Module: AstroChart::Pure::Vsop87Data

Defined in:

lib/astro_chart/pure/vsop87_data.rb

Overview

Vsop87Data -- truncated VSOP87D periodic series (heliocentric ecliptic longitude L / latitude B / radius vector R, ecliptic and equinox of date).

Source: P. Bretagnon & G. Francou, "Planetary theories in rectangular and spherical variables: VSOP87 solutions", Astronomy & Astrophysics 202, 309-315 (1988). Series data files (VSOP87D.*) are publicly distributed by IMCCE and are used here under their published terms. No Swiss Ephemeris code or data was consulted or copied.

Truncation: terms kept per (planet, variable) until the summed effective amplitude (A * Tmax**order, Tmax = 1.1 Julian millennia) of the dropped tail falls below a per-variable residual target chosen for <= 0.01 deg apparent geocentric longitude accuracy over 1900-2100 (see repo tmp/verify_vsop87.rb for empirical check against ground truth).

Layout: SERIES[var] = [order0, order1, ...] where each order is a flat Float array of consecutive (A, B, C) triples:

value = sum over orders k of T**k * sum_i A_i * cos(B_i + C_i*T)

with T in Julian millennia of TDB(~TT) from J2000.0; L/B in radians, R in au. This file is generated -- do not hand edit.

Constant Summary

SERIES =

{
    mercury: {
      l: [
        [4.40250710144e+00, 0.00000000000e+00, 0.00000000000e+00, 4.09894149760e-01, 1.48302034194e+00, 2.60879031416e+04, 5.04629419900e-02, 4.47785489540e+00, 5.21758062831e+04, 8.55346843000e-03, 1.16520322351e+00, 7.82637094247e+04, 1.65590362000e-03, 4.11969163181e+00, 1.04351612566e+05, 3.45618970000e-04, 7.79307658170e-01, 1.30439515708e+05, 7.58347600000e-05, 3.71348400510e+00, 1.56527418849e+05, 3.55974000000e-05, 1.51202669419e+00, 1.10937855209e+03, 1.80346300000e-05, 4.10333178410e+00, 5.66133204915e+03, 1.72601200000e-05, 3.58322399080e-01, 1.82615321991e+05, 1.58992300000e-05, 2.99510417815e+00, 2.50285212114e+04, 1.36468200000e-05, 4.59918318745e+00, 2.71972816937e+04, 1.01733200000e-05, 8.80314390400e-01, 3.17492351907e+04, 7.14182000000e-06, 1.54144865265e+00, 2.49785245895e+04, 6.43759000000e-06, 5.30266110787e+00, 2.15359496445e+04, 4.51137000000e-06, 6.04989275289e+00, 5.11164243530e+04, 4.04200000000e-06, 3.28228847025e+00, 2.08703225133e+05, 3.52441000000e-06, 5.24156297101e+00, 2.04265710924e+04, 3.45212000000e-06, 2.79211901539e+00, 1.58746175954e+04, 3.43313000000e-06, 5.76531885335e+00, 9.55599741609e+02, 3.39214000000e-06, 5.86327765000e+00, 2.55582121765e+04, 3.25335000000e-06, 1.33674334780e+00, 5.32851848352e+04, 2.72947000000e-06, 2.49451163975e+00, 5.29690965095e+02, 2.64336000000e-06, 3.91705094013e+00, 5.78371383323e+04, 2.59587000000e-06, 9.87324281840e-01, 4.55195349706e+03, 2.38793000000e-06, 1.13439533780e-01, 1.05938193019e+03, 2.34830000000e-06, 2.66721189000e-01, 1.13226640983e+04, 2.16645000000e-06, 6.59872073480e-01, 1.35217514416e+04, 2.08995000000e-06, 2.09178234008e+00, 4.76238527861e+04, 1.83359000000e-06, 2.62878670784e+00, 2.70435028832e+04, 1.81629000000e-06, 2.43413502466e+00, 2.56613049507e+04, 1.75965000000e-06, 4.53636829858e+00, 5.10664277311e+04, 1.72643000000e-06, 2.45200164173e+00, 2.44988302463e+04, 1.42316000000e-06, 3.36003948842e+00, 3.74105672399e+04, 1.37942000000e-06, 2.90984478490e-01, 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9.74700000000e-08, 3.83976857418e+00, 2.60840218062e+04, 9.67700000000e-08, 2.98527809776e+00, 5.94144818747e+04, 9.66400000000e-08, 5.77941968495e+00, 2.59383399444e+04, 9.36200000000e-08, 5.44291958209e+00, 3.86540548416e+04, 9.26400000000e-08, 4.02987000812e+00, 4.67964990354e+02, 9.00100000000e-08, 6.23396256413e+00, 2.50214076644e+04, 8.97700000000e-08, 3.47888073089e+00, 9.17854608663e+04, 8.96100000000e-08, 1.10625261140e-01, 6.23890918294e+04, 8.85500000000e-08, 2.84672636028e+00, 2.50356347584e+04, 8.34300000000e-08, 5.34499871294e+00, 1.93171925403e+04, 8.18100000000e-08, 5.77857196635e+00, 4.08531421848e+04, 8.12600000000e-08, 1.12294634635e+00, 2.60950166886e+04, 8.03300000000e-08, 2.45692824195e+00, 1.29380133778e+05].freeze,
        [2.60881470622e+04, 0.00000000000e+00, 0.00000000000e+00, 1.12600783200e-02, 6.21703970996e+00, 2.60879031416e+04, 3.03471395000e-03, 3.05565472363e+00, 5.21758062831e+04, 8.05384520000e-04, 6.10454743366e+00, 7.82637094247e+04, 2.12450350000e-04, 2.83531934452e+00, 1.04351612566e+05, 5.59209400000e-05, 5.82675673328e+00, 1.30439515708e+05, 1.47223300000e-05, 2.51845458395e+00, 1.56527418849e+05, 3.88318000000e-06, 5.48039225891e+00, 1.82615321991e+05, 3.52244000000e-06, 3.05238094403e+00, 1.10937855209e+03, 1.02743000000e-06, 2.14879173777e+00, 2.08703225133e+05, 9.35400000000e-07, 6.11791163931e+00, 2.71972816937e+04, 9.05790000000e-07, 4.54816690000e-04, 2.49785245895e+04, 5.19410000000e-07, 5.62107554052e+00, 5.66133204915e+03, 4.43700000000e-07, 4.57348500464e+00, 2.50285212114e+04, 2.80700000000e-07, 3.04195430989e+00, 5.10664277311e+04, 2.72950000000e-07, 5.09210138837e+00, 2.34791128274e+05, 2.20030000000e-07, 8.64753712430e-01, 9.55599741609e+02, 2.04250000000e-07, 3.71509622702e+00, 2.04265710924e+04, 2.02210000000e-07, 5.19340472950e-01, 2.15359496445e+04, 1.74960000000e-07, 5.72663608620e+00, 4.55195349706e+03, 1.66800000000e-07, 1.35134428173e+00, 5.29690965095e+02, 1.53980000000e-07, 5.74263453989e+00, 1.96697608998e+01, 1.53060000000e-07, 1.79184360652e+00, 1.13226640983e+04, 1.39640000000e-07, 3.59426938083e+00, 2.44988302463e+04, 1.28220000000e-07, 2.69591798562e+00, 5.32851848352e+04, 1.26210000000e-07, 3.89530641889e+00, 3.88133535800e+00, 1.25660000000e-07, 4.70537436663e+00, 1.05938193019e+03, 8.63900000000e-08, 6.06360282793e+00, 7.71543308726e+04, 8.02400000000e-08, 3.92723313702e+00, 2.70435028832e+04, 7.97400000000e-08, 4.17682324505e+00, 2.66175941067e+04, 7.92900000000e-08, 5.04268043180e-01, 4.65144742340e+04, 7.66500000000e-08, 2.48158305355e+00, 5.78371383323e+04, 7.28500000000e-08, 1.74581868954e+00, 2.60879031416e+05].freeze,
        [5.30498450000e-04, 0.00000000000e+00, 0.00000000000e+00, 1.69036580000e-04, 4.69072300649e+00, 2.60879031416e+04, 7.39671100000e-05, 1.34735624669e+00, 5.21758062831e+04, 3.01829700000e-05, 4.45643539705e+00, 7.82637094247e+04, 1.10741900000e-05, 1.26226537554e+00, 1.04351612566e+05, 3.78173000000e-06, 4.31998055900e+00, 1.30439515708e+05, 1.22998000000e-06, 1.06868541052e+00, 1.56527418849e+05, 3.86630000000e-07, 4.08011610182e+00, 1.82615321991e+05, 1.48980000000e-07, 4.63343085810e+00, 1.10937855209e+03, 1.18610000000e-07, 7.91876464390e-01, 2.08703225133e+05].freeze,
        [1.88077000000e-06, 3.46683011700e-02, 5.21758062831e+04, 1.42152000000e-06, 3.12505452600e+00, 2.60879031416e+04, 9.68770000000e-07, 3.00378171915e+00, 7.82637094247e+04, 4.36690000000e-07, 6.01867965826e+00, 1.04351612566e+05, 3.53950000000e-07, 0.00000000000e+00, 0.00000000000e+00, 1.80450000000e-07, 2.77538373991e+00, 1.30439515708e+05, 6.97100000000e-08, 5.81808665742e+00, 1.56527418849e+05].freeze,
        [1.14078000000e-06, 3.14159265359e+00, 0.00000000000e+00].freeze,
      ].freeze,
      b: [
        [1.17375289620e-01, 1.98357498767e+00, 2.60879031416e+04, 2.38807699600e-02, 5.03738959685e+00, 5.21758062831e+04, 1.22283953200e-02, 3.14159265359e+00, 0.00000000000e+00, 5.43251810000e-03, 1.79644363963e+00, 7.82637094247e+04, 1.29778770000e-03, 4.83232503961e+00, 1.04351612566e+05, 3.18669270000e-04, 1.58088495667e+00, 1.30439515708e+05, 7.96330100000e-05, 4.60972126348e+00, 1.56527418849e+05, 2.01418900000e-05, 1.35324164694e+00, 1.82615321991e+05, 5.13953000000e-06, 4.37835409309e+00, 2.08703225133e+05, 2.08584000000e-06, 2.02020294153e+00, 2.49785245895e+04, 2.07674000000e-06, 4.91772564073e+00, 2.71972816937e+04, 1.32013000000e-06, 1.11908492283e+00, 2.34791128274e+05, 1.21395000000e-06, 1.81271752059e+00, 5.32851848352e+04, 1.00454000000e-06, 5.65684734206e+00, 2.04265710924e+04, 9.92140000000e-07, 9.39188709700e-02, 5.11164243530e+04, 9.45740000000e-07, 1.24184909234e+00, 3.17492351907e+04, 9.15660000000e-07, 2.28163128692e+00, 2.50285212114e+04, 8.42640000000e-07, 5.08510388314e+00, 5.10664277311e+04, 7.87850000000e-07, 4.40725880000e+00, 5.78371383323e+04, 7.77470000000e-07, 5.25570617490e-01, 1.05938193019e+03, 4.99480000000e-07, 3.49752993688e+00, 5.66133204915e+03, 4.64540000000e-07, 3.23739270829e+00, 7.72043274945e+04, 4.47670000000e-07, 4.87849816734e+00, 7.93730879768e+04, 4.07660000000e-07, 2.46558332165e+00, 4.65144742340e+04, 3.73780000000e-07, 4.45768797944e+00, 4.55195349706e+03, 3.59110000000e-07, 1.09057317869e+00, 1.10937855209e+03, 3.40820000000e-07, 4.14209210575e+00, 2.60879031416e+05, 3.19530000000e-07, 1.18516389747e+00, 8.39250414739e+04, 3.18080000000e-07, 2.41474588439e+00, 4.76238527861e+04, 3.09540000000e-07, 3.50328027210e+00, 2.15359496445e+04, 2.86910000000e-07, 1.84828614269e+00, 7.71543308726e+04, 2.57650000000e-07, 2.77593370583e+00, 2.70435028832e+04, 2.51990000000e-07, 3.59062266460e+00, 2.71472850718e+04, 2.02440000000e-07, 3.06833797229e+00, 5.16461153181e+04, 2.00990000000e-07, 4.06593040301e+00, 2.51323034000e+04, 1.85910000000e-07, 5.58427274440e+00, 7.37117559277e+04, 1.70020000000e-07, 6.13739392193e+00, 4.19625207369e+04, 1.69710000000e-07, 2.79127655100e-02, 1.03292230636e+05, 1.57950000000e-07, 3.79629547258e+00, 5.29690965095e+02, 1.55770000000e-07, 6.07693643204e+00, 5.31314060248e+04, 1.49840000000e-07, 1.64717994813e+00, 1.05460991118e+05].freeze,
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        [1.18309340000e-04, 4.79065585784e+00, 2.60879031416e+04, 1.91351600000e-05, 0.00000000000e+00, 0.00000000000e+00, 1.04480100000e-05, 1.21216540536e+00, 5.21758062831e+04, 2.66213000000e-06, 4.43418336532e+00, 7.82637094247e+04, 1.70280000000e-06, 1.62255638714e+00, 1.04351612566e+05, 9.63000000000e-07, 4.80023692017e+00, 1.30439515708e+05, 4.46920000000e-07, 1.60758267772e+00, 1.56527418849e+05, 1.83160000000e-07, 4.66904655377e+00, 1.82615321991e+05].freeze,
        [2.35423000000e-06, 3.53875246040e-01, 2.60879031416e+04, 1.60537000000e-06, 0.00000000000e+00, 0.00000000000e+00, 1.89040000000e-07, 4.36275460261e+00, 5.21758062831e+04].freeze,
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