[2.728, 5.89052930055, 213.95348674380],
[3.411, 2.24137878065, 734.45573129830],
[2.623, 0.54340876464, 1586.10394986720],
[3.169, 5.84871429991, 1049.51188609290],
[2.430, 2.34595493263, 450.45594840240],
[2.907, 5.58085498481, 597.57146498220],
[3.300, 0.94221473935, 58.17051448570],
[2.543, 5.30426930256, 419.48464387520],
[3.175, 2.32600231924, 339.28641933650],
[2.858, 2.36621678719, 32.50396134530],
[2.712, 5.79983621237, 1587.58842257550],
[3.340, 1.36950315448, 384.27236954420],
[3.301, 5.83023910521, 51.77517430280],
[2.415, 0.69446923670, 489.55219188670],
[2.736, 5.74320864965, 1167.84314626940],
[2.956, 5.22962139507, 199.85389872910],
[3.262, 0.01501002027, 1545.31078535350],
[2.506, 4.84043333582, 943.49835056750],
[3.240, 2.46676155925, 1016.79547642650],
[3.148, 4.62079057738, 233.53351624200],
[2.327, 4.10421417326, 70.11573212130],
[2.371, 4.79963943424, 271.14528701800],
[3.006, 3.66877796077, 1476.15826107870],
[2.537, 5.66681769885, 21.14944454070],
[3.006, 0.93048909480, 21.97952594320],
[3.033, 0.67157488690, 292.48592802040],
[2.344, 1.83547256266, 492.30868898220],
[3.117, 2.76268894894, 1473.18931566210],
[2.323, 2.88799980853, 533.62311835770],
[2.340, 4.44862573253, 490.80716993140],
[2.511, 0.99467349084, 266.10116806210],
[2.919, 4.75889516601, 1511.32235129990],
[2.493, 6.10541658597, 1225.94997028030],
[2.798, 3.06162629894, 419.74527630610],
[2.691, 3.20679023131, 463.50738623640],
[2.291, 5.81534758547, 246.97871295090],
[2.319, 6.05514281470, 525.75881183150],
[3.112, 0.89712836583, 314.90739694830],
[3.085, 5.84605938859, 1192.22216865760],
[2.897, 0.54747024257, 20350.30502114640],
[3.067, 2.22206306288, 248.46318565920],
[2.252, 0.87483094907, 61.02758531770],
[2.392, 3.62837597194, 439.19779981740],
[2.817, 2.73562306571, 16.67477455640],
[2.379, 6.17876088396, 467.65198782060],
[2.598, 4.82643304253, 384.58118608490],
[2.718, 1.01823841209, 215.95922431390],
[2.998, 1.09755715300, 1964.74724511890],
[2.884, 2.97813466834, 383.09671337660],
[2.231, 4.48841493844, 4.14460158420],
[2.203, 2.23336308907, 481.26298871830],
[2.260, 2.35404913660, 659.61044225620],
[2.491, 1.70236357070, 445.34813897170],
[3.041, 5.55577674116, 674.80074410430],
[2.289, 1.18497528002, 1552.42433235430],
[2.975, 0.48272389481, 1052.48083150950],
[2.339, 0.75318738767, 478.81530816350],
[3.011, 0.16359500858, 54.28654533240],
[2.820, 6.18522693724, 556.51766803760],
[2.266, 5.91286000054, 3.49021027840],
[2.231, 1.45038594906, 196.50670080260],
],
# R1
[
[236338.502, 0.70498011235, 38.13303563780],
[13220.279, 3.32015499895, 1.48447270830],
[8621.863, 6.21628951630, 35.16409022120],
[2701.740, 1.88140666779, 39.61750834610],
[2153.150, 5.16873840979, 76.26607127560],
[2154.735, 2.09431198086, 2.96894541660],
[1463.924, 1.18417031047, 33.67961751290],
[1603.165, 0.00000000000, 0.00000000000],
[1135.773, 3.91891199655, 36.64856292950],
[897.650, 5.24122933533, 388.46515523820],
[789.908, 0.53315484580, 168.05251279940],
[760.030, 0.02051033644, 182.27960680100],
[607.183, 1.07706500350, 1021.24889455140],
[571.622, 3.40060785432, 484.44438245600],
[560.790, 2.88685815667, 498.67147645760],
[490.190, 3.46830928696, 137.03302416240],
[264.093, 0.86220057976, 4.45341812490],
[270.526, 3.27355867939, 71.81265315070],
[203.524, 2.41820674409, 32.19514480460],
[155.438, 0.36537064534, 41.10198105440],
[132.766, 3.60157672619, 9.56122755560],
[93.626, 0.66670888163, 46.20979048510],
[83.317, 3.25992461673, 98.89998852460],
[72.205, 4.47717435693, 601.76425067620],
[68.983, 1.46326969479, 74.78159856730],
[86.953, 5.77228651853, 381.35160823740],
[68.717, 4.52563942435, 70.32818044240],
[64.724, 3.85477388838, 73.29712585900],
[68.377, 3.39509945953, 108.46121608020],
[53.375, 5.43650770516, 395.57870223900],
[44.453, 3.61409723545, 2.44768055480],
[41.243, 4.73866592865, 8.07675484730],
[48.331, 1.98568593981, 175.16605980020],
[41.744, 4.94257598763, 31.01948863700],
[44.102, 1.41744904844, 1550.93985964600],
[41.170, 1.41999374753, 490.07345674850],
[41.099, 4.86312637841, 493.04240216510],
[36.267, 5.30764043577, 312.19908396260],
[36.284, 0.38187812797, 77.75054398390],
[40.619, 2.27237172464, 529.69096509460],
[32.360, 5.91123007786, 5.93789083320],
[31.197, 2.70549944134, 1014.13534755060],
[32.730, 5.22147683115, 41.05379694460],
[36.079, 4.87817494829, 491.55792945680],
[30.181, 3.63273193845, 30.71067209630],
[29.991, 3.30769367603, 1028.36244155220],
[27.048, 1.77647060739, 44.72531777680],
[27.756, 4.55583165091, 7.11354700080],
[27.475, 0.97228280623, 33.94024994380],
[24.944, 3.10083391185, 144.14657116320],
[25.958, 2.99724758632, 60.76695288680],
[21.369, 4.71270048898, 278.25883401880],
[21.283, 0.68957829113, 251.43213107580],
[23.727, 5.12044184469, 176.65053250850],
[21.392, 0.86286397645, 4.19278569400],
[23.373, 1.64955088447, 173.68158709190],
[24.163, 3.56602004577, 145.10977900970],
[20.238, 5.61479765982, 24.11838995730],
[26.958, 4.14294870704, 453.42489381900],
[24.048, 1.00718363213, 213.29909543800],
[18.322, 1.98028683488, 72.07328558160],
[18.266, 6.17260374467, 189.39315380180],
[19.201, 4.65162168927, 106.97674337190],
[17.606, 1.60307551767, 62.25142559510],
[16.545, 1.69931816587, 357.44566660120],
[20.132, 3.29520553529, 114.39910691340],
[15.425, 4.38812302799, 25.60286266560],
[19.173, 2.20014267311, 343.21857259960],
[15.077, 3.66802659382, 0.52126486180],
[14.029, 0.55336333290, 129.91947716160],
[13.361, 5.85751083720, 68.84370773410],
[15.357, 4.20731277007, 567.82400073240],
[12.746, 3.52815836608, 477.33083545520],
[11.724, 5.57647263460, 31.23193695810],
[11.533, 0.89138506506, 594.65070367540],
[10.508, 4.35552732772, 32.71640966640],
[10.826, 5.21826226871, 26.82670294300],
[10.085, 1.98102855874, 40.58071619260],
[10.518, 5.27281360238, 2.92076130680],
[9.207, 0.50092534158, 64.95973858080],
[9.231, 0.68180977710, 160.93896579860],
[8.735, 5.80657503476, 6.59228213900],
[10.114, 4.51164596694, 28.57180808220],
[10.392, 5.18877536013, 42.58645376270],
[9.873, 3.76512158080, 181.75834193920],
[8.350, 2.82449631025, 43.24084506850],
[9.838, 1.49438763600, 47.69426319340],
[7.645, 4.07503370297, 389.94962794650],
[8.004, 2.78082277326, 505.78502345840],
[7.440, 2.35731983047, 11.04570026390],
[7.342, 1.62279119952, 135.54855145410],
[9.450, 0.27241261915, 426.59819087600],
[7.192, 0.82841201068, 911.04257333200],
[6.979, 1.86753914872, 206.18554843720],
[6.874, 0.83802906828, 82.85835341460],
[7.897, 1.86554246391, 38.65430049960],
[6.729, 3.98338053636, 12.53017297220],
[6.357, 0.90093123522, 487.36514376280],
[6.720, 1.33936040700, 220.41264243880],
[7.695, 5.13312500855, 23.90594163620],
[7.059, 5.99832463494, 639.89728631400],
[8.302, 3.85960902325, 37.61177077600],
[6.412, 2.41743702679, 1059.38193018920],
[6.751, 1.96860894470, 45.24658263860],
[6.431, 4.07813226506, 35.68535508300],
[5.517, 3.81325790890, 815.06334611420],
[5.562, 0.41619602150, 563.63121503840],
[6.115, 2.10934525342, 697.74347789400],
[6.216, 4.79301628209, 143.62530630140],
[5.346, 3.13071964722, 386.98068252990],
[5.245, 6.06245070403, 171.23390653710],
[5.129, 0.79394555531, 179.09821306330],
[5.168, 4.73765992885, 522.57741809380],
[6.422, 0.64684316894, 350.33211960040],
[5.006, 2.37645082899, 77.22927912210],
[5.005, 4.70632786971, 460.53844081980],
[5.167, 5.20246616570, 446.31134681820],
[5.119, 2.17338058771, 494.73932319450],
[5.025, 4.21265519856, 536.80451209540],
[4.722, 6.22814313946, 63.73589830340],
[5.125, 5.38138329172, 179.31066138440],
[4.918, 4.09031782903, 488.37653571910],
[4.652, 5.10765073368, 274.06604832480],
[4.711, 5.56542374115, 42.32582133180],
[4.459, 1.30784829830, 69.36497259590],
[5.485, 3.88088464259, 218.40690486870],
[4.416, 3.05353893868, 27.08733537390],
[4.559, 4.92224120952, 285.37238101960],
[4.393, 4.18047835584, 5.41662597140],
[4.687, 2.21401153210, 1029.84691426050],
[4.644, 1.87902594973, 1433.61999142580],
[5.639, 3.05596737234, 983.11585891360],
[6.045, 5.68817982786, 351.81659230870],
[4.430, 3.37768805833, 377.41945497430],
[4.683, 2.14346624864, 97.41551581630],
[5.845, 4.62301099402, 1024.21783996800],
[4.536, 2.45860473853, 496.01134758170],
[4.398, 5.65312496227, 3.93215326310],
[4.287, 0.66340266603, 1012.65087484230],
[4.086, 0.14551174994, 385.28376150050],
[4.029, 5.98399329775, 178.34745353790],
[4.276, 3.68205082970, 348.84764689210],
[5.257, 3.75263242432, 379.86713552910],
[4.012, 0.42559540783, 104313.47953065898],
[4.025, 2.40645188238, 84.34282612290],
[3.957, 0.86846121055, 171.98466606250],
[3.961, 3.04953080906, 1017.31674128830],
[5.559, 0.77714806229, 1447.84708542740],
[5.071, 2.61075526868, 1536.71276564440],
[4.052, 5.00014006312, 391.64654897590],
[5.182, 4.73444634983, 382.83608094570],
[3.763, 4.29449373755, 313.68355667090],
[4.038, 2.82857942788, 1661.14618086540],
[4.067, 5.73169928960, 169.53698550770],
[3.841, 1.62580928420, 0.96320784650],
[3.901, 2.70874386576, 14.01464568050],
[3.721, 1.20062375429, 1026.87796884390],
[3.911, 3.01809123569, 100.38446123290],
[3.489, 4.28865448963, 1025.18104781450],
[3.714, 5.05021268365, 292.48592802040],
[3.816, 3.93084933114, 39.09624348430],
[3.988, 2.82832650224, 134.11226285560],
[3.745, 4.24728135115, 180.79513409270],
[3.836, 1.02685786071, 1018.27994913480],
[3.941, 5.21895739331, 183.76407950930],
[4.669, 4.38080962573, 1066.49547719000],
[3.780, 6.03723468132, 1022.73336725970],
[3.647, 3.98130320367, 608.87779767700],
[3.456, 5.54052355058, 846.08283475120],
[4.047, 3.71041480907, 1018.06750081370],
[3.865, 4.76002199091, 166.56804009110],
[3.629, 3.29053233846, 447.79581952650],
[3.564, 4.36703678321, 397.06317494730],
[3.304, 1.49289552229, 1505.69327700740],
[3.976, 2.42476188945, 106.01353552540],
[4.217, 4.21677652639, 1052.26838318840],
[3.294, 0.42088065654, 22.63391724900],
[3.615, 3.68096122231, 494.52687487340],
[3.230, 5.10786091356, 69.15252427480],
[3.280, 3.62226152032, 531.17543780290],
[3.337, 2.72502876320, 481.47543703940],
[3.187, 0.08677634706, 399.51085550210],
[3.389, 1.79454271219, 1519.92037100900],
[3.179, 3.40418030121, 423.62924545940],
[3.154, 3.69356460843, 470.21728845440],
[3.706, 2.79048710497, 462.02291352810],
[3.136, 4.38015969606, 385.49620982160],
[3.122, 0.48346644637, 79.18683258240],
[3.392, 0.48037804731, 521.09294538550],
[3.465, 0.93152295589, 2183.72359895920],
[3.735, 0.98809808606, 487.41332787260],
[3.998, 3.38773325131, 6283.07584999140],
[2.998, 2.61728063127, 487.62577619370],
[3.295, 2.53821501556, 4.66586644600],
[2.964, 3.66274645375, 495.49008271990],
[3.901, 1.65463523144, 210.33015002140],
[2.950, 1.99904237956, 872.90953769420],
[2.948, 2.90769224206, 391.43410065480],
[2.971, 0.31626092637, 5.10780943070],
[3.085, 0.95725590904, 109.94568878850],
[2.995, 3.34433305798, 394.09422953070],
[3.126, 5.89472116854, 105.49227066360],
[3.904, 3.01022809543, 556.51766803760],
[3.388, 6.24936444215, 535.32003938710],
[2.930, 6.15005257333, 164.12035953630],
[3.267, 4.19718045293, 518.38463239980],
[3.946, 2.88842759670, 151.26011816400],
[3.076, 6.04134449219, 142.14083359310],
[2.823, 0.60712626756, 214.78356814630],
[2.917, 2.74502617182, 138.51749687070],
[3.347, 6.09373507569, 6246.42728706190],
[3.659, 5.12211619716, 79.23501669220],
[3.010, 0.24656411754, 91.78644152380],
[2.861, 6.17465663902, 422.40540518200],
[2.989, 2.31620917965, 485.92885516430],
[3.088, 2.29186342974, 110.20632121940],
[3.030, 3.69866149100, 532.61172640140],
[3.020, 2.36422658177, 290.21955801940],
[3.170, 1.23078934548, 10176.63698328150],
[2.652, 3.35836234807, 148.07872442630],
[2.673, 6.03366372927, 196.50670080260],
[2.630, 0.46957619348, 1970.42450352120],
[2.599, 4.86022081674, 439.19779981740],
[2.878, 2.61946597178, 488.58898404020],
[2.720, 1.71836225398, 364.55921360200],
[3.333, 3.25126857354, 30.05628079050],
[3.053, 2.49346960035, 6243.45834164530],
[3.062, 6.23776299963, 419.48464387520],
[2.786, 0.83078219939, 497.18700374930],
[2.834, 3.52926079424, 457.87831194390],
[2.932, 1.80245810977, 500.15594916590],
[3.030, 5.10152500393, 367.97010200330],
[2.956, 5.76230870725, 986.08480433020],
[3.116, 2.20042242739, 495.70253104100],
[2.554, 0.65945973992, 67.35923502580],
[2.901, 3.91891656185, 10173.66803786490],
[2.840, 1.34453183591, 482.95990974770],
[2.458, 1.20012815574, 489.11024890200],
[2.556, 3.86921927085, 487.10451133190],
[2.614, 1.51881085312, 463.50738623640],
[2.386, 4.58400538443, 615.99134467780],
[2.438, 5.19827220476, 501.11915701240],
[2.537, 1.64802783144, 519.60847267720],
[2.444, 3.87859489652, 185.24855221760],
[2.795, 4.04265752580, 255.05546779820],
[2.895, 3.26202698812, 1646.91908686380],
[2.225, 5.75197574692, 605.95703637020],
[2.324, 3.99503920129, 481.26298871830],
[2.962, 1.74151265966, 2080.63082474060],
[2.621, 1.74442251671, 35.21227433100],
],
# R2
[
[4247.412, 5.89910679117, 38.13303563780],
[217.570, 0.34581829080, 1.48447270830],
[163.025, 2.23872947130, 168.05251279940],
[156.285, 4.59414467342, 182.27960680100],
[117.940, 5.10295026024, 484.44438245600],
[112.429, 1.19000583596, 498.67147645760],
[127.141, 2.84786298079, 35.16409022120],
[99.467, 3.41578558739, 175.16605980020],
[64.814, 3.46214064840, 388.46515523820],
[77.286, 0.01659281785, 491.55792945680],
[49.509, 4.06995509133, 76.26607127560],
[39.330, 6.09521855958, 1021.24889455140],
[36.450, 5.17130059988, 137.03302416240],
[37.080, 5.97288967681, 2.96894541660],
[30.484, 3.58259801313, 33.67961751290],
[21.099, 0.76843555176, 36.64856292950],
[13.886, 3.59248623971, 395.57870223900],
[13.117, 5.09263515697, 98.89998852460],
[11.379, 1.18060018898, 381.35160823740],
[9.132, 2.34787658568, 601.76425067620],
[8.527, 5.25134685897, 2.44768055480],
[8.136, 4.96270726986, 4.45341812490],
[7.417, 4.46775409796, 189.39315380180],
[7.225, 1.92287508629, 9.56122755560],
[7.289, 1.65519525780, 1028.36244155220],
[8.076, 5.84268048311, 220.41264243880],
[9.654, 0.00000000000, 0.00000000000],
[6.554, 0.69397520733, 144.14657116320],
[7.782, 1.14341656235, 1059.38193018920],
[5.665, 6.25378258571, 74.78159856730],
[5.628, 5.23383764266, 46.20979048510],
[5.523, 4.59041448911, 1014.13534755060],
[5.177, 5.23116646157, 477.33083545520],
[5.503, 3.49522319102, 183.76407950930],
[4.878, 3.52934357721, 39.61750834610],
[4.787, 2.08260524745, 41.10198105440],
[5.055, 0.19949888617, 166.56804009110],
[4.751, 1.18054948270, 169.53698550770],
[4.747, 1.50608965076, 73.29712585900],
[6.113, 6.18326155595, 71.81265315070],
[4.606, 3.91970908886, 587.53715667460],
[5.756, 2.23667359233, 176.65053250850],
[4.536, 2.84337336954, 7.11354700080],
[4.338, 0.51553847388, 446.31134681820],
[3.891, 0.26338839265, 1550.93985964600],
[4.465, 3.01487041298, 129.91947716160],
[3.727, 2.37977930658, 160.93896579860],
[3.840, 3.79290381880, 111.43016149680],
[4.142, 1.70293820961, 983.11585891360],
[3.296, 1.07748822909, 505.78502345840],
[4.008, 0.30663868827, 494.73932319450],
[3.974, 5.97351783840, 488.37653571910],
[3.925, 4.85736421123, 60.76695288680],
[2.966, 2.01608546009, 822.17689311500],
[3.972, 1.07780371834, 374.23806123660],
[3.843, 5.23002047199, 350.33211960040],
[2.848, 6.17799253802, 704.85702489480],
[3.527, 0.79317138165, 274.06604832480],
[2.828, 1.32275775835, 386.98068252990],
[2.773, 5.37132330836, 251.43213107580],
[3.113, 5.12622288690, 426.59819087600],
[3.344, 5.61433537548, 1124.34166877000],
[2.597, 0.67759426519, 312.19908396260],
[2.581, 3.55847612121, 567.82400073240],
[2.578, 1.45603792456, 1035.47598855300],
[2.541, 5.19427579702, 1227.43444298860],
[2.510, 4.12148891512, 171.23390653710],
[2.511, 2.71606957319, 179.09821306330],
[2.342, 0.96469916587, 1019.76442184310],
[2.500, 0.70282276030, 707.77778620160],
[2.480, 4.59623030219, 693.55069220000],
[2.253, 0.74334306011, 976.00231191280],
],
# R3
[
[166.297, 4.55243893489, 38.13303563780],
[22.380, 3.94830879358, 168.05251279940],
[21.348, 2.86296778794, 182.27960680100],
[16.233, 0.54226725872, 484.44438245600],
[15.623, 5.75702251906, 498.67147645760],
[11.867, 4.40280192710, 1.48447270830],
[6.448, 5.19003066847, 31.01948863700],
[3.655, 5.91335292846, 1007.02180054980],
[3.681, 1.62865545676, 388.46515523820],
[3.198, 0.70197118575, 1558.05340664680],
[3.243, 1.88035665980, 522.57741809380],
[3.269, 2.94301808574, 76.26607127560],
[2.688, 1.87062743473, 402.69224923980],
[3.246, 0.79381356193, 536.80451209540],
[2.650, 5.76858449026, 343.21857259960],
[2.644, 4.64542905401, 500.15594916590],
[2.541, 4.79217120822, 482.95990974770],
[2.523, 1.72869889780, 395.57870223900],
[2.690, 2.21096415618, 446.31134681820],
[2.355, 5.77381398401, 485.92885516430],
[2.874, 6.19643340540, 815.06334611420],
[2.278, 3.66579603119, 497.18700374930],
],
# R4
[
[4.227, 2.40375758563, 477.33083545520],
[4.333, 0.10459484545, 395.57870223900],
[3.545, 4.78431259422, 1028.36244155220],
[3.154, 3.88192942366, 505.78502345840],
[3.016, 1.03609346831, 189.39315380180],
[2.294, 1.10879658603, 182.27960680100],
[2.295, 5.67776133184, 168.05251279940],
],
]
"""This table contains Neptune'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
page 454."""
ORBITAL_ELEM = [
[304.348665, 219.8833092, 0.00030882, 0.000000018], # L
[30.110386869, -0.0000001663, 0.00000000069, 0.0], # a
[0.00945575, 0.000006033, 0.0, -0.00000000005], # e
[1.769953, -0.0093082, -0.00000708, 0.000000027], # i
[131.748057, 1.1022039, 0.00025952, -0.000000637], # Omega
[48.120276, 1.4262957, 0.00038434, 0.00000002] # pie
]
"""This table contains the parameters to compute Neptune's orbital elements for
the mean equinox of date. Based in Table 31.A, page 213"""
ORBITAL_ELEM_J2000 = [
[304.348665, 218.4862002, 0.00000059, -0.000000002], # L
[1.769953, 0.0002256, 0.00000023, 0.0], # i
[131.748057, -0.0061651, -0.00000219, -0.000000078], # Omega
[48.120276, 0.0291866, 0.0000761, 0.0] # pie
]
"""This table contains the parameters to compute Neptune's orbital elements for
the standard equinox J2000.0. Based on Table 31.B, page 215"""
[docs]class Neptune(object):
"""
Class Neptune models that planet.
"""
[docs] @staticmethod
def geometric_heliocentric_position(epoch, tofk5=True):
"""This method computes the geometric heliocentric position of planet
Neptune for a given epoch, using the VSOP87 theory.
:param epoch: Epoch to compute Neptune position, as an Epoch object
:type epoch: :py:class:`Epoch`
:param tofk5: Whether or not the small correction to convert to the FK5
system will be applied or not
:type tofk5: bool
:returns: A tuple with the heliocentric longitude and latitude (as
:py:class:`Angle` objects), and the radius vector (as a float,
in astronomical units), in that order
:rtype: tuple
:raises: TypeError if input values are of wrong type.
>>> epoch = Epoch(2018, 10, 27.0)
>>> l, b, r = Neptune.geometric_heliocentric_position(epoch)
>>> print(round(l.to_positive(), 4))
345.3776
>>> print(round(b, 4))
-0.9735
>>> print(round(r, 5))
29.93966
"""
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
Neptune for a given epoch, using the VSOP87 theory.
:param epoch: Epoch to compute Neptune position, as an Epoch object
:type epoch: :py:class:`Epoch`
:returns: A tuple with the heliocentric longitude and latitude (as
:py:class:`Angle` objects), and the radius vector (as a float,
in astronomical units), in that order
:rtype: tuple
:raises: TypeError if input values are of wrong type.
"""
return apparent_vsop_pos(epoch, VSOP87_L, VSOP87_B, VSOP87_R)
[docs] @staticmethod
def orbital_elements_mean_equinox(epoch):
"""This method computes the orbital elements of Neptune for the mean
equinox of the date for a given epoch.
:param epoch: Epoch to compute orbital elements, as an Epoch object
:type epoch: :py:class:`Epoch`
:returns: A tuple containing the following six orbital elements:
- Mean longitude of the planet (Angle)
- Semimajor axis of the orbit (float, astronomical units)
- eccentricity of the orbit (float)
- inclination on the plane of the ecliptic (Angle)
- longitude of the ascending node (Angle)
- argument of the perihelion (Angle)
:rtype: tuple
:raises: TypeError if input values are of wrong type.
>>> epoch = Epoch(2065, 6, 24.0)
>>> l, a, e, i, ome, arg = Neptune.orbital_elements_mean_equinox(epoch)
>>> print(round(l, 6))
88.321947
>>> print(round(a, 8))
30.11038676
>>> print(round(e, 7))
0.0094597
>>> print(round(i, 6))
1.763855
>>> print(round(ome, 5))
132.46986
>>> print(round(arg, 6))
-83.415521
"""
return orbital_elements(epoch, ORBITAL_ELEM, ORBITAL_ELEM)
[docs] @staticmethod
def orbital_elements_j2000(epoch):
"""This method computes the orbital elements of Neptune for the
standard equinox J2000.0 for a given epoch.
:param epoch: Epoch to compute orbital elements, as an Epoch object
:type epoch: :py:class:`Epoch`
:returns: A tuple containing the following six orbital elements:
- Mean longitude of the planet (Angle)
- Semimajor axis of the orbit (float, astronomical units)
- eccentricity of the orbit (float)
- inclination on the plane of the ecliptic (Angle)
- longitude of the ascending node (Angle)
- argument of the perihelion (Angle)
:rtype: tuple
:raises: TypeError if input values are of wrong type.
>>> epoch = Epoch(2065, 6, 24.0)
>>> l, a, e, i, ome, arg = Neptune.orbital_elements_j2000(epoch)
>>> print(round(l, 6))
87.407029
>>> print(round(a, 8))
30.11038676
>>> print(round(e, 7))
0.0094597
>>> print(round(i, 6))
1.770101
>>> print(round(ome, 5))
131.74402
>>> print(round(arg, 6))
-83.6046
"""
return orbital_elements(epoch, ORBITAL_ELEM, ORBITAL_ELEM_J2000)
[docs] @staticmethod
def geocentric_position(epoch):
"""This method computes the geocentric position of Neptune (right
ascension and declination) for the given epoch, as well as the
elongation angle.
:param epoch: Epoch to compute geocentric position, as an Epoch object
:type epoch: :py:class:`Epoch`
:returns: A tuple containing the right ascension, the declination and
the elongation angle as Angle objects
:rtype: tuple
:raises: TypeError if input value is of wrong type.
>>> epoch = Epoch(1992, 12, 20.0)
>>> ra, dec, elon = Neptune.geocentric_position(epoch)
>>> print(ra.ra_str(n_dec=1))
19h 17' 14.5''
>>> print(dec.dms_str(n_dec=1))
-21d 34' 15.1''
>>> print(elon.dms_str(n_dec=1))
19d 44' 59.6''
"""
# First check that input value is of correct types
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input type")
# Compute the heliocentric position of Neptune
l, b, r = Neptune.geometric_heliocentric_position(epoch, tofk5=False)
# Compute the heliocentric position of the Earth
l0, b0, r0 = Earth.geometric_heliocentric_position(epoch, tofk5=False)
# Convert to radians
lr = l.rad()
br = b.rad()
l0r = l0.rad()
b0r = b0.rad()
# Compute first iteration
x = r * cos(br) * cos(lr) - r0 * cos(b0r) * cos(l0r)
y = r * cos(br) * sin(lr) - r0 * cos(b0r) * sin(l0r)
z = r * sin(br) - r0 * sin(b0r)
delta = sqrt(x * x + y * y + z * z)
tau = 0.0057755183 * delta
# Adjust the epoch for light-time
epoch -= tau
# Compute again Neptune coordinates with this correction
l, b, r = Neptune.geometric_heliocentric_position(epoch, tofk5=False)
# Compute second iteration
lr = l.rad()
br = b.rad()
x = r * cos(br) * cos(lr) - r0 * cos(b0r) * cos(l0r)
y = r * cos(br) * sin(lr) - r0 * cos(b0r) * sin(l0r)
z = r * sin(br) - r0 * sin(b0r)
# Compute longitude and latitude
lamb = atan2(y, x)
beta = atan2(z, sqrt(x * x + y * y))
# Now, let's compute the aberration effect
t = (epoch - JDE2000) / 36525
e = 0.016708634 + t * (-0.000042037 - t * 0.0000001267)
pie = 102.93735 + t * (1.71946 + t * 0.00046)
pie = radians(pie)
lon = l0 + 180.0
lon = lon.rad()
k = 20.49552 # The constant of aberration
deltal1 = k * (-cos(lon - lamb) + e * cos(pie - lamb)) / cos(beta)
deltab1 = -k * sin(beta) * (sin(lon - lamb) - e * sin(pie - lamb))
deltal1 = Angle(0, 0, deltal1)
deltab1 = Angle(0, 0, deltab1)
# Correction to FK5 system
lamb = Angle(lamb, radians=True)
lamb = lamb.to_positive()
beta = Angle(beta, radians=True)
l_prime = lamb - t * (1.397 + t * 0.00031)
deltal2 = Angle(0, 0, -0.09033)
a = 0.03916 * (cos(l_prime.rad()) + sin(l_prime.rad()))
a = a * tan(b.rad())
deltal2 += Angle(0, 0, a)
deltab2 = 0.03916 * (cos(l_prime.rad()) - sin(l_prime.rad()))
deltab2 = Angle(0, 0, deltab2)
# Apply the corrections
lamb = lamb + deltal1 + deltal2
beta = beta + deltab1 + deltab2
# Correction for nutation
dpsi = nutation_longitude(epoch)
lamb += dpsi
e = true_obliquity(epoch)
ra, dec = ecliptical2equatorial(lamb, beta, e)
# Let's compute the elongation angle
lons, lats, rs = Sun.apparent_geocentric_position(epoch)
lambr = lamb.rad()
lsr = lons.rad()
betar = beta.rad()
elon = acos(cos(betar) * cos(lambr - lsr))
elon = Angle(elon, radians=True)
return ra, dec, elon
[docs] @staticmethod
def conjunction(epoch):
"""This method computes the time of the conjunction closest to the
given epoch.
:param epoch: Epoch close to the desired conjunction
:type epoch: :py:class:`Epoch`
:returns: The time when the conjunction happens, as an Epoch
:rtype: :py:class:`Epoch`
:raises: TypeError if input value is of wrong type.
:raises: ValueError if input epoch outside the -2000/4000 range.
>>> epoch = Epoch(1993, 10, 1.0)
>>> conj = Neptune.conjunction(epoch)
>>> y, m, d = conj.get_date()
>>> print(y)
1994
>>> print(m)
1
>>> print(round(d, 4))
11.3057
"""
# First check that input value is of correct types
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input type")
# Check that the input epoch is within valid range
y = epoch.year()
if y < -2000.0 or y > 4000.0:
raise ValueError("Epoch outside the -2000/4000 range")
# Set some specific constants for Neptune's conjunction
a = 2451569.379
b = 367.486703
m0 = 21.5569
m1 = 2.194998
k = round((365.2425 * y + 1721060.0 - a) / b)
jde0 = a + k * b
m = m0 + k * m1
m = Angle(m).to_positive()
m = m.rad()
t = (jde0 - 2451545.0) / 36525.0
# Compute a couple auxiliary angles
ee = 207.83 + 8.51 * t
gg = 276.74 + 209.98 * t
# Convert to radians
ee = Angle(ee).rad()
gg = Angle(gg).rad()
corr = (0.0168
+ sin(m) * (-2.5606 + t * (0.0088 + t * 0.00002))
+ cos(m) * (-0.8611 + t * (-0.0037 + t * 0.00002))
+ sin(2.0 * m) * (0.0118 + t * (-0.0004 + t * 0.00001))
+ cos(2.0 * m) * (0.0307 - t * 0.0003)
+ cos(ee) * (-0.5964)
+ cos(gg) * (0.0728))
to_return = jde0 + corr
return Epoch(to_return)
[docs] @staticmethod
def opposition(epoch):
"""This method computes the time of the opposition closest to the given
epoch.
:param epoch: Epoch close to the desired opposition
:type epoch: :py:class:`Epoch`
:returns: The time when the opposition happens, as an Epoch
:rtype: :py:class:`Epoch`
:raises: TypeError if input value is of wrong type.
:raises: ValueError if input epoch outside the -2000/4000 range.
>>> epoch = Epoch(1846, 8, 1)
>>> oppo = Neptune.opposition(epoch)
>>> y, m, d = oppo.get_date()
>>> print(y)
1846
>>> print(m)
8
>>> print(round(d, 4))
20.1623
"""
# First check that input value is of correct types
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input type")
# Check that the input epoch is within valid range
y = epoch.year()
if y < -2000.0 or y > 4000.0:
raise ValueError("Epoch outside the -2000/4000 range")
# Set some specific constants for Neptune's opposition
a = 2451753.122
b = 367.486703
m0 = 202.6544
m1 = 2.194998
k = round((365.2425 * y + 1721060.0 - a) / b)
jde0 = a + k * b
m = m0 + k * m1
m = Angle(m).to_positive()
m = m.rad()
t = (jde0 - 2451545.0) / 36525.0
# Compute a couple auxiliary angles
ee = 207.83 + 8.51 * t
gg = 276.74 + 209.98 * t
# Convert to radians
ee = Angle(ee).rad()
gg = Angle(gg).rad()
corr = (-0.014 + t * t * 0.00001
+ sin(m) * (-1.3486 + t * (0.001 + t * 0.00001))
+ cos(m) * (0.8597 + t * 0.0037)
+ sin(2.0 * m) * (-0.0082 + t * (-0.0002 + t * 0.00001))
+ cos(2.0 * m) * (0.0037 - t * 0.0003)
+ cos(ee) * (-0.5964)
+ cos(gg) * (0.0728))
to_return = jde0 + corr
return Epoch(to_return)
[docs] @staticmethod
def magnitude(sun_dist, earth_dist):
"""This function computes the approximate magnitude of Neptune.
:param sun_dist: Distance from Neptune to Sun, in Astronomical Units
:type sun_dist: float
:param earth_dist: Distance Neptune to Earth, in Astronomical Units
:type earth_dist: float
:returns: Neptune's magnitude
:rtype: float
:raises: TypeError if input values are of wrong type.
"""
if not (isinstance(sun_dist, float) and isinstance(earth_dist, float)):
raise TypeError("Invalid input types")
m = -7.05 + 5.0 * log10(sun_dist * earth_dist)
return round(m, 1)
def main():
# Let's define a small helper function
def print_me(msg, val):
print("{}: {}".format(msg, val))
# Let's show some uses of Neptune class
print("\n" + 35 * "*")
print("*** Use of Neptune class")
print(35 * "*" + "\n")
# Let's now compute the heliocentric position for a given epoch
epoch = Epoch(2018, 10, 27.0)
lon, lat, r = Neptune.geometric_heliocentric_position(epoch)
print_me("Geometric Heliocentric Longitude", lon.to_positive())
print_me("Geometric Heliocentric Latitude", lat)
print_me("Radius vector", r)
print("")
# Compute the geocentric position for 1992/12/20:
epoch = Epoch(1992, 12, 20.0)
ra, dec, elon = Neptune.geocentric_position(epoch)
print_me("Right ascension", ra.ra_str(n_dec=1))
print_me("Declination", dec.dms_str(n_dec=1))
print_me("Elongation", elon.dms_str(n_dec=1))
print("")
# Print mean orbital elements for Neptune at 2065.6.24
epoch = Epoch(2065, 6, 24.0)
l, a, e, i, ome, arg = Neptune.orbital_elements_mean_equinox(epoch)
print_me("Mean longitude of the planet", round(l, 6)) # 88.321947
print_me("Semimajor axis of the orbit (UA)", round(a, 8)) # 30.11038676
print_me("Eccentricity of the orbit", round(e, 7)) # 0.0094597
print_me("Inclination on plane of the ecliptic", round(i, 6)) # 1.763855
print_me("Longitude of the ascending node", round(ome, 5)) # 132.46986
print_me("Argument of the perihelion", round(arg, 6)) # -83.415521
print("")
# Compute the time of the conjunction close to 1993/10/1
epoch = Epoch(1993, 10, 1.0)
conj = Neptune.conjunction(epoch)
y, m, d = conj.get_date()
d = round(d, 4)
date = "{}/{}/{}".format(y, m, d)
print_me("Conjunction date", date)
# Compute the time of the opposition close to 1846/8/1
epoch = Epoch(1846, 8, 1)
oppo = Neptune.opposition(epoch)
y, m, d = oppo.get_date()
d = round(d, 4)
date = "{}/{}/{}".format(y, m, d)
print_me("Opposition date", date)
if __name__ == "__main__":
main()