4662 lines
214 KiB
Python
4662 lines
214 KiB
Python
# -*- coding: utf-8 -*-
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# PyMeeus: Python module implementing astronomical algorithms.
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# Copyright (C) 2018 Dagoberto Salazar
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#
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# This program is free software: you can redistribute it and/or modify
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# it under the terms of the GNU Lesser General Public License as published by
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# the Free Software Foundation, either version 3 of the License, or
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# (at your option) any later version.
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#
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# This program is distributed in the hope that it will be useful,
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# but WITHOUT ANY WARRANTY; without even the implied warranty of
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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# GNU Lesser General Public License for more details.
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#
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# You should have received a copy of the GNU Lesser General Public License
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# along with this program. If not, see <https://www.gnu.org/licenses/>.
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from math import sin, cos, tan, acos, atan2, sqrt, radians, log10
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from pymeeus.Angle import Angle
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from pymeeus.Epoch import Epoch, JDE2000
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from pymeeus.Interpolation import Interpolation
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from pymeeus.Coordinates import (
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geometric_vsop_pos, apparent_vsop_pos, orbital_elements,
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nutation_longitude, true_obliquity, ecliptical2equatorial,
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passage_nodes_elliptic
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)
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from pymeeus.Earth import Earth
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from pymeeus.Sun import Sun
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"""
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.. module:: Uranus
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:synopsis: Class to model Uranus planet
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:license: GNU Lesser General Public License v3 (LGPLv3)
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.. moduleauthor:: Dagoberto Salazar
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"""
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VSOP87_L = [
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# L0
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[
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[548129294.299, 0.00000000000, 0.00000000000],
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[9260408.252, 0.89106421530, 74.78159856730],
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[1504247.826, 3.62719262195, 1.48447270830],
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[365981.718, 1.89962189068, 73.29712585900],
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[272328.132, 3.35823710524, 149.56319713460],
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[70328.499, 5.39254431993, 63.73589830340],
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[68892.609, 6.09292489045, 76.26607127560],
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[61998.592, 2.26952040469, 2.96894541660],
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[61950.714, 2.85098907565, 11.04570026390],
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[26468.869, 3.14152087888, 71.81265315070],
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[25710.505, 6.11379842935, 454.90936652730],
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[21078.897, 4.36059465144, 148.07872442630],
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[17818.665, 1.74436982544, 36.64856292950],
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[14613.471, 4.73732047977, 3.93215326310],
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[11162.535, 5.82681993692, 224.34479570190],
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[10997.934, 0.48865493179, 138.51749687070],
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[9527.487, 2.95516893093, 35.16409022120],
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[7545.543, 5.23626440666, 109.94568878850],
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[4220.170, 3.23328535514, 70.84944530420],
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[4051.850, 2.27754158724, 151.04766984290],
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[3354.607, 1.06549008887, 4.45341812490],
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[2926.671, 4.62903695486, 9.56122755560],
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[3490.352, 5.48305567292, 146.59425171800],
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[3144.093, 4.75199307603, 77.75054398390],
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[2922.410, 5.35236743380, 85.82729883120],
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[2272.790, 4.36600802756, 70.32818044240],
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[2051.209, 1.51773563459, 0.11187458460],
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[2148.599, 0.60745800902, 38.13303563780],
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[1991.726, 4.92437290826, 277.03499374140],
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[1376.208, 2.04281409054, 65.22037101170],
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[1666.910, 3.62744580852, 380.12776796000],
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[1284.183, 3.11346336879, 202.25339517410],
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[1150.416, 0.93344454002, 3.18139373770],
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[1533.223, 2.58593414266, 52.69019803950],
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[1281.641, 0.54269869505, 222.86032299360],
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[1372.100, 4.19641615561, 111.43016149680],
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[1220.998, 0.19901396193, 108.46121608020],
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[946.195, 1.19249463066, 127.47179660680],
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[1150.993, 4.17898207045, 33.67961751290],
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[1244.342, 0.91612680579, 2.44768055480],
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[1072.008, 0.23564502877, 62.25142559510],
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[1090.461, 1.77501638912, 12.53017297220],
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[707.875, 5.18285226584, 213.29909543800],
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[653.401, 0.96586909116, 78.71375183040],
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[627.562, 0.18210181975, 984.60033162190],
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[524.495, 2.01276706996, 299.12639426920],
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[559.370, 3.35776737704, 0.52126486180],
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[606.827, 5.43209728952, 529.69096509460],
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[404.891, 5.98689011389, 8.07675484730],
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[467.211, 0.41484068933, 145.10977900970],
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[471.288, 1.40664336447, 184.72728735580],
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[483.219, 2.10553990154, 0.96320784650],
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[395.614, 5.87039580949, 351.81659230870],
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[433.532, 5.52142978255, 183.24281464750],
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[309.885, 5.83301304674, 145.63104387150],
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[378.609, 2.34975805006, 56.62235130260],
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[398.996, 0.33810765436, 415.55249061210],
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[300.379, 5.64353974146, 22.09140052780],
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[249.229, 4.74617120584, 225.82926841020],
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[239.334, 2.35045874708, 137.03302416240],
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[294.172, 5.83916826225, 39.61750834610],
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[216.480, 4.77847481363, 340.77089204480],
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[251.792, 1.63696775578, 221.37585028530],
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[219.621, 1.92212987979, 67.66805156650],
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[201.963, 1.29693040865, 0.04818410980],
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[224.097, 0.51574863468, 84.34282612290],
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[216.549, 6.14211862702, 5.93789083320],
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[222.588, 2.84309380331, 0.26063243090],
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[207.828, 5.58020570040, 68.84370773410],
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[187.474, 1.31924326253, 0.16005869440],
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[158.028, 0.73811997211, 54.17467074780],
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[199.146, 0.95634155010, 152.53214255120],
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[168.648, 5.87874000882, 18.15924726470],
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[170.300, 3.67717520688, 5.41662597140],
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[193.652, 1.88800122606, 456.39383923560],
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[192.998, 0.91616058506, 453.42489381900],
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[181.934, 3.53624029238, 79.23501669220],
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[173.145, 1.53860728054, 160.60889739850],
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[164.588, 1.42379714838, 106.97674337190],
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[171.968, 5.67952685533, 219.89137757700],
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[162.792, 3.05029377666, 112.91463420510],
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[146.653, 1.26300172265, 59.80374504030],
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[139.453, 5.38597723400, 32.19514480460],
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[138.585, 4.25994786673, 909.81873305460],
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[143.058, 1.29995487555, 35.42472265210],
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[123.840, 1.37359990336, 7.11354700080],
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[104.414, 5.02820888813, 0.75075952540],
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[103.277, 0.68095301267, 14.97785352700],
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[94.741, 0.90674090409, 74.66972398270],
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[82.978, 2.92828718445, 265.98929347750],
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[110.163, 2.02685778976, 554.06998748280],
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[94.226, 3.94266328260, 74.89347315190],
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[79.858, 1.01446829180, 6.59228213900],
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[109.376, 5.70581833286, 77.96299230500],
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[85.876, 1.70649435603, 82.85835341460],
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[103.562, 1.45770270246, 24.37902238820],
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[74.667, 4.63177552576, 69.36497259590],
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[79.919, 3.00974084247, 297.64192156090],
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[84.502, 0.36887189574, 186.21176006410],
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[88.810, 0.52481330563, 181.75834193920],
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[70.303, 1.18986880009, 66.70484372000],
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[69.965, 0.87476081875, 305.34616939270],
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[69.927, 3.76102749315, 131.40394986990],
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[84.604, 5.88725183325, 256.53994050650],
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[74.341, 6.24271323846, 447.79581952650],
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[62.310, 0.16901376623, 479.28838891550],
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[72.726, 2.84892775693, 462.02291352810],
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[69.060, 4.43934854374, 39.35687591520],
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[76.568, 4.58721110340, 6.21977512350],
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[73.387, 4.27603448634, 87.31177153950],
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[55.307, 1.49636544147, 71.60020482960],
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[57.291, 1.63015165542, 143.62530630140],
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[61.661, 3.18604743524, 77.22927912210],
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[57.634, 3.67180685401, 51.20572533120],
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[50.289, 1.12279384633, 20.60692781950],
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[53.744, 5.51890986247, 128.95626931510],
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[57.894, 2.66877593418, 381.61224066830],
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[58.112, 1.58629352171, 60.76695288680],
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[45.382, 0.48053933052, 14.01464568050],
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[37.581, 6.06822931932, 211.81462272970],
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[38.640, 3.43597050177, 153.49535039770],
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[46.087, 4.36201639577, 75.74480641380],
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[40.088, 4.57333927519, 46.20979048510],
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[34.229, 2.93967782207, 140.00196957900],
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[38.669, 5.58941074168, 99.16062095550],
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[34.827, 1.02792863024, 203.73786788240],
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[40.024, 0.69889667397, 218.40690486870],
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[32.538, 4.21625657443, 200.76892246580],
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[31.865, 5.50961503408, 72.33391801250],
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[41.695, 3.82438031124, 81.00137369080],
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[34.795, 0.39363490236, 1.37259812370],
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[39.775, 6.05600836903, 293.18850343600],
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[27.577, 2.18261286374, 125.98732389850],
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[36.279, 1.66586085405, 258.02441321480],
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[35.442, 1.96652806541, 835.03713448730],
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[35.361, 3.72258690030, 692.58748435350],
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[27.323, 2.10164372072, 209.36694217490],
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[26.530, 4.48265986115, 373.90799283650],
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[34.472, 1.07907945481, 191.20769491020],
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[29.915, 3.87358632506, 259.50888592310],
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[26.233, 3.63172504384, 490.33408917940],
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[25.848, 0.54461409359, 41.64449777560],
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[26.989, 6.27711247734, 28.57180808220],
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[26.391, 5.81110061049, 75.30286342910],
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[34.227, 6.05617272657, 275.55052103310],
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[24.279, 3.18776564878, 81.37388070630],
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[29.937, 1.88789751816, 269.92144674060],
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[26.235, 6.20105251336, 134.58534360760],
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[22.754, 0.92919725789, 288.08069400530],
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[25.180, 5.42547381962, 116.42609634290],
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[22.715, 0.53098783687, 1514.29129671650],
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[26.485, 4.77176167929, 284.14854074220],
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[27.008, 4.75281624832, 41.10198105440],
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[21.972, 4.58613057386, 404.50679034820],
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[22.012, 1.84389287183, 617.80588578620],
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[24.694, 4.70875195490, 378.64329525170],
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[28.949, 0.17127584792, 528.20649238630],
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[20.492, 0.10285646641, 195.13984817330],
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[20.696, 5.62143477633, 55.65914345610],
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[25.843, 0.74627159338, 278.51946644970],
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[22.990, 3.58378694661, 1.59634729290],
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[21.843, 0.05733533568, 173.94221952280],
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[19.050, 2.30351091243, 5.10780943070],
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[20.675, 2.64113858585, 105.49227066360],
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[21.856, 5.87352402691, 45.57665103870],
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[21.120, 1.98081790016, 114.39910691340],
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[19.279, 2.84304025179, 159.12442469020],
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[19.061, 0.50598371738, 67.35923502580],
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[20.434, 3.77601951414, 135.54855145410],
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[17.326, 4.47793157645, 120.35824960600],
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[20.547, 0.88695598555, 255.05546779820],
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[19.320, 1.48569290504, 0.89377187730],
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[21.331, 2.74470023060, 28.31117565130],
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[17.582, 4.09139636700, 296.15744885260],
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[15.918, 3.94525074972, 17.52610781830],
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[15.562, 0.92748407689, 300.61086697750],
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[16.439, 0.30868798605, 30.71067209630],
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[15.237, 4.93048601827, 7.42236354150],
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[19.284, 6.21950083268, 329.83706636550],
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[13.860, 0.56255266406, 144.14657116320],
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[16.206, 2.30292598693, 344.70304530790],
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[16.041, 0.19723295436, 103.09277421860],
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[14.414, 2.57606243208, 230.56457082540],
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[16.789, 4.93540052916, 565.11568774670],
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[17.052, 1.81844925116, 294.67297614430],
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[16.766, 0.27542186330, 73.81839072080],
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[15.428, 1.91577056305, 96.87299909510],
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[15.718, 3.87095025861, 98.89998852460],
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[11.923, 6.17545505441, 44.72531777680],
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[12.407, 6.22419970167, 80.19822453870],
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[13.040, 1.99652993223, 27.08733537390],
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[13.229, 3.43782440072, 227.31374111850],
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[11.669, 4.31526860843, 426.59819087600],
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[14.378, 5.78353646474, 1059.38193018920],
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[15.879, 0.98454960055, 6208.29425142410],
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[11.158, 1.74417430690, 220.41264243880],
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[11.989, 5.84388657950, 13.33332212430],
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[11.386, 2.55925734515, 19.12245511120],
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[13.281, 5.39472153462, 391.17346822390],
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[12.295, 4.57340278496, 23.57587323610],
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[12.827, 1.77410269070, 180.27386923090],
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[11.651, 4.29138607818, 142.44965013380],
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[12.248, 2.44241346243, 100.38446123290],
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[12.421, 2.32591770919, 80.71948940050],
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[9.774, 0.39898140151, 7.86430652620],
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[13.172, 2.74099358938, 177.87437278590],
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[12.262, 5.42795591646, 831.10498122420],
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[10.272, 5.90194483926, 74.52096613640],
|
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[9.317, 3.75869700774, 74.82978267710],
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[10.701, 4.00709797731, 235.39049596580],
|
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[9.243, 5.38492199672, 20.44686912510],
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[9.461, 2.60126707172, 92.30770638560],
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[12.066, 5.52163100220, 74.26033370550],
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[10.836, 1.88393779293, 241.61027108930],
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[9.317, 1.16483658310, 74.73341445750],
|
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[10.718, 5.50310449842, 187.69623277240],
|
|
[12.057, 6.02120050390, 154.01661525950],
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[9.124, 1.15458738606, 0.63313944640],
|
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[11.526, 6.26425302826, 155.78297225810],
|
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[12.200, 5.79400179483, 1364.72809958190],
|
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[10.979, 5.76614513865, 628.85158605010],
|
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[8.532, 5.18016456150, 1.64453140270],
|
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[8.660, 3.78133822411, 74.94165726170],
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[11.227, 1.30788626675, 604.47256366190],
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[10.531, 1.05867421534, 291.70403072770],
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[8.446, 3.52020067595, 756.32338265690],
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[10.291, 5.30493908317, 75.04223099820],
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[8.015, 6.24347048958, 543.02428721890],
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[7.796, 5.23497582886, 58.10682401090],
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[9.310, 1.65210713729, 24.11838995730],
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[8.642, 1.14285691458, 74.62153987290],
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[7.797, 4.00208030502, 31.49256938900],
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[8.915, 3.63129389881, 408.43894361130],
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[7.191, 4.24536221306, 110.20632121940],
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[9.764, 0.10205649809, 366.48562929500],
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[8.710, 2.25910759480, 451.94042111070],
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[9.430, 2.00492467431, 331.32153907380],
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[9.008, 1.63146330622, 443.86366626340],
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[7.247, 4.35313018726, 88.11492069160],
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[7.659, 0.61918159043, 50.40257617910],
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[6.836, 5.12190844483, 0.80314915210],
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[9.367, 1.42664537007, 414.06801790380],
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[8.136, 0.45279998999, 25.60286266560],
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[9.199, 2.41000352664, 10138.50394764370],
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[6.896, 5.85017813531, 339.28641933650],
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[6.487, 6.03397141885, 1.22384027740],
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[7.186, 4.00480285222, 157.63995198190],
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[8.130, 0.21907525983, 422.66603761290],
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[8.022, 2.09953974305, 92.94084583200],
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[6.371, 4.47820781123, 79.88940799800],
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[7.957, 5.86499639179, 760.25553592000],
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[8.383, 2.33782809093, 417.03696332040],
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[7.931, 3.41952210669, 7.70424783180],
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[6.613, 1.39197711439, 16.67477455640],
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[7.142, 5.57864813931, 4.73530241520],
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[7.441, 0.48121969777, 68.18931642830],
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[7.187, 0.50441238918, 457.87831194390],
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[6.613, 2.84628770892, 142.14083359310],
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|
[0.284, 1.59495665161, 336.83873878170],
|
|
[0.255, 5.85817353877, 229.34073054800],
|
|
[0.260, 5.92834225312, 455.06942522170],
|
|
[0.274, 0.53977064975, 380.23964254460],
|
|
[0.259, 3.15728797958, 454.74930783290],
|
|
[0.303, 0.17851964142, 384.58118608490],
|
|
[0.285, 1.29732672572, 25.12978191360],
|
|
[0.273, 4.18776699292, 177.30492381430],
|
|
[0.326, 1.68159391466, 161.72086309130],
|
|
[0.321, 2.36931686576, 2274.54683263650],
|
|
[0.241, 3.57660492473, 150.31395666000],
|
|
[0.273, 3.78780099400, 380.01589337540],
|
|
[0.265, 3.02540120552, 454.79749194270],
|
|
[0.265, 6.06087280189, 455.02124111190],
|
|
[0.279, 3.82392760479, 31.54075349880],
|
|
[0.273, 2.64820862667, 838.00607990390],
|
|
[0.238, 5.17487170793, 263.02034806090],
|
|
[0.299, 3.94906046599, 531.97858695500],
|
|
[0.317, 2.28289083599, 44.07092647100],
|
|
[0.250, 1.35950829789, 304.12232911530],
|
|
[0.312, 2.73327875294, 442.37919355510],
|
|
[0.314, 3.86400459047, 734.45573129830],
|
|
[0.251, 0.15148137746, 221.16340196420],
|
|
[0.272, 5.71864670101, 164.54105066160],
|
|
[0.305, 4.96642198943, 1140.38330388000],
|
|
[0.282, 5.46073788901, 550.13783421970],
|
|
[0.273, 5.68721459468, 92.41958097020],
|
|
[0.256, 0.88787970870, 418.52143602870],
|
|
[0.229, 5.02021405557, 144.89733068860],
|
|
[0.231, 5.70236752870, 132.88842257820],
|
|
[0.218, 2.05623736180, 303.05854753230],
|
|
[0.300, 1.76109447754, 371.52974825090],
|
|
[0.216, 2.97122807313, 176.65053250850],
|
|
[0.224, 3.12798198868, 188.92007304980],
|
|
[0.212, 1.30757526083, 74.14845912090],
|
|
[0.238, 4.65119406609, 385.75684225250],
|
|
[0.216, 0.07086910120, 893.35640681930],
|
|
[0.262, 5.78959872639, 635.96513305090],
|
|
[0.250, 4.47327859711, 551.10104206620],
|
|
[0.222, 1.64692618955, 76.42612997000],
|
|
[0.254, 2.61838408005, 525.23754696970],
|
|
[0.284, 4.13290731223, 544.50875992720],
|
|
[0.262, 2.82476092056, 971.10695080320],
|
|
[0.266, 4.12467258610, 375.67434983510],
|
|
[0.212, 3.61675003296, 75.41473801370],
|
|
[0.253, 3.14224867483, 270.18207917150],
|
|
[0.250, 4.32883971376, 346.44815044710],
|
|
[0.273, 1.95676918609, 402.21916848780],
|
|
[0.259, 1.96371242284, 968.13800538660],
|
|
[0.238, 1.29663338057, 421.18156490460],
|
|
[0.243, 5.94961177434, 117.36805233000],
|
|
[0.241, 4.70849619029, 406.95447090300],
|
|
[0.216, 3.31232425021, 190.66517818900],
|
|
[0.201, 1.23733749784, 799.61241183520],
|
|
[0.223, 0.98087204684, 627.36711334180],
|
|
[0.226, 1.66139333004, 1366.21257229020],
|
|
[0.205, 0.33839683950, 143.34342201110],
|
|
[0.240, 0.71559872262, 525.75881183150],
|
|
[0.223, 2.57722930616, 981.63138620530],
|
|
[0.193, 4.48974066435, 172.19711438360],
|
|
[0.221, 2.88670838151, 238.90195810360],
|
|
[0.177, 3.87122035013, 389.68899551560],
|
|
[0.175, 5.85737374379, 170.71264167530],
|
|
[0.233, 0.63169996424, 980.66817835880],
|
|
[0.225, 4.81504648561, 88.27497938600],
|
|
[0.210, 2.49819501106, 128.43500445330],
|
|
[0.172, 0.91255921858, 210.85141488320],
|
|
[0.176, 3.85133296117, 605.95703637020],
|
|
[0.211, 1.72999855867, 10213.28554621100],
|
|
[0.170, 1.61405340100, 1512.80682400820],
|
|
[0.216, 1.54874566441, 1060.86640289750],
|
|
[0.194, 6.07381783144, 520.12973753900],
|
|
[0.170, 2.58526747515, 1515.77576942480],
|
|
[0.172, 1.45073604378, 995.64603188580],
|
|
[0.160, 4.20015913513, 433.71173787680],
|
|
[0.219, 1.63985385568, 630.33605875840],
|
|
[0.219, 1.96273394194, 313.68355667090],
|
|
[0.159, 3.62343846627, 73.97844941520],
|
|
[0.206, 0.83764718449, 104.83787935780],
|
|
[0.203, 0.68701289007, 1363.24362687360],
|
|
[0.158, 0.81666479221, 987.56927703850],
|
|
[0.172, 2.97938676702, 327.43756992050],
|
|
[0.147, 2.15517092627, 73.24894174920],
|
|
[0.156, 1.29643469200, 216.26804085460],
|
|
[0.153, 3.77492020946, 768.85355562910],
|
|
[0.147, 4.74903152642, 73.34530996880],
|
|
[0.198, 2.80749830888, 225.30800354840],
|
|
[0.179, 0.35410767087, 421.22974901440],
|
|
[0.204, 3.47423038287, 564.85505531580],
|
|
[0.172, 2.88420642820, 233.53351624200],
|
|
[0.195, 3.09114364733, 294.30046912880],
|
|
[0.181, 4.75684139861, 71.15826184490],
|
|
[0.160, 3.16134209902, 70.04629615210],
|
|
[0.155, 2.07144269719, 91.24392480260],
|
|
[0.154, 3.37462128317, 138.40562228610],
|
|
[0.192, 6.19629054455, 312.19908396260],
|
|
[0.162, 0.60896273267, 73.03649342810],
|
|
[0.172, 2.01712700688, 973.55463135800],
|
|
[0.145, 1.72582731815, 302.37722397610],
|
|
[0.170, 2.97437423989, 3191.04922956520],
|
|
[0.153, 0.11158566352, 138.62937145530],
|
|
[0.164, 5.37129563471, 457.35704708210],
|
|
[0.132, 3.15466226029, 523.47118997110],
|
|
[0.137, 2.88313323946, 765.88461021250],
|
|
[0.128, 1.75773421717, 77.70235987410],
|
|
[0.173, 5.03552846066, 415.29185818120],
|
|
[0.137, 4.77137510538, 73.45718455340],
|
|
[0.163, 0.99316178485, 94.42531854030],
|
|
[0.138, 4.68330115148, 517.16079212240],
|
|
[0.133, 2.95376828791, 75.15410558280],
|
|
[0.134, 1.35779558361, 249.94765836750],
|
|
[0.168, 4.73164542970, 108.72184851110],
|
|
[0.119, 1.48229220689, 237.41748539530],
|
|
[0.134, 1.52277177920, 154.67100656530],
|
|
[0.117, 5.48642273610, 437.64389113990],
|
|
[0.131, 5.76525548944, 75.43598987310],
|
|
[0.127, 2.38309227230, 208.84567731310],
|
|
[0.115, 4.38951350436, 343.21857259960],
|
|
[0.114, 4.48142283161, 224.86606056370],
|
|
[0.117, 5.37802827323, 293.70976829780],
|
|
[0.136, 2.80772094137, 374.49869366750],
|
|
],
|
|
# L1
|
|
[
|
|
[7502543121.646, 0.00000000000, 0.00000000000],
|
|
[154458.244, 5.24201658072, 74.78159856730],
|
|
[24456.413, 1.71255705309, 1.48447270830],
|
|
[9257.828, 0.42844639064, 11.04570026390],
|
|
[8265.977, 1.50220035110, 63.73589830340],
|
|
[7841.715, 1.31983607251, 149.56319713460],
|
|
[3899.105, 0.46483574024, 3.93215326310],
|
|
[2283.777, 4.17367533997, 76.26607127560],
|
|
[1926.600, 0.53013080152, 2.96894541660],
|
|
[1232.727, 1.58634458237, 70.84944530420],
|
|
[791.206, 5.43641224143, 3.18139373770],
|
|
[766.954, 1.99555409575, 73.29712585900],
|
|
[481.671, 2.98401996914, 85.82729883120],
|
|
[449.798, 4.13826237508, 138.51749687070],
|
|
[445.600, 3.72300400331, 224.34479570190],
|
|
[426.554, 4.73126059388, 71.81265315070],
|
|
[347.735, 2.45372261286, 9.56122755560],
|
|
[353.752, 2.58324496886, 148.07872442630],
|
|
[317.084, 5.57855232072, 52.69019803950],
|
|
[179.920, 5.68367730922, 12.53017297220],
|
|
[171.084, 3.00060075287, 78.71375183040],
|
|
[205.585, 2.36263144251, 2.44768055480],
|
|
[158.029, 2.90931969498, 0.96320784650],
|
|
[189.068, 4.20242881378, 56.62235130260],
|
|
[154.670, 5.59083925605, 4.45341812490],
|
|
[183.762, 0.28371004654, 151.04766984290],
|
|
[143.464, 2.59049246726, 62.25142559510],
|
|
[151.984, 2.94217326890, 77.75054398390],
|
|
[153.515, 4.65186885939, 35.16409022120],
|
|
[121.452, 4.14839204920, 127.47179660680],
|
|
[115.546, 3.73224603791, 65.22037101170],
|
|
[102.022, 4.18754517993, 145.63104387150],
|
|
[101.718, 6.03385875009, 0.11187458460],
|
|
[88.202, 3.99035787994, 18.15924726470],
|
|
[87.549, 6.15520787584, 202.25339517410],
|
|
[80.530, 2.64124743934, 22.09140052780],
|
|
[72.047, 6.04545933578, 70.32818044240],
|
|
[68.570, 4.05071895264, 77.96299230500],
|
|
[59.173, 3.70413919082, 67.66805156650],
|
|
[47.267, 3.54312460519, 351.81659230870],
|
|
[42.534, 5.72357370899, 5.41662597140],
|
|
[44.339, 5.90865821911, 7.11354700080],
|
|
[35.605, 3.29197259183, 8.07675484730],
|
|
[35.524, 3.32784616138, 71.60020482960],
|
|
[36.116, 5.89964278801, 33.67961751290],
|
|
[30.608, 5.46414592601, 160.60889739850],
|
|
[31.454, 5.62015632303, 984.60033162190],
|
|
[38.544, 4.91519003848, 222.86032299360],
|
|
[34.996, 5.08034112149, 38.13303563780],
|
|
[30.811, 5.49591403863, 59.80374504030],
|
|
[28.947, 4.51867390414, 84.34282612290],
|
|
[26.627, 5.54127301037, 131.40394986990],
|
|
[29.866, 1.65980844667, 447.79581952650],
|
|
[29.206, 1.14722640419, 462.02291352810],
|
|
[25.753, 4.99362028417, 137.03302416240],
|
|
[25.373, 5.73584678604, 380.12776796000],
|
|
[21.672, 2.80556379586, 69.36497259590],
|
|
[26.605, 6.14640604128, 299.12639426920],
|
|
[22.995, 2.24925345862, 111.43016149680],
|
|
[19.246, 3.55645739672, 54.17467074780],
|
|
[21.780, 0.93285892393, 213.29909543800],
|
|
[19.338, 1.86249384092, 108.46121608020],
|
|
[16.153, 3.10208165842, 14.97785352700],
|
|
[13.126, 1.95385539499, 87.31177153950],
|
|
[13.907, 1.54149045800, 340.77089204480],
|
|
[13.549, 4.38455126720, 5.93789083320],
|
|
[13.102, 5.88301410143, 6.21977512350],
|
|
[11.810, 0.32615567587, 35.42472265210],
|
|
[10.980, 1.69230280951, 45.57665103870],
|
|
[12.351, 0.32823896833, 51.20572533120],
|
|
[10.906, 5.97068444790, 265.98929347750],
|
|
[11.446, 3.37831545858, 72.33391801250],
|
|
[12.013, 3.60395709253, 269.92144674060],
|
|
[11.662, 1.74504271366, 79.23501669220],
|
|
[13.777, 2.69028726334, 225.82926841020],
|
|
[12.006, 5.34430562395, 152.53214255120],
|
|
[9.866, 5.50316093605, 153.49535039770],
|
|
[10.436, 4.16875643286, 24.37902238820],
|
|
[10.632, 3.06875158069, 284.14854074220],
|
|
[9.613, 0.49590148788, 209.36694217490],
|
|
[9.283, 3.54479191952, 41.64449777560],
|
|
[9.536, 5.60054956443, 82.85835341460],
|
|
[9.740, 1.01087744586, 68.84370773410],
|
|
[9.187, 4.49472579228, 20.60692781950],
|
|
[10.159, 3.51765739489, 529.69096509460],
|
|
[8.612, 3.88869873588, 60.76695288680],
|
|
[10.030, 4.64790204580, 77.22927912210],
|
|
[8.689, 1.96813580258, 195.13984817330],
|
|
[8.370, 4.40914764204, 134.58534360760],
|
|
[9.273, 3.93291227900, 39.61750834610],
|
|
[7.784, 5.35626068469, 75.74480641380],
|
|
[7.724, 5.77176047568, 73.81839072080],
|
|
[7.683, 4.44252070929, 14.01464568050],
|
|
[8.355, 2.44425910430, 146.59425171800],
|
|
[7.954, 5.73093878181, 184.72728735580],
|
|
[7.465, 2.18972405572, 145.10977900970],
|
|
[6.430, 0.84582374839, 32.19514480460],
|
|
[6.257, 2.17085130003, 74.89347315190],
|
|
[7.911, 0.17275924476, 120.35824960600],
|
|
[7.036, 4.12047266896, 191.20769491020],
|
|
[6.860, 2.13462553365, 116.42609634290],
|
|
[5.191, 3.11155355454, 106.97674337190],
|
|
[4.798, 2.25093144226, 46.20979048510],
|
|
[4.566, 3.45427648666, 0.75075952540],
|
|
[4.401, 3.94058045671, 6.59228213900],
|
|
[4.214, 5.17805765625, 144.14657116320],
|
|
[4.409, 0.24427052932, 92.94084583200],
|
|
[4.866, 1.15344187054, 112.91463420510],
|
|
[4.744, 5.18229292013, 81.00137369080],
|
|
[4.332, 2.52429167546, 99.16062095550],
|
|
[3.876, 2.78430217652, 565.11568774670],
|
|
[3.801, 0.75133837939, 58.10682401090],
|
|
[4.146, 5.84943984597, 221.37585028530],
|
|
[3.885, 4.95626104286, 125.98732389850],
|
|
[3.815, 3.23004401930, 479.28838891550],
|
|
[3.679, 5.28098232097, 66.91729204110],
|
|
[3.479, 2.95514470947, 74.66972398270],
|
|
[3.514, 4.90090391308, 28.31117565130],
|
|
[4.515, 4.15474629145, 344.70304530790],
|
|
[4.036, 2.28903172191, 109.94568878850],
|
|
[4.266, 2.68534591099, 7.86430652620],
|
|
[3.428, 0.02846652682, 140.00196957900],
|
|
[3.644, 5.32002093810, 408.43894361130],
|
|
[3.252, 1.44975192429, 128.95626931510],
|
|
[4.143, 1.89070487241, 277.03499374140],
|
|
[3.177, 0.04197149544, 220.41264243880],
|
|
[3.901, 6.25926496244, 0.89377187730],
|
|
[3.787, 0.02516903921, 152.74459087230],
|
|
[3.200, 0.52009458683, 2.28762186040],
|
|
[2.995, 1.94615440691, 80.19822453870],
|
|
[4.029, 5.24603808726, 96.87299909510],
|
|
[3.302, 4.81033551060, 422.66603761290],
|
|
[3.189, 6.26156603400, 456.39383923560],
|
|
[2.804, 1.35626949052, 404.50679034820],
|
|
[2.970, 0.54327361056, 159.12442469020],
|
|
[3.465, 5.88337990735, 16.67477455640],
|
|
[3.518, 4.99649404130, 36.64856292950],
|
|
[3.081, 2.82772472086, 453.42489381900],
|
|
[3.320, 1.56223495893, 23.57587323610],
|
|
[2.573, 6.19617997586, 135.54855145410],
|
|
[2.547, 5.19937103778, 173.94221952280],
|
|
[2.534, 1.85452635674, 490.33408917940],
|
|
[3.106, 6.07067928601, 142.44965013380],
|
|
[3.302, 1.02846689671, 297.64192156090],
|
|
[2.429, 1.33640100979, 211.81462272970],
|
|
[2.792, 3.89897022917, 358.93013930950],
|
|
[2.947, 5.31528985588, 55.13787859430],
|
|
[2.449, 3.44007536754, 206.18554843720],
|
|
[2.407, 4.38551271701, 60.55450456570],
|
|
[2.425, 2.22643225523, 66.70484372000],
|
|
[2.295, 2.31690029267, 31.49256938900],
|
|
[2.225, 0.41365126245, 81.37388070630],
|
|
[2.196, 0.76281798713, 17.52610781830],
|
|
[2.301, 3.60815987923, 288.08069400530],
|
|
[2.557, 0.73679737974, 200.76892246580],
|
|
[2.158, 2.61924330277, 13.33332212430],
|
|
[2.048, 6.27204714771, 98.89998852460],
|
|
[2.054, 3.61072687338, 333.65734504400],
|
|
[2.190, 2.49696729700, 76.47851959670],
|
|
[2.092, 1.66496421654, 235.39049596580],
|
|
[2.206, 2.35938756479, 347.88443904560],
|
|
[2.469, 4.70656858928, 186.21176006410],
|
|
[2.226, 5.97327738150, 1514.29129671650],
|
|
[1.851, 2.19455296942, 203.73786788240],
|
|
[1.865, 4.98207204280, 5.10780943070],
|
|
[2.171, 5.49034081907, 373.01422095920],
|
|
[1.999, 5.80509154216, 146.38180339690],
|
|
[1.903, 4.32950489567, 49.50880430180],
|
|
[1.732, 3.94794012202, 24.11838995730],
|
|
[1.747, 2.46883637489, 55.65914345610],
|
|
[1.833, 3.35110048460, 143.62530630140],
|
|
[1.686, 1.28621563322, 103.09277421860],
|
|
[1.720, 2.35857527806, 1.64453140270],
|
|
[1.641, 2.99507314472, 391.17346822390],
|
|
[1.610, 0.97420709262, 977.48678462110],
|
|
[1.696, 4.98332661473, 387.24131496080],
|
|
[1.527, 3.15107379811, 7.42236354150],
|
|
[1.570, 1.61119571428, 991.71387862270],
|
|
[1.497, 2.89637638984, 19.64371997300],
|
|
[1.507, 3.32822127349, 909.81873305460],
|
|
[1.375, 5.75263837916, 19.12245511120],
|
|
[1.407, 2.20244941425, 67.35923502580],
|
|
[1.364, 4.40006421418, 27.08733537390],
|
|
[1.357, 4.33780029649, 70.11573212130],
|
|
[1.311, 4.62202930578, 81.89514556810],
|
|
[1.307, 2.79964247834, 25.60286266560],
|
|
[1.312, 3.73623252660, 628.85158605010],
|
|
[1.286, 3.96557527092, 61.28821774860],
|
|
[1.723, 4.56068809303, 305.34616939270],
|
|
[1.313, 4.90611014973, 617.80588578620],
|
|
[1.508, 6.25017976193, 604.47256366190],
|
|
[1.235, 5.93779486368, 415.55249061210],
|
|
[1.278, 3.21119872139, 92.04707395470],
|
|
[1.357, 0.72647086107, 546.95644048200],
|
|
[1.552, 5.05296247763, 10.29494073850],
|
|
[1.230, 1.52077038294, 157.63995198190],
|
|
[1.210, 2.63049415027, 426.59819087600],
|
|
[1.206, 4.83219370572, 100.38446123290],
|
|
[1.234, 4.46203104116, 162.09337010680],
|
|
[1.174, 5.32356191090, 17.26547538740],
|
|
[1.431, 6.18138614295, 14.22709400160],
|
|
[1.244, 0.16929250603, 29.20494752860],
|
|
[1.180, 4.09719023908, 443.86366626340],
|
|
[1.180, 3.31438239649, 44.72531777680],
|
|
[1.259, 1.88793196065, 0.65439130580],
|
|
[1.263, 3.49967730885, 230.56457082540],
|
|
[1.168, 2.04071854201, 30.71067209630],
|
|
[1.523, 2.28101186489, 373.90799283650],
|
|
[1.429, 2.05075136274, 181.75834193920],
|
|
[1.065, 2.95960854361, 241.61027108930],
|
|
[1.253, 0.23639539817, 561.18353448360],
|
|
[1.255, 1.25819925760, 155.78297225810],
|
|
[1.044, 2.89293032709, 543.02428721890],
|
|
[1.062, 3.26314901318, 28.57180808220],
|
|
[1.124, 1.06535506684, 88.11492069160],
|
|
[1.186, 5.73445278027, 329.72519178090],
|
|
[1.190, 2.82438170535, 41.10198105440],
|
|
[1.067, 0.27101806190, 58.31927233200],
|
|
[1.017, 4.30527610005, 67.88049988760],
|
|
[0.959, 5.20504598622, 42.53826965290],
|
|
[0.984, 4.90934403664, 465.95506679120],
|
|
[0.944, 0.66925769374, 88.79624424780],
|
|
[1.017, 4.37095088461, 13.49338081870],
|
|
[1.222, 5.13450955699, 300.61086697750],
|
|
[0.989, 0.53937909300, 80.71948940050],
|
|
[0.890, 3.09802121989, 110.20632121940],
|
|
[1.095, 1.70637576740, 43.12897048390],
|
|
[0.992, 4.17968869928, 154.01661525950],
|
|
[0.950, 0.09841899432, 273.10284047830],
|
|
[0.870, 4.77500238443, 33.13710079170],
|
|
[0.867, 4.22078052532, 20.44686912510],
|
|
[0.830, 5.23785245773, 472.17484191470],
|
|
[0.884, 4.34377463442, 105.49227066360],
|
|
[0.812, 3.53258780148, 39.35687591520],
|
|
[1.055, 1.52219418153, 227.31374111850],
|
|
[0.963, 1.87806076896, 259.50888592310],
|
|
[0.859, 0.57844232244, 152.01087768940],
|
|
[0.861, 4.69213709412, 1059.38193018920],
|
|
[1.084, 2.79612346618, 48.75804477640],
|
|
[0.994, 2.87052008214, 454.90936652730],
|
|
[0.831, 1.62068330602, 554.06998748280],
|
|
[0.891, 2.85026036860, 32.24332891440],
|
|
[0.876, 0.83921717739, 4.73530241520],
|
|
[0.707, 6.16918394997, 3.62333672240],
|
|
[0.787, 1.95585343912, 16.46232623530],
|
|
[0.702, 5.49557046240, 558.00214074590],
|
|
[0.817, 0.38724470336, 378.64329525170],
|
|
[0.804, 2.25693582099, 16.04163511000],
|
|
[0.866, 1.80814575866, 258.87574647670],
|
|
[0.651, 3.72120167607, 286.59622129700],
|
|
[0.672, 1.00052727778, 522.57741809380],
|
|
[0.631, 4.14839739363, 141.69889060840],
|
|
[0.748, 4.19441869839, 486.40193591630],
|
|
[0.668, 0.77754011576, 120.99138905240],
|
|
[0.619, 4.31040053492, 455.87257437380],
|
|
[0.619, 4.77556598202, 453.94615868080],
|
|
[0.647, 5.74952736928, 119.50691634410],
|
|
[0.609, 0.24149609998, 117.91056905120],
|
|
[0.630, 1.79018649942, 440.68227252570],
|
|
[0.601, 1.41196883461, 218.92816973050],
|
|
[0.719, 4.27398947015, 50.40257617910],
|
|
[0.594, 3.92150462249, 25.27279426550],
|
|
[0.710, 0.45768559438, 536.80451209540],
|
|
[0.706, 6.15599144951, 258.02441321480],
|
|
[0.617, 2.80636989892, 68.56182344380],
|
|
[0.587, 5.47247350993, 767.36908292080],
|
|
[0.690, 3.48978614301, 835.03713448730],
|
|
[0.537, 4.06668446648, 450.97721326420],
|
|
[0.511, 0.60155300709, 264.50482076920],
|
|
[0.694, 1.18127476921, 129.91947716160],
|
|
[0.584, 1.94104733057, 106.27416795630],
|
|
[0.522, 5.95180617510, 518.64526483070],
|
|
[0.507, 4.39658523394, 121.84272231430],
|
|
[0.627, 2.24582628581, 218.40690486870],
|
|
[0.485, 0.02058107411, 106.01353552540],
|
|
[0.592, 2.06072766194, 296.15744885260],
|
|
[0.587, 0.18557470860, 458.09076026500],
|
|
[0.483, 1.50333774574, 150.52640498110],
|
|
[0.474, 4.99848521665, 458.84151979040],
|
|
[0.566, 1.94435189030, 699.70103135430],
|
|
[0.472, 1.86519720200, 180.16199464630],
|
|
[0.472, 0.07145793467, 216.48048917570],
|
|
[0.571, 6.01195273302, 47.06112374700],
|
|
[0.460, 3.76890954025, 342.25536475310],
|
|
[0.489, 2.96084966272, 385.75684225250],
|
|
[0.458, 1.99730631732, 275.55052103310],
|
|
[0.460, 5.75982407113, 89.75945209430],
|
|
[0.549, 1.43219978325, 171.65459766240],
|
|
[0.544, 0.04821904056, 114.39910691340],
|
|
[0.450, 1.94933296558, 148.59998928810],
|
|
[0.444, 2.94093732205, 692.58748435350],
|
|
[0.442, 2.15938034999, 173.68158709190],
|
|
[0.543, 2.61197342701, 451.72797278960],
|
|
[0.465, 0.31777753866, 756.32338265690],
|
|
[0.441, 2.82271922049, 32.71640966640],
|
|
[0.538, 2.39420182072, 339.28641933650],
|
|
[0.569, 0.84686482736, 260.99335863140],
|
|
[0.572, 5.40379754526, 278.51946644970],
|
|
[0.422, 4.61520857062, 40.16002506730],
|
|
[0.451, 4.50911201020, 142.14083359310],
|
|
[0.501, 0.18290112601, 331.32153907380],
|
|
[0.468, 0.97688759019, 760.25553592000],
|
|
[0.443, 4.58896013561, 149.67507171920],
|
|
[0.428, 1.02564850231, 469.13646052890],
|
|
[0.500, 4.34235307579, 166.82867252200],
|
|
[0.412, 5.69502940499, 92.30770638560],
|
|
[0.404, 5.18855270166, 22.63391724900],
|
|
[0.396, 3.98515136901, 31.23193695810],
|
|
[0.421, 5.47567810199, 104.00779795530],
|
|
[0.425, 3.50702044406, 180.27386923090],
|
|
[0.415, 1.52291071520, 497.44763618020],
|
|
[0.430, 2.39159932023, 39.09624348430],
|
|
[0.401, 0.55271143649, 95.38852638680],
|
|
[0.384, 2.48712922138, 210.33015002140],
|
|
[0.422, 1.02056886848, 468.24268865160],
|
|
[0.465, 5.72323435231, 183.24281464750],
|
|
[0.383, 2.63486938783, 685.47393735270],
|
|
[0.367, 5.39331524988, 874.39401040250],
|
|
[0.461, 3.57961254790, 187.69623277240],
|
|
[0.409, 4.21780704807, 181.05576652360],
|
|
[0.440, 0.36380766054, 367.97010200330],
|
|
[0.392, 5.44355925956, 26.02355379090],
|
|
[0.431, 3.83885208954, 254.94359321360],
|
|
[0.366, 2.92275490656, 291.26208774300],
|
|
[0.416, 2.54190330826, 255.05546779820],
|
|
[0.348, 0.35176743482, 46.47042291600],
|
|
[0.413, 2.41518097006, 483.22054217860],
|
|
[0.386, 4.76483292968, 268.43697403230],
|
|
[0.344, 0.20350283971, 184.09414790940],
|
|
[0.350, 1.24205287122, 97.41551581630],
|
|
[0.361, 5.68393391400, 353.30106501700],
|
|
[0.359, 2.62171903648, 162.89651925890],
|
|
[0.381, 3.38777292581, 114.94162363460],
|
|
[0.352, 2.76374792259, 295.19424100610],
|
|
[0.340, 1.34666360560, 34.20088237470],
|
|
[0.433, 1.90504858871, 123.53964334370],
|
|
[0.389, 2.41268196916, 381.61224066830],
|
|
[0.383, 3.20416581825, 79.44746501330],
|
|
[0.369, 2.15185889720, 555.55446019110],
|
|
[0.370, 2.19402183275, 562.66800719190],
|
|
[0.327, 3.40081544565, 309.27832265580],
|
|
[0.378, 5.75737470182, 916.93228005540],
|
|
[0.318, 4.53066393124, 350.33211960040],
|
|
[0.376, 1.74845257914, 545.47196777370],
|
|
[0.346, 4.15815107375, 282.66406803390],
|
|
[0.319, 4.38123849114, 154.97982310600],
|
|
[0.320, 0.81846631878, 610.69233878540],
|
|
[0.327, 5.07873875355, 189.72322220190],
|
|
[0.306, 1.71903179875, 394.35486196160],
|
|
[0.329, 1.82999432252, 706.81457835510],
|
|
[0.335, 4.78622577105, 109.31254934210],
|
|
[0.310, 5.08120849869, 376.19561469690],
|
|
[0.327, 1.87637598331, 207.88246946660],
|
|
[0.323, 1.88845451800, 192.69216761850],
|
|
[0.284, 2.88222063053, 384.05992122310],
|
|
[0.283, 4.63187254084, 332.17287233570],
|
|
[0.294, 2.84554743359, 267.47376618580],
|
|
[0.285, 0.97965330777, 113.87784205160],
|
|
[0.319, 5.09582764612, 285.63301345050],
|
|
[0.280, 0.67871105907, 312.45971639350],
|
|
[0.300, 5.93285242876, 124.29040286910],
|
|
[0.320, 4.86151247369, 448.68959140380],
|
|
[0.310, 3.75000484412, 253.57099508990],
|
|
[0.311, 5.59686590720, 271.40591944890],
|
|
[0.316, 1.89686876211, 228.27694896500],
|
|
[0.269, 0.14585942744, 142.66209845490],
|
|
[0.270, 2.12904548682, 778.41478318470],
|
|
[0.267, 0.96560769114, 90.82323367730],
|
|
[0.308, 1.38454900684, 375.39246554480],
|
|
[0.298, 3.99595366039, 451.94042111070],
|
|
[0.278, 3.38339026214, 346.39996633730],
|
|
[0.287, 1.01918432834, 905.88657979150],
|
|
[0.263, 0.16921968622, 124.50285119020],
|
|
[0.283, 5.95865378023, 362.86229257260],
|
|
[0.266, 3.07331582044, 193.65537546500],
|
|
[0.264, 5.47114459575, 133.10087089930],
|
|
[0.288, 2.78232740152, 1812.52391910840],
|
|
[0.361, 4.30140629884, 198.32124191100],
|
|
[0.257, 1.60206491208, 369.08206769610],
|
|
[0.274, 2.88347680082, 233.90602325750],
|
|
[0.267, 4.90554019072, 681.54178408960],
|
|
[0.305, 1.55983861329, 49.72125262290],
|
|
[0.253, 0.50457429429, 316.39186965660],
|
|
[0.258, 5.81453094409, 630.33605875840],
|
|
[0.280, 1.15452517706, 986.08480433020],
|
|
[0.265, 4.93584097286, 831.10498122420],
|
|
[0.246, 1.25186233620, 134.06407874580],
|
|
[0.298, 5.75927878031, 902.70518605380],
|
|
[0.240, 2.84888261768, 44.09217833040],
|
|
[0.261, 2.20643594285, 73.08467753790],
|
|
[0.321, 3.46864827820, 372.42352012820],
|
|
[0.234, 6.06783988023, 147.11551657980],
|
|
[0.262, 2.69623862046, 167.72244439930],
|
|
[0.267, 4.05985113852, 75.30286342910],
|
|
[0.240, 0.48471871511, 172.19711438360],
|
|
[0.261, 4.64354183979, 535.32003938710],
|
|
[0.244, 5.85987959874, 507.59956456680],
|
|
[0.237, 4.79666486485, 377.15882254340],
|
|
[0.224, 1.94589447357, 593.42686339800],
|
|
[0.226, 3.71637531808, 449.28029223480],
|
|
[0.233, 5.98739382153, 219.89137757700],
|
|
[0.240, 2.71609791875, 227.52618943960],
|
|
[0.221, 2.23218400256, 460.53844081980],
|
|
[0.226, 2.74516124394, 446.31134681820],
|
|
[0.221, 3.20339807670, 463.50738623640],
|
|
[0.203, 5.04975483055, 457.87831194390],
|
|
[0.191, 4.24841510229, 4.66586644600],
|
|
[0.169, 0.59358171769, 983.11585891360],
|
|
[0.179, 4.12060524413, 310.17209453310],
|
|
[0.187, 6.22165475247, 294.67297614430],
|
|
[0.162, 1.30776665222, 248.72381809010],
|
|
[0.219, 4.17413407057, 303.86169668440],
|
|
[0.193, 1.64715944768, 91.45637312370],
|
|
[0.170, 2.18067759964, 66.18357885820],
|
|
[0.156, 4.92094728667, 68.18931642830],
|
|
[0.145, 5.51404722738, 280.96714700450],
|
|
[0.144, 5.81835834612, 75.53235809270],
|
|
[0.153, 0.48549989656, 144.89733068860],
|
|
[0.168, 5.81402201452, 149.45132255000],
|
|
[0.150, 4.66632209585, 306.83064210100],
|
|
[0.131, 1.01359934164, 175.16605980020],
|
|
[0.174, 3.03279013213, 298.23262239190],
|
|
[0.163, 1.97665571311, 221.16340196420],
|
|
[0.144, 2.59058085010, 217.23124870110],
|
|
[0.167, 2.74604167580, 69.15252427480],
|
|
[0.129, 2.87574897902, 156.15547927360],
|
|
],
|
|
# L2
|
|
[
|
|
[53033.277, 0.00000000000, 0.00000000000],
|
|
[2357.636, 2.26014661705, 74.78159856730],
|
|
[769.129, 4.52561041823, 11.04570026390],
|
|
[551.533, 3.25814281023, 63.73589830340],
|
|
[541.532, 2.27573907424, 3.93215326310],
|
|
[529.473, 4.92348433826, 1.48447270830],
|
|
[257.521, 3.69059216858, 3.18139373770],
|
|
[238.835, 5.85806638405, 149.56319713460],
|
|
[181.904, 6.21763603405, 70.84944530420],
|
|
[49.401, 6.03101301723, 56.62235130260],
|
|
[53.504, 1.44225240953, 76.26607127560],
|
|
[38.222, 1.78467827781, 52.69019803950],
|
|
[44.753, 3.90904910523, 2.44768055480],
|
|
[44.530, 0.81152639478, 85.82729883120],
|
|
[37.403, 4.46228598032, 2.96894541660],
|
|
[33.029, 0.86388149962, 9.56122755560],
|
|
[24.292, 2.10702559049, 18.15924726470],
|
|
[29.423, 5.09818697708, 73.29712585900],
|
|
[22.135, 4.81730808582, 78.71375183040],
|
|
[22.491, 5.99320728691, 138.51749687070],
|
|
[17.226, 2.53537183199, 145.63104387150],
|
|
[21.392, 2.39880709309, 77.96299230500],
|
|
[20.578, 2.16918786539, 224.34479570190],
|
|
[16.777, 3.46631344086, 12.53017297220],
|
|
[12.012, 0.01941361902, 22.09140052780],
|
|
[10.466, 4.45556032593, 62.25142559510],
|
|
[11.010, 0.08496274370, 127.47179660680],
|
|
[8.668, 4.25550086984, 7.11354700080],
|
|
[10.476, 5.16453084068, 71.60020482960],
|
|
[7.160, 1.24903906391, 5.41662597140],
|
|
[8.387, 5.50115930045, 67.66805156650],
|
|
[6.087, 5.44611674384, 65.22037101170],
|
|
[6.013, 4.51836836347, 151.04766984290],
|
|
[5.718, 1.82933915340, 202.25339517410],
|
|
[6.109, 3.36320161279, 447.79581952650],
|
|
[6.003, 5.72500086735, 462.02291352810],
|
|
[5.111, 3.52374555791, 59.80374504030],
|
|
[5.155, 1.05810305746, 131.40394986990],
|
|
[5.969, 5.61147374852, 148.07872442630],
|
|
[5.065, 3.36477113418, 4.45341812490],
|
|
[4.845, 1.20298837109, 71.81265315070],
|
|
[3.979, 0.67629577193, 77.75054398390],
|
|
[3.673, 1.76315074166, 351.81659230870],
|
|
[3.149, 3.83590892865, 45.57665103870],
|
|
[3.036, 3.32062892682, 160.60889739850],
|
|
[3.033, 6.14532331482, 77.22927912210],
|
|
[3.596, 4.57256025582, 454.90936652730],
|
|
[2.664, 5.36121614612, 269.92144674060],
|
|
[2.498, 1.04819496324, 69.36497259590],
|
|
[2.307, 2.69282373897, 84.34282612290],
|
|
[2.249, 5.07693376112, 14.97785352700],
|
|
[2.228, 1.38937510191, 284.14854074220],
|
|
[2.064, 4.34647674542, 984.60033162190],
|
|
[2.105, 2.32047802326, 120.35824960600],
|
|
[1.864, 5.70354779393, 54.17467074780],
|
|
[2.005, 3.87177765185, 195.13984817330],
|
|
[1.622, 5.07964536529, 209.36694217490],
|
|
[1.597, 0.48807990368, 137.03302416240],
|
|
[1.583, 2.90536212187, 51.20572533120],
|
|
[1.725, 6.25703202673, 41.64449777560],
|
|
[2.073, 1.24032244487, 35.16409022120],
|
|
[1.543, 2.15414338268, 70.32818044240],
|
|
[1.671, 6.28283232471, 277.03499374140],
|
|
[1.494, 6.04572758571, 87.31177153950],
|
|
[1.418, 1.15843502159, 213.29909543800],
|
|
[1.239, 4.63223076077, 92.94084583200],
|
|
[1.238, 2.65969680342, 134.58534360760],
|
|
[1.273, 5.87964059822, 60.55450456570],
|
|
[1.160, 1.03320781667, 153.49535039770],
|
|
[1.430, 4.68022239016, 299.12639426920],
|
|
[1.117, 2.62506108047, 72.33391801250],
|
|
[1.142, 4.64615099782, 152.74459087230],
|
|
[0.974, 2.85233132493, 222.86032299360],
|
|
[1.046, 4.81299135934, 116.42609634290],
|
|
[0.872, 3.49659835508, 340.77089204480],
|
|
[0.952, 2.10837480840, 20.60692781950],
|
|
[0.964, 2.46471453524, 380.12776796000],
|
|
[0.843, 6.12869288891, 49.50880430180],
|
|
[0.821, 0.27134156683, 191.20769491020],
|
|
[0.813, 4.08930465981, 14.22709400160],
|
|
[0.796, 6.17066846300, 344.70304530790],
|
|
[0.924, 2.11096444289, 14.01464568050],
|
|
[0.791, 2.38927423348, 58.10682401090],
|
|
[0.781, 0.74223115950, 408.43894361130],
|
|
[0.759, 3.77564054479, 80.19822453870],
|
|
[0.884, 1.99930014838, 265.98929347750],
|
|
[0.722, 3.10001033669, 422.66603761290],
|
|
[0.750, 2.33167721991, 358.93013930950],
|
|
[0.687, 2.02866342040, 33.67961751290],
|
|
[0.603, 1.10391172652, 55.13787859430],
|
|
[0.655, 3.85415269764, 16.67477455640],
|
|
[0.606, 0.15052747979, 28.31117565130],
|
|
[0.639, 5.16714934188, 23.57587323610],
|
|
[0.658, 0.75636229109, 76.47851959670],
|
|
[0.590, 1.73778850095, 8.07675484730],
|
|
[0.565, 4.92645232089, 35.42472265210],
|
|
[0.656, 2.34273264083, 38.13303563780],
|
|
[0.542, 5.97968975563, 146.59425171800],
|
|
[0.518, 3.19086220901, 152.53214255120],
|
|
[0.536, 4.52808465499, 220.41264243880],
|
|
[0.489, 4.80633294199, 159.12442469020],
|
|
[0.491, 0.85765309118, 565.11568774670],
|
|
[0.483, 3.52583593251, 144.14657116320],
|
|
[0.521, 5.21561656321, 206.18554843720],
|
|
[0.477, 4.25420753202, 365.90067395840],
|
|
[0.466, 5.13219663072, 297.64192156090],
|
|
[0.557, 0.98387565952, 225.82926841020],
|
|
[0.531, 4.22534657450, 29.20494752860],
|
|
[0.500, 3.49663062387, 128.95626931510],
|
|
[0.445, 2.60797570173, 96.87299909510],
|
|
[0.466, 6.05585106742, 70.11573212130],
|
|
[0.425, 1.04692398351, 19.64371997300],
|
|
[0.491, 2.26123398680, 152.01087768940],
|
|
[0.455, 5.45520675000, 333.65734504400],
|
|
[0.458, 0.91654899383, 373.01422095920],
|
|
[0.520, 5.72828536642, 111.43016149680],
|
|
[0.432, 1.04604024916, 125.98732389850],
|
|
[0.387, 2.82547341355, 200.76892246580],
|
|
[0.383, 1.91679738697, 5.62907429250],
|
|
[0.504, 1.95816731769, 415.55249061210],
|
|
[0.370, 3.21958844151, 387.24131496080],
|
|
[0.379, 2.75940848661, 81.89514556810],
|
|
[0.345, 2.98021540638, 429.77958461370],
|
|
[0.368, 6.20331898497, 456.39383923560],
|
|
[0.335, 5.29062985955, 13.33332212430],
|
|
[0.320, 0.74685222907, 347.88443904560],
|
|
[0.307, 1.65925943351, 99.16062095550],
|
|
[0.284, 2.09437476480, 129.91947716160],
|
|
[0.275, 0.62680026669, 31.49256938900],
|
|
[0.339, 1.65968150805, 142.44965013380],
|
|
[0.270, 2.79378345550, 977.48678462110],
|
|
[0.284, 2.42261530322, 546.95644048200],
|
|
[0.271, 0.59225635449, 1894.41906467650],
|
|
[0.263, 3.49309481771, 440.68227252570],
|
|
[0.295, 0.43376026627, 373.90799283650],
|
|
[0.271, 4.82853730065, 561.18353448360],
|
|
[0.248, 5.72379940676, 79.23501669220],
|
|
[0.252, 5.76728095309, 235.39049596580],
|
|
[0.261, 0.09830739366, 991.71387862270],
|
|
[0.238, 1.14634663242, 288.08069400530],
|
|
[0.220, 5.12386263728, 479.28838891550],
|
|
[0.263, 1.52366362053, 146.38180339690],
|
|
[0.230, 0.35983101967, 109.94568878850],
|
|
[0.214, 2.94388765580, 184.72728735580],
|
|
[0.198, 5.72107161521, 453.42489381900],
|
|
[0.185, 4.71600176780, 108.46121608020],
|
|
[0.139, 2.99832472431, 211.81462272970],
|
|
[0.167, 1.19643522280, 39.61750834610],
|
|
[0.180, 0.80198096578, 183.24281464750],
|
|
[0.131, 2.73236351123, 522.57741809380],
|
|
[0.142, 5.03489222377, 536.80451209540],
|
|
],
|
|
# L3
|
|
[
|
|
[120.936, 0.02418789918, 74.78159856730],
|
|
[68.064, 4.12084267733, 3.93215326310],
|
|
[52.828, 2.38964061260, 11.04570026390],
|
|
[43.754, 2.95965039734, 1.48447270830],
|
|
[45.300, 2.04423798410, 3.18139373770],
|
|
[45.806, 0.00000000000, 0.00000000000],
|
|
[24.969, 4.88741307918, 63.73589830340],
|
|
[21.061, 4.54511486862, 70.84944530420],
|
|
[19.897, 2.31320314136, 149.56319713460],
|
|
[8.901, 1.57548871761, 56.62235130260],
|
|
[4.271, 0.22777319552, 18.15924726470],
|
|
[3.613, 5.39244611308, 76.26607127560],
|
|
[3.488, 4.97622811775, 85.82729883120],
|
|
[3.479, 4.12969359977, 52.69019803950],
|
|
[3.572, 0.95052448578, 77.96299230500],
|
|
[2.328, 0.85770961794, 145.63104387150],
|
|
[2.696, 0.37287796344, 78.71375183040],
|
|
[1.946, 2.67997393431, 7.11354700080],
|
|
[2.156, 5.65647821519, 9.56122755560],
|
|
[1.363, 4.86983744746, 224.34479570190],
|
|
[1.333, 1.25032115614, 12.53017297220],
|
|
[1.613, 0.48764377311, 71.60020482960],
|
|
[1.475, 5.19957293069, 73.29712585900],
|
|
[1.225, 3.93406822032, 22.09140052780],
|
|
[0.911, 2.18921999026, 127.47179660680],
|
|
[0.811, 3.98323855938, 462.02291352810],
|
|
[0.808, 5.06374463008, 447.79581952650],
|
|
[0.718, 0.34600103024, 5.62907429250],
|
|
[0.722, 1.05856935832, 138.51749687070],
|
|
[0.687, 2.93752748595, 131.40394986990],
|
|
[0.463, 1.58927254512, 151.04766984290],
|
|
[0.414, 4.32904287620, 120.35824960600],
|
|
[0.372, 0.73596518002, 269.92144674060],
|
|
[0.345, 3.05968942771, 561.18353448360],
|
|
[0.338, 5.94221536204, 284.14854074220],
|
|
[0.343, 4.01891371998, 546.95644048200],
|
|
[0.382, 5.93515231196, 45.57665103870],
|
|
[0.276, 3.44212110991, 202.25339517410],
|
|
[0.300, 1.13119175675, 160.60889739850],
|
|
[0.268, 3.24615387968, 536.80451209540],
|
|
[0.358, 1.10916640253, 333.65734504400],
|
|
[0.236, 4.65292396535, 387.24131496080],
|
|
[0.204, 5.81663798296, 373.01422095920],
|
|
[0.145, 2.75632381347, 92.94084583200],
|
|
[0.149, 0.13764106563, 71.81265315070],
|
|
[0.156, 2.90936922804, 153.49535039770],
|
|
],
|
|
# L4
|
|
[
|
|
[113.855, 3.14159265359, 0.00000000000],
|
|
[5.599, 4.57882424417, 74.78159856730],
|
|
[3.203, 0.34623003207, 11.04570026390],
|
|
[1.217, 3.42199121826, 56.62235130260],
|
|
[0.634, 4.65759668097, 18.15924726470],
|
|
[0.171, 3.80393539303, 149.56319713460],
|
|
[0.133, 4.35519131657, 63.73589830340],
|
|
],
|
|
# L5
|
|
[
|
|
[0.873, 3.14159265359, 0.00000000000]
|
|
],
|
|
]
|
|
"""This table contains Uranus' 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
|
|
445-448."""
|
|
|
|
|
|
VSOP87_B = [
|
|
# B0
|
|
[
|
|
[1346277.639, 2.61877810545, 74.78159856730],
|
|
[62341.405, 5.08111175856, 149.56319713460],
|
|
[61601.203, 3.14159265359, 0.00000000000],
|
|
[9963.744, 1.61603876357, 76.26607127560],
|
|
[9926.151, 0.57630387917, 73.29712585900],
|
|
[3259.455, 1.26119385960, 224.34479570190],
|
|
[2972.318, 2.24367035538, 1.48447270830],
|
|
[2010.257, 6.05550401088, 148.07872442630],
|
|
[1522.172, 0.27960386377, 63.73589830340],
|
|
[924.055, 4.03822927853, 151.04766984290],
|
|
[760.624, 6.14000431923, 71.81265315070],
|
|
[420.265, 5.21279984788, 11.04570026390],
|
|
[430.668, 3.55445034854, 213.29909543800],
|
|
[436.843, 3.38082524317, 529.69096509460],
|
|
[522.309, 3.32085194770, 138.51749687070],
|
|
[434.625, 0.34065281858, 77.75054398390],
|
|
[462.630, 0.74256727574, 85.82729883120],
|
|
[232.649, 2.25716421383, 222.86032299360],
|
|
[215.838, 1.59121704940, 38.13303563780],
|
|
[244.698, 0.78795150326, 2.96894541660],
|
|
[179.935, 3.72487952673, 299.12639426920],
|
|
[174.895, 1.23550262213, 146.59425171800],
|
|
[173.667, 1.93654269131, 380.12776796000],
|
|
[160.368, 5.33635436463, 111.43016149680],
|
|
[144.064, 5.96239326415, 35.16409022120],
|
|
[102.049, 2.61876256513, 78.71375183040],
|
|
[116.363, 5.73877190007, 70.84944530420],
|
|
[106.441, 0.94103112994, 70.32818044240],
|
|
[86.163, 0.70262506622, 39.61750834610],
|
|
[72.617, 0.20564696113, 225.82926841020],
|
|
[71.172, 0.83343269975, 109.94568878850],
|
|
[57.502, 2.67039425415, 108.46121608020],
|
|
[54.255, 3.35166579613, 184.72728735580],
|
|
[44.470, 2.74408231138, 152.53214255120],
|
|
[38.591, 5.17394663303, 202.25339517410],
|
|
[39.157, 2.17108251341, 351.81659230870],
|
|
[41.346, 3.22134319551, 160.60889739850],
|
|
[35.140, 4.00111634363, 112.91463420510],
|
|
[33.073, 3.61378095742, 221.37585028530],
|
|
[31.315, 2.71969470781, 145.10977900970],
|
|
[37.336, 4.02053241202, 52.69019803950],
|
|
[32.028, 1.29160071142, 145.63104387150],
|
|
[27.574, 3.70064266960, 36.64856292950],
|
|
[24.277, 2.84989187496, 127.47179660680],
|
|
[24.635, 1.11645461259, 3.93215326310],
|
|
[24.315, 5.48987913644, 79.23501669220],
|
|
[21.418, 0.63722900407, 277.03499374140],
|
|
[19.826, 2.59334182230, 84.34282612290],
|
|
[22.373, 5.73687615457, 4.45341812490],
|
|
[19.137, 1.30214105578, 62.25142559510],
|
|
[19.789, 4.72260849557, 297.64192156090],
|
|
[20.299, 1.06070151806, 454.90936652730],
|
|
[19.768, 5.77906142568, 305.34616939270],
|
|
[21.348, 1.01350946382, 33.67961751290],
|
|
[15.142, 2.91786832554, 426.59819087600],
|
|
[16.000, 1.95535748902, 186.21176006410],
|
|
[13.819, 2.67163927171, 74.66972398270],
|
|
[11.463, 5.73391138419, 41.10198105440],
|
|
[10.741, 3.73401569675, 1059.38193018920],
|
|
[11.450, 3.98177764866, 106.97674337190],
|
|
[10.360, 4.75567608732, 183.24281464750],
|
|
[10.232, 6.18772866993, 373.90799283650],
|
|
[13.803, 5.70712120608, 74.89347315190],
|
|
[10.553, 3.78602881738, 490.33408917940],
|
|
[11.838, 5.96756415681, 87.31177153950],
|
|
[10.030, 1.74828757238, 22.09140052780],
|
|
[10.107, 0.92911975959, 65.22037101170],
|
|
[9.127, 5.11093790809, 153.49535039770],
|
|
[12.093, 2.53736362742, 9.56122755560],
|
|
[8.646, 4.18351923569, 12.53017297220],
|
|
[9.978, 5.83600622359, 604.47256366190],
|
|
[11.352, 2.12645777694, 68.84370773410],
|
|
[8.472, 3.36885457285, 72.33391801250],
|
|
[7.797, 5.11771906359, 77.96299230500],
|
|
[8.302, 5.19247905162, 77.22927912210],
|
|
[7.696, 3.25189037096, 71.60020482960],
|
|
[7.513, 2.98265970100, 114.39910691340],
|
|
[6.947, 3.31871016057, 56.62235130260],
|
|
[6.490, 0.88434578474, 288.08069400530],
|
|
[6.394, 3.51142812432, 220.41264243880],
|
|
[6.211, 0.58222518453, 340.77089204480],
|
|
[6.772, 4.09374798222, 137.03302416240],
|
|
[5.595, 5.68643434536, 259.50888592310],
|
|
[5.309, 2.65421183211, 300.61086697750],
|
|
[4.950, 4.99672086239, 219.89137757700],
|
|
[6.419, 0.44895727879, 140.00196957900],
|
|
[4.975, 4.06722486039, 143.62530630140],
|
|
[5.692, 3.76563463180, 67.66805156650],
|
|
[4.853, 2.03383592524, 415.55249061210],
|
|
[3.796, 1.26231186682, 75.30286342910],
|
|
[3.807, 2.24787582155, 909.81873305460],
|
|
[3.812, 3.10475682509, 181.75834193920],
|
|
[3.764, 5.20052090560, 227.31374111850],
|
|
[3.445, 5.91769433069, 296.15744885260],
|
|
[3.517, 5.44397685665, 628.85158605010],
|
|
[3.943, 4.95136058926, 265.98929347750],
|
|
[3.472, 0.34737998380, 131.40394986990],
|
|
[3.390, 0.53497504164, 206.18554843720],
|
|
[3.038, 4.68314286209, 159.12442469020],
|
|
[3.190, 5.68929316349, 235.39049596580],
|
|
[3.303, 2.09359507373, 73.81839072080],
|
|
[3.069, 4.49065085092, 66.70484372000],
|
|
[3.285, 0.00780313833, 75.74480641380],
|
|
[2.917, 4.21615078632, 258.02441321480],
|
|
[3.747, 0.82999983666, 74.26033370550],
|
|
[2.814, 3.96708337625, 82.85835341460],
|
|
[2.474, 3.81319259323, 7.11354700080],
|
|
[2.394, 2.21483198491, 54.17467074780],
|
|
[2.555, 2.97023907145, 378.64329525170],
|
|
[2.631, 1.55153254691, 154.01661525950],
|
|
[2.633, 2.28385552693, 32.19514480460],
|
|
[2.643, 3.96832729680, 381.61224066830],
|
|
[2.206, 3.06995275892, 59.80374504030],
|
|
[2.635, 0.53987945692, 211.81462272970],
|
|
[2.071, 1.97429082033, 18.15924726470],
|
|
[2.485, 3.55433846990, 96.87299909510],
|
|
[2.061, 4.50102695788, 5.93789083320],
|
|
[1.916, 1.60538526374, 80.19822453870],
|
|
[2.480, 0.63321072542, 187.69623277240],
|
|
[2.039, 2.97351088965, 191.20769491020],
|
|
[1.833, 1.95824865568, 81.89514556810],
|
|
[1.719, 2.22526635038, 479.28838891550],
|
|
[1.745, 3.22821992592, 218.40690486870],
|
|
[1.857, 1.66304484985, 984.60033162190],
|
|
[1.766, 5.24239122261, 105.49227066360],
|
|
[1.524, 6.05374020264, 99.16062095550],
|
|
[1.519, 0.94716867229, 372.42352012820],
|
|
[1.614, 3.39986066169, 230.56457082540],
|
|
[1.711, 3.44237080993, 522.57741809380],
|
|
[1.504, 1.34653259405, 74.52096613640],
|
|
[1.577, 4.38020936720, 80.71948940050],
|
|
[1.360, 5.48691240270, 74.82978267710],
|
|
[1.364, 4.56045715617, 42.58645376270],
|
|
[1.398, 0.33827838973, 142.44965013380],
|
|
[1.709, 3.63188407264, 554.06998748280],
|
|
[1.360, 2.89305157919, 74.73341445750],
|
|
[1.260, 5.50922979275, 74.94165726170],
|
|
[1.374, 4.39897993200, 260.99335863140],
|
|
[1.366, 2.15288773765, 162.09337010680],
|
|
[1.244, 4.97789913094, 149.45132255000],
|
|
[1.269, 0.84167691738, 767.36908292080],
|
|
[1.278, 4.53585702916, 294.67297614430],
|
|
[1.342, 5.11117141196, 51.20572533120],
|
|
[1.180, 0.79882196802, 116.42609634290],
|
|
[1.495, 0.74986873597, 75.04223099820],
|
|
[1.207, 3.67288675913, 20.60692781950],
|
|
[1.181, 4.39598416757, 180.27386923090],
|
|
[1.248, 3.13312504066, 67.35923502580],
|
|
[1.263, 2.87116663203, 74.62153987290],
|
|
[1.380, 3.76141611602, 92.94084583200],
|
|
[1.113, 3.87133607367, 39.35687591520],
|
|
[1.018, 6.20393099094, 835.03713448730],
|
|
[0.962, 3.30343472839, 255.05546779820],
|
|
[1.238, 1.73023505315, 149.67507171920],
|
|
[0.970, 1.71236273285, 115.88357962170],
|
|
[1.001, 5.49914631698, 256.53994050650],
|
|
[0.921, 3.07729879788, 8.07675484730],
|
|
[0.914, 0.00764291274, 536.80451209540],
|
|
[0.911, 6.23753038018, 200.76892246580],
|
|
[0.956, 5.76811833839, 128.95626931510],
|
|
[0.999, 0.33400530567, 404.50679034820],
|
|
[0.952, 3.00456073496, 14.97785352700],
|
|
[0.765, 3.45454533660, 214.78356814630],
|
|
[0.800, 3.20912932090, 28.31117565130],
|
|
[0.799, 4.11425365829, 125.98732389850],
|
|
[1.021, 1.79905869707, 3.18139373770],
|
|
[0.706, 5.80210566917, 157.63995198190],
|
|
[0.715, 5.56313177065, 146.38180339690],
|
|
[0.689, 1.84748347121, 41.64449777560],
|
|
[0.682, 5.16479782395, 74.03083904190],
|
|
[0.673, 2.65544175682, 75.53235809270],
|
|
[0.723, 4.75905991606, 331.32153907380],
|
|
[0.730, 2.25510749124, 453.42489381900],
|
|
[0.691, 3.58561635364, 362.86229257260],
|
|
[0.641, 5.77408891198, 110.20632121940],
|
|
[0.671, 5.96862039131, 135.54855145410],
|
|
[0.631, 1.97807297205, 639.89728631400],
|
|
[0.774, 0.42035450706, 565.11568774670],
|
|
[0.705, 2.94649553712, 60.76695288680],
|
|
[0.663, 5.32574112049, 142.14083359310],
|
|
[0.612, 2.01741578932, 195.13984817330],
|
|
[0.749, 5.56828487823, 2.44768055480],
|
|
[0.798, 0.90969731665, 152.01087768940],
|
|
[0.747, 5.07639466593, 89.75945209430],
|
|
[0.650, 4.56215718085, 216.92243216040],
|
|
[0.651, 2.80626026285, 50.40257617910],
|
|
[0.593, 1.89556258897, 203.73786788240],
|
|
[0.550, 2.90625551534, 68.18931642830],
|
|
[0.548, 3.75628845322, 617.80588578620],
|
|
[0.554, 2.78135114877, 14.01464568050],
|
|
[0.530, 3.51385025328, 291.70403072770],
|
|
[0.506, 4.94619342366, 81.37388070630],
|
|
[0.649, 5.74895589744, 141.48644228730],
|
|
[0.593, 5.40734033998, 692.58748435350],
|
|
[0.544, 2.99910512780, 152.74459087230],
|
|
[0.485, 2.36317665443, 448.68959140380],
|
|
[0.481, 5.81647231299, 134.58534360760],
|
|
[0.517, 4.97759795528, 387.24131496080],
|
|
[0.573, 2.46311368783, 81.00137369080],
|
|
[0.470, 1.30184316812, 228.27694896500],
|
|
[0.475, 0.53480492526, 303.86169668440],
|
|
[0.485, 6.21247575899, 5.41662597140],
|
|
[0.468, 0.55881267334, 23.57587323610],
|
|
[0.585, 4.67924542643, 88.79624424780],
|
|
[0.512, 5.86200059955, 293.18850343600],
|
|
[0.445, 2.50076311432, 905.88657979150],
|
|
[0.501, 4.79997295899, 306.83064210100],
|
|
[0.418, 5.21379084769, 35.42472265210],
|
|
[0.408, 5.69107313998, 284.14854074220],
|
|
[0.474, 3.03149617428, 286.59622129700],
|
|
[0.432, 4.20907682097, 278.51946644970],
|
|
[0.506, 2.05348204197, 373.01422095920],
|
|
[0.410, 5.30637634877, 95.38852638680],
|
|
[0.478, 2.41106642594, 358.93013930950],
|
|
[0.536, 1.82614772260, 114.13847448250],
|
|
[0.383, 5.54541241459, 419.48464387520],
|
|
[0.413, 0.03813081773, 103.09277421860],
|
|
[0.368, 4.08526832792, 1589.07289528380],
|
|
[0.369, 1.82533858431, 334.29048449040],
|
|
[0.491, 5.58913582973, 68.56182344380],
|
|
[0.387, 0.56619310480, 602.98809095360],
|
|
[0.427, 5.08349119654, 367.97010200330],
|
|
[0.475, 0.17507881032, 120.35824960600],
|
|
[0.342, 5.27187859255, 28.57180808220],
|
|
[0.407, 2.00853504718, 679.25416222920],
|
|
[0.381, 4.61366060949, 329.72519178090],
|
|
[0.388, 0.88856038803, 483.22054217860],
|
|
[0.376, 1.28856348513, 155.78297225810],
|
|
[0.326, 6.09140263554, 456.39383923560],
|
|
[0.318, 0.09996195379, 69.36497259590],
|
|
[0.292, 5.11578046796, 375.39246554480],
|
|
[0.299, 6.04121646505, 332.80601178210],
|
|
[0.328, 3.47252263966, 73.40900044360],
|
|
[0.283, 1.81773059325, 647.01083331480],
|
|
[0.308, 3.50154864071, 30.71067209630],
|
|
[0.283, 1.88910019831, 24.37902238820],
|
|
[0.278, 3.85507901929, 760.25553592000],
|
|
[0.273, 4.22941219477, 391.17346822390],
|
|
[0.293, 5.44464406156, 477.91579079180],
|
|
[0.289, 3.85492516765, 209.36694217490],
|
|
[0.309, 1.97045147502, 543.02428721890],
|
|
[0.324, 5.57191515554, 501.37978944330],
|
|
[0.248, 2.17741598681, 611.58611066270],
|
|
[0.245, 1.04008534095, 1332.48477066750],
|
|
[0.248, 6.19516038159, 1134.16352875650],
|
|
[0.242, 1.37720813333, 121.25202148330],
|
|
[0.233, 0.50933224249, 462.02291352810],
|
|
[0.319, 4.24219881040, 328.35259365720],
|
|
[0.244, 6.00644853640, 295.19424100610],
|
|
[0.228, 0.72608678727, 233.90602325750],
|
|
[0.223, 5.35785607671, 983.11585891360],
|
|
[0.304, 5.68101077712, 189.18070548070],
|
|
[0.223, 2.04168197187, 370.93904741990],
|
|
[0.245, 4.69742022955, 316.39186965660],
|
|
[0.217, 4.33845164683, 269.92144674060],
|
|
[0.267, 0.15744446718, 10213.28554621100],
|
|
[0.210, 5.84975171904, 147.11551657980],
|
|
[0.224, 3.04829549918, 1439.50969814920],
|
|
[0.226, 0.72248476212, 45.57665103870],
|
|
[0.202, 1.37341689387, 302.09533968580],
|
|
[0.207, 6.13936312021, 344.70304530790],
|
|
[0.228, 2.33602531859, 150.52640498110],
|
|
[0.203, 2.38070591912, 275.55052103310],
|
|
[0.194, 5.11344829813, 1215.16490244730],
|
|
[0.259, 2.78974616768, 144.14657116320],
|
|
[0.199, 3.21010368905, 7.42236354150],
|
|
[0.246, 6.15106498377, 6.21977512350],
|
|
[0.180, 4.70377036870, 518.64526483070],
|
|
[0.186, 3.85070006482, 46.20979048510],
|
|
[0.175, 3.72163733058, 150.08446199640],
|
|
[0.165, 1.87245210311, 310.17209453310],
|
|
[0.166, 3.24028819042, 173.94221952280],
|
|
[0.181, 0.39521867351, 0.96320784650],
|
|
[0.144, 1.78180338482, 531.17543780290],
|
|
[0.137, 6.20635855175, 369.45457471160],
|
|
[0.136, 4.00164375048, 526.72201967800],
|
|
[0.141, 4.02238453909, 350.33211960040],
|
|
[0.125, 5.28865037145, 329.83706636550],
|
|
[0.134, 3.97421067761, 228.79821382680],
|
|
[0.132, 4.52023845365, 148.59998928810],
|
|
[0.125, 4.24724390191, 248.72381809010],
|
|
[0.120, 4.08565783859, 154.97982310600],
|
|
[0.133, 3.16576403244, 262.47783133970],
|
|
],
|
|
# B1
|
|
[
|
|
[206366.162, 4.12394311407, 74.78159856730],
|
|
[8563.230, 0.33819986165, 149.56319713460],
|
|
[1725.703, 2.12193159895, 73.29712585900],
|
|
[1368.860, 3.06861722047, 76.26607127560],
|
|
[1374.449, 0.00000000000, 0.00000000000],
|
|
[399.847, 2.84767037795, 224.34479570190],
|
|
[450.639, 3.77656180977, 1.48447270830],
|
|
[307.214, 1.25456766737, 148.07872442630],
|
|
[154.336, 3.78575467747, 63.73589830340],
|
|
[110.888, 5.32888676461, 138.51749687070],
|
|
[112.432, 5.57299891505, 151.04766984290],
|
|
[83.493, 3.59152795558, 71.81265315070],
|
|
[55.573, 3.40135416354, 85.82729883120],
|
|
[41.377, 4.45476669141, 78.71375183040],
|
|
[53.690, 1.70455769943, 77.75054398390],
|
|
[41.912, 1.21476607434, 11.04570026390],
|
|
[31.959, 3.77446207748, 222.86032299360],
|
|
[30.297, 2.56371683644, 2.96894541660],
|
|
[26.977, 5.33695500294, 213.29909543800],
|
|
[26.222, 0.41620628369, 380.12776796000],
|
|
[20.094, 5.93085633510, 529.69096509460],
|
|
[22.992, 2.48887389394, 146.59425171800],
|
|
[19.590, 5.37213500014, 299.12639426920],
|
|
[20.408, 3.70179681605, 70.84944530420],
|
|
[19.102, 1.09213276596, 111.43016149680],
|
|
[19.411, 3.83015453768, 38.13303563780],
|
|
[10.847, 2.66326308043, 3.93215326310],
|
|
[10.249, 2.31278807720, 109.94568878850],
|
|
[9.405, 2.76950513184, 39.61750834610],
|
|
[7.660, 1.81108462850, 225.82926841020],
|
|
[8.082, 4.69064168719, 184.72728735580],
|
|
[6.584, 5.50417589189, 35.16409022120],
|
|
[7.410, 1.17879753422, 65.22037101170],
|
|
[6.451, 4.98294064391, 71.60020482960],
|
|
[6.089, 1.31830108565, 52.69019803950],
|
|
[4.768, 5.90574941745, 145.63104387150],
|
|
[4.840, 4.86390682412, 221.37585028530],
|
|
[4.192, 3.29643787103, 77.96299230500],
|
|
[4.711, 4.24289069791, 152.53214255120],
|
|
[4.894, 6.01164167429, 160.60889739850],
|
|
[3.738, 4.75287390209, 70.32818044240],
|
|
[3.481, 0.64108927026, 153.49535039770],
|
|
[3.758, 3.94715595219, 351.81659230870],
|
|
[3.114, 0.10537144899, 112.91463420510],
|
|
[2.788, 4.24118032837, 74.66972398270],
|
|
[2.505, 0.04576283378, 297.64192156090],
|
|
[2.563, 4.15665405963, 305.34616939270],
|
|
[2.544, 5.25903565788, 56.62235130260],
|
|
[2.247, 4.24726481845, 36.64856292950],
|
|
[2.541, 0.40106060407, 77.22927912210],
|
|
[2.212, 2.88960413468, 277.03499374140],
|
|
[2.299, 3.57748029365, 186.21176006410],
|
|
[2.661, 0.53230319176, 79.23501669220],
|
|
[2.157, 2.10150995852, 127.47179660680],
|
|
[2.265, 1.41055702214, 4.45341812490],
|
|
[2.103, 4.27438518414, 22.09140052780],
|
|
[1.861, 3.75619999278, 145.10977900970],
|
|
[1.759, 2.10240976488, 131.40394986990],
|
|
[1.661, 4.84483054269, 62.25142559510],
|
|
[1.496, 1.72084298116, 220.41264243880],
|
|
[1.659, 5.86539712478, 454.90936652730],
|
|
[1.428, 0.31508367934, 137.03302416240],
|
|
[1.522, 1.00801468633, 75.74480641380],
|
|
[1.459, 6.17427145114, 426.59819087600],
|
|
[1.463, 5.14953143442, 84.34282612290],
|
|
[1.453, 2.22988903923, 206.18554843720],
|
|
[1.358, 5.85111427068, 183.24281464750],
|
|
[1.405, 2.43582184515, 87.31177153950],
|
|
[1.495, 5.55621838458, 67.66805156650],
|
|
[1.317, 1.91178535183, 140.00196957900],
|
|
[1.068, 1.51430678116, 373.90799283650],
|
|
[1.439, 0.99170994448, 74.89347315190],
|
|
[1.065, 4.15616015505, 288.08069400530],
|
|
[1.096, 1.63909426062, 41.10198105440],
|
|
[1.189, 0.90595784409, 33.67961751290],
|
|
[0.961, 5.48175535705, 490.33408917940],
|
|
[0.851, 0.95029849401, 909.81873305460],
|
|
[0.820, 0.78610123063, 259.50888592310],
|
|
[0.881, 4.31294603221, 9.56122755560],
|
|
[0.708, 0.00007309836, 81.89514556810],
|
|
[0.709, 3.18853632737, 80.19822453870],
|
|
[0.786, 5.18884635415, 114.39910691340],
|
|
[0.822, 0.01949759759, 18.15924726470],
|
|
[0.656, 6.16899483115, 96.87299909510],
|
|
[0.879, 1.82006610038, 73.81839072080],
|
|
[0.872, 0.30134022304, 12.53017297220],
|
|
[0.860, 0.21225398802, 3.18139373770],
|
|
[0.637, 2.64378420008, 75.30286342910],
|
|
[0.727, 0.02846968582, 66.70484372000],
|
|
[0.600, 4.42462853209, 415.55249061210],
|
|
[0.590, 4.17885957237, 300.61086697750],
|
|
[0.610, 6.07202921132, 219.89137757700],
|
|
[0.611, 0.97629869063, 296.15744885260],
|
|
[0.635, 2.21125075603, 74.26033370550],
|
|
[0.529, 2.35940463062, 7.11354700080],
|
|
[0.622, 2.21801944850, 211.81462272970],
|
|
[0.519, 2.01872911223, 142.44965013380],
|
|
[0.489, 1.83419944488, 92.94084583200],
|
|
[0.445, 2.51784247184, 604.47256366190],
|
|
[0.413, 5.36482818305, 82.85835341460],
|
|
[0.445, 0.33164113115, 227.31374111850],
|
|
[0.456, 2.44190834824, 381.61224066830],
|
|
[0.378, 1.91873737843, 202.25339517410],
|
|
[0.509, 5.83556856314, 191.20769491020],
|
|
[0.455, 5.15414537021, 522.57741809380],
|
|
[0.419, 2.80644155875, 72.33391801250],
|
|
[0.333, 0.32014837950, 2.44768055480],
|
|
[0.360, 1.47248643716, 378.64329525170],
|
|
[0.306, 0.15517399606, 159.12442469020],
|
|
[0.301, 4.46417652272, 536.80451209540],
|
|
[0.353, 0.48749845867, 128.95626931510],
|
|
[0.351, 6.24769322491, 5.93789083320],
|
|
[0.298, 1.71815652029, 235.39049596580],
|
|
[0.315, 2.44922921309, 187.69623277240],
|
|
[0.318, 0.70176359510, 181.75834193920],
|
|
[0.314, 4.68400251693, 14.97785352700],
|
|
[0.282, 3.70093718573, 108.46121608020],
|
|
[0.272, 3.91340553608, 617.80588578620],
|
|
[0.273, 3.29483889428, 387.24131496080],
|
|
[0.323, 4.90410549341, 258.02441321480],
|
|
[0.288, 4.42249612833, 195.13984817330],
|
|
[0.250, 1.23231297183, 703.63318461740],
|
|
[0.338, 2.84645768890, 154.01661525950],
|
|
[0.297, 1.16538119842, 146.38180339690],
|
|
[0.248, 4.90614051989, 41.64449777560],
|
|
[0.275, 5.35665949805, 80.71948940050],
|
|
[0.257, 1.82441994046, 230.56457082540],
|
|
[0.234, 0.27679874465, 33.13710079170],
|
|
[0.280, 1.73679618032, 265.98929347750],
|
|
[0.229, 0.49529839431, 74.82978267710],
|
|
[0.229, 4.18462288684, 74.73341445750],
|
|
[0.253, 2.63817804331, 74.52096613640],
|
|
[0.252, 2.04143912495, 75.04223099820],
|
|
[0.213, 4.16218259902, 74.62153987290],
|
|
[0.212, 0.51761494342, 74.94165726170],
|
|
[0.201, 4.54140547837, 20.60692781950],
|
|
[0.194, 4.17282454759, 116.42609634290],
|
|
[0.213, 2.29528235429, 32.19514480460],
|
|
[0.174, 3.15418942153, 228.27694896500],
|
|
[0.194, 0.06960211137, 42.58645376270],
|
|
[0.173, 5.59700344643, 68.84370773410],
|
|
[0.159, 4.91721631097, 143.62530630140],
|
|
[0.150, 0.92771324396, 404.50679034820],
|
|
[0.136, 2.51083022906, 372.42352012820],
|
|
[0.134, 3.22507836958, 479.28838891550],
|
|
[0.124, 0.42063711585, 149.45132255000],
|
|
[0.122, 1.20639876458, 5.41662597140],
|
|
[0.119, 0.45375065997, 74.03083904190],
|
|
[0.146, 5.08207330360, 294.67297614430],
|
|
[0.118, 4.22640788890, 75.53235809270],
|
|
[0.118, 1.50613822829, 344.70304530790],
|
|
[0.121, 2.13544759505, 209.36694217490],
|
|
[0.121, 6.08239076370, 260.99335863140],
|
|
[0.154, 4.18369977366, 39.35687591520],
|
|
],
|
|
# B2
|
|
[
|
|
[9211.656, 5.80044305785, 74.78159856730],
|
|
[556.926, 0.00000000000, 0.00000000000],
|
|
[286.265, 2.17729776353, 149.56319713460],
|
|
[94.969, 3.84237569809, 73.29712585900],
|
|
[45.419, 4.87822046064, 76.26607127560],
|
|
[20.107, 5.46264485369, 1.48447270830],
|
|
[14.793, 0.87983715652, 138.51749687070],
|
|
[13.963, 5.07234043994, 63.73589830340],
|
|
[14.261, 2.84517742687, 148.07872442630],
|
|
[10.122, 5.00290894862, 224.34479570190],
|
|
[8.299, 6.26655615197, 78.71375183040],
|
|
[4.729, 5.16274174929, 71.81265315070],
|
|
[3.816, 6.28224514574, 85.82729883120],
|
|
[3.488, 3.53472172445, 11.04570026390],
|
|
[2.555, 1.44444215715, 151.04766984290],
|
|
[2.353, 4.23069776466, 3.93215326310],
|
|
[2.585, 0.41383633246, 71.60020482960],
|
|
[1.394, 4.13126838571, 146.59425171800],
|
|
[1.183, 3.68471361409, 77.75054398390],
|
|
[1.103, 5.54212014132, 222.86032299360],
|
|
[1.205, 5.05109252937, 380.12776796000],
|
|
[1.146, 1.95280464754, 529.69096509460],
|
|
[0.977, 1.52652616357, 77.96299230500],
|
|
[1.025, 4.33698643491, 2.96894541660],
|
|
[0.858, 2.78728745263, 111.43016149680],
|
|
[0.868, 5.55175791193, 38.13303563780],
|
|
[0.633, 0.41074353315, 213.29909543800],
|
|
[0.596, 5.39265533517, 127.47179660680],
|
|
[0.586, 4.00404667232, 109.94568878850],
|
|
[0.543, 2.40369406419, 153.49535039770],
|
|
[0.486, 2.05237757516, 299.12639426920],
|
|
[0.557, 3.13408880388, 65.22037101170],
|
|
[0.457, 3.96543219832, 454.90936652730],
|
|
[0.481, 2.81511187371, 160.60889739850],
|
|
[0.421, 2.16819778071, 56.62235130260],
|
|
[0.326, 4.52920012430, 39.61750834610],
|
|
[0.308, 6.26508780547, 70.32818044240],
|
|
[0.338, 5.14594268587, 3.18139373770],
|
|
[0.288, 0.47061435406, 22.09140052780],
|
|
[0.336, 4.23512034174, 35.16409022120],
|
|
[0.316, 3.93430525759, 52.69019803950],
|
|
[0.306, 1.10359318443, 70.84944530420],
|
|
[0.250, 3.58780257084, 202.25339517410],
|
|
[0.239, 4.77679306080, 87.31177153950],
|
|
[0.227, 2.74138067839, 12.53017297220],
|
|
[0.263, 1.59203582407, 84.34282612290],
|
|
[0.215, 3.88195737361, 131.40394986990],
|
|
[0.216, 5.80700510713, 74.66972398270],
|
|
[0.264, 1.82574036051, 77.22927912210],
|
|
[0.222, 0.04111883550, 184.72728735580],
|
|
[0.197, 1.56602555362, 9.56122755560],
|
|
[0.193, 2.26416938160, 75.74480641380],
|
|
[0.179, 2.69065316892, 145.63104387150],
|
|
[0.170, 2.75844544119, 73.81839072080],
|
|
[0.155, 3.55393249110, 18.15924726470],
|
|
[0.174, 4.76111441901, 277.03499374140],
|
|
[0.140, 0.28714762870, 221.37585028530],
|
|
[0.134, 1.29065526326, 206.18554843720],
|
|
[0.127, 6.17908901556, 62.25142559510],
|
|
[0.116, 6.26646620658, 220.41264243880],
|
|
],
|
|
# B3
|
|
[
|
|
[267.832, 1.25097888291, 74.78159856730],
|
|
[11.048, 3.14159265359, 0.00000000000],
|
|
[6.154, 4.00663614486, 149.56319713460],
|
|
[3.361, 5.77804694935, 73.29712585900],
|
|
[1.602, 1.05657834344, 63.73589830340],
|
|
[1.265, 1.66795295537, 78.71375183040],
|
|
[1.183, 2.58856450374, 138.51749687070],
|
|
[1.087, 0.28687213135, 76.26607127560],
|
|
[0.640, 1.87238784591, 71.60020482960],
|
|
[0.590, 0.80206040001, 1.48447270830],
|
|
[0.467, 4.42872012006, 148.07872442630],
|
|
[0.272, 4.00684090176, 85.82729883120],
|
|
[0.203, 0.60406901282, 71.81265315070],
|
|
[0.180, 5.55657564049, 3.93215326310],
|
|
[0.168, 4.67745630044, 70.84944530420],
|
|
[0.170, 2.93672195979, 11.04570026390],
|
|
],
|
|
# B4
|
|
[
|
|
[5.719, 2.85499529315, 74.78159856730],
|
|
[0.300, 3.14159265359, 0.00000000000]
|
|
],
|
|
]
|
|
"""This table contains Uranus' periodic terms (all of them) from the planetary
|
|
theory VSOP87 for the heliocentric latitude at the equinox of date (taken from
|
|
the 'D' solution). In Meeus' book a shortened version can be found in pages
|
|
448-449."""
|
|
|
|
|
|
VSOP87_R = [
|
|
# R0
|
|
[
|
|
[1921264847.881, 0.00000000000, 0.00000000000],
|
|
[88784984.055, 5.60377526994, 74.78159856730],
|
|
[3440835.545, 0.32836098991, 73.29712585900],
|
|
[2055653.495, 1.78295170028, 149.56319713460],
|
|
[649321.851, 4.52247298119, 76.26607127560],
|
|
[602248.144, 3.86003820462, 63.73589830340],
|
|
[496404.171, 1.40139934716, 454.90936652730],
|
|
[338525.522, 1.58002682946, 138.51749687070],
|
|
[243508.222, 1.57086595074, 71.81265315070],
|
|
[190521.915, 1.99809364502, 1.48447270830],
|
|
[161858.251, 2.79137863469, 148.07872442630],
|
|
[143705.902, 1.38368574483, 11.04570026390],
|
|
[93192.359, 0.17437193645, 36.64856292950],
|
|
[71424.265, 4.24509327405, 224.34479570190],
|
|
[89805.842, 3.66105366329, 109.94568878850],
|
|
[39009.624, 1.66971128869, 70.84944530420],
|
|
[46677.322, 1.39976563936, 35.16409022120],
|
|
[39025.681, 3.36234710692, 277.03499374140],
|
|
[36755.160, 3.88648934736, 146.59425171800],
|
|
[30348.875, 0.70100446346, 151.04766984290],
|
|
[29156.264, 3.18056174556, 77.75054398390],
|
|
[20471.584, 1.55588961500, 202.25339517410],
|
|
[25620.360, 5.25656292802, 380.12776796000],
|
|
[25785.805, 3.78537741503, 85.82729883120],
|
|
[22637.152, 0.72519137745, 529.69096509460],
|
|
[20473.163, 2.79639811626, 70.32818044240],
|
|
[17900.561, 0.55455488605, 2.96894541660],
|
|
[12328.151, 5.96039150918, 127.47179660680],
|
|
[14701.566, 4.90434406648, 108.46121608020],
|
|
[11494.701, 0.43774027872, 65.22037101170],
|
|
[15502.809, 5.35405037603, 38.13303563780],
|
|
[10792.699, 1.42104858472, 213.29909543800],
|
|
[11696.085, 3.29825599114, 3.93215326310],
|
|
[11959.355, 1.75044072173, 984.60033162190],
|
|
[12896.507, 2.62154018241, 111.43016149680],
|
|
[11852.996, 0.99342814582, 52.69019803950],
|
|
[9111.446, 4.99638600045, 62.25142559510],
|
|
[8420.550, 5.25350716616, 222.86032299360],
|
|
[7449.125, 0.79491905956, 351.81659230870],
|
|
[8402.147, 5.03877516489, 415.55249061210],
|
|
[6046.370, 5.67960948357, 78.71375183040],
|
|
[5524.133, 3.11499484161, 9.56122755560],
|
|
[7329.454, 3.97277527840, 183.24281464750],
|
|
[5444.878, 5.10575635361, 145.10977900970],
|
|
[5238.103, 2.62960141797, 33.67961751290],
|
|
[4079.167, 3.22064788674, 340.77089204480],
|
|
[3801.606, 6.10985558505, 184.72728735580],
|
|
[3919.476, 4.25015288873, 39.61750834610],
|
|
[2940.492, 2.14637460319, 137.03302416240],
|
|
[3781.219, 3.45840272873, 456.39383923560],
|
|
[2942.239, 0.42393808854, 299.12639426920],
|
|
[3686.787, 2.48718116535, 453.42489381900],
|
|
[3101.743, 4.14031063896, 219.89137757700],
|
|
[2962.641, 0.82977991995, 56.62235130260],
|
|
[2937.799, 3.67657450930, 140.00196957900],
|
|
[2865.128, 0.30996903761, 12.53017297220],
|
|
[2538.032, 4.85457831993, 131.40394986990],
|
|
[1962.510, 5.24342224065, 84.34282612290],
|
|
[2363.550, 0.44253328372, 554.06998748280],
|
|
[1979.394, 6.12836181686, 106.97674337190],
|
|
[2182.572, 2.94040431638, 305.34616939270],
|
|
[1962.974, 0.04114739120, 221.37585028530],
|
|
[1829.560, 4.01105771632, 68.84370773410],
|
|
[1642.920, 0.35564102554, 67.66805156650],
|
|
[1584.850, 3.16267171762, 225.82926841020],
|
|
[1848.655, 2.91111759376, 909.81873305460],
|
|
[1632.430, 4.23061792837, 22.09140052780],
|
|
[1401.390, 1.39084023521, 265.98929347750],
|
|
[1403.717, 5.63563637532, 4.45341812490],
|
|
[1655.866, 1.96431297431, 79.23501669220],
|
|
[1248.978, 5.44027380866, 54.17467074780],
|
|
[1563.447, 1.47917835549, 112.91463420510],
|
|
[1248.054, 4.88984353601, 479.28838891550],
|
|
[1197.439, 2.52185744943, 145.63104387150],
|
|
[1506.952, 5.24186185583, 181.75834193920],
|
|
[1481.746, 5.66203046912, 152.53214255120],
|
|
[1438.838, 1.53046287618, 447.79581952650],
|
|
[1408.514, 4.41921749601, 462.02291352810],
|
|
[1477.112, 4.32214690647, 256.53994050650],
|
|
[1228.314, 5.97703331040, 59.80374504030],
|
|
[1249.958, 6.24484546141, 160.60889739850],
|
|
[906.468, 5.62025869483, 74.66972398270],
|
|
[1090.681, 4.15393813845, 77.96299230500],
|
|
[844.931, 0.12943398585, 82.85835341460],
|
|
[900.363, 2.37315925843, 74.89347315190],
|
|
[1071.957, 1.74286714339, 528.20649238630],
|
|
[689.708, 3.08097059985, 69.36497259590],
|
|
[593.798, 4.50074517056, 8.07675484730],
|
|
[718.559, 4.00047509264, 128.95626931510],
|
|
[699.574, 0.03987168068, 143.62530630140],
|
|
[575.656, 5.89552672641, 66.70484372000],
|
|
[759.004, 2.13700057433, 692.58748435350],
|
|
[710.449, 5.41605755095, 218.40690486870],
|
|
[548.672, 5.62811496970, 3.18139373770],
|
|
[651.632, 4.42340061551, 18.15924726470],
|
|
[539.825, 6.20788667166, 71.60020482960],
|
|
[544.539, 5.69375108253, 203.73786788240],
|
|
[710.276, 4.21967260022, 381.61224066830],
|
|
[593.819, 3.83805798523, 32.19514480460],
|
|
[710.134, 4.48972171999, 293.18850343600],
|
|
[705.482, 0.45521177725, 835.03713448730],
|
|
[588.000, 5.08252923316, 186.21176006410],
|
|
[598.231, 0.35815291076, 269.92144674060],
|
|
[641.914, 2.71127457036, 87.31177153950],
|
|
[495.621, 2.65094755989, 200.76892246580],
|
|
[630.252, 4.46146214548, 275.55052103310],
|
|
[575.195, 5.57862480486, 2.44768055480],
|
|
[569.870, 1.63930932740, 77.22927912210],
|
|
[556.672, 1.07231961344, 1059.38193018920],
|
|
[449.439, 0.27981733949, 617.80588578620],
|
|
[463.608, 1.43448297993, 297.64192156090],
|
|
[436.547, 0.52802035072, 209.36694217490],
|
|
[463.938, 2.35443114417, 211.81462272970],
|
|
[435.943, 2.10077211065, 1514.29129671650],
|
|
[515.534, 3.23274579379, 284.14854074220],
|
|
[454.879, 4.08364210459, 99.16062095550],
|
|
[477.430, 2.89397217998, 39.35687591520],
|
|
[542.331, 5.39481705077, 278.51946644970],
|
|
[410.087, 3.04968860441, 404.50679034820],
|
|
[367.848, 0.71159607058, 125.98732389850],
|
|
[503.096, 5.83931251717, 191.20769491020],
|
|
[487.532, 0.06402454583, 60.76695288680],
|
|
[455.043, 2.59321186669, 490.33408917940],
|
|
[436.291, 2.08183813746, 51.20572533120],
|
|
[435.803, 2.79445203085, 75.74480641380],
|
|
[323.546, 4.82899980859, 195.13984817330],
|
|
[359.363, 0.00868012078, 35.42472265210],
|
|
[429.314, 3.08031550488, 41.10198105440],
|
|
[320.021, 5.48625497747, 14.97785352700],
|
|
[414.331, 0.09012800478, 258.02441321480],
|
|
[379.715, 0.05832815311, 378.64329525170],
|
|
[420.062, 2.25393983318, 81.00137369080],
|
|
[357.721, 4.71414305625, 173.94221952280],
|
|
[358.922, 0.35213227553, 426.59819087600],
|
|
[405.410, 6.12263257999, 24.37902238820],
|
|
[365.158, 5.59483211224, 255.05546779820],
|
|
[308.102, 3.92355394354, 116.42609634290],
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|
|
[3.173, 5.68964342749, 4.19278569400],
|
|
[3.181, 2.87968862974, 9914.15915194180],
|
|
[3.355, 5.45857968674, 73.08467753790],
|
|
[2.899, 5.12928266291, 448.31708438830],
|
|
[3.706, 2.47342147635, 64.25716316520],
|
|
[3.796, 4.29502458131, 164.54105066160],
|
|
[3.534, 4.42464754991, 46.47042291600],
|
|
[3.488, 5.62713714766, 3189.56475685690],
|
|
[2.940, 4.33606107945, 78263.70942472259],
|
|
[3.309, 3.10770680369, 519.60847267720],
|
|
[4.030, 4.41794838679, 772.58876693610],
|
|
[2.867, 5.17129632099, 346.18751801620],
|
|
[3.842, 1.87994191354, 299.71709510020],
|
|
[3.846, 5.38315286213, 980.14691349700],
|
|
[3.724, 4.94511644698, 984.48845703730],
|
|
[2.814, 2.17260061398, 191.31956949480],
|
|
[3.392, 3.08552116090, 245.49424024260],
|
|
[2.923, 0.37358823115, 6.48040755440],
|
|
[3.025, 1.19297242418, 104.83787935780],
|
|
[3.470, 1.89084704021, 44.61344319220],
|
|
[2.931, 0.78809830626, 540.05534180230],
|
|
[3.707, 4.14868763219, 6136.48159827340],
|
|
[3.931, 5.52289695589, 6171.64568849460],
|
|
[3.056, 2.97000936733, 250.60204967330],
|
|
[3.117, 0.76332399369, 229.45260513260],
|
|
[3.091, 4.91941279780, 221.16340196420],
|
|
[3.378, 3.82658652472, 25936.85547173129],
|
|
[3.041, 2.14503983522, 6604.95878212400],
|
|
[2.865, 0.53734608663, 273.85360000370],
|
|
[2.845, 0.34922064899, 85.93917341580],
|
|
[3.657, 6.02755271763, 340.88276662940],
|
|
[2.818, 4.44508352472, 369.34270012700],
|
|
[2.861, 2.19284349075, 295.19424100610],
|
|
[2.865, 3.21935127992, 3.82027867850],
|
|
[2.797, 5.97725967979, 2014.02655475710],
|
|
[3.280, 0.74832416123, 422.71422172270],
|
|
[3.509, 1.92501559437, 343.47920503050],
|
|
[2.962, 2.29867992492, 661.15860543930],
|
|
[3.485, 4.53205302380, 676.28521681260],
|
|
[2.836, 1.20779683660, 1119.18567522950],
|
|
[3.603, 2.72183511139, 508.62646288810],
|
|
[3.620, 5.57691156197, 10066.69129449300],
|
|
[2.731, 0.96663411770, 582.38116313410],
|
|
[3.306, 6.20620840278, 11.56696512570],
|
|
[3.279, 6.13563821647, 276.07178589490],
|
|
[2.747, 4.57476263020, 226.63241756230],
|
|
[2.825, 1.24120423378, 989.05374974680],
|
|
[2.707, 0.46257342768, 1458.47209456600],
|
|
[2.755, 5.43548338507, 246.97871295090],
|
|
[3.338, 3.98641322371, 488.58898404020],
|
|
[2.960, 5.31788128818, 1467.07011427510],
|
|
[3.062, 1.93542241882, 987.78172535960],
|
|
[3.504, 4.10521239427, 6280.10690457480],
|
|
[3.584, 3.12196206517, 108.72184851110],
|
|
[2.975, 0.13746189123, 9987.45627780080],
|
|
[2.634, 5.61201014857, 412.37109687440],
|
|
[3.702, 0.66231252049, 10101.85538471420],
|
|
[3.261, 4.39228048501, 75.37229939830],
|
|
[2.939, 3.26319979850, 130.55261660800],
|
|
[2.742, 6.24317126103, 447.20511869550],
|
|
[3.008, 4.24451493185, 170.17012495410],
|
|
[3.001, 2.45489658954, 230.82520325630],
|
|
[2.722, 4.98348297926, 754.03576079650],
|
|
[2.928, 5.73784691627, 14.66903698630],
|
|
[2.699, 2.98043546816, 27.72047482030],
|
|
[3.678, 3.46436124301, 26468.03090953420],
|
|
[3.500, 4.41810854452, 322.61164478010],
|
|
[2.943, 3.58544468129, 12489.88562870720],
|
|
[2.894, 2.26999120840, 1615.89959822680],
|
|
[2.679, 1.32002304425, 236.19364511790],
|
|
[2.711, 1.25250599577, 52250.58788171570],
|
|
[2.573, 4.41371056719, 262.05714021440],
|
|
[3.483, 1.97113718781, 655.93892142400],
|
|
[2.600, 3.80107226970, 70.63699698310],
|
|
[3.280, 1.75059058234, 683.98946464440],
|
|
[3.260, 3.46047977615, 74.19089773630],
|
|
[3.097, 5.47452034532, 302.37722397610],
|
|
[2.565, 3.47443238116, 2042.49778910280],
|
|
[3.158, 4.58160924364, 12492.85457412380],
|
|
[3.373, 5.52806001629, 10210.31660079440],
|
|
[2.619, 4.43681016753, 949.17560896980],
|
|
[3.290, 1.35055242247, 515.67631941410],
|
|
[3.180, 4.49938964982, 694.83822295220],
|
|
[2.558, 5.07921716363, 197.79997704920],
|
|
[2.902, 2.61388996483, 115.36231475990],
|
|
[2.586, 4.09771865336, 1448.91086701040],
|
|
[3.160, 4.82168102018, 714.67888488130],
|
|
[3.016, 3.16691101108, 385.75684225250],
|
|
[3.001, 3.24181300229, 1618.86854364340],
|
|
[3.319, 5.98200177347, 533.83556667880],
|
|
[3.307, 3.31452419197, 732.97125859000],
|
|
[2.530, 0.13809025963, 591.94239068970],
|
|
[2.975, 5.72770980032, 1011.42703456490],
|
|
[2.857, 4.11031053901, 2267.43328563570],
|
|
[3.091, 4.87979664891, 582.64179556500],
|
|
[3.422, 6.18592254593, 281.48841186630],
|
|
[2.501, 0.50645055144, 29.22619938800],
|
|
[3.502, 0.17203520151, 371.52974825090],
|
|
[2.607, 3.51828908958, 112.39336934330],
|
|
[2.547, 4.45612695304, 901.22071334550],
|
|
[2.778, 4.97805873371, 132.57960603750],
|
|
[2.476, 1.55163657371, 1234.12729886410],
|
|
[2.929, 2.34725672182, 273.15102458810],
|
|
[2.724, 5.73177362443, 688.65533109040],
|
|
[2.667, 6.13733078138, 161.41204655060],
|
|
[2.877, 5.47506403197, 1436.54075273260],
|
|
[2.779, 1.54196175338, 680.05731138130],
|
|
[2.427, 4.64913431310, 392.65794093220],
|
|
[3.223, 2.57976952494, 267.58564077040],
|
|
[2.750, 1.29662662582, 108.98248094200],
|
|
[3.220, 1.06290187940, 388.72578766910],
|
|
[3.236, 3.47802643973, 283.62727588040],
|
|
[3.027, 5.38233284458, 44.09217833040],
|
|
[2.830, 5.70274947128, 327.43756992050],
|
|
[2.768, 5.42256168790, 482.25733433210],
|
|
[3.230, 5.65661970187, 134.37289528650],
|
|
[2.685, 5.03687735302, 763.22448133660],
|
|
[2.441, 5.19830386978, 380.23964254460],
|
|
[2.608, 3.11386505876, 578.44900987100],
|
|
[2.465, 1.49242672830, 141.69889060840],
|
|
[2.332, 3.19371804203, 683.02625679790],
|
|
[2.307, 4.07685834192, 78.92620015150],
|
|
[2.280, 2.52476606956, 156.67674413540],
|
|
[2.260, 6.23958645351, 400.57463708510],
|
|
[2.301, 2.47762267951, 107.91869935900],
|
|
[3.089, 5.69639540598, 537.39521292640],
|
|
[3.074, 1.16740737548, 58.62808887270],
|
|
[2.846, 0.02430566936, 563.37058260750],
|
|
[2.423, 4.24559706691, 27.74172667970],
|
|
[2.670, 3.48404619442, 123.01837848190],
|
|
[2.228, 3.33159258912, 1257.70317210020],
|
|
[2.445, 2.29979337782, 280.21638747910],
|
|
[2.260, 3.85026258012, 753.14198891920],
|
|
[2.195, 4.94038065567, 1222.27844944810],
|
|
[2.579, 1.76841912074, 710.74673161820],
|
|
[2.402, 4.47942458428, 569.04784100980],
|
|
[2.181, 5.39048760967, 318.67949151700],
|
|
[2.317, 6.27946729049, 493.04240216510],
|
|
[2.420, 3.66436222896, 3.62333672240],
|
|
],
|
|
# R1
|
|
[
|
|
[1479896.370, 3.67205705317, 74.78159856730],
|
|
[71212.085, 6.22601006675, 63.73589830340],
|
|
[68626.972, 6.13411265052, 149.56319713460],
|
|
[20857.262, 5.24625494219, 11.04570026390],
|
|
[21468.152, 2.60176704270, 76.26607127560],
|
|
[24059.649, 3.14159265359, 0.00000000000],
|
|
[11405.346, 0.01848461561, 70.84944530420],
|
|
[7496.775, 0.42360033283, 73.29712585900],
|
|
[4243.800, 1.41692350371, 85.82729883120],
|
|
[3505.936, 2.58354048851, 138.51749687070],
|
|
[3228.835, 5.25499602896, 3.93215326310],
|
|
[3926.694, 3.15513991323, 71.81265315070],
|
|
[3060.010, 0.15321893225, 1.48447270830],
|
|
[3578.446, 2.31160668309, 224.34479570190],
|
|
[2564.251, 0.98076846352, 148.07872442630],
|
|
[2429.445, 3.99440122468, 52.69019803950],
|
|
[1644.719, 2.65349313124, 127.47179660680],
|
|
[1583.766, 1.43045619196, 78.71375183040],
|
|
[1413.112, 4.57461892062, 202.25339517410],
|
|
[1489.525, 2.67559167316, 56.62235130260],
|
|
[1403.237, 1.36985349744, 77.75054398390],
|
|
[1228.220, 1.04703640149, 62.25142559510],
|
|
[1508.028, 5.05996325425, 151.04766984290],
|
|
[992.085, 2.17168865909, 65.22037101170],
|
|
[1032.731, 0.26459059027, 131.40394986990],
|
|
[861.867, 5.05530802218, 351.81659230870],
|
|
[744.445, 3.07640148939, 35.16409022120],
|
|
[604.362, 0.90717667985, 984.60033162190],
|
|
[646.851, 4.47290422910, 70.32818044240],
|
|
[574.710, 3.23070708457, 447.79581952650],
|
|
[687.470, 2.49912565674, 77.96299230500],
|
|
[623.602, 0.86253073820, 9.56122755560],
|
|
[527.794, 5.15136007084, 2.96894541660],
|
|
[561.839, 2.71778158980, 462.02291352810],
|
|
[530.364, 5.91655309045, 213.29909543800],
|
|
[460.080, 4.22302465979, 12.53017297220],
|
|
[494.280, 0.46291078127, 145.63104387150],
|
|
[487.336, 0.70614146398, 380.12776796000],
|
|
[380.908, 3.85089591694, 3.18139373770],
|
|
[444.352, 2.15558291251, 67.66805156650],
|
|
[338.800, 2.53820897704, 18.15924726470],
|
|
[372.947, 5.05141251694, 529.69096509460],
|
|
[348.345, 1.74874852104, 71.60020482960],
|
|
[405.881, 1.22961727600, 22.09140052780],
|
|
[268.913, 6.24069521597, 340.77089204480],
|
|
[255.585, 2.95695013627, 84.34282612290],
|
|
[259.465, 3.92053708924, 59.80374504030],
|
|
[224.731, 3.90961468562, 160.60889739850],
|
|
[221.710, 3.64727173951, 137.03302416240],
|
|
[254.591, 3.50411592815, 38.13303563780],
|
|
[238.290, 2.04879982674, 269.92144674060],
|
|
[272.355, 3.38363105223, 222.86032299360],
|
|
[200.648, 1.24861003313, 69.36497259590],
|
|
[234.153, 0.27825220612, 108.46121608020],
|
|
[188.515, 4.41307507326, 265.98929347750],
|
|
[211.691, 0.68027381802, 111.43016149680],
|
|
[205.946, 1.53379817229, 284.14854074220],
|
|
[196.179, 4.77152996605, 299.12639426920],
|
|
[153.102, 5.21761881347, 209.36694217490],
|
|
[162.563, 4.34054353610, 33.67961751290],
|
|
[150.563, 1.98966326297, 54.17467074780],
|
|
[137.012, 0.40323866041, 195.13984817330],
|
|
[117.171, 0.39649791652, 87.31177153950],
|
|
[127.913, 2.40333045173, 39.61750834610],
|
|
[104.218, 2.92152185788, 134.58534360760],
|
|
[103.862, 1.81622936156, 72.33391801250],
|
|
[105.741, 0.17067407327, 79.23501669220],
|
|
[106.419, 0.69799543514, 2.44768055480],
|
|
[95.326, 4.02880266738, 82.85835341460],
|
|
[104.772, 4.43616414428, 305.34616939270],
|
|
[93.825, 5.01823592717, 51.20572533120],
|
|
[103.739, 2.57553519741, 191.20769491020],
|
|
[106.679, 1.22996874093, 225.82926841020],
|
|
[93.452, 3.09274255916, 77.22927912210],
|
|
[97.398, 3.81380841075, 152.53214255120],
|
|
[84.583, 5.72473747348, 68.84370773410],
|
|
[77.395, 0.08281157747, 45.57665103870],
|
|
[76.207, 4.20384370842, 73.81839072080],
|
|
[86.249, 0.53131085736, 145.10977900970],
|
|
[75.795, 3.78559826812, 75.74480641380],
|
|
[77.592, 1.63628139623, 479.28838891550],
|
|
[84.612, 0.61662456010, 116.42609634290],
|
|
[100.209, 4.94084867643, 120.35824960600],
|
|
[72.142, 4.30505812564, 565.11568774670],
|
|
[70.733, 2.38450718488, 60.76695288680],
|
|
[71.585, 3.93906647867, 153.49535039770],
|
|
[84.566, 5.56037336584, 344.70304530790],
|
|
[63.556, 1.93742986679, 41.64449777560],
|
|
[71.619, 3.71213491656, 408.43894361130],
|
|
[61.594, 3.90006698249, 4.45341812490],
|
|
[64.973, 1.55845503407, 106.97674337190],
|
|
[59.913, 0.60110866128, 74.89347315190],
|
|
[62.000, 4.39369268007, 453.42489381900],
|
|
[63.361, 4.19159979468, 184.72728735580],
|
|
[62.301, 3.23773103318, 422.66603761290],
|
|
[54.427, 3.72545550857, 7.11354700080],
|
|
[52.474, 6.08562717749, 404.50679034820],
|
|
[59.073, 1.55568469603, 456.39383923560],
|
|
[52.597, 3.50492233970, 125.98732389850],
|
|
[52.835, 5.20100035142, 358.93013930950],
|
|
[58.123, 5.33480562448, 220.41264243880],
|
|
[52.909, 4.44819701196, 426.59819087600],
|
|
[50.934, 0.52638534200, 490.33408917940],
|
|
[54.968, 1.60146090981, 14.97785352700],
|
|
[49.491, 4.25534603275, 5.41662597140],
|
|
[51.303, 0.36772379136, 206.18554843720],
|
|
[51.821, 1.75832999538, 8.07675484730],
|
|
[56.964, 0.84114552694, 146.59425171800],
|
|
[49.109, 0.94061875871, 99.16062095550],
|
|
[46.361, 5.35115472594, 152.74459087230],
|
|
[48.023, 1.97249712347, 288.08069400530],
|
|
[43.772, 3.03713403879, 20.60692781950],
|
|
[49.493, 5.84619560979, 112.91463420510],
|
|
[41.987, 0.04620500196, 128.95626931510],
|
|
[48.628, 3.62817742782, 81.00137369080],
|
|
[41.472, 2.33730376429, 277.03499374140],
|
|
[39.983, 5.09525356576, 35.42472265210],
|
|
[41.948, 2.51050760642, 24.37902238820],
|
|
[38.325, 3.61946898382, 173.94221952280],
|
|
[38.385, 2.06003220130, 333.65734504400],
|
|
[42.597, 1.26088737300, 1514.29129671650],
|
|
[38.855, 0.74239364306, 347.88443904560],
|
|
[38.535, 4.95064283065, 92.94084583200],
|
|
[33.234, 1.38358507432, 74.66972398270],
|
|
[33.788, 3.68407945156, 66.91729204110],
|
|
[38.953, 5.49236040328, 200.76892246580],
|
|
[31.850, 0.53990592534, 203.73786788240],
|
|
[33.320, 6.26012644668, 1059.38193018920],
|
|
[30.806, 2.53797566903, 977.48678462110],
|
|
[29.198, 5.43116906000, 58.10682401090],
|
|
[30.059, 0.19481555617, 387.24131496080],
|
|
[28.997, 3.10546504714, 991.71387862270],
|
|
[35.640, 3.72863820177, 96.87299909510],
|
|
[27.607, 0.37142052647, 80.19822453870],
|
|
[32.492, 4.38403518987, 221.37585028530],
|
|
[27.029, 1.35552416596, 0.96320784650],
|
|
[31.276, 0.79566430555, 373.01422095920],
|
|
[31.122, 2.05381353845, 230.56457082540],
|
|
[25.883, 3.46808071409, 144.14657116320],
|
|
[30.201, 0.71392007232, 109.94568878850],
|
|
[24.688, 3.04162764358, 14.01464568050],
|
|
[27.882, 4.76559523368, 415.55249061210],
|
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|
|
[4.077, 0.07273073033, 1190.03512053370],
|
|
[3.020, 2.64998251178, 20.44686912510],
|
|
[3.926, 1.41612569694, 346.18751801620],
|
|
[3.110, 1.11431255827, 1044.40407666220],
|
|
[2.836, 0.62522723719, 749.20983565610],
|
|
[2.831, 4.78996738581, 820.05928096030],
|
|
[2.824, 0.87232289414, 30.71067209630],
|
|
[3.114, 1.79734939525, 414.06801790380],
|
|
[2.801, 3.99301180541, 10063.72234907640],
|
|
[3.489, 1.86982946081, 371.52974825090],
|
|
[3.725, 1.68366366742, 683.98946464440],
|
|
[3.763, 3.28247771799, 432.81796599950],
|
|
[3.493, 0.98765698465, 9988.94075050910],
|
|
[3.523, 5.12512607932, 105.38039607900],
|
|
[2.839, 4.22662576295, 990.22940591440],
|
|
[3.432, 2.80483162230, 764.18768918310],
|
|
[2.733, 0.42373696972, 354.99798604640],
|
|
[3.146, 5.19208910201, 417.03696332040],
|
|
[3.041, 5.75641149588, 409.92341631960],
|
|
[3.379, 5.47448876584, 1396.22066897090],
|
|
[3.102, 0.41684444780, 521.09294538550],
|
|
[2.863, 0.41519700992, 894.84087952760],
|
|
[2.707, 3.60084311477, 621.73803904930],
|
|
[3.128, 5.23384180625, 424.15051032120],
|
|
[3.107, 2.44919355737, 4.66586644600],
|
|
[2.683, 3.88682711832, 133.10087089930],
|
|
[2.660, 4.78670985324, 362.86229257260],
|
|
[3.200, 1.88004939357, 331.20966448920],
|
|
[2.730, 4.12217979791, 600.54041039880],
|
|
[3.414, 4.93712749827, 1140.38330388000],
|
|
[2.653, 5.10283251074, 118.02244363580],
|
|
[3.222, 4.76521772319, 294.67297614430],
|
|
[3.289, 4.26401031509, 544.50875992720],
|
|
[3.100, 5.47928527930, 701.18550406260],
|
|
[2.785, 5.19343849039, 144.89733068860],
|
|
[2.607, 4.72531286187, 122.47586176070],
|
|
[2.581, 6.27329466695, 908.33426034630],
|
|
[3.285, 1.95972622670, 372.42352012820],
|
|
[2.897, 0.37378090180, 582.38116313410],
|
|
[2.615, 2.25516923974, 74.99404688840],
|
|
[3.582, 1.27992264402, 987.56927703850],
|
|
[3.115, 5.10929689813, 459.05396811150],
|
|
[2.857, 5.90256930211, 525.23754696970],
|
|
[2.589, 1.83177157032, 657.16276170140],
|
|
[2.539, 4.14968938109, 74.73341445750],
|
|
[2.797, 2.82242772664, 2036.86871481030],
|
|
[2.688, 2.16500211397, 262.80789973980],
|
|
[2.744, 1.54445470732, 28.57180808220],
|
|
[2.539, 0.46036497385, 74.82978267710],
|
|
[3.322, 3.50108539407, 82.64590509350],
|
|
[2.810, 6.06709915335, 374.49869366750],
|
|
[2.504, 3.52394801700, 1183.67233305830],
|
|
[2.565, 1.64023845161, 73.40900044360],
|
|
[2.531, 3.50486296784, 293.18850343600],
|
|
[2.663, 4.23321349902, 421.18156490460],
|
|
[2.793, 2.00644423849, 75.04223099820],
|
|
[2.430, 1.56119387576, 136.06981631590],
|
|
[2.553, 1.25909246207, 670.49608382570],
|
|
[2.604, 3.87350462519, 74.03083904190],
|
|
[2.510, 3.35948960782, 464.99185894470],
|
|
[3.005, 0.81031349171, 73.88782669000],
|
|
[3.110, 6.14956891318, 118.87377689770],
|
|
[3.234, 2.45751141361, 98.35747180340],
|
|
[2.774, 6.26134027482, 1022.31267613440],
|
|
[2.402, 4.38353347008, 1303.27982313890],
|
|
[3.296, 3.84350963765, 511.53171782990],
|
|
[2.800, 2.60339313269, 74.52096613640],
|
|
[3.005, 0.76247280223, 75.67537044460],
|
|
[2.434, 4.94784679430, 969.62247809490],
|
|
[2.632, 0.63557110200, 227.52618943960],
|
|
[2.669, 0.73340228210, 73.08467753790],
|
|
[2.465, 1.30648773380, 77.06922042770],
|
|
[3.237, 3.19110274211, 1887.30551767570],
|
|
[2.395, 2.76580569447, 768.85355562910],
|
|
[3.230, 0.01981320255, 881.50755740330],
|
|
[2.747, 5.59085990261, 388.72578766910],
|
|
[3.008, 5.65955463660, 1969.20066324380],
|
|
[3.008, 0.91409756228, 2118.76386037840],
|
|
[2.465, 0.26629856014, 72.49397670690],
|
|
[2.629, 4.00618677646, 26.02355379090],
|
|
[2.272, 2.77069357315, 515.46387109300],
|
|
[2.360, 4.12736987374, 74.62153987290],
|
|
[2.255, 3.36574443950, 286.59622129700],
|
|
[2.211, 5.18239546182, 59.28248017850],
|
|
[2.994, 2.83179016989, 184.98791978670],
|
|
[2.492, 1.19872353228, 383.09671337660],
|
|
[2.355, 0.48259604722, 74.94165726170],
|
|
[2.185, 6.07997119980, 63.62402371880],
|
|
[2.228, 1.42452148910, 6219.33995168800],
|
|
],
|
|
# R2
|
|
[
|
|
[22439.904, 0.69953118760, 74.78159856730],
|
|
[4727.037, 1.69901641488, 63.73589830340],
|
|
[1681.903, 4.64833551727, 70.84944530420],
|
|
[1433.755, 3.52119917947, 149.56319713460],
|
|
[1649.559, 3.09660078980, 11.04570026390],
|
|
[770.188, 0.00000000000, 0.00000000000],
|
|
[461.009, 0.76676632849, 3.93215326310],
|
|
[500.429, 6.17229032223, 76.26607127560],
|
|
[390.371, 4.49605283502, 56.62235130260],
|
|
[389.945, 5.52673426377, 85.82729883120],
|
|
[292.097, 0.20389012095, 52.69019803950],
|
|
[272.898, 3.84707823651, 138.51749687070],
|
|
[286.579, 3.53357683270, 73.29712585900],
|
|
[205.449, 3.24758017121, 78.71375183040],
|
|
[219.674, 1.96418942891, 131.40394986990],
|
|
[215.788, 0.84812474187, 77.96299230500],
|
|
[128.834, 2.08146849515, 3.18139373770],
|
|
[148.554, 4.89840863841, 127.47179660680],
|
|
[117.452, 4.93414907433, 447.79581952650],
|
|
[112.690, 1.01361852218, 462.02291352810],
|
|
[98.875, 6.15817742611, 224.34479570190],
|
|
[91.379, 0.67973399531, 18.15924726470],
|
|
[89.217, 0.23425778826, 202.25339517410],
|
|
[88.206, 2.93094837724, 62.25142559510],
|
|
[114.066, 4.78741873960, 145.63104387150],
|
|
[103.858, 3.58561789629, 71.60020482960],
|
|
[61.819, 3.29964272893, 351.81659230870],
|
|
[57.782, 4.90737420887, 22.09140052780],
|
|
[64.369, 3.39006689398, 1.48447270830],
|
|
[71.110, 6.10490061068, 454.90936652730],
|
|
[50.990, 3.86691997779, 65.22037101170],
|
|
[63.537, 3.96202309168, 67.66805156650],
|
|
[58.957, 5.55530463687, 9.56122755560],
|
|
[48.700, 3.74709235789, 269.92144674060],
|
|
[43.584, 1.92568752002, 59.80374504030],
|
|
[42.170, 2.61650997054, 151.04766984290],
|
|
[42.420, 6.13634453301, 284.14854074220],
|
|
[44.340, 5.89997845114, 71.81265315070],
|
|
[37.328, 5.91300114911, 984.60033162190],
|
|
[36.201, 5.40315761474, 77.75054398390],
|
|
[41.989, 2.09071623849, 12.53017297220],
|
|
[31.411, 4.59200004835, 148.07872442630],
|
|
[31.289, 2.26696307388, 195.13984817330],
|
|
[27.150, 3.53242984046, 209.36694217490],
|
|
[28.152, 4.57845964163, 77.22927912210],
|
|
[26.097, 0.65978256272, 120.35824960600],
|
|
[24.372, 5.86680440531, 69.36497259590],
|
|
[23.037, 1.03776963677, 84.34282612290],
|
|
[22.679, 1.71434243970, 160.60889739850],
|
|
[27.650, 4.91488946525, 277.03499374140],
|
|
[20.816, 2.19643268155, 45.57665103870],
|
|
[19.961, 2.32077356180, 2.44768055480],
|
|
[16.584, 4.77529536873, 213.29909543800],
|
|
[16.578, 1.85615182154, 340.77089204480],
|
|
[17.196, 4.36852462522, 54.17467074780],
|
|
[16.053, 3.64619586667, 152.74459087230],
|
|
[14.806, 5.43824503068, 408.43894361130],
|
|
[13.872, 3.38531100784, 358.93013930950],
|
|
[13.328, 5.25179190495, 137.03302416240],
|
|
[13.286, 1.26285812368, 134.58534360760],
|
|
[12.890, 3.03270380745, 92.94084583200],
|
|
[12.467, 1.33213558369, 51.20572533120],
|
|
[13.450, 1.53176996919, 422.66603761290],
|
|
[16.442, 0.40190549188, 265.98929347750],
|
|
[11.996, 5.10426418352, 191.20769491020],
|
|
[12.898, 4.43242192513, 87.31177153950],
|
|
[11.449, 2.02645622099, 7.11354700080],
|
|
[11.826, 4.65645290272, 41.64449777560],
|
|
[12.045, 3.23910807852, 116.42609634290],
|
|
[11.680, 3.73278249629, 220.41264243880],
|
|
[11.573, 4.16500659139, 60.55450456570],
|
|
[10.175, 0.32936886913, 70.32818044240],
|
|
[11.332, 1.07613885149, 72.33391801250],
|
|
[9.655, 3.05950236129, 2.96894541660],
|
|
[9.279, 2.43997351068, 565.11568774670],
|
|
[8.986, 5.18839740735, 225.82926841020],
|
|
[10.284, 1.18602582060, 344.70304530790],
|
|
[8.844, 6.00894470528, 5.41662597140],
|
|
[8.508, 5.24741470216, 347.88443904560],
|
|
[8.319, 3.71723808749, 14.97785352700],
|
|
[8.276, 2.27408171672, 299.12639426920],
|
|
[8.064, 5.71681525179, 55.13787859430],
|
|
[7.830, 0.90313686798, 222.86032299360],
|
|
[8.335, 4.48600419464, 70.11573212130],
|
|
[8.763, 5.81519440120, 153.49535039770],
|
|
[8.472, 3.91387041805, 333.65734504400],
|
|
[9.874, 5.96526143660, 35.16409022120],
|
|
[9.647, 0.38872626737, 415.55249061210],
|
|
[7.106, 1.50598488470, 991.71387862270],
|
|
[6.596, 1.18068235818, 96.87299909510],
|
|
[8.065, 2.25930653257, 206.18554843720],
|
|
[6.479, 2.99461362786, 380.12776796000],
|
|
[9.012, 6.05343622530, 146.38180339690],
|
|
[6.131, 0.05596259493, 99.16062095550],
|
|
[5.799, 0.82465326137, 142.44965013380],
|
|
[5.816, 4.63029217647, 49.50880430180],
|
|
[5.608, 0.66268449799, 58.10682401090],
|
|
[5.966, 2.48916255408, 373.01422095920],
|
|
[5.710, 2.23566160404, 80.19822453870],
|
|
[5.272, 5.06746739956, 440.68227252570],
|
|
[5.162, 4.36457872885, 977.48678462110],
|
|
[5.428, 0.85181859845, 546.95644048200],
|
|
[5.766, 0.34229025692, 536.80451209540],
|
|
[5.924, 5.48443563529, 76.47851959670],
|
|
[5.340, 3.73073116400, 23.57587323610],
|
|
[5.174, 4.13873402677, 132.88842257820],
|
|
[5.310, 6.14059082194, 39.61750834610],
|
|
[5.790, 3.39593613152, 458.09076026500],
|
|
[5.007, 4.25821412289, 522.57741809380],
|
|
[4.967, 4.79184817938, 387.24131496080],
|
|
[5.183, 3.25775152471, 561.18353448360],
|
|
[4.602, 1.69262282455, 152.53214255120],
|
|
[5.302, 1.83522660093, 124.29040286910],
|
|
[5.005, 0.36630565950, 60.76695288680],
|
|
[4.454, 2.30288945184, 312.45971639350],
|
|
[4.457, 0.45775730382, 33.13710079170],
|
|
[5.722, 0.89523844278, 81.89514556810],
|
|
[5.842, 0.92039543147, 20.60692781950],
|
|
[5.743, 0.66226484448, 38.13303563780],
|
|
[4.255, 3.55373860346, 479.28838891550],
|
|
[4.190, 4.37674804409, 79.23501669220],
|
|
[4.194, 1.64986267170, 128.95626931510],
|
|
[5.125, 1.40553011416, 144.14657116320],
|
|
[4.045, 6.07362424798, 19.64371997300],
|
|
[3.984, 5.77178406410, 288.08069400530],
|
|
[5.017, 2.99521887648, 29.20494752860],
|
|
[3.842, 2.60024827897, 426.59819087600],
|
|
[3.861, 3.19886211335, 159.12442469020],
|
|
[3.870, 4.43713601497, 141.69889060840],
|
|
[5.316, 4.07970979457, 111.43016149680],
|
|
[4.553, 0.01384318412, 298.23262239190],
|
|
[3.737, 5.28319518103, 353.30106501700],
|
|
[3.939, 5.27301148162, 521.09294538550],
|
|
[3.710, 5.15385470848, 490.33408917940],
|
|
[4.039, 0.60924359087, 152.01087768940],
|
|
[3.861, 1.34394383700, 535.32003938710],
|
|
[4.385, 0.62057680100, 827.17282796110],
|
|
[3.567, 4.71986443303, 6.90109867970],
|
|
[3.576, 3.24526237368, 230.56457082540],
|
|
[3.469, 0.79054323335, 983.11585891360],
|
|
[4.524, 2.86819565712, 129.91947716160],
|
|
[3.648, 5.59395544992, 774.48262992160],
|
|
[3.513, 4.49630054276, 376.19561469690],
|
|
[3.432, 2.55614913808, 258.87574647670],
|
|
[4.352, 2.09804374929, 404.50679034820],
|
|
[3.336, 0.89628904042, 469.13646052890],
|
|
[3.274, 3.86236880159, 42.53826965290],
|
|
[3.201, 2.76459652868, 248.72381809010],
|
|
[3.184, 0.07709843451, 1514.29129671650],
|
|
[3.783, 5.29835962126, 369.08206769610],
|
|
[3.266, 2.24754480216, 73.81839072080],
|
|
[3.055, 2.60120354415, 433.71173787680],
|
|
[3.051, 4.54953369151, 980.66817835880],
|
|
[3.062, 1.27089879603, 200.76892246580],
|
|
[3.055, 1.70878161343, 639.89728631400],
|
|
[3.110, 3.63187411723, 16.67477455640],
|
|
[3.472, 4.93521260607, 411.62033734900],
|
|
[3.531, 4.49372794858, 881.50755740330],
|
|
[3.284, 5.59170577331, 472.17484191470],
|
|
[3.015, 6.02967446446, 291.26208774300],
|
|
[3.467, 2.17484439267, 554.06998748280],
|
|
[3.138, 0.52367930477, 1094.80665284130],
|
|
[3.257, 2.49339546514, 451.72797278960],
|
|
[2.881, 0.50481204892, 305.34616939270],
|
|
[3.082, 4.20145474081, 146.59425171800],
|
|
[2.883, 2.44983947531, 135.33610313300],
|
|
[2.965, 0.39294995530, 25.27279426550],
|
|
[2.831, 2.52728803131, 867.28046340170],
|
|
[2.728, 5.29491477549, 125.98732389850],
|
|
[2.857, 4.71106805785, 218.92816973050],
|
|
[2.763, 4.27510031656, 350.33211960040],
|
|
[2.730, 1.98552777251, 82.85835341460],
|
|
[2.857, 3.08706426922, 216.48048917570],
|
|
[3.365, 3.67691210011, 661.09491496450],
|
|
[2.925, 1.43646759644, 381.61224066830],
|
|
[2.753, 0.39468041761, 33.67961751290],
|
|
[2.756, 4.62672498840, 1357.61455258110],
|
|
[3.450, 2.12911756067, 685.47393735270],
|
|
[2.571, 5.92862393284, 89.75945209430],
|
|
[2.677, 0.76342313946, 486.40193591630],
|
|
[2.689, 4.16436463826, 235.39049596580],
|
|
[2.646, 3.81808560938, 550.88859374510],
|
|
[3.369, 3.17071565345, 108.46121608020],
|
|
[2.613, 5.68333838067, 24.37902238820],
|
|
[2.736, 1.87107584495, 529.69096509460],
|
|
[2.606, 4.36605237304, 1080.57955883970],
|
|
[2.407, 3.07343136742, 391.17346822390],
|
|
[2.446, 5.73846381540, 535.91074021810],
|
|
[2.334, 5.18878243102, 1059.38193018920],
|
|
[2.568, 1.09886876369, 913.00012679230],
|
|
[2.236, 6.10115874045, 140.00196957900],
|
|
[3.053, 5.35047433775, 681.54178408960],
|
|
],
|
|
# R3
|
|
[
|
|
[1164.382, 4.73453291602, 74.78159856730],
|
|
[212.367, 3.34255734999, 63.73589830340],
|
|
[196.408, 2.98004616318, 70.84944530420],
|
|
[104.527, 0.95807937648, 11.04570026390],
|
|
[71.681, 0.02528455665, 56.62235130260],
|
|
[72.540, 0.99701907912, 149.56319713460],
|
|
[54.875, 2.59436811267, 3.93215326310],
|
|
[34.029, 3.81553325635, 76.26607127560],
|
|
[32.081, 3.59825177840, 131.40394986990],
|
|
[29.641, 3.44111535957, 85.82729883120],
|
|
[36.377, 5.65035573017, 77.96299230500],
|
|
[27.663, 0.42836001470, 3.18139373770],
|
|
[27.464, 2.55126467481, 52.69019803950],
|
|
[24.569, 5.14034173566, 78.71375183040],
|
|
[19.390, 5.13477648625, 18.15924726470],
|
|
[15.767, 0.37116951743, 447.79581952650],
|
|
[15.441, 5.57271837433, 462.02291352810],
|
|
[15.232, 3.85998573509, 73.29712585900],
|
|
[15.475, 2.97496547327, 145.63104387150],
|
|
[17.951, 0.00000000000, 0.00000000000],
|
|
[15.958, 5.19915553904, 71.60020482960],
|
|
[11.056, 6.03152659562, 138.51749687070],
|
|
[10.529, 3.58261852497, 224.34479570190],
|
|
[7.606, 1.44542030704, 1.48447270830],
|
|
[8.121, 2.61579604319, 22.09140052780],
|
|
[7.107, 5.43946774526, 269.92144674060],
|
|
[6.459, 4.37142319461, 284.14854074220],
|
|
[6.818, 0.01396812984, 151.04766984290],
|
|
[8.101, 0.29563819537, 127.47179660680],
|
|
[5.768, 4.22672716593, 373.01422095920],
|
|
[5.022, 1.84154937974, 202.25339517410],
|
|
[4.692, 2.78404575440, 120.35824960600],
|
|
[5.087, 0.77745294804, 62.25142559510],
|
|
[4.160, 1.83820502779, 72.33391801250],
|
|
[3.922, 1.88900691473, 209.36694217490],
|
|
[5.201, 4.15791319343, 195.13984817330],
|
|
[3.636, 1.99709010456, 65.22037101170],
|
|
[3.582, 3.92592140377, 124.29040286910],
|
|
[3.808, 1.04818660873, 92.94084583200],
|
|
[4.241, 3.95755998904, 9.56122755560],
|
|
[3.497, 1.54139696251, 148.07872442630],
|
|
[3.195, 2.98608971329, 387.24131496080],
|
|
[3.950, 1.85721204932, 152.74459087230],
|
|
[3.277, 1.40881404192, 351.81659230870],
|
|
[3.605, 1.17366167402, 153.49535039770],
|
|
[2.940, 6.03594958459, 12.53017297220],
|
|
[2.744, 5.64674283515, 134.58534360760],
|
|
[2.800, 0.79480255927, 572.22923474750],
|
|
[3.054, 5.84310939105, 160.60889739850],
|
|
[2.662, 1.98593312104, 450.97721326420],
|
|
[2.700, 2.77036653988, 213.29909543800],
|
|
[2.323, 1.67918985468, 358.93013930950],
|
|
[2.254, 5.77129530133, 84.34282612290],
|
|
[2.291, 4.81424601600, 536.80451209540],
|
|
[2.213, 2.20360299816, 465.95506679120],
|
|
],
|
|
# R4
|
|
[
|
|
[52.996, 3.00838033088, 74.78159856730],
|
|
[9.887, 1.91399083603, 56.62235130260],
|
|
[7.008, 5.08677527404, 11.04570026390],
|
|
[6.728, 5.42924958121, 149.56319713460],
|
|
[3.703, 5.22728581851, 131.40394986990],
|
|
[3.361, 1.29695290266, 85.82729883120],
|
|
[2.664, 0.44064577837, 63.73589830340],
|
|
[2.309, 0.92380720934, 145.63104387150],
|
|
[2.383, 6.21390585593, 358.93013930950],
|
|
[2.288, 2.23425399117, 440.68227252570],
|
|
[3.093, 3.14159265359, 0.00000000000],
|
|
],
|
|
]
|
|
"""This table contains Uranus' 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 449-451."""
|
|
|
|
|
|
ORBITAL_ELEM = [
|
|
[314.055005, 429.8640561, 0.0003039, 0.000000026], # L
|
|
[19.218446062, -0.0000000372, 0.00000000098, 0.0], # a
|
|
[0.04638122, -0.000027293, 0.0000000789, 0.00000000024], # e
|
|
[0.773197, 0.0007744, 0.00003749, -0.000000092], # i
|
|
[74.005957, 0.5211278, 0.00133947, 0.000018484], # Omega
|
|
[173.005291, 1.486379, 0.00021406, 0.000000434] # pie
|
|
]
|
|
"""This table contains the parameters to compute Uranus's orbital elements for
|
|
the mean equinox of date. Based in Table 31.A, page 213"""
|
|
|
|
|
|
ORBITAL_ELEM_J2000 = [
|
|
[314.055005, 428.4669983, -0.00000486, 0.000000006], # L
|
|
[0.773197, -0.0016869, 0.00000349, 0.000000016], # i
|
|
[74.005957, 0.0741431, 0.00040539, 0.000000119], # Omega
|
|
[173.005291, 0.0893212, -0.0000947, 0.000000414] # pie
|
|
]
|
|
"""This table contains the parameters to compute Uranus's orbital elements for
|
|
the standard equinox J2000.0. Based on Table 31.B, page 215"""
|
|
|
|
|
|
class Uranus(object):
|
|
"""
|
|
Class Uranus models that planet.
|
|
"""
|
|
|
|
@staticmethod
|
|
def geometric_heliocentric_position(epoch, tofk5=True):
|
|
"""This method computes the geometric heliocentric position of planet
|
|
Uranus for a given epoch, using the VSOP87 theory.
|
|
|
|
:param epoch: Epoch to compute Uranus 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 = Uranus.geometric_heliocentric_position(epoch)
|
|
>>> print(round(l.to_positive(), 4))
|
|
30.5888
|
|
>>> print(round(b, 4))
|
|
-0.5315
|
|
>>> print(round(r, 5))
|
|
19.86964
|
|
"""
|
|
|
|
return geometric_vsop_pos(epoch, VSOP87_L, VSOP87_B, VSOP87_R, tofk5)
|
|
|
|
@staticmethod
|
|
def apparent_heliocentric_position(epoch):
|
|
"""This method computes the apparent heliocentric position of planet
|
|
Uranus for a given epoch, using the VSOP87 theory.
|
|
|
|
:param epoch: Epoch to compute Uranus 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)
|
|
|
|
@staticmethod
|
|
def orbital_elements_mean_equinox(epoch):
|
|
"""This method computes the orbital elements of Uranus 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 = Uranus.orbital_elements_mean_equinox(epoch)
|
|
>>> print(round(l, 6))
|
|
235.517526
|
|
>>> print(round(a, 8))
|
|
19.21844604
|
|
>>> print(round(e, 7))
|
|
0.0463634
|
|
>>> print(round(i, 6))
|
|
0.77372
|
|
>>> print(round(ome, 5))
|
|
74.34776
|
|
>>> print(round(arg, 6))
|
|
99.630865
|
|
"""
|
|
|
|
return orbital_elements(epoch, ORBITAL_ELEM, ORBITAL_ELEM)
|
|
|
|
@staticmethod
|
|
def orbital_elements_j2000(epoch):
|
|
"""This method computes the orbital elements of Uranus 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 = Uranus.orbital_elements_j2000(epoch)
|
|
>>> print(round(l, 6))
|
|
234.602641
|
|
>>> print(round(a, 8))
|
|
19.21844604
|
|
>>> print(round(e, 7))
|
|
0.0463634
|
|
>>> print(round(i, 6))
|
|
0.772094
|
|
>>> print(round(ome, 5))
|
|
74.05468
|
|
>>> print(round(arg, 6))
|
|
99.009058
|
|
"""
|
|
|
|
return orbital_elements(epoch, ORBITAL_ELEM, ORBITAL_ELEM_J2000)
|
|
|
|
@staticmethod
|
|
def geocentric_position(epoch):
|
|
"""This method computes the geocentric position of Uranus (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 = Uranus.geocentric_position(epoch)
|
|
>>> print(ra.ra_str(n_dec=1))
|
|
19h 13' 48.7''
|
|
>>> print(dec.dms_str(n_dec=1))
|
|
-22d 46' 13.0''
|
|
>>> print(elon.dms_str(n_dec=1))
|
|
18d 44' 18.7''
|
|
"""
|
|
|
|
# First check that input value is of correct types
|
|
if not isinstance(epoch, Epoch):
|
|
raise TypeError("Invalid input type")
|
|
# Compute the heliocentric position of Uranus
|
|
l, b, r = Uranus.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 Uranus coordinates with this correction
|
|
l, b, r = Uranus.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
|
|
|
|
@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 = Uranus.conjunction(epoch)
|
|
>>> y, m, d = conj.get_date()
|
|
>>> print(y)
|
|
1994
|
|
>>> print(m)
|
|
1
|
|
>>> print(round(d, 4))
|
|
12.7365
|
|
"""
|
|
|
|
# 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 Uranus' conjunction
|
|
a = 2451579.489
|
|
b = 369.656035
|
|
m0 = 31.5219
|
|
m1 = 4.333093
|
|
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
|
|
ff = 108.84 + 419.96 * t
|
|
# Convert to radians
|
|
ee = Angle(ee).rad()
|
|
ff = Angle(ff).rad()
|
|
corr = (-0.0859 + t * 0.0003 +
|
|
sin(m) * (-3.8179 + t * (-0.0148 + t * 0.00003)) +
|
|
cos(m) * (5.1228 + t * (-0.0105 - t * 0.00002)) +
|
|
sin(2.0 * m) * (-0.0803 + t * 0.0011) +
|
|
cos(2.0 * m) * (-0.1905 - t * 0.0006) +
|
|
sin(3.0 * m) * (0.0088 + t * 0.0001) +
|
|
cos(ee) * (0.885) +
|
|
cos(ff) * (0.2153))
|
|
to_return = jde0 + corr
|
|
return Epoch(to_return)
|
|
|
|
@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(1780, 12, 1.0)
|
|
>>> oppo = Uranus.opposition(epoch)
|
|
>>> y, m, d = oppo.get_date()
|
|
>>> print(y)
|
|
1780
|
|
>>> print(m)
|
|
12
|
|
>>> print(round(d, 4))
|
|
17.5998
|
|
"""
|
|
|
|
# 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 Uranus' opposition
|
|
a = 2451764.317
|
|
b = 369.656035
|
|
m0 = 213.6884
|
|
m1 = 4.333093
|
|
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
|
|
ff = 108.84 + 419.96 * t
|
|
# Convert to radians
|
|
ee = Angle(ee).rad()
|
|
ff = Angle(ff).rad()
|
|
corr = (0.0844 - t * 0.0006 +
|
|
sin(m) * (-0.1048 + t * 0.0246) +
|
|
cos(m) * (-5.1221 + t * (0.0104 + t * 0.00003)) +
|
|
sin(2.0 * m) * (-0.1428 + t * 0.0005) +
|
|
cos(2.0 * m) * (-0.0148 - t * 0.0013) +
|
|
cos(3.0 * m) * (0.0055) +
|
|
cos(ee) * (0.885) +
|
|
cos(ff) * (0.2153))
|
|
to_return = jde0 + corr
|
|
return Epoch(to_return)
|
|
|
|
@staticmethod
|
|
def perihelion_aphelion(epoch, perihelion=True):
|
|
"""This method computes the time of Perihelion (or Aphelion) closer to
|
|
a given epoch.
|
|
|
|
:param epoch: Epoch close to the desired Perihelion (or Aphelion)
|
|
:type epoch: :py:class:`Epoch`
|
|
:param peihelion: If True, the epoch of the closest Perihelion is
|
|
computed, if False, the epoch of the closest Aphelion is found.
|
|
:type bool:
|
|
|
|
:returns: The epoch of the desired Perihelion (or Aphelion)
|
|
:rtype: :py:class:`Epoch`
|
|
:raises: TypeError if input values are of wrong type.
|
|
|
|
.. note:: The solution provided by this method may have several days of
|
|
error.
|
|
|
|
>>> epoch = Epoch(1880, 1, 1.0)
|
|
>>> e = Uranus.perihelion_aphelion(epoch)
|
|
>>> y, m, d = e.get_date()
|
|
>>> print(y)
|
|
1882
|
|
>>> print(m)
|
|
3
|
|
>>> print(int(d))
|
|
18
|
|
>>> epoch = Epoch(2090, 1, 1.0)
|
|
>>> e = Uranus.perihelion_aphelion(epoch, perihelion=False)
|
|
>>> y, m, d = e.get_date()
|
|
>>> print(y)
|
|
2092
|
|
>>> print(m)
|
|
11
|
|
>>> print(int(d))
|
|
22
|
|
"""
|
|
|
|
if not isinstance(epoch, Epoch):
|
|
raise TypeError("Invalid input value")
|
|
# First approximation
|
|
k = 0.0119 * (epoch.year() - 2051.1)
|
|
if perihelion:
|
|
k = round(k)
|
|
else:
|
|
k = round(k + 0.5) - 0.5
|
|
jde = 2470213.5 + k * (30694.8767 - k * 0.00541)
|
|
# Compute the epochs 1 year before and after
|
|
jde_before = jde - 360.0
|
|
jde_after = jde + 360.0
|
|
# Compute the Sun-Uranus distance for each epoch
|
|
l, b, r_b = Uranus.geometric_heliocentric_position(Epoch(jde_before))
|
|
l, b, r = Uranus.geometric_heliocentric_position(Epoch(jde))
|
|
l, b, r_a = Uranus.geometric_heliocentric_position(Epoch(jde_after))
|
|
# Call an interpolation object
|
|
m = Interpolation([jde_before, jde, jde_after], [r_b, r, r_a])
|
|
sol = m.minmax()
|
|
return Epoch(sol)
|
|
|
|
@staticmethod
|
|
def passage_nodes(epoch, ascending=True):
|
|
"""This function computes the time of passage by the nodes (ascending
|
|
or descending) of Uranus, nearest to the given epoch.
|
|
|
|
:param epoch: Epoch closest to the node passage
|
|
:type epoch: :py:class:`Epoch`
|
|
:param ascending: Whether the time of passage by the ascending (True)
|
|
or descending (False) node will be computed
|
|
:type ascending: bool
|
|
|
|
:returns: Tuple containing:
|
|
- Time of passage through the node (:py:class:`Epoch`)
|
|
- Radius vector when passing through the node (in AU, float)
|
|
:rtype: tuple
|
|
:raises: TypeError if input values are of wrong type.
|
|
|
|
>>> epoch = Epoch(2019, 1, 1)
|
|
>>> time, r = Uranus.passage_nodes(epoch)
|
|
>>> year, month, day = time.get_date()
|
|
>>> print(year)
|
|
2028
|
|
>>> print(month)
|
|
8
|
|
>>> print(round(day, 1))
|
|
23.2
|
|
>>> print(round(r, 4))
|
|
19.3201
|
|
"""
|
|
|
|
if not isinstance(epoch, Epoch):
|
|
raise TypeError("Invalid input types")
|
|
# Get the orbital parameters
|
|
l, a, e, i, ome, arg = Uranus.orbital_elements_mean_equinox(epoch)
|
|
# Compute the time of passage through perihelion
|
|
t = Uranus.perihelion_aphelion(epoch)
|
|
# Get the time of passage through the node
|
|
time, r = passage_nodes_elliptic(arg, e, a, t, ascending)
|
|
return time, r
|
|
|
|
@staticmethod
|
|
def magnitude(sun_dist, earth_dist):
|
|
"""This function computes the approximate magnitude of Uranus.
|
|
|
|
:param sun_dist: Distance from Uranus to Sun, in Astronomical Units
|
|
:type sun_dist: float
|
|
:param earth_dist: Distance from Uranus to Earth, in Astronomical Units
|
|
:type earth_dist: float
|
|
|
|
:returns: Uranus'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 = -6.85 + 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 Uranus class
|
|
print("\n" + 35 * "*")
|
|
print("*** Use of Uranus class")
|
|
print(35 * "*" + "\n")
|
|
|
|
# Let's now compute the heliocentric position for a given epoch
|
|
epoch = Epoch(2018, 10, 27.0)
|
|
lon, lat, r = Uranus.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 = Uranus.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 Uranus at 2065.6.24
|
|
epoch = Epoch(2065, 6, 24.0)
|
|
l, a, e, i, ome, arg = Uranus.orbital_elements_mean_equinox(epoch)
|
|
print_me("Mean longitude of the planet", round(l, 6)) # 235.517526
|
|
print_me("Semimajor axis of the orbit (UA)", round(a, 8)) # 19.21844604
|
|
print_me("Eccentricity of the orbit", round(e, 7)) # 0.0463634
|
|
print_me("Inclination on plane of the ecliptic", round(i, 6)) # 0.77372
|
|
print_me("Longitude of the ascending node", round(ome, 5)) # 74.34776
|
|
print_me("Argument of the perihelion", round(arg, 6)) # 99.630865
|
|
|
|
print("")
|
|
|
|
# Compute the time of the conjunction close to 1993/10/1
|
|
epoch = Epoch(1993, 10, 1.0)
|
|
conj = Uranus.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 1780/12/1
|
|
epoch = Epoch(1780, 12, 1.0)
|
|
oppo = Uranus.opposition(epoch)
|
|
y, m, d = oppo.get_date()
|
|
d = round(d, 4)
|
|
date = "{}/{}/{}".format(y, m, d)
|
|
print_me("Opposition date", date)
|
|
|
|
print("")
|
|
|
|
# Find the epoch of the Perihelion closer to 1780/1/1
|
|
epoch = Epoch(1780, 1, 1.0)
|
|
e = Uranus.perihelion_aphelion(epoch)
|
|
y, m, d = e.get_date()
|
|
peri = str(y) + '/' + str(m) + '/' + str(int(d))
|
|
print_me("The Perihelion closest to 1780/1/1 happened on", peri)
|
|
|
|
print("")
|
|
|
|
# Compute the time of passage through an ascending node
|
|
epoch = Epoch(2019, 1, 1)
|
|
time, r = Uranus.passage_nodes(epoch)
|
|
y, m, d = time.get_date()
|
|
d = round(d, 1)
|
|
print("Time of passage through ascending node: {}/{}/{}".format(y, m, d))
|
|
# 2028/8/23.2
|
|
print("Radius vector at ascending node: {}".format(round(r, 4))) # 19.3201
|
|
|
|
|
|
if __name__ == "__main__":
|
|
|
|
main()
|