Forum der Vereinigung der Sternfreunde

# planetVsop.py
# Beispielprogramm zur Berechnung des Planetenorts:
# heliozentrisch, geozentrisch und topozentrisch.
# die Numerik steckt im Modul planpos.py

from math import *
from planpos import *

def printDegMinSec(w):
        # formatiert drucken ohne Zeilenwechsel
        # print("%5.3f " % (j * dt),end="")
        signum = ' '
        if (w < 0):
                signum = '-'
                w = -w
        bruchteil, deg = modf(w)
        w = 60 * (bruchteil)
        bruchteil, min = modf(w)
        w = 60 * (bruchteil)
        print(signum,end=" ")
        print(int(deg), end=" ")
        print(int(min), end=" ")
        print(w, end="   ")


# Main
# berechneHeliozentrisch(planet, JD)
# berechneGeozentrisch(pnr, JD, epoche2000)
# def berechneTopozentrisch(JD, alpha, delta, phi, L, h):

# Leipzig 
phi = 51.38579; 
L = -12.43629/15; 
h = 110; 

JD = 2452879.636806;
print("Ausgabe: l b r   a d D   aT dT")
print("JD=",JD)
for j in range(0,8):
        x, y, z, l, b, r = berechneHeliozentrisch(j, JD)
        print("Planet:",j)
        printDegMinSec(l)
        printDegMinSec(b)
        print(r, end="   ")
        if (j != 2):
                alpha, delta, Delta = berechneGeozentrisch(j, JD, 0)
                printDegMinSec(alpha)
                printDegMinSec(delta)
                print(Delta, end="   ")
                alphaT, deltaT=berechneTopozentrisch(JD, alpha, delta, Delta, phi, L, h)
                printDegMinSec(alphaT)
                printDegMinSec(deltaT)
        print("")

# Prompt am Ende
ende = input("Fertig.")

# planpos.py
# Planetenpositionen besser 1"
# analog Meuus Kap. 32, S. 219 und Appendix II, S. 413
# hier sind aber mehr Koeffizienten drinnen

from math import *


# Winkelfunktionen in Gradmaß, wie im Meeus
def Sin(w): return sin(pi * w / 180)
def Cos(w): return cos(pi * w / 180)
def Tan(w): return tan(pi * w / 180) 
def Atan2(y, x): return 180 * atan2(y, x) / pi 
def Atan(x): return 180 * atan(x) / pi 
def Asin(x): return 180 * asin(x) / pi 
def to360(w):
        gebrochen, ganz=modf(w/360.0)
        w = 360 * gebrochen
        return w
def To360(w):
	w = to360(w)
	if (w < 0): w = w+360
	return w


def sq(x):
    return x*x    

def sunNewcomb(JD):
        T = (JD - 2415020) / 36525           # Time since 0.5 Jan 1900 (Julian centuries)
        DLP = (1.882e0 - .016e0 * T) * Sin((57.24e0 + 150.27e0 * T)) + 6.400e0 * Sin((231.19e0 + 20.20e0 * T))+ 0.266e0 * Sin((31.80e0 + 119.00e0 * T))
        G = 358.4758333e0 + to360(35999.e0 * T) + (T * (179.10e0 - .54e0 * T) + DLP) / 3600.e0
        #-------
        # LO = DLO+SLO
        DLO = 279.6966778e0 + to360(36000.e0 * T)
        SLO = T * (2768.13e0 + 1.089e0 * T) + 0.202e0 * Sin(315.6e0 + 893.3e0 * T) + DLP
        DL = (6910.057e0 - 17.240e0 * T) * Sin(G) + (72.338e0 - 0.361e0 * T) * Sin(2.0e0 * G) + 1.054e0 * Sin(3.0e0 * G)
        rDis = (0.00003057e0 - 0.00000015e0 * T) + (-0.00727412e0 + 0.00001814e0 * T) * Cos(G) + (-0.00009138e0 + 0.00000046e0 * T) * Cos(2.0e0 * G) + (-0.00000145e0) * Cos(3.0e0 * G)
        rLat = 0.0e0
        G2 = 212.45e0 + 58517.493e0 * T
        G4 = 319.58e0 + 19139.977e0 * T
        G5 = 225.28e0 + 3034.583e0 * T + 1300.0e0 * Sin(133.775e0 + 39.804e0 * T) / 3600.0e0
        G6 = 175.60e0 + 1221.794e0 * T
        D = 350.737486e0 + 445267.114217e0 * T
        A = 296.104608e0 + 477198.849108e0 * T
        U = 11.250889e0 + 483202.025150e0 * T
        #-------
        # DL2 (Venus)
        DL = DL\
                + 4.838e0 * Cos(299.102e0 + G2 - G) \
                + 0.116e0 * Cos(148.900e0 + 2.0e0 * G2 - G) \
                + 5.526e0 * Cos(148.313e0 + 2.0e0 * G2 - 2.0e0 * G)\
                + 2.497e0 * Cos(315.943e0 + 2.0e0 * G2 - 3.0e0 * G)\
                + 0.666e0 * Cos(177.710e0 + 3.0e0 * G2 - 3.0e0 * G)\
                + 1.559e0 * Cos(345.253e0 + 3.0e0 * G2 - 4.0e0 * G)\
                + 1.024e0 * Cos(318.150e0 + 3.0e0 * G2 - 5.0e0 * G)\
                + 0.210e0 * Cos(206.200e0 + 4.0e0 * G2 - 4.0e0 * G)\
                + 0.144e0 * Cos(195.400e0 + 4.0e0 * G2 - 5.0e0 * G)\
                + 0.152e0 * Cos(343.800e0 + 4.0e0 * G2 - 6.0e0 * G)\
                + 0.123e0 * Cos(195.300e0 + 5.0e0 * G2 - 7.0e0 * G)\
                + 0.154e0 * Cos(359.600e0 + 5.0e0 * G2 - 8.0e0 * G)
        #-------
        # DL4 (Mars)
        DL = DL\
                + 0.273e0 * Cos(217.700e0 - G4 + G)\
                + 2.043e0 * Cos(343.888e0 - 2.0e0 * G4 + 2.0e0 * G)\
                + 1.770e0 * Cos(200.402e0 - 2.0e0 * G4 + G)\
                + 0.129e0 * Cos(294.200e0 - 3.0e0 * G4 + 3.0e0 * G)\
                + 0.425e0 * Cos(338.880e0 - 3.0e0 * G4 + 2.0e0 * G)\
                + 0.500e0 * Cos(105.180e0 - 4.0e0 * G4 + 3.0e0 * G)\
                + 0.585e0 * Cos(334.060e0 - 4.0e0 * G4 + 2.0e0 * G)\
                + 0.204e0 * Cos(100.800e0 - 5.0e0 * G4 + 3.0e0 * G)\
                + 0.154e0 * Cos(227.400e0 - 6.0e0 * G4 + 4.0e0 * G)\
                + 0.101e0 * Cos(96.300e0 - 6.0e0 * G4 + 3.0e0 * G)\
                + 0.106e0 * Cos(222.700e0 - 7.0e0 * G4 + 4.0e0 * G)
        #-------
        # DL5 (Jupiter)
        DL = DL\
                + 0.163e0 * Cos(198.600e0 - G5 + 2.0e0 * G)\
                + 7.208e0 * Cos(179.532e0 - G5 + G)\
                + 2.600e0 * Cos(263.217e0 - G5)\
                + 2.731e0 * Cos(87.145e0 - 2.0e0 * G5 + 2.0e0 * G)\
                + 1.610e0 * Cos(109.493e0 - 2.0e0 * G5 + G)\
                + 0.164e0 * Cos(170.500e0 - 3.0e0 * G5 + 3.0e0 * G)\
                + 0.556e0 * Cos(82.650e0 - 3.0e0 * G5 + 2.0e0 * G)\
                + 0.210e0 * Cos(98.500e0 - 3.0e0 * G5 + G)
        #-------
        # DL6 (Saturn)
        DL = DL\
                + 0.419e0 * Cos(100.580e0 - G6 + G)\
                + 0.320e0 * Cos(269.460e0 - G6)\
                + 0.108e0 * Cos(290.600e0 - 2.0e0 * G6 + 2.0e0 * G)\
                + 0.112e0 * Cos(293.600e0 - 2.0e0 * G6 + G)
        #-------
        # DLM (Moon)
        DL = DL\
                + 6.454e0 * Sin(D)\
                + 0.177e0 * Sin(D + A)\
                - 0.424e0 * Sin(D - A)\
                + 0.172e0 * Sin(D - G)
        #-------
        # DR2 (Venus)
        R1 =\
                2359.0e0 * Cos(209.080e0 + G2 - G)\
                + 160.0e0 * Cos(58.400e0 + 2.0e0 * G2 - G)\
                + 6842.0e0 * Cos(58.318e0 + 2.0e0 * G2 - 2.0e0 * G)\
                + 869.0e0 * Cos(226.700e0 + 2.0e0 * G2 - 3.0e0 * G)\
                + 1045.0e0 * Cos(87.570e0 + 3.0e0 * G2 - 3.0e0 * G)\
                + 1497.0e0 * Cos(255.250e0 + 3.0e0 * G2 - 4.0e0 * G)\
                + 194.0e0 * Cos(49.500e0 + 3.0e0 * G2 - 5.0e0 * G)\
                + 376.0e0 * Cos(116.280e0 + 4.0e0 * G2 - 4.0e0 * G)\
                + 196.0e0 * Cos(105.200e0 + 4.0e0 * G2 - 5.0e0 * G)\
                + 163.0e0 * Cos(145.400e0 + 5.0e0 * G2 - 5.0e0 * G)\
                + 141.0e0 * Cos(105.400e0 + 5.0e0 * G2 - 7.0e0 * G)
        #-------
        # DR4 (Mars)
        R1 = R1\
                + 150.0e0 * Cos(127.700e0 - G4 + G)\
                + 2057.0e0 * Cos(253.828e0 - 2.0e0 * G4 + 2.0e0 * G)\
                + 151.0e0 * Cos(295.000e0 - 2.0e0 * G4 + G)\
                + 168.0e0 * Cos(203.500e0 - 3.0e0 * G4 + 3.0e0 * G)\
                + 215.0e0 * Cos(249.000e0 - 3.0e0 * G4 + 2.0e0 * G)\
                + 478.0e0 * Cos(15.170e0 - 4.0e0 * G4 + 3.0e0 * G)\
                + 105.0e0 * Cos(65.900e0 - 4.0e0 * G4 + 2.0e0 * G)\
                + 107.0e0 * Cos(324.600e0 - 5.0e0 * G4 + 4.0e0 * G)\
                + 139.0e0 * Cos(137.300e0 - 6.0e0 * G4 + 4.0e0 * G)
        #-------
        # DR5 (Jupiter)
        R1 = R1\
                + 208.0e0 * Cos(112.000e0 - G5 + 2.0e0 * G)\
                + 7067.0e0 * Cos(89.545e0 - G5 + G)\
                + 244.0e0 * Cos(338.600e0 - G5)\
                + 103.0e0 * Cos(350.500e0 - 2.0e0 * G5 + 3.0e0 * G)\
                + 4026.0e0 * Cos(357.108e0 - 2.0e0 * G5 + 2.0e0 * G)\
                + 1459.0e0 * Cos(19.467e0 - 2.0e0 * G5 + G)\
                + 281.0e0 * Cos(81.200e0 - 3.0e0 * G5 + 3.0e0 * G)\
                + 803.0e0 * Cos(352.560e0 - 3.0e0 * G5 + 2.0e0 * G)\
                + 174.0e0 * Cos(8.600e0 - 3.0e0 * G5 + G)\
                + 113.0e0 * Cos(347.700e0 - 4.0e0 * G5 + 2.0e0 * G)
        #-------
        # DR6 (Saturn)
        R1 = R1\
                + 429.0e0 * Cos(10.600e0 - G6 + G)\
                + 162.0e0 * Cos(200.600e0 - 2.0e0 * G6 + 2.0e0 * G)\
                + 112.0e0 * Cos(203.100e0 - 2.0e0 * G6 + G)
        #-------
        # DRM (Moon)
        R1 = R1\
                + 13360.0e0 * Cos(D)\
                + 370.0e0 * Cos(D + A)\
                - 1330.0e0 * Cos(D - A)\
                - 140.0e0 * Cos(D + G)\
                + 360.0e0 * Cos(D - G)
        rDis = rDis + R1 * 1.e-9
        rLat =\
                -0.210e0 * Cos(151.800e0 + 3.0e0 * G2 - 4.0e0 * G)\
                - 0.166e0 * Cos(265.500e0 - 2.0e0 * G5 + G)\
                + 0.576e0 * Sin(U)

        # Berechnungen der Länge und Breite erfolgten in Bogensekunden
        rLng = DLO + (SLO + DL) / 3600.0e0  # Länge in Grad
        rLng = to360(rLng)
        if (rLng < 0):
                                rLng += 360
        rLat /= 3600.0 # Breite in Grad

        rDis = pow(10, rDis)
        x = rDis * Cos(rLng) * Cos(rLat)
        y = rDis * Sin(rLng) * Cos(rLat)
        z = rDis * Sin(rLat)

        return rLng, rLat, rDis, x, y, z 

# Zu den Koeffizienten sind die erreichbaren Genauigkeiten für JD2000+-4000 Jahre angegeben
#Erde 0,1" 0,1e-6AE
p2 = [ 10000000000, # Der Divisionsfaktor
# es folgen die Indizes für den Beginn von L0...R5
20, 578, 920, 1100, 1124, 1136, 1148, 1217, 1226, 1229, 1229, 1229, 1229, 1937, 2363, 2618, 2633, 2660, 2666,
17534704567, 0.00000000000, 0.00000000000, 334165646, 4.669256804, 6283.075849991, 3489428, 4.6261024, 12566.1517000, 349706, 2.744118, 5753.384885, 341757, 2.828866, 3.523118, 313590, 3.627670, 77713.771468, 267622, 4.418084, 7860.419392, 234269, 6.135162, 3930.209696, 132429, 0.742464, 11506.769770, 127317, 2.037097, 529.690965, 119917, 1.109629, 1577.343542, 99025, 5.23268, 5884.92685, 90186, 2.04505, 26.29832, 85722, 3.50849, 398.14900, 77979, 1.17883, 5223.69392, 75314, 2.53339, 5507.55324, 50526, 4.58293, 18849.22755, 49238, 4.20507, 775.52261, 35666, 2.91954, 0.06731, 31709, 5.84902, 11790.62909, 28413, 1.89869, 796.29801, 27104, 0.31489, 10977.07880, 24281, 0.34481, 5486.77784, 20616, 4.80647, 2544.31442, 20539, 1.86948, 5573.14280, 20226, 2.45768, 6069.77675, 15552, 0.83306, 213.29910, 13221, 3.41118, 2942.46342, 12618, 1.08303, 20.77540, 11513, 0.64545, 0.98032, 10285, 0.63600, 4694.00295, 10190, 0.97569, 15720.83878, 10172, 4.26680, 7.11355, 9921, 6.2099, 2146.1654, 9761, 0.6810, 155.4204, 8580, 5.9832, 161000.6857, 8513, 1.2987, 6275.9623, 8471, 3.6708, 71430.6956, 7964, 1.8079, 17260.1547, 7876, 3.0370, 12036.4607, 7465, 1.7551, 5088.6288, 7387, 3.5032, 3154.6871, 7355, 4.6793, 801.8209, 6963, 0.8330, 9437.7629, 6245, 3.9776, 8827.3903, 6115, 1.8184, 7084.8968, 5696, 2.7843, 6286.5990, 5612, 4.3869, 14143.4952, 5558, 3.4701, 6279.5527, 5199, 0.1891, 12139.5535, 5161, 1.3328, 1748.0164, 5115, 0.2831, 5856.4777, 4900, 0.4874, 1194.4470, 4104, 5.3682, 8429.2413, 4094, 2.3985, 19651.0485, 3920, 6.1683, 10447.3878, 3677, 6.0413, 10213.2855, 3660, 2.5696, 1059.3819, 3595, 1.7088, 2352.8662, 3557, 1.7760, 6812.7668, 3329, 0.5931, 17789.8456, 3041, 0.4429, 83996.8473, 3005, 2.7398, 1349.8674, 2535, 3.1647, 4690.4798, 2474, 0.2148, 3.5904, 2366, 0.4847, 8031.0923, 2357, 2.0653, 3340.6124, 2282, 5.2220, 4705.7323, 2189, 5.5559, 553.5694, 2142, 1.4256, 16730.4637, 2109, 4.1483, 951.7184, 2030, 0.3713, 283.8593, 1992, 5.2221, 12168.0027, 1986, 5.7747, 6309.3742, 1912, 3.8222, 23581.2582, 1889, 5.3863, 149854.4001, 1790, 2.2149, 13367.9726, 1748, 4.5605, 135.0651, 1622, 5.9884, 11769.8537, 1508, 4.1957, 6256.7775, 1442, 4.1932, 242.7286, 1435, 3.7236, 38.0277, 1397, 4.4014, 6681.2249, 1362, 1.8893, 7632.9433, 1250, 1.1305, 5.5229, 1205, 2.6223, 955.5997, 1200, 1.0035, 632.7837, 1129, 0.1774, 4164.3120, 1083, 0.3273, 103.0928, 1052, 0.9387, 11926.2544, 1050, 5.3591, 1592.5960, 1033, 6.1998, 6438.4962, 1001, 6.0291, 5746.2713, 980, 0.999, 11371.705, 980, 5.244, 27511.468, 938, 2.624, 5760.498, 923, 0.483, 522.577, 922, 4.571, 4292.331, 905, 5.337, 6386.169, 862, 4.165, 7058.598, 841, 3.299, 7234.794, 836, 4.539, 25132.303, 813, 6.112, 4732.031, 812, 6.271, 426.598, 801, 5.821, 28.449, 787, 0.996, 5643.179, 776, 2.957, 23013.540, 769, 3.121, 7238.676, 758, 3.974, 11499.656, 735, 4.386, 316.392, 731, 0.607, 11513.883, 719, 3.998, 74.782, 706, 0.323, 263.084, 676, 5.911, 90955.552, 663, 3.665, 17298.182, 653, 5.791, 18073.705, 630, 4.717, 6836.645, 615, 1.458, 233141.314, 612, 1.075, 19804.827, 596, 3.321, 6283.009, 596, 2.876, 6283.143, 555, 2.452, 12352.853, 541, 5.392, 419.485, 531, 0.382, 31441.678, 519, 4.065, 6208.294, 513, 2.361, 10973.556, 494, 5.737, 9917.697, 450, 3.272, 11015.106, 449, 3.653, 206.186, 447, 2.064, 7079.374, 435, 4.423, 5216.580, 421, 1.906, 245.832, 413, 0.921, 3738.761, 402, 0.840, 20.355, 387, 1.826, 11856.219, 379, 2.344, 3.881, 374, 2.954, 3128.389, 370, 5.031, 536.805, 365, 1.018, 16200.773, 365, 1.083, 88860.057, 352, 5.978, 3894.182, 352, 2.056, 244287.600, 351, 3.713, 6290.189, 340, 1.106, 14712.317, 339, 0.978, 8635.942, 339, 3.202, 5120.601, 333, 0.837, 6496.375, 325, 3.479, 6133.513, 316, 5.089, 21228.392, 316, 1.328, 10873.986, 309, 3.646, 10.637, 303, 1.802, 35371.887, 296, 3.397, 9225.539, 288, 6.026, 154717.610, 281, 2.585, 14314.168, 262, 3.856, 266.607, 262, 2.579, 22483.849, 257, 1.561, 23543.231, 255, 3.949, 1990.745, 251, 3.744, 10575.407, 240, 1.161, 10984.192, 238, 0.106, 7.046, 236, 4.272, 6040.347, 234, 3.577, 10969.965, 211, 3.714, 65147.620, 210, 0.754, 13521.751, 207, 4.228, 5650.292, 202, 0.814, 170.673, 201, 4.629, 6037.244, 200, 0.381, 6172.870, 199, 3.933, 6206.810, 199, 5.197, 6262.300, 197, 1.046, 18209.330, 195, 1.070, 5230.807, 195, 4.869, 36.028, 194, 4.313, 6244.943, 192, 1.229, 709.933, 192, 5.595, 6282.096, 192, 0.602, 6284.056, 189, 3.744, 23.878, 188, 1.904, 15.252, 188, 0.867, 22003.915, 182, 3.681, 15110.466, 181, 0.491, 1.484, 179, 3.222, 39302.097, 179, 1.259, 12559.038,
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10301861, 1.10748970, 6283.07584999, 172124, 1.064423, 12566.151700, 70222, 3.14159, 0.00000, 3235, 1.0217, 18849.2275, 3080, 2.8435, 5507.5532, 2497, 1.3191, 5223.6939, 1849, 1.4243, 1577.3435, 1008, 5.9138, 10977.0788, 865, 1.420, 6275.962, 863, 0.271, 5486.778, 507, 1.686, 5088.629, 499, 6.014, 6286.599, 467, 5.987, 529.691, 440, 0.518, 4694.003, 410, 1.084, 9437.763, 387, 4.750, 2544.314, 375, 5.071, 796.298, 352, 0.023, 83996.847, 344, 0.949, 71430.696, 341, 5.412, 775.523, 322, 6.156, 2146.165, 286, 5.484, 10447.388, 284, 3.420, 2352.866, 255, 6.132, 6438.496, 252, 0.243, 398.149, 243, 3.092, 4690.480, 225, 3.689, 7084.897, 220, 4.952, 6812.767, 219, 0.420, 8031.092, 209, 1.282, 1748.016, 193, 5.314, 8429.241, 185, 1.820, 7632.943, 175, 3.229, 6279.553, 173, 1.537, 4705.732, 158, 4.097, 11499.656, 158, 5.539, 3154.687, 150, 3.633, 11513.883, 148, 3.222, 7234.794, 147, 3.653, 1194.447, 144, 0.817, 14143.495, 135, 6.151, 5746.271, 134, 4.644, 6836.645, 128, 2.693, 1349.867, 123, 5.650, 5760.498, 118, 2.577, 13367.973, 113, 3.357, 17789.846, 110, 4.497, 4292.331, 108, 5.828, 12036.461, 102, 5.621, 6256.778, 99, 1.14, 1059.38, 98, 0.66, 5856.48, 93, 2.32, 10213.29, 92, 0.77, 16730.46, 88, 1.50, 11926.25, 86, 1.42, 5753.38, 85, 0.66, 155.42, 81, 1.64, 6681.22, 80, 4.11, 951.72, 66, 4.55, 5216.58, 65, 0.98, 25132.30, 64, 4.19, 6040.35, 64, 0.52, 6290.19, 63, 1.51, 5643.18, 59, 6.18, 4164.31, 57, 2.30, 10973.56, 55, 2.32, 11506.77, 55, 2.20, 1592.60, 55, 5.27, 3340.61, 54, 5.54, 553.57, 53, 5.04, 9917.70, 53, 0.92, 11371.70, 52, 3.98, 17298.18, 52, 3.60, 10969.97, 49, 5.91, 3894.18, 49, 2.51, 6127.66, 48, 1.67, 12168.00, 46, 0.31, 801.82, 42, 3.70, 10575.41, 42, 4.05, 10984.19, 40, 2.17, 7860.42, 40, 4.17, 26.30, 38, 5.82, 7058.60, 37, 3.39, 6496.37, 36, 1.08, 6309.37, 36, 5.34, 7079.37, 34, 3.62, 11790.63, 32, 0.32, 16200.77, 31, 4.24, 3738.76, 29, 4.55, 11856.22, 29, 1.26, 8635.94, 27, 3.45, 5884.93, 26, 5.08, 10177.26, 26, 5.38, 21228.39, 24, 2.26, 11712.96, 24, 1.05, 242.73, 24, 5.59, 6069.78, 23, 3.63, 6284.06, 23, 1.64, 4732.03, 22, 3.46, 213.30, 21, 1.05, 3496.03, 21, 3.92, 13916.02, 21, 4.01, 5230.81, 20, 5.16, 12352.85, 20, 0.69, 1990.75, 19, 2.73, 6062.66, 19, 5.01, 11015.11, 18, 6.04, 6283.01, 18, 2.85, 7238.68, 18, 5.60, 6283.14, 18, 5.16, 17253.04, 18, 2.54, 14314.17, 17, 1.58, 7.11, 17, 0.98, 3930.21, 17, 4.75, 17267.27, 16, 2.19, 6076.89, 16, 2.19, 18073.70, 16, 6.12, 3.52, 16, 4.61, 9623.69, 16, 3.40, 16496.36, 15, 0.19, 9779.11, 15, 5.30, 13517.87, 15, 4.26, 3128.39, 15, 0.81, 709.93, 14, 0.50, 25158.60, 14, 4.38, 4136.91, 13, 0.98, 65147.62, 13, 3.31, 154717.61, 13, 2.11, 1589.07, 13, 1.92, 22483.85, 12, 6.03, 9225.54, 12, 1.53, 12559.04, 12, 5.82, 6282.10, 12, 5.61, 5642.20, 12, 2.38, 167283.76, 12, 0.39, 12132.44, 12, 3.98, 4686.89, 12, 5.81, 12569.67, 12, 0.56, 5849.36, 11, 0.45, 6172.87, 11, 5.80, 16858.48, 11, 6.22, 12146.67, 11, 2.27, 5429.88,
435939, 5.784551, 6283.075850, 12363, 5.57935, 12566.15170, 1234, 3.1416, 0.0000, 879, 3.628, 77713.771, 569, 1.870, 5573.143, 330, 5.470, 18849.228, 147, 4.480, 5507.553, 110, 2.842, 161000.686, 101, 2.815, 5223.694, 85, 3.11, 1577.34, 65, 5.47, 775.52, 61, 1.38, 6438.50, 50, 4.42, 6286.60, 47, 3.66, 7084.90, 46, 5.39, 149854.40, 42, 0.90, 10977.08, 40, 3.20, 5088.63, 35, 1.81, 5486.78, 32, 5.35, 3154.69, 30, 3.52, 796.30, 29, 4.62, 4690.48, 28, 1.84, 4694.00, 27, 3.14, 71430.70, 27, 6.17, 6836.65, 26, 1.42, 2146.17, 25, 2.81, 1748.02, 24, 2.18, 155.42, 23, 4.76, 7234.79, 21, 3.38, 7632.94, 21, 0.22, 4705.73, 20, 4.22, 1349.87, 20, 2.01, 1194.45, 20, 4.58, 529.69, 19, 1.59, 6309.37, 18, 5.70, 6040.35, 18, 6.03, 4292.33, 17, 2.90, 9437.76, 17, 2.00, 8031.09, 17, 5.78, 83996.85, 16, 0.05, 2544.31, 15, 0.95, 6127.66, 14, 0.36, 10447.39, 14, 1.48, 2352.87, 13, 0.77, 553.57, 13, 5.48, 951.72, 13, 5.27, 6279.55, 13, 3.76, 6812.77, 11, 5.41, 6256.78, 10, 0.68, 1592.60, 10, 4.95, 398.15, 10, 1.15, 3894.18, 10, 5.20, 244287.60, 10, 1.94, 11856.22, 9, 5.39, 25132.30, 8, 6.18, 1059.38, 8, 0.69, 8429.24, 8, 5.85, 242.73, 7, 5.26, 14143.50, 7, 0.52, 801.82, 6, 2.24, 8635.94, 6, 4.00, 13367.97, 6, 2.77, 90955.55, 6, 5.17, 7058.60, 5, 1.46, 233141.31, 5, 4.13, 7860.42, 5, 3.91, 26.30, 5, 3.89, 12036.46, 5, 5.58, 6290.19, 5, 5.54, 1990.75, 5, 0.83, 11506.77, 5, 6.22, 6681.22, 4, 5.26, 10575.41, 4, 1.91, 7477.52, 4, 0.43, 10213.29, 4, 1.09, 709.93, 4, 5.09, 11015.11, 4, 4.22, 88860.06, 4, 3.57, 7079.37, 4, 1.98, 6284.06, 4, 3.93, 10973.56, 4, 6.18, 9917.70, 4, 0.36, 10177.26, 4, 2.75, 3738.76, 4, 3.33, 5643.18, 4, 5.36, 25158.60,
14459, 4.27319, 6283.07585, 673, 3.917, 12566.152, 77, 0.00, 0.00, 25, 3.73, 18849.23, 4, 2.80, 6286.60,
386, 2.564, 6283.076, 31, 2.27, 12566.15, 5, 3.44, 5573.14, 2, 2.05, 18849.23, 1, 2.06, 77713.77, 1, 4.41, 161000.69, 1, 3.82, 149854.40, 1, 4.08, 6127.66, 1, 5.26, 6438.50,
9, 1.22, 6283.08, 1, 0.66, 12566.15]

# Merkur 0.2" 0.2e-6 AE
p0 = [1000000000,
20, 443, 710, 761, 791, 818, 824, 1043, 1106, 1142, 1169, 1190, 1196, 1550, 1742, 1781, 1808, 1823, 1823,
4402507101, 0.0000000000, 0.0000000000, 409894150, 1.483020342, 26087.903141574, 50462942, 4.47785490, 52175.80628315, 8553468, 1.1652032, 78263.7094247, 1655904, 4.1196916, 104351.6125663, 345619, 0.779308, 130439.515708, 75835, 3.71348, 156527.41885, 35597, 1.51203, 1109.37855, 18035, 4.10333, 5661.33205, 17260, 0.35832, 182615.32199, 15899, 2.99510, 25028.52121, 13647, 4.59918, 27197.28169, 10173, 0.88031, 31749.23519, 7142, 1.5414, 24978.5246, 6438, 5.3027, 21535.9496, 4511, 6.0499, 51116.4244, 4042, 3.2823, 208703.2251, 3524, 5.2416, 20426.5711, 3452, 2.7921, 15874.6176, 3433, 5.7653, 955.5997, 3392, 5.8633, 25558.2122, 3253, 1.3367, 53285.1848, 2729, 2.4945, 529.6910, 2643, 3.9171, 57837.1383, 2596, 0.9873, 4551.9535, 2388, 0.1134, 1059.3819, 2348, 0.2667, 11322.6641, 2166, 0.6599, 13521.7514, 2090, 2.0918, 47623.8528, 1834, 2.6288, 27043.5029, 1816, 2.4341, 25661.3050, 1760, 4.5364, 51066.4277, 1726, 2.4520, 24498.8302, 1423, 3.3600, 37410.5672, 1379, 0.2910, 10213.2855, 1252, 3.7208, 39609.6546, 1182, 2.7815, 77204.3275, 1064, 4.2057, 19804.8273, 969, 6.204, 234791.128, 900, 5.852, 41962.521, 883, 5.413, 26617.594, 868, 2.642, 51646.115, 867, 1.960, 46514.474, 850, 4.331, 79373.088, 697, 3.572, 25132.303, 692, 4.194, 19.670, 685, 0.634, 83925.041, 648, 0.048, 33326.579, 635, 3.147, 7238.676, 595, 2.747, 16983.996, 565, 5.119, 73711.756, 554, 4.053, 30639.857, 544, 3.143, 27147.285, 515, 5.478, 50586.733, 496, 3.990, 6770.711, 480, 5.493, 51749.208, 476, 5.497, 3.881, 447, 1.224, 77154.331, 419, 5.193, 6283.076, 418, 5.642, 53131.406, 380, 2.431, 12566.152, 360, 1.424, 2218.757, 356, 0.814, 32858.614, 354, 3.370, 36301.189, 340, 0.475, 65697.558, 340, 2.786, 14765.239, 308, 5.770, 103292.231, 306, 5.840, 43071.899, 295, 0.698, 213.299, 285, 0.650, 426.598, 275, 0.980, 45892.730, 271, 0.085, 63498.470, 268, 1.061, 3442.575, 263, 0.648, 1589.073, 262, 5.242, 22645.328, 243, 4.400, 7.114, 237, 2.842, 260879.031, 229, 2.585, 68050.424, 224, 1.025, 105460.991, 223, 5.653, 77734.018, 223, 2.179, 52705.497, 222, 3.224, 25448.006, 220, 4.934, 72602.377, 186, 4.527, 28306.660, 178, 3.612, 110012.945, 176, 4.717, 25874.604, 172, 0.284, 51220.207, 172, 3.261, 153.779, 149, 1.835, 99799.659, 144, 0.966, 26107.573, 144, 1.910, 23969.139, 142, 5.142, 26068.233, 142, 6.124, 53235.188, 140, 2.302, 76674.637, 134, 4.518, 26080.790, 134, 0.766, 56727.760, 124, 2.223, 77837.111, 120, 6.205, 18849.228, 116, 2.385, 79219.309, 115, 4.178, 103242.234, 112, 2.048, 32370.979, 111, 3.783, 26301.202, 100, 2.046, 48733.231, 98, 2.27, 26091.78, 97, 3.84, 26084.02, 97, 2.99, 59414.48, 97, 5.78, 25938.34, 94, 5.44, 38654.05, 93, 4.03, 467.96, 90, 6.23, 25021.41, 90, 3.48, 91785.46, 90, 0.11, 62389.09, 89, 2.85, 25035.63, 83, 5.34, 19317.19, 82, 5.78, 40853.14, 81, 1.12, 26095.02, 80, 2.46, 129380.13, 76, 0.18, 12432.04, 74, 4.71, 6.63, 70, 3.99, 71980.63, 70, 1.63, 23869.15, 66, 3.66, 26514.50, 61, 3.67, 27676.98, 60, 0.00, 51535.91, 59, 3.99, 131548.89, 59, 4.12, 29530.48, 59, 5.57, 94138.33, 59, 5.76, 286966.93, 59, 6.13, 26011.64, 59, 2.14, 20760.43, 58, 2.35, 103821.92, 58, 4.45, 19406.68, 57, 3.02, 89586.37, 57, 5.18, 78793.40, 57, 1.61, 98690.28, 52, 3.29, 38519.95, 51, 3.78, 58946.52, 46, 0.29, 136100.85, 45, 1.50, 51962.51, 45, 4.89, 50057.04, 44, 3.25, 77308.11,
26088147062227, 0.000000000000, 0.000000000000, 11260078, 6.21703971, 26087.90314157, 3034714, 3.0556547, 52175.8062831, 805385, 6.104547, 78263.709425, 212450, 2.835319, 104351.612566, 55921, 5.82676, 130439.51571, 14722, 2.51845, 156527.41885, 3883, 5.4804, 182615.3220, 3522, 3.0524, 1109.3786, 1027, 2.1488, 208703.2251, 935, 6.118, 27197.282, 906, 0.000, 24978.525, 519, 5.621, 5661.332, 444, 4.573, 25028.521, 281, 3.042, 51066.428, 273, 5.092, 234791.128, 220, 0.865, 955.600, 204, 3.715, 20426.571, 202, 0.519, 21535.950, 175, 5.727, 4551.953, 167, 1.351, 529.691, 154, 5.743, 19.670, 153, 1.792, 11322.664, 140, 3.594, 24498.830, 128, 2.696, 53285.185, 126, 3.895, 3.881, 126, 4.705, 1059.382, 86, 6.06, 77154.33, 80, 3.93, 27043.50, 80, 4.18, 26617.59, 79, 0.50, 46514.47, 77, 2.48, 57837.14, 73, 1.75, 260879.03, 72, 2.98, 2218.76, 68, 2.77, 7.11, 66, 5.53, 6770.71, 64, 2.14, 25132.30, 59, 2.20, 13521.75, 58, 4.28, 16984.00, 50, 3.94, 25661.30, 50, 2.48, 30639.86, 49, 4.85, 37410.57, 46, 0.82, 25558.21, 46, 1.56, 27147.29, 45, 5.79, 3442.57, 44, 4.94, 213.30, 43, 5.09, 10213.29, 42, 5.54, 83925.04, 37, 1.40, 77204.33, 36, 2.34, 32858.61, 35, 3.59, 26068.23, 34, 0.50, 22645.33, 33, 5.23, 25448.01, 32, 1.26, 14765.24, 31, 6.21, 26080.79, 31, 6.07, 28306.66, 30, 4.45, 7238.68, 30, 0.14, 50586.73, 29, 1.64, 25021.41, 29, 0.67, 26091.78, 28, 2.51, 26107.57, 28, 3.54, 72602.38, 27, 5.64, 1589.07, 27, 0.88, 52705.50, 26, 2.78, 103242.23, 25, 5.80, 26095.02, 25, 4.35, 41962.52, 24, 1.16, 25035.63, 23, 5.44, 26084.02, 23, 1.85, 36301.19, 21, 5.16, 51220.21, 21, 1.07, 43071.90, 20, 2.96, 23969.14, 20, 4.44, 103292.23, 20, 0.84, 12566.15, 20, 4.68, 286966.93, 18, 1.81, 26301.20, 18, 5.18, 426.60, 17, 2.29, 110012.94, 17, 4.63, 53235.19, 17, 1.26, 33326.58, 16, 5.53, 56727.76, 16, 0.08, 23869.15, 16, 4.66, 79373.09, 16, 3.76, 73711.76, 14, 1.14, 68050.42, 14, 1.45, 51646.12, 13, 3.80, 19317.19, 13, 1.73, 12432.04,
530498, 0.000000, 0.000000, 169037, 4.690723, 26087.903142, 73967, 1.34736, 52175.80628, 30183, 4.45644, 78263.70942, 11074, 1.26227, 104351.61257, 3782, 4.3200, 130439.5157, 1230, 1.0687, 156527.4188, 387, 4.080, 182615.322, 149, 4.633, 1109.379, 119, 0.792, 208703.225, 52, 4.72, 24978.52, 36, 3.77, 234791.13, 26, 1.44, 27197.28, 20, 1.50, 51066.43, 11, 0.46, 260879.03, 10, 1.80, 955.60, 8, 4.54, 77154.33,
1881, 0.0347, 52175.8063, 1422, 3.1251, 26087.9031, 969, 3.004, 78263.709, 437, 6.019, 104351.613, 354, 0.000, 0.000, 180, 2.775, 130439.516, 70, 5.82, 156527.42, 26, 2.57, 182615.32, 9, 5.59, 208703.23, 3, 2.32, 234791.13,
1141, 3.1416, 0.0000, 32, 2.03, 26087.90, 19, 1.42, 78263.71, 17, 4.50, 52175.81, 12, 4.50, 104351.61, 6, 1.27, 130439.52, 3, 4.31, 156527.42, 1, 1.06, 182615.32, 1, 4.09, 208703.23,
9, 3.14, 0.00, 1, 3.38, 52175.81,
117375290, 1.983574988, 26087.903141574, 23880770, 5.03738960, 52175.80628315, 12228395, 3.14159265, 0.00000000, 5432518, 1.7964436, 78263.7094247, 1297788, 4.8323250, 104351.6125663, 318669, 1.580885, 130439.515708, 79633, 4.60972, 156527.41885, 20142, 1.35324, 182615.32199, 5140, 4.3784, 208703.2251, 2086, 2.0202, 24978.5246, 2077, 4.9177, 27197.2817, 1320, 1.1191, 234791.1283, 1214, 1.8127, 53285.1848, 1005, 5.6568, 20426.5711, 992, 0.094, 51116.424, 946, 1.242, 31749.235, 916, 2.282, 25028.521, 843, 5.085, 51066.428, 788, 4.407, 57837.138, 777, 0.526, 1059.382, 499, 3.498, 5661.332, 465, 3.237, 77204.327, 448, 4.878, 79373.088, 408, 2.466, 46514.474, 374, 4.458, 4551.953, 359, 1.091, 1109.379, 341, 4.142, 260879.031, 320, 1.185, 83925.041, 318, 2.415, 47623.853, 310, 3.503, 21535.950, 287, 1.848, 77154.331, 258, 2.776, 27043.503, 252, 3.591, 27147.285, 202, 3.068, 51646.115, 201, 4.066, 25132.303, 186, 5.584, 73711.756, 170, 6.137, 41962.521, 170, 0.028, 103292.231, 158, 3.796, 529.691, 156, 6.077, 53131.406, 150, 1.647, 105460.991, 142, 0.331, 10213.286, 140, 5.528, 72602.377, 130, 3.480, 37410.567, 129, 4.817, 30639.857, 124, 4.051, 39609.655, 123, 3.166, 14765.239, 113, 0.113, 13521.751, 112, 0.557, 63498.470, 110, 5.797, 51749.208, 110, 4.232, 110012.945, 107, 1.537, 25661.305, 105, 5.830, 50586.733, 102, 2.879, 12566.152, 99, 0.95, 65697.56, 98, 1.66, 24498.83, 94, 1.82, 15874.62, 92, 6.16, 77734.02, 91, 4.89, 103242.23, 90, 1.04, 426.60, 89, 0.40, 53235.19, 88, 0.88, 286966.93, 88, 5.81, 11322.66, 87, 3.04, 68050.42, 85, 1.05, 1589.07, 83, 5.27, 25558.21, 82, 0.84, 51220.21, 76, 3.44, 36301.19, 73, 2.37, 99799.66, 71, 5.74, 26617.59, 66, 2.67, 52705.50, 58, 6.25, 33326.58, 57, 2.87, 79219.31,
4291514, 3.5016978, 26087.9031416, 1462337, 3.1415927, 0.0000000, 226753, 0.015154, 52175.806283, 108950, 0.485402, 78263.709425, 63535, 3.42944, 104351.61257, 24957, 0.16051, 130439.51571, 8596, 3.1845, 156527.4188, 2775, 6.2102, 182615.3220, 862, 2.952, 208703.225, 277, 0.291, 27197.282, 261, 5.977, 234791.128, 128, 3.377, 53285.185, 127, 0.538, 24978.525, 78, 2.72, 260879.03, 75, 3.58, 51066.43, 62, 2.92, 31749.24, 55, 1.97, 51116.42, 35, 0.11, 79373.09, 34, 0.35, 77154.33, 29, 5.95, 57837.14, 27, 0.99, 25028.52,
118309, 4.790656, 26087.903142, 19135, 0.00000, 0.00000, 10448, 1.21217, 52175.80628, 2662, 4.4342, 78263.7094, 1703, 1.6226, 104351.6126, 963, 4.800, 130439.516, 447, 1.608, 156527.419, 183, 4.669, 182615.322, 69, 1.43, 208703.23, 25, 4.47, 234791.13, 17, 1.83, 27197.28, 9, 1.23, 260879.03,
2354, 0.3539, 26087.9031, 1605, 0.0000, 0.0000, 189, 4.363, 52175.806, 64, 2.51, 78263.71, 46, 6.14, 104351.61, 31, 3.12, 130439.52, 17, 6.27, 156527.42, 9, 3.08, 182615.32, 4, 6.15, 208703.23,
43, 1.75, 26087.90, 10, 3.14, 0.00, 4, 4.03, 52175.81, 3, 0.21, 78263.71, 1, 3.75, 104351.61, 1, 1.18, 130439.52, 1, 4.55, 156527.42,
1, 3.95, 26087.90, 1, 3.14, 0.00,
395282717, 0.000000000, 0.000000000, 78341318, 6.19233723, 26087.90314157, 7955256, 2.9598969, 52175.8062831, 1212818, 6.0106415, 78263.7094247, 219220, 2.778201, 104351.612566, 43541, 5.82895, 130439.51571, 9182, 2.5965, 156527.4188, 2900, 1.4244, 25028.5212, 2600, 3.0282, 27197.2817, 2019, 5.6473, 182615.3220, 2015, 5.5923, 31749.2352, 1420, 6.2526, 24978.5246, 1001, 3.7344, 21535.9496, 776, 3.670, 20426.571, 755, 4.474, 51116.424, 668, 2.525, 5661.332, 633, 4.299, 25558.212, 630, 4.766, 1059.382, 483, 6.068, 53285.185, 457, 2.415, 208703.225, 442, 1.220, 15874.618, 408, 2.359, 57837.138, 372, 0.517, 47623.853, 352, 1.059, 27043.503, 339, 0.864, 25661.305, 309, 0.884, 24498.830, 301, 1.795, 37410.567, 284, 3.021, 51066.428, 261, 2.150, 39609.655, 213, 5.369, 13521.751, 194, 4.984, 10213.286, 187, 4.965, 11322.664, 171, 1.241, 77204.327, 169, 3.888, 26617.594, 163, 2.633, 19804.827, 151, 0.445, 46514.474, 150, 4.282, 41962.521, 140, 4.771, 33326.579, 139, 1.626, 27147.285, 139, 2.000, 25132.303, 134, 1.077, 51646.115, 128, 6.064, 1109.379, 128, 2.076, 529.691, 121, 2.850, 79373.088, 119, 2.365, 4551.953, 106, 5.466, 234791.128, 95, 0.84, 12566.15, 94, 5.41, 83925.04, 91, 1.21, 14765.24, 89, 3.88, 50586.73, 85, 3.57, 73711.76, 77, 3.92, 51749.21, 75, 2.45, 30639.86, 75, 5.53, 32858.61, 72, 1.17, 16984.00, 71, 5.33, 426.60, 69, 5.31, 1589.07, 69, 1.82, 36301.19, 66, 4.28, 43071.90, 65, 6.07, 77154.33, 59, 4.07, 53131.41, 54, 5.20, 65697.56, 52, 3.57, 6283.08, 44, 5.69, 45892.73, 41, 1.65, 25448.01, 41, 3.68, 22645.33, 41, 4.29, 103292.23, 36, 2.96, 28306.66, 34, 0.65, 52705.50, 34, 3.49, 72602.38, 33, 3.14, 25874.60, 33, 1.03, 68050.42, 31, 4.13, 77734.02, 30, 5.91, 105460.99, 28, 4.63, 18849.23, 28, 5.05, 51220.21, 28, 5.68, 26107.57, 27, 4.68, 53235.19, 27, 4.75, 63498.47, 27, 3.57, 26068.23, 26, 2.95, 26080.79, 25, 0.35, 23969.14, 25, 2.23, 260879.03, 23, 0.50, 32370.98, 23, 2.18, 110012.94, 21, 0.85, 76674.64, 21, 2.19, 26301.20, 20, 0.34, 99799.66, 20, 0.47, 48733.23, 20, 3.77, 19317.19, 20, 1.37, 7238.68, 19, 2.37, 6770.71, 19, 0.69, 26091.78, 19, 3.93, 38654.05, 19, 2.27, 26084.02, 18, 4.21, 25938.34, 18, 0.92, 79219.31, 18, 5.51, 56727.76, 17, 0.68, 77837.11, 17, 4.29, 40853.14, 17, 2.15, 26514.50, 17, 4.98, 9103.91, 16, 4.66, 25021.41, 16, 1.28, 25035.63, 16, 5.85, 26095.02, 16, 2.84, 103242.23, 15, 1.55, 955.60, 15, 2.16, 27676.98, 14, 0.06, 23869.15, 14, 4.85, 62389.09, 12, 1.97, 91785.46, 12, 1.73, 38519.95, 11, 4.56, 26011.64, 10, 2.78, 213.30, 10, 1.06, 129380.13, 10, 2.44, 71980.63, 10, 4.71, 51535.91, 10, 2.54, 29530.48,
2173477, 4.6561716, 26087.9031416, 441418, 1.423855, 52175.806283, 100945, 4.474663, 78263.709425, 24328, 1.24226, 104351.61257, 16244, 0.00000, 0.00000, 6040, 4.2930, 130439.5157, 1529, 1.0606, 156527.4188, 392, 4.111, 182615.322, 180, 4.712, 24978.525, 178, 4.544, 27197.282, 102, 0.879, 208703.225, 81, 3.01, 25028.52, 44, 2.14, 20426.57, 44, 1.48, 51066.43, 35, 3.21, 1059.38, 31, 5.24, 21535.95, 27, 3.93, 234791.13, 25, 2.03, 24498.83, 20, 1.24, 53285.18, 20, 4.05, 5661.33, 15, 2.62, 26617.59, 15, 2.36, 27043.50, 14, 1.38, 1109.38, 13, 5.19, 46514.47, 13, 0.56, 25132.30, 12, 0.21, 11322.66, 12, 4.53, 77154.33, 11, 0.86, 57837.14, 11, 6.24, 27147.29, 10, 3.28, 37410.57, 9, 2.37, 25661.30, 9, 5.55, 25558.21, 8, 5.96, 14765.24, 7, 0.78, 32858.61, 7, 4.07, 1589.07, 7, 2.71, 16984.00, 7, 0.93, 30639.86, 7, 0.70, 260879.03, 7, 2.02, 26068.23, 6, 0.86, 4551.95, 6, 3.66, 25448.01, 6, 4.50, 28306.66, 6, 4.65, 26080.79, 6, 3.50, 10213.29, 6, 0.63, 13521.75, 5, 5.38, 26091.78, 5, 0.94, 26107.57, 5, 5.22, 22645.33, 5, 0.06, 25021.41, 5, 3.89, 83925.04, 5, 4.84, 50586.73, 5, 5.55, 12566.15, 5, 4.24, 26095.02, 5, 6.01, 77204.33, 5, 0.73, 529.69, 4, 3.87, 26084.02, 4, 5.87, 25035.63, 4, 5.79, 43071.90, 4, 0.26, 36301.19, 4, 2.78, 41962.52, 4, 5.60, 52705.50, 4, 3.82, 426.60, 4, 1.96, 72602.38, 4, 6.00, 33326.58,
31179, 3.08232, 26087.90314, 12454, 6.15183, 52175.80628, 4248, 2.9258, 78263.7094, 1361, 5.9798, 104351.6126, 422, 2.749, 130439.516, 218, 3.142, 0.000, 128, 5.801, 156527.419, 38, 2.57, 182615.32, 11, 5.62, 208703.23, 10, 3.15, 24978.52, 5, 6.14, 27197.28, 3, 2.39, 234791.13, 3, 6.21, 51066.43,
327, 1.680, 26087.903, 242, 4.634, 52175.806, 121, 1.390, 78263.709, 51, 4.44, 104351.61, 20, 1.21, 130439.52, 15, 3.14, 0.00, 7, 4.26, 156527.42, 3, 1.03, 182615.32, 1, 4.08, 208703.23,
4, 0.37, 26087.90, 4, 3.19, 52175.81, 3, 6.17, 78263.71, 1, 2.92, 104351.61, 1, 5.96, 130439.52 ]

# Venus 0,1" 0.2e-6 AE
p1 = [1000000000,
20, 257, 374, 425, 437, 449, 458, 566, 629, 641, 653, 665, 668, 929, 1040, 1082, 1091, 1094, 1094,
3176146668, 0.0000000000, 0.0000000000, 13539684, 5.59313320, 10213.28554621, 898916, 5.306500, 20426.571092, 54772, 4.41631, 7860.41939, 34557, 2.69964, 11790.62909, 23721, 2.99378, 3930.20970, 16641, 4.25019, 1577.34354, 14383, 4.15745, 9683.59458, 13171, 5.18668, 26.29832, 12005, 6.15357, 30639.85664, 7693, 0.8163, 9437.7629, 7614, 1.9501, 529.6910, 7077, 1.0647, 775.5226, 5848, 3.9984, 191.4483, 4999, 4.1234, 15720.8388, 4295, 3.5864, 19367.1892, 3270, 5.6774, 5507.5532, 3262, 4.5906, 10404.7338, 2319, 3.1625, 9153.9036, 1797, 4.6534, 1109.3786, 1555, 5.5704, 19651.0485, 1283, 4.2260, 20.7754, 1279, 0.9621, 5661.3320, 1055, 1.5372, 801.8209, 991, 0.833, 213.299, 988, 5.394, 13367.973, 880, 3.889, 9999.986, 857, 0.356, 3154.687, 821, 3.216, 18837.498, 716, 0.111, 11015.106, 702, 0.675, 23581.258, 561, 4.240, 7.114, 508, 0.245, 11322.664, 461, 5.316, 18073.705, 446, 6.063, 40853.142, 426, 1.800, 7084.897, 426, 5.329, 2352.866, 412, 0.362, 382.897, 357, 2.704, 10206.172, 339, 2.023, 6283.076, 333, 2.100, 27511.468, 302, 4.942, 13745.346, 299, 4.022, 10239.584, 293, 3.514, 283.859, 291, 3.592, 22003.915, 285, 2.224, 1059.382, 263, 0.541, 17298.182, 244, 2.702, 8624.213, 243, 4.278, 5.523, 237, 4.829, 6872.673, 205, 0.585, 38.028, 203, 3.795, 14143.495, 191, 6.120, 29050.784, 190, 4.138, 4551.953, 183, 3.047, 19999.973, 171, 3.522, 31441.678, 159, 1.501, 8635.942, 137, 4.413, 3532.061, 118, 1.913, 21228.392, 116, 5.810, 19896.880, 110, 2.584, 9786.687, 110, 2.846, 18307.807, 106, 0.854, 10596.182, 101, 2.343, 10742.977, 99, 1.09, 7064.12, 94, 4.95, 35371.89, 92, 5.52, 12566.15, 89, 1.97, 10186.99, 82, 1.92, 15.25, 70, 1.00, 632.78, 68, 4.40, 8662.24, 67, 1.55, 14945.32, 64, 2.18, 10988.81, 63, 0.36, 103.09, 60, 5.05, 245.83, 60, 2.97, 4732.03, 58, 1.93, 3340.61, 56, 0.49, 522.58, 55, 3.37, 25158.60,
10213529430529, 0.000000000000, 0.000000000000, 957077, 2.464244, 10213.285546, 144450, 0.516246, 20426.571092, 2134, 1.7955, 30639.8566, 1739, 2.6554, 26.2983, 1517, 6.1064, 1577.3435, 822, 5.702, 191.448, 697, 2.681, 9437.763, 524, 3.600, 775.523, 383, 1.034, 529.691, 296, 1.251, 5507.553, 251, 6.107, 10404.734, 178, 6.194, 1109.379, 165, 2.643, 7.114, 142, 5.451, 9153.904, 126, 1.245, 40853.142, 126, 1.881, 382.897, 116, 4.976, 213.299, 89, 0.95, 13367.97, 74, 4.39, 10206.17, 67, 5.06, 801.82, 66, 2.28, 2352.87, 63, 4.08, 3154.69, 49, 3.45, 11015.11, 43, 0.08, 6283.08, 41, 4.12, 18837.50, 37, 2.48, 5661.33, 36, 1.48, 1059.38, 35, 6.20, 5.52, 34, 1.77, 11322.66, 30, 2.24, 18073.70, 30, 0.39, 15.25, 30, 5.35, 7084.90, 28, 1.46, 10239.58, 26, 0.35, 22003.91, 24, 2.36, 10596.18, 23, 2.37, 17298.18, 22, 2.08, 8635.94, 21, 4.47, 8624.21,
541271, 0.000000, 0.000000, 38915, 0.34514, 10213.28555, 13379, 2.02011, 20426.57109, 238, 2.046, 26.298, 193, 3.535, 30639.857, 100, 3.971, 775.523, 70, 1.52, 1577.34, 60, 1.00, 191.45, 32, 4.36, 9437.76, 21, 2.66, 40853.14, 19, 3.39, 382.90, 15, 6.05, 529.69, 13, 2.95, 5507.55, 12, 3.73, 3154.69, 10, 3.53, 11015.11, 10, 1.41, 10404.73, 10, 5.11, 801.82,
1357, 4.8039, 10213.2855, 778, 3.669, 20426.571, 260, 0.000, 0.000, 12, 5.32, 30639.86,
1140, 3.1416, 0.0000, 32, 5.21, 20426.57, 17, 2.51, 10213.29, 1, 0.71, 30639.86,
9, 3.14, 0.00, 1, 1.91, 10213.29, 1, 0.55, 20426.57,
59236385, 0.26702776, 10213.28554621, 401080, 1.147372, 20426.571092, 328149, 3.141593, 0.000000, 10114, 1.08946, 30639.85664, 1495, 6.2539, 18073.7049, 1378, 0.8602, 1577.3435, 1300, 3.6715, 9437.7629, 1195, 3.7047, 2352.8662, 1080, 4.5390, 22003.9146, 920, 1.540, 9153.904, 530, 2.281, 5507.553, 456, 0.723, 10239.584, 435, 6.140, 11790.629, 417, 5.991, 19896.880, 396, 3.868, 8635.942, 392, 3.950, 529.691, 389, 2.934, 10186.987, 333, 4.832, 14143.495, 237, 2.906, 10988.808, 235, 2.008, 13367.973, 218, 2.697, 19651.048, 207, 0.987, 775.523, 186, 1.805, 40853.142, 178, 5.963, 25934.124, 170, 4.137, 10021.837, 154, 3.296, 11015.106, 149, 5.611, 10404.734, 131, 5.707, 9683.595, 129, 5.427, 29580.475, 120, 3.576, 10742.977, 118, 1.191, 8624.213, 115, 5.128, 6283.076, 98, 0.15, 20618.02, 95, 2.75, 191.45, 86, 0.43, 9786.69, 81, 1.31, 15720.84,
5133476, 1.8036431, 10213.2855462, 43801, 3.38616, 20426.57109, 1992, 0.0000, 0.0000, 1966, 2.5300, 30639.8566, 140, 2.271, 9437.763, 130, 1.507, 18073.705, 119, 5.605, 1577.344, 103, 5.242, 2352.866, 93, 6.08, 22003.91, 80, 0.29, 9153.90, 75, 5.08, 10186.99, 74, 1.50, 11790.63, 47, 3.88, 10239.58, 47, 0.75, 5507.55, 44, 3.59, 40853.14, 40, 1.28, 10404.73, 38, 4.33, 19651.05, 36, 1.26, 19896.88, 35, 5.51, 529.69, 34, 4.89, 10988.81, 29, 0.09, 14143.50,
223777, 3.385091, 10213.285546, 2817, 0.0000, 0.0000, 1732, 5.2556, 20426.5711, 269, 3.870, 30639.857,
6467, 4.9917, 10213.2855, 200, 3.142, 0.000, 55, 0.77, 20426.57, 25, 5.44, 30639.86,
141, 0.315, 10213.286, 2, 3.14, 0.00, 2, 2.35, 20426.57, 2, 0.74, 30639.86,
2, 2.05, 10213.29,
723348209, 0.000000000, 0.000000000, 4898242, 4.0215183, 10213.2855462, 16581, 4.90207, 20426.57109, 16321, 2.84549, 7860.41939, 13780, 1.12847, 11790.62909, 4984, 2.5868, 9683.5946, 3740, 1.4231, 3930.2097, 2636, 5.5294, 9437.7629, 2375, 2.5514, 15720.8388, 2220, 2.0135, 19367.1892, 1259, 2.7277, 1577.3435, 1195, 3.0198, 10404.7338, 853, 3.986, 19651.048, 762, 1.596, 9153.904, 743, 4.120, 5507.553, 425, 3.819, 13367.973, 419, 1.643, 18837.498, 394, 5.390, 23581.258, 313, 2.318, 9999.986, 290, 5.677, 5661.332, 276, 5.724, 775.523, 273, 4.822, 11015.106, 198, 0.532, 27511.468, 197, 4.962, 11322.664, 162, 0.565, 529.691, 136, 3.755, 18073.705, 132, 3.372, 13745.346, 131, 5.244, 17298.182, 129, 1.134, 10206.172, 118, 5.090, 3154.687, 117, 0.234, 7084.897, 114, 4.568, 29050.784, 108, 2.450, 10239.584, 107, 1.955, 31441.678, 104, 1.202, 15874.618, 96, 1.47, 19999.97, 93, 1.62, 2352.87, 91, 3.07, 1109.38, 84, 5.78, 30639.86, 82, 1.95, 22003.91, 76, 1.14, 8624.21, 65, 2.17, 14143.50, 64, 0.84, 6283.08, 62, 3.26, 6872.67, 61, 0.35, 21228.39, 60, 3.38, 35371.89, 59, 0.01, 8635.94, 56, 3.95, 12566.15, 55, 1.27, 18307.81, 45, 4.73, 19896.88, 45, 2.48, 191.45, 43, 2.60, 4551.95, 40, 0.00, 801.82, 39, 5.57, 10596.18, 39, 1.01, 9786.69, 35, 4.80, 39302.10, 33, 0.71, 10742.98, 32, 0.40, 10186.99, 32, 1.81, 25158.60, 31, 6.26, 14945.32, 30, 4.21, 28521.09, 27, 5.80, 7064.12, 25, 0.69, 10988.81, 24, 3.78, 21535.95, 22, 2.83, 8662.24, 21, 6.22, 43232.31, 20, 5.42, 16496.36, 20, 2.21, 19786.67, 19, 2.86, 3532.06, 19, 2.63, 29580.47, 19, 1.50, 10021.84, 18, 3.23, 29088.81, 18, 0.42, 4705.73, 17, 3.68, 26.30, 15, 0.00, 17277.41, 15, 2.48, 31749.24, 14, 5.86, 9676.48, 14, 5.18, 10316.38, 13, 2.49, 9690.71, 13, 1.36, 47162.52, 13, 5.25, 19360.08, 12, 1.88, 19374.30, 12, 5.56, 6770.71, 12, 1.42, 4732.03, 12, 1.43, 18875.53, 11, 5.92, 13936.79, 11, 4.64, 33019.02,
345510, 0.891987, 10213.285546, 2342, 1.7722, 20426.5711, 2340, 3.1416, 0.0000, 239, 1.113, 9437.763, 106, 4.592, 1577.344, 91, 4.54, 10404.73, 66, 5.98, 5507.55, 47, 3.88, 9153.90, 38, 5.66, 13367.97, 27, 2.82, 10206.17, 22, 2.05, 775.52, 21, 2.55, 18837.50, 18, 1.88, 11015.11, 18, 2.65, 30639.86, 13, 0.21, 11322.66, 12, 0.79, 17298.18, 11, 4.95, 6283.08, 10, 6.17, 10239.58, 9, 4.60, 1109.38, 9, 0.81, 10596.18, 9, 2.48, 3154.69, 9, 0.67, 18073.70, 8, 5.59, 12566.15, 8, 0.44, 8635.94, 8, 5.49, 529.69, 8, 3.75, 7084.90, 8, 0.90, 5661.33, 7, 2.87, 8624.21, 7, 5.07, 22003.91, 6, 4.10, 191.45, 6, 3.14, 10186.99, 6, 2.25, 21228.39, 6, 2.17, 18307.81, 5, 5.87, 2352.87, 5, 5.33, 14143.50, 5, 4.34, 9786.69, 5, 5.56, 10742.98,
14066, 5.06366, 10213.28555, 155, 5.473, 20426.571, 131, 0.000, 0.000, 11, 2.79, 9437.76, 5, 6.28, 1577.34, 4, 1.95, 11015.11, 4, 2.33, 775.52, 4, 6.12, 10404.73, 3, 1.39, 5507.55, 2, 5.63, 10239.58, 2, 6.17, 30639.86, 2, 1.11, 13367.97, 2, 3.64, 7084.90, 2, 2.22, 3154.69,
496, 3.223, 10213.286, 8, 3.21, 20426.57, 1, 3.14, 0.00,
6, 0.92, 10213.29 ]

# Mars 0,5", 1e-6AE
p3 = [1000000000,
20, 596, 1028, 1289, 1385, 1427, 1454, 1586, 1670, 1694, 1709, 1718, 1724, 2360, 2873, 3155, 3239, 3275, 3287,
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134, 0.000, 0.000, 113, 3.457, 3340.612, 7, 0.50, 6681.22,
5, 4.87, 3340.61, 1, 5.31, 6681.22,
1530334883, 0.0000000000, 0.0000000000, 141849532, 3.479712835, 3340.612426700, 6607764, 3.8178344, 6681.2248534, 461791, 4.155953, 10021.837280, 81097, 5.55958, 2810.92146, 74853, 1.77239, 5621.84292, 55232, 1.36436, 2281.23050, 38252, 4.49407, 13362.44971, 24844, 4.92546, 2942.46342, 23065, 0.09082, 2544.31442, 19994, 5.36060, 3337.08931, 19602, 4.74249, 3344.13555, 11671, 2.11262, 5092.15196, 11028, 5.00908, 398.14900, 9923, 5.8386, 6151.5339, 8991, 4.4079, 529.6910, 8073, 2.1022, 1059.3819, 7979, 3.4484, 796.2980, 7410, 1.4991, 2146.1654, 7256, 1.2452, 8432.7644, 6923, 2.1338, 8962.4553, 6331, 0.8935, 3340.5952, 6331, 2.9243, 3340.6297, 6300, 1.2874, 1751.5395, 5744, 0.8290, 2914.0142, 5262, 5.3829, 3738.7614, 4728, 5.1985, 3127.3133, 3481, 4.8322, 16703.0621, 2837, 2.9069, 3532.0607, 2796, 5.2575, 6283.0758, 2755, 1.2177, 6254.6267, 2752, 2.9082, 1748.0164, 2699, 3.7639, 5884.9268, 2391, 2.0367, 1194.4470, 2338, 5.1055, 5486.7778, 2281, 3.2553, 6872.6731, 2232, 4.1986, 3149.1642, 2194, 5.5834, 191.4483, 2083, 4.8463, 3340.6797, 2083, 5.2548, 3340.5451, 1862, 5.6987, 6677.7017, 1827, 5.0806, 6684.7480, 1786, 4.1842, 3333.4989, 1760, 5.9534, 3870.3034, 1635, 3.7989, 4136.9104, 1443, 0.2130, 5088.6288, 1418, 2.4779, 4562.4610, 1331, 1.5391, 7903.0734, 1286, 5.4988, 8827.3903, 1188, 2.1218, 1589.0729, 1149, 4.3175, 1349.8674, 1115, 0.5534, 11243.6858, 1021, 6.1814, 9492.1463, 867, 1.750, 2700.715, 853, 1.616, 4690.480, 845, 0.623, 1592.596, 832, 0.616, 8429.241, 825, 1.622, 11773.377, 718, 2.475, 12303.068, 686, 2.402, 4399.994, 665, 2.213, 6041.328, 636, 2.673, 426.598, 620, 1.101, 1221.849, 590, 3.262, 6681.242, 590, 1.232, 6681.208, 586, 4.721, 213.299, 558, 1.233, 3185.192, 557, 5.447, 3723.509, 550, 5.727, 951.718, 524, 3.024, 4292.331, 516, 5.723, 7079.374, 489, 5.616, 3553.912, 454, 5.433, 6467.926, 446, 2.015, 8031.092, 443, 5.003, 5614.729, 433, 1.037, 11769.854, 424, 2.266, 155.420, 422, 1.633, 5628.956, 392, 1.242, 3339.632, 390, 2.578, 3341.593, 364, 4.439, 3894.182, 360, 1.160, 2288.344, 353, 5.490, 1990.745, 336, 5.170, 20043.675, 331, 0.855, 553.569, 323, 2.382, 4535.059, 320, 1.940, 382.897, 319, 4.593, 2274.117, 319, 4.375, 3.523, 303, 2.442, 11371.705, 294, 4.060, 3097.884, 279, 4.258, 3191.049, 275, 1.577, 9595.239, 262, 5.585, 9623.688, 252, 0.814, 10713.995, 248, 5.390, 2818.035, 247, 2.580, 2803.808, 234, 6.015, 3496.033, 228, 3.417, 7632.943, 221, 0.857, 3319.837, 213, 6.192, 14054.607, 210, 2.385, 4989.059, 206, 2.987, 3361.388, 204, 4.536, 6489.777, 199, 2.735, 5099.266, 197, 1.863, 3443.705, 195, 6.038, 10018.314, 194, 5.185, 6681.292, 194, 5.594, 6681.158, 191, 5.420, 10025.360, 191, 0.226, 13745.346, 186, 4.073, 2388.894, 183, 5.796, 7064.121, 182, 5.613, 7.114, 180, 2.814, 4032.770, 172, 3.671, 3205.547, 172, 3.188, 3347.726, 171, 1.550, 2957.716, 170, 6.155, 10404.734, 167, 4.521, 6674.111, 165, 4.141, 7477.523, 165, 3.845, 10973.556, 165, 2.866, 14712.317, 163, 6.282, 7210.916, 163, 1.923, 7373.382, 161, 0.928, 14584.298, 160, 4.584, 3264.346, 154, 2.208, 2118.764, 151, 2.654, 2787.043, 137, 1.686, 3337.022, 134, 2.128, 3344.203, 131, 4.275, 14314.168, 119, 0.799, 3265.831, 119, 4.821, 7234.794, 118, 0.197, 3475.678, 118, 3.229, 5828.028, 112, 0.239, 12832.759, 110, 0.445, 10213.286, 106, 1.740, 639.897, 102, 5.748, 242.729, 102, 2.665, 2487.416, 101, 5.375, 5085.038, 101, 0.789, 9381.940, 101, 2.451, 4929.685, 90, 0.96, 4933.21, 90, 1.99, 15113.99, 90, 4.18, 9225.54, 83, 1.94, 1648.45, 83, 0.95, 2906.90, 82, 5.25, 10575.41, 80, 3.92, 2921.13, 79, 2.81, 15643.68, 78, 2.05, 1758.65, 75, 5.68, 13916.02, 74, 6.10, 3583.34, 74, 0.84, 692.16, 70, 3.32, 3230.41, 68, 4.69, 17654.78, 65, 6.12, 135.07, 65, 2.74, 7740.61, 64, 4.20, 5202.36, 63, 3.32, 3767.21, 63, 4.50, 8425.65, 62, 6.11, 17256.63, 62, 4.48, 22747.29, 62, 4.59, 6531.66, 62, 1.57, 10021.82, 62, 3.60, 10021.85, 61, 0.00, 6836.65, 57, 0.14, 13524.92, 55, 5.75, 12168.00, 55, 6.06, 10419.99, 54, 5.22, 5305.45, 54, 5.08, 2707.83, 53, 4.55, 1744.43, 52, 2.70, 4459.37, 51, 1.57, 6525.80, 51, 1.29, 8439.88, 50, 2.34, 1052.27, 50, 4.68, 522.58, 47, 0.01, 3325.36, 47, 5.78, 9808.54, 47, 3.06, 5518.75, 47, 5.15, 1066.50, 45, 1.44, 3369.06, 45, 5.95, 6894.52, 44, 5.57, 16865.53, 44, 0.82, 3302.48, 43, 3.11, 4569.57, 43, 2.79, 3503.08, 42, 1.91, 263.08, 41, 4.40, 3074.01, 41, 5.49, 2699.73, 41, 5.47, 3120.20, 40, 1.34, 6247.51, 40, 1.84, 3134.43, 40, 3.83, 3355.86, 39, 1.98, 8969.57, 39, 1.49, 9168.64, 39, 0.38, 10177.26, 39, 1.23, 16858.48, 39, 3.48, 20618.02, 38, 0.80, 13517.87, 38, 0.27, 17395.22, 37, 4.25, 6261.74, 37, 1.58, 6680.24, 36, 2.95, 6144.42, 36, 5.55, 632.78, 36, 2.92, 6682.21, 36, 3.68, 5724.94, 36, 0.15, 2178.14, 35, 1.18, 10184.30,
11074333, 2.03250525, 3340.61242670, 1031759, 2.3707185, 6681.2248534, 128772, 0.000000, 0.000000, 108159, 2.708881, 10021.837280, 11946, 3.04702, 13362.44971, 4386, 2.8884, 2281.2305, 3957, 3.4232, 3344.1355, 1826, 1.5843, 2544.3144, 1359, 3.3851, 16703.0621, 1284, 6.0434, 3337.0893, 1282, 0.6299, 1059.3819, 1271, 1.9539, 796.2980, 1184, 2.9976, 2146.1654, 875, 3.421, 398.149, 830, 3.856, 3738.761, 756, 4.451, 6151.534, 720, 2.764, 529.691, 665, 2.549, 1751.540, 664, 4.406, 1748.016, 575, 0.544, 1194.447, 543, 0.678, 8962.455, 510, 3.726, 6684.748, 494, 5.730, 3340.595, 494, 1.477, 3340.630, 483, 2.581, 3149.164, 479, 2.285, 2914.014, 390, 2.319, 4136.910, 372, 5.814, 1349.867, 364, 6.027, 3185.192, 360, 5.895, 3333.499, 311, 0.978, 191.448, 272, 5.414, 1592.596, 243, 3.758, 155.420, 228, 1.748, 5088.629, 223, 0.939, 951.718, 217, 3.836, 6283.076, 216, 4.569, 3532.061, 213, 0.780, 1589.073, 204, 3.135, 4690.480, 182, 0.413, 5486.778, 180, 4.219, 3870.303, 169, 4.537, 4292.331, 168, 5.549, 3097.884, 165, 0.968, 4399.994, 165, 3.539, 2700.715, 163, 3.808, 3340.545, 163, 3.399, 3340.680, 162, 2.349, 553.569, 158, 4.757, 9492.146, 157, 3.724, 20043.675, 147, 5.953, 3894.182, 143, 3.999, 1990.745, 132, 0.415, 5614.729, 130, 5.142, 6677.702, 127, 0.690, 3723.509, 125, 1.032, 3341.593, 124, 6.231, 5628.956, 122, 4.223, 7079.374, 118, 6.253, 2274.117, 113, 1.024, 12303.068, 112, 1.318, 3496.033, 104, 1.233, 426.598, 103, 0.901, 4535.059, 98, 3.45, 382.90, 92, 1.82, 6681.24, 92, 6.07, 6681.21, 92, 3.90, 3553.91, 90, 2.58, 2388.89, 88, 2.20, 1221.85, 86, 1.16, 2787.04, 79, 5.74, 2288.34, 78, 4.15, 6041.33, 77, 1.01, 8432.76, 73, 4.27, 2803.81, 72, 3.70, 2818.04, 71, 3.51, 8031.09, 68, 4.05, 10025.36, 68, 0.24, 11773.38, 67, 4.26, 242.73, 65, 0.04, 2957.72, 65, 2.12, 8429.24, 65, 2.76, 3339.63, 63, 1.90, 5621.84, 63, 1.60, 3347.73, 60, 2.96, 6489.78, 57, 3.14, 213.30, 55, 4.91, 7632.94, 55, 4.61, 3583.34, 53, 3.78, 5092.15, 52, 2.67, 7477.52, 51, 3.98, 7.11, 47, 0.91, 5099.27, 46, 1.82, 2810.92, 40, 4.14, 9623.69, 40, 4.91, 2942.46, 39, 0.54, 5884.93, 39, 3.08, 3.52, 39, 0.67, 3127.31, 38, 0.03, 7234.79, 37, 0.09, 6525.80, 36, 5.77, 4933.21, 32, 4.55, 2487.42, 31, 1.00, 2118.76, 30, 2.59, 2906.90, 30, 4.15, 6681.16, 30, 3.74, 6681.29, 30, 0.83, 5085.04, 29, 4.66, 7210.92, 28, 1.01, 7064.12, 28, 0.05, 639.90, 28, 3.98, 6467.93, 28, 5.17, 5828.03, 27, 0.69, 2699.73, 26, 5.34, 10973.56, 26, 5.01, 10018.31, 26, 1.09, 4929.69, 26, 5.09, 12832.76, 25, 1.53, 6836.65, 24, 3.94, 11371.70, 22, 0.19, 9595.24, 21, 5.69, 3191.05, 21, 1.30, 7740.61, 21, 3.54, 1066.50, 21, 6.24, 6674.11, 20, 6.16, 1744.43, 20, 0.46, 10575.41, 19, 5.02, 3475.68, 19, 1.37, 15643.68, 18, 4.06, 23384.29, 18, 6.16, 8425.65, 18, 5.68, 3319.84, 18, 2.31, 3355.86, 18, 5.87, 3320.26, 17, 4.58, 10419.99, 17, 2.22, 2921.13, 17, 1.93, 3767.21, 16, 4.34, 5331.36, 16, 5.93, 8439.88, 15, 1.54, 3361.39, 15, 0.35, 8969.57, 14, 2.15, 10021.85, 14, 0.12, 10021.82, 14, 0.56, 15113.99, 14, 1.39, 6682.21, 14, 4.65, 4562.46, 14, 1.50, 3325.36, 14, 0.15, 1758.65, 13, 1.25, 7875.67, 13, 1.87, 692.16, 13, 1.45, 6254.63, 13, 5.79, 14584.30, 13, 1.35, 10404.73, 12, 6.03, 3264.35, 12, 1.88, 10177.26, 12, 0.85, 3120.20, 12, 4.30, 6894.52, 12, 0.90, 13916.02, 12, 4.18, 3360.97, 12, 3.00, 6247.51, 11, 0.15, 3134.43, 11, 2.84, 640.88, 11, 2.58, 6261.74, 11, 0.49, 11243.69, 11, 0.25, 3337.02, 11, 0.13, 522.58, 11, 0.68, 3344.20, 10, 4.06, 6158.65, 10, 5.70, 536.80, 10, 5.77, 14314.17, 10, 1.28, 4569.57, 10, 2.92, 5729.51,
442422, 0.479306, 3340.612427, 81380, 0.86998, 6681.22485, 12749, 1.22594, 10021.83728, 1874, 1.5730, 13362.4497, 524, 3.142, 0.000, 407, 1.971, 3344.136, 266, 1.917, 16703.062, 178, 4.435, 2281.230, 117, 4.525, 3185.192, 102, 5.391, 1059.382, 100, 0.419, 796.298, 92, 4.54, 2146.17, 78, 5.93, 1748.02, 73, 3.14, 2544.31, 72, 2.29, 6684.75, 68, 5.27, 155.42, 67, 5.30, 1194.45, 65, 2.31, 3738.76, 58, 1.05, 1349.87, 54, 1.00, 3149.16, 47, 0.77, 3097.88, 46, 0.81, 4136.91, 44, 2.46, 951.72, 43, 3.90, 1592.60, 39, 3.86, 553.57, 37, 2.26, 20043.67, 36, 1.32, 3333.50, 35, 1.85, 398.15, 34, 3.82, 1751.54, 32, 2.12, 5614.73, 31, 4.55, 5628.96, 30, 2.86, 6151.53, 29, 1.19, 529.69, 29, 1.20, 3894.18, 28, 2.49, 1990.75, 27, 2.92, 3496.03, 27, 6.07, 4292.33, 24, 4.68, 4690.48, 24, 5.94, 2787.04, 23, 2.56, 191.45, 22, 1.85, 3337.09, 22, 5.37, 8962.46, 22, 1.07, 2388.89, 21, 2.75, 242.73, 20, 3.82, 2914.01, 20, 5.76, 3341.59, 20, 5.76, 4399.99, 20, 4.17, 3340.60, 20, 6.21, 3340.63, 20, 3.11, 3583.34, 18, 5.69, 1589.07, 18, 3.32, 5088.63, 16, 5.68, 4535.06, 15, 4.96, 382.90, 15, 2.23, 3723.51, 14, 2.70, 7079.37, 14, 5.19, 2700.72, 13, 4.88, 6525.80, 13, 4.82, 2957.72, 12, 2.62, 10025.36, 12, 0.93, 2810.92, 12, 3.27, 9492.15, 10, 6.27, 3347.73, 10, 3.40, 5621.84, 10, 2.11, 3870.30, 9, 1.40, 6489.78, 9, 5.81, 12303.07, 9, 2.20, 2699.73, 9, 5.96, 426.60, 8, 2.26, 6283.08, 8, 2.24, 3553.91, 8, 1.17, 7477.52, 8, 2.01, 5092.15, 8, 0.23, 3532.06, 8, 2.06, 5486.78, 7, 4.26, 4933.21, 7, 0.30, 6681.24, 7, 4.55, 6681.21, 7, 2.34, 7.11, 7, 3.99, 6677.70, 7, 0.16, 7632.94, 6, 2.25, 3340.55, 6, 1.84, 3340.68, 6, 1.55, 7234.79, 6, 3.30, 1221.85, 6, 5.06, 8031.09, 5, 4.26, 3339.63, 5, 2.60, 23384.29, 5, 3.08, 6836.65, 4, 1.34, 640.88, 4, 4.96, 8969.57, 4, 2.85, 5331.36, 4, 6.27, 2487.42, 4, 6.10, 7740.61,
11131, 5.14987, 3340.61243, 4244, 5.6134, 6681.2249, 1000, 5.9973, 10021.8373, 196, 0.076, 13362.450, 47, 3.14, 0.00, 35, 0.43, 16703.06, 29, 0.45, 3344.14, 24, 3.02, 3185.19, 7, 0.81, 6684.75, 6, 0.78, 20043.67, 5, 3.87, 1059.38, 5, 1.61, 3583.34, 5, 4.52, 3496.03, 4, 5.72, 3149.16, 4, 4.42, 2787.04, 4, 5.56, 4136.91, 3, 3.38, 6525.80, 3, 0.76, 3738.76, 2, 2.14, 3097.88, 2, 5.83, 2388.89, 2, 0.57, 155.42, 2, 4.20, 3341.59, 2, 0.97, 1990.75, 2, 2.35, 1592.60, 2, 4.15, 4535.06, 2, 3.76, 1194.45, 2, 1.14, 10025.36, 2, 5.13, 796.30,
196, 3.582, 3340.612, 163, 4.051, 6681.225, 58, 4.46, 10021.84, 15, 4.84, 13362.45, 4, 1.51, 3185.19, 3, 5.21, 16703.06, 2, 5.16, 3344.14, 1, 0.00, 0.00, 1, 2.19, 3496.03, 1, 0.10, 3583.34, 1, 5.55, 20043.67, 1, 1.87, 6525.80,
5, 2.48, 6681.22, 3, 2.92, 10021.84, 1, 1.77, 3340.61, 1, 3.31, 13362.45 ]

# Jupiter 0,5", 3e-6 AE
p4 = [100000000,
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79645, 1.35866, 529.69097, 8252, 5.7777, 522.5774, 7030, 3.2748, 536.8045, 5314, 1.8384, 1059.3819, 1861, 2.9768, 7.1135, 964, 5.480, 515.464, 836, 4.199, 419.485, 498, 3.142, 0.000, 427, 2.228, 639.897, 406, 3.783, 1066.495, 377, 2.242, 1589.073, 363, 5.368, 206.186, 342, 6.099, 1052.268, 339, 6.127, 625.670, 333, 0.003, 426.598, 280, 4.262, 412.371, 257, 0.963, 632.784, 230, 0.705, 735.877, 201, 3.069, 543.918, 200, 4.429, 103.093, 139, 2.932, 14.227, 114, 0.787, 728.763, 95, 1.70, 838.97, 86, 5.14, 323.51, 83, 0.06, 309.28, 80, 2.98, 742.99, 75, 1.60, 956.29, 70, 1.51, 213.30, 67, 5.47, 199.07, 62, 6.10, 1045.15, 56, 0.96, 1162.47, 52, 5.58, 942.06, 50, 2.72, 532.87, 45, 5.52, 508.35, 44, 0.27, 526.51, 40, 5.95, 95.98, 30, 0.94, 1155.36, 29, 1.79, 831.86, 28, 2.88, 525.76, 27, 2.65, 2118.76, 27, 2.81, 1169.59, 26, 4.27, 1596.19, 23, 0.18, 302.16, 22, 1.89, 1272.68, 21, 4.35, 316.39, 21, 0.54, 1265.57, 20, 0.04, 949.18, 20, 1.16, 533.62, 20, 0.06, 1581.96, 18, 4.15, 846.08, 17, 5.89, 1258.45, 17, 0.53, 1368.66, 13, 0.79, 110.21, 13, 3.90, 433.71, 12, 2.23, 220.41, 12, 0.41, 1361.55, 12, 4.44, 405.26, 10, 1.00, 1471.75, 10, 6.01, 853.20, 9, 1.51, 1148.25, 9, 1.60, 1692.17, 9, 6.27, 519.40, 9, 3.52, 1073.61, 8, 5.60, 1574.85, 8, 0.18, 1685.05, 8, 0.65, 1478.87, 7, 0.88, 88.87, 7, 0.89, 721.65, 7, 4.44, 330.62, 6, 2.50, 3.18, 5, 0.85, 1788.14, 5, 2.79, 21.34, 5, 2.98, 1375.77, 5, 0.05, 1677.94, 5, 0.86, 3.93, 5, 2.28, 1485.98, 4, 1.28, 1464.64, 4, 0.41, 629.60, 4, 1.61, 635.97, 4, 2.71, 551.03, 3, 2.45, 539.99, 3, 0.55, 1795.26, 3, 1.19, 1905.46, 3, 6.19, 1038.04, 3, 5.55, 191.96, 3, 6.23, 2001.44, 3, 4.82, 416.30, 3, 0.55, 2104.54, 3, 3.24, 1062.56, 3, 0.03, 1898.35, 3, 1.24, 2221.86, 3, 2.40, 227.53, 2, 0.07, 750.10, 2, 4.28, 963.40, 2, 1.95, 824.74, 2, 6.19, 1994.33, 2, 1.72, 628.85, 2, 5.33, 1891.24, 2, 1.05, 1781.03, 2, 3.33, 1699.28, 2, 4.62, 423.42, 2, 0.29, 636.72, 2, 0.29, 2111.65, 2, 0.32, 295.05, 2, 3.44, 647.01, 2, 2.79, 1802.37, 2, 3.14, 611.44, 2, 1.12, 618.56, 2, 4.72, 2125.88, 2, 1.60, 2008.56, 2, 3.01, 2648.45, 2, 2.32, 440.83, 2, 5.89, 2317.84, 2, 2.42, 10.29, 2, 0.37, 1056.20, 2, 3.52, 1055.45, 2, 5.83, 422.67, 2, 5.76, 117.32, 1, 0.08, 1382.89, 1, 0.18, 2420.93, 1, 1.20, 1063.31, 1, 0.76, 2097.42, 1, 5.99, 2310.72, 1, 1.59, 380.13, 1, 4.20, 547.85, 1, 4.23, 934.95, 1, 3.86, 1603.30, 1, 1.35, 732.70, 1, 1.55, 2324.95, 1, 5.60, 99.91, 1, 6.18, 945.99, 1, 1.03, 81.75, 1, 0.09, 2737.32, 1, 2.54, 6283.08, 1, 1.15, 952.36, 1, 5.22, 2207.63, 1, 6.01, 511.53, 1, 3.03, 3046.60, 1, 2.71, 3370.10, 1, 6.01, 2214.74, 1, 5.00, 319.57, 1, 3.91, 10213.29, 1, 2.52, 3679.38, 1, 4.69, 5746.27, 1, 2.39, 3267.01, 1, 0.77, 5760.50, 1, 6.12, 9676.48, 1, 3.99, 337.73, 1, 2.19, 9690.71, 1, 1.12, 739.81, 1, 5.93, 2634.23, 1, 1.15, 2641.34, 1, 0.73, 1354.43, 1, 0.65, 2538.25, 1, 4.84, 860.31, 1, 4.23, 9683.59, 1, 1.20, 124.43, 1, 5.44, 107.02, 1, 0.90, 106.27, 1, 2.22, 2015.67, 1, 6.00, 501.24, 1, 5.12, 3156.81, 1, 1.24, 3803.82, 1, 2.43, 739.06, 1, 2.98, 1262.39, 1, 6.00, 1049.09, 1, 1.85, 453.42, 1, 6.19, 1987.22, 1, 5.33, 2751.55, 1, 4.92, 447.80, 1, 1.00, 462.02, 1, 4.77, 3473.20, 1, 5.61, 2524.02, 1, 5.82, 2627.11, 1, 2.43, 3686.50, 1, 3.89, 2516.91, 1, 3.55, 3178.15, 1, 3.29, 4.67, 1, 5.36, 9.56,
3519, 6.0580, 529.6910, 1073, 1.6732, 536.8045, 916, 1.413, 522.577, 342, 0.523, 1059.382, 255, 1.196, 7.114, 222, 0.952, 515.464, 90, 3.14, 0.00, 69, 2.27, 1066.50, 58, 1.41, 543.92, 58, 0.53, 639.90, 51, 5.98, 412.37, 47, 1.58, 625.67, 43, 6.12, 419.48, 37, 1.18, 14.23, 34, 1.67, 1052.27, 34, 0.85, 206.19, 31, 1.04, 1589.07, 30, 4.63, 426.60, 21, 2.50, 728.76, 15, 0.89, 199.07, 14, 0.96, 508.35, 13, 1.50, 1045.15, 12, 2.61, 735.88, 12, 3.56, 323.51, 11, 1.79, 309.28, 11, 6.28, 956.29, 10, 6.26, 103.09, 9, 3.45, 838.97, 7, 1.28, 742.99, 7, 0.92, 942.06, 7, 3.45, 831.86, 7, 1.87, 302.16, 6, 1.38, 95.98, 5, 2.83, 1596.19, 4, 1.21, 1169.59, 4, 5.99, 213.30, 4, 6.11, 405.26, 3, 2.33, 1155.36, 2, 0.35, 1272.68, 2, 1.87, 532.87, 2, 0.43, 220.41, 2, 5.97, 1162.47, 2, 1.95, 1073.61, 2, 0.09, 632.78, 2, 1.59, 2118.76, 2, 1.51, 1258.45, 2, 1.07, 21.34, 2, 2.16, 433.71, 2, 5.94, 110.21, 2, 3.17, 1148.25, 2, 2.55, 88.87, 2, 2.70, 721.65, 2, 2.26, 1361.55, 2, 1.98, 525.76, 2, 2.71, 330.62, 2, 0.44, 533.62, 2, 4.46, 853.20, 2, 0.47, 526.51, 2, 0.12, 949.18, 1, 0.67, 551.03, 1, 1.17, 1038.04, 1, 3.02, 963.40, 1, 1.16, 1574.85, 1, 2.55, 846.08, 1, 1.79, 1581.96, 1, 1.07, 227.53, 1, 2.70, 519.40, 1, 4.17, 2627.11, 1, 3.69, 824.74, 1, 4.91, 1670.83, 1, 2.93, 1368.66, 1, 0.60, 539.99, 1, 4.52, 750.10, 1, 0.94, 191.96, 1, 4.87, 611.44, 1, 0.21, 1141.13, 1, 3.23, 2125.88, 1, 2.39, 2317.84, 1, 2.25, 2538.25, 1, 5.80, 1485.98, 1, 2.27, 1699.28, 1, 0.67, 440.83, 1, 2.48, 1265.57, 1, 5.51, 2413.82, 1, 4.41, 1382.89, 1, 6.14, 1279.79, 1, 1.93, 2634.23, 1, 2.18, 1062.56, 1, 1.96, 1677.94, 1, 2.32, 1471.75, 1, 2.05, 295.05, 1, 2.50, 2207.63, 1, 0.19, 10.29,
129, 0.084, 536.805, 113, 4.249, 529.691, 83, 3.30, 522.58, 38, 2.73, 515.46, 27, 5.69, 7.11, 18, 5.40, 1059.38, 13, 6.02, 543.92, 9, 0.77, 1066.50, 8, 5.68, 14.23, 7, 1.43, 412.37, 6, 5.12, 639.90, 5, 3.34, 625.67, 3, 3.40, 1052.27, 3, 4.16, 728.76, 3, 2.90, 426.60, 2, 6.22, 1589.07, 2, 3.12, 1045.15, 2, 1.89, 419.48, 2, 2.60, 199.07, 2, 0.00, 0.00, 2, 2.81, 206.19, 2, 1.33, 1596.19, 1, 5.16, 831.86, 1, 4.42, 956.29, 1, 5.47, 220.41, 1, 0.67, 1361.55, 1, 1.87, 1148.25, 1, 3.17, 508.35, 1, 5.79, 1169.59, 1, 1.48, 1272.68, 1, 2.42, 117.32, 1, 2.20, 942.06, 1, 5.31, 551.03, 1, 0.50, 1073.61, 1, 2.85, 191.96, 1, 3.72, 88.87, 1, 3.53, 302.16, 1, 1.84, 10.29, 1, 1.59, 3.18, 1, 3.82, 618.56, 1, 0.86, 330.62, 1, 5.26, 21.34, 1, 1.83, 647.01, 1, 0.24, 433.71, 1, 4.44, 110.21,
11, 4.75, 536.80, 4, 5.92, 522.58, 2, 5.57, 515.46, 2, 4.30, 543.92, 2, 3.69, 7.11, 2, 4.13, 1059.38, 2, 5.49, 1066.50, 1, 3.78, 14.23, 1, 4.51, 529.69 ]

# Saturn 0.5" 5e-6 AE
p5 = [100000000,
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20315, 3.02187, 213.29910, 8924, 3.1914, 220.4126, 6909, 4.3517, 206.1855, 4087, 4.2241, 7.1135, 3879, 2.0106, 426.5982, 1071, 4.2036, 199.0720, 907, 2.283, 433.712, 606, 3.175, 227.526, 597, 4.135, 14.227, 483, 1.173, 639.897, 393, 0.000, 0.000, 229, 4.698, 419.485, 188, 4.590, 110.206, 150, 3.202, 103.093, 121, 3.768, 323.505, 102, 4.710, 95.979, 101, 5.819, 412.371, 93, 1.44, 647.01, 84, 2.63, 216.48, 73, 4.15, 117.32, 62, 2.31, 440.83, 55, 0.31, 853.20, 50, 2.39, 209.37, 45, 4.37, 191.96, 41, 0.69, 522.58, 40, 1.84, 302.16, 38, 5.94, 88.87, 32, 4.01, 21.34, 28, 5.77, 210.12, 25, 0.73, 515.46, 25, 3.06, 234.64, 21, 4.93, 625.67, 18, 1.46, 309.28, 17, 5.73, 728.76, 17, 3.53, 3.18, 13, 3.36, 330.62, 12, 5.99, 735.88, 11, 3.37, 224.34, 11, 3.42, 956.29, 11, 6.07, 405.26, 10, 0.28, 838.97, 10, 0.58, 860.31, 10, 1.59, 202.25, 9, 2.57, 223.59, 9, 2.94, 124.43, 9, 4.65, 632.78, 9, 1.76, 429.78, 8, 4.48, 742.99, 8, 4.20, 195.14, 8, 0.44, 831.86, 8, 1.46, 654.12, 7, 4.51, 942.06, 7, 5.47, 1045.15, 7, 1.52, 422.67, 7, 4.83, 316.39, 7, 3.42, 10.29, 6, 6.01, 1066.50, 6, 2.34, 269.92, 6, 0.83, 217.23, 6, 1.15, 284.15, 6, 4.18, 529.69, 6, 2.47, 536.80, 5, 2.12, 295.05, 4, 0.92, 203.00, 4, 3.23, 1272.68, 4, 0.11, 1155.36, 4, 6.01, 1052.27, 4, 0.06, 81.75, 3, 4.33, 1258.45, 3, 0.19, 1148.25, 3, 2.19, 447.94, 3, 1.89, 149.56, 3, 5.64, 3.93, 3, 5.41, 1361.55, 3, 4.97, 1677.94, 3, 0.92, 508.35, 3, 3.00, 1589.07, 3, 2.31, 543.92, 3, 3.71, 408.44, 2, 4.24, 1059.38, 2, 3.22, 319.57, 2, 5.73, 313.21, 2, 1.30, 184.84, 2, 5.88, 721.65, 2, 0.52, 416.30, 2, 6.18, 1464.64, 2, 6.23, 1471.75, 2, 2.41, 337.73, 2, 5.17, 2854.64, 2, 2.41, 131.55, 2, 5.62, 11.05, 2, 0.54, 635.97, 2, 5.59, 1038.04, 2, 1.82, 436.89, 2, 1.51, 750.10, 2, 6.12, 1073.61, 2, 4.58, 1994.33, 2, 0.03, 423.42, 2, 2.58, 2090.31, 2, 2.95, 437.64, 2, 1.75, 195.89, 2, 5.97, 1781.03, 2, 0.56, 2324.95, 2, 6.15, 490.33, 2, 0.61, 210.85, 2, 3.85, 1251.34, 1, 0.27, 497.45, 1, 0.99, 643.08, 1, 5.35, 1354.43, 1, 3.29, 1884.12, 1, 1.50, 430.53, 1, 0.85, 415.55, 1, 5.33, 2538.25, 1, 4.12, 1574.85, 1, 5.58, 1382.89, 1, 0.70, 867.42, 1, 3.79, 1567.73, 1, 2.29, 2420.93, 1, 1.41, 2634.23, 1, 0.48, 824.74, 1, 2.97, 241.75, 1, 3.11, 2200.52, 1, 5.13, 25.27, 1, 4.70, 113.39, 1, 1.80, 618.56, 1, 3.96, 1891.24, 1, 3.78, 1375.77, 1, 3.73, 131.40, 1, 4.48, 2214.74, 1, 0.79, 127.47, 1, 5.42, 1279.79, 1, 0.05, 63.74, 1, 4.80, 1987.22, 1, 5.85, 215.75, 1, 4.06, 231.46, 1, 1.09, 362.86, 1, 4.23, 1802.37, 1, 5.33, 2428.04, 1, 5.91, 265.99, 1, 0.74, 16.67, 1, 6.26, 2015.67, 1, 5.99, 2524.02, 1, 1.92, 483.22, 1, 2.66, 145.63, 1, 2.97, 934.95, 1, 6.26, 2.45, 1, 3.16, 2207.63, 1, 0.09, 628.85, 1, 1.24, 74.78, 1, 5.87, 1368.66, 1, 2.90, 2008.56, 1, 2.38, 2228.97, 1, 2.28, 1478.87, 1, 1.16, 3053.71, 1, 4.70, 1670.83, 1, 5.92, 1685.05, 1, 3.13, 56.62,
1202, 1.4150, 220.4126, 708, 1.162, 213.299, 516, 6.240, 206.186, 427, 2.469, 7.114, 268, 0.187, 426.598, 170, 5.959, 199.072, 150, 0.480, 433.712, 145, 1.442, 227.526, 121, 2.405, 14.227, 47, 5.57, 639.90, 19, 5.86, 647.01, 17, 0.53, 440.83, 16, 2.90, 110.21, 15, 0.30, 419.48, 14, 1.30, 412.37, 13, 2.09, 323.51, 11, 0.22, 95.98, 11, 2.46, 117.32, 10, 3.14, 0.00, 9, 1.56, 88.87, 9, 2.28, 21.34, 9, 0.68, 216.48, 8, 1.27, 234.64, 8, 4.49, 853.20, 8, 3.59, 302.16, 6, 5.17, 103.09, 5, 2.59, 515.46, 4, 4.97, 860.31, 4, 0.02, 191.96, 4, 5.97, 654.12, 4, 1.60, 330.62, 4, 1.60, 405.26, 4, 3.30, 210.12, 3, 2.73, 522.58, 3, 0.75, 209.37, 3, 1.32, 728.76, 2, 1.19, 124.43, 2, 0.49, 447.94, 2, 3.28, 203.00, 2, 0.73, 625.67, 2, 6.15, 429.78, 2, 0.75, 295.05, 2, 3.89, 1066.50, 2, 2.00, 831.86, 2, 0.09, 942.06, 2, 0.82, 223.59, 2, 1.40, 224.34, 2, 3.02, 184.84, 2, 5.41, 824.74, 2, 5.96, 422.67, 1, 2.12, 529.69, 1, 0.72, 536.80, 1, 1.65, 17.41, 1, 1.90, 956.29, 1, 5.97, 195.14, 1, 1.12, 838.97, 1, 0.89, 721.65, 1, 1.59, 735.88, 1, 3.06, 1574.85, 1, 1.01, 1045.15, 1, 5.36, 316.39, 1, 4.93, 56.62, 1, 2.72, 508.35, 1, 1.11, 1169.59,
129, 5.913, 220.413, 32, 0.69, 7.11, 27, 5.91, 227.53, 20, 4.95, 433.71, 20, 0.67, 14.23, 14, 2.67, 206.19, 14, 1.46, 199.07, 13, 4.59, 426.60, 7, 4.63, 213.30, 5, 3.61, 639.90, 4, 4.90, 440.83, 3, 4.07, 647.01, 3, 4.66, 191.96, 3, 0.49, 323.51, 3, 3.18, 419.48, 2, 3.70, 88.87, 2, 3.32, 95.98, 2, 0.56, 117.32, 2, 5.33, 302.16, 2, 0.00, 0.00, 2, 2.67, 853.20, 2, 0.86, 515.46, 1, 5.83, 234.64, 1, 0.16, 412.37, 1, 5.98, 3.18, 1, 5.23, 216.48, 1, 5.05, 124.43, 1, 0.37, 28.45 ]

# Uranus 1", 20e-6 AE
p6 = [100000000,
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98.900, 170, 4.950, 206.186, 170, 4.510, 288.081, 169, 4.043, 55.659, 168, 5.258, 518.645, 167, 4.922, 422.666, 164, 5.225, 67.359, 162, 3.273, 443.864, 162, 4.995, 73.818, 161, 3.823, 451.940, 157, 0.663, 220.413, 155, 4.320, 760.256, 154, 4.278, 45.577, 154, 4.707, 543.024, 152, 4.647, 155.783, 146, 2.657, 465.955, 143, 2.078, 457.878, 142, 1.270, 159.124, 134, 5.309, 14.015, 133, 2.889, 373.908, 129, 0.363, 96.873, 127, 0.424, 331.322, 125, 4.305, 339.286, 123, 2.383, 141.486, 117, 3.950, 74.260, 117, 1.837, 1289.947, 116, 4.435, 5.938, 116, 2.512, 296.157, 115, 6.249, 767.369, 113, 4.654, 80.198, 113, 0.831, 100.384, 113, 0.081, 558.002, 112, 1.212, 329.725, 111, 0.750, 80.719, 111, 0.387, 216.922, 108, 3.773, 142.450, 107, 2.394, 347.884, 107, 1.821, 306.831, 106, 0.816, 1087.693, 105, 5.945, 328.353, 104, 2.994, 6.220, 103, 0.698, 358.930, 101, 1.057, 92.308, 99, 4.33, 74.52, 98, 3.73, 75.04, 97, 0.69, 977.49, 96, 5.55, 969.62, 95, 0.80, 342.26, 94, 4.54, 28.57, 94, 4.99, 403.13, 91, 5.17, 144.15, 91, 0.22, 333.66, 90, 0.37, 0.96, 90, 3.80, 986.08, 89, 2.19, 74.83, 89, 5.88, 74.73, 89, 4.74, 604.47, 89, 4.44, 154.02, 87, 5.62, 300.61, 86, 2.83, 983.12, 85, 5.80, 6.59, 85, 1.26, 142.14, 84, 1.84, 227.31, 83, 1.88, 387.24, 83, 2.21, 74.94, 83, 5.86, 74.62, 80, 2.98, 526.72, 79, 5.67, 267.47, 78, 2.73, 110.21, 76, 2.78, 88.11, 76, 4.66, 101.87, 76, 5.41, 50.40, 75, 5.37, 373.01, 75, 1.35, 350.33, 74, 6.21, 312.46, 73, 0.58, 367.97, 71, 3.17, 23.58, 71, 3.65, 894.84, 71, 0.56, 92.94, 71, 4.66, 44.73, 70, 1.52, 552.59, 70, 3.74, 546.96, 70, 3.95, 187.70, 69, 2.45, 555.55, 69, 2.42, 235.39, 69, 4.77, 991.71, 67, 0.86, 522.58, 66, 5.05, 30.71, 65, 4.24, 771.30, 65, 0.69, 152.74, 65, 3.74, 536.80, 65, 5.27, 68.19, 64, 2.37, 157.64, 64, 0.10, 681.54, 63, 4.60, 67.88, 63, 2.90, 79.89, 63, 0.29, 119.51, 63, 5.36, 92.05, 63, 0.34, 561.18, 62, 2.68, 130.44, 62, 2.32, 74.03, 61, 0.58, 253.57,
1479896, 3.6720571, 74.7815986, 71212, 6.22601, 63.73590, 68627, 6.13411, 149.56320, 24060, 3.14159, 0.00000, 21468, 2.60177, 76.26607, 20857, 5.24625, 11.04570, 11405, 0.01848, 70.84945, 7497, 0.4236, 73.2971, 4244, 1.4169, 85.8273, 3927, 3.1551, 71.8127, 3578, 2.3116, 224.3448, 3506, 2.5835, 138.5175, 3229, 5.2550, 3.9322, 3060, 0.1532, 1.4845, 2564, 0.9808, 148.0787, 2429, 3.9944, 52.6902, 1645, 2.6535, 127.4718, 1584, 1.4305, 78.7138, 1508, 5.0600, 151.0477, 1490, 2.6756, 56.6224, 1413, 4.5746, 202.2534, 1403, 1.3699, 77.7505, 1228, 1.0470, 62.2514, 1033, 0.2646, 131.4039, 992, 2.172, 65.220, 862, 5.055, 351.817, 744, 3.076, 35.164, 687, 2.499, 77.963, 647, 4.473, 70.328, 624, 0.863, 9.561, 604, 0.907, 984.600, 575, 3.231, 447.796, 562, 2.718, 462.023, 530, 5.917, 213.299, 528, 5.151, 2.969, 494, 0.463, 145.631, 487, 0.706, 380.128, 460, 4.223, 12.530, 444, 2.156, 67.668, 406, 1.230, 22.091, 381, 3.851, 3.181, 373, 5.051, 529.691, 348, 1.749, 71.600, 339, 2.538, 18.159, 272, 3.384, 222.860, 269, 6.241, 340.771, 259, 3.921, 59.804, 256, 2.957, 84.343, 255, 3.504, 38.133, 238, 2.049, 269.921, 234, 0.278, 108.461, 225, 3.910, 160.609, 222, 3.647, 137.033, 212, 0.680, 111.430, 206, 1.534, 284.149, 201, 1.249, 69.365, 196, 4.772, 299.126, 189, 4.413, 265.989, 163, 4.341, 33.680, 153, 5.218, 209.367, 151, 1.990, 54.175, 137, 0.403, 195.140, 128, 2.403, 39.618, 117, 0.396, 87.312, 107, 1.230, 225.829, 106, 0.698, 2.448, 106, 0.171, 79.235, 105, 4.436, 305.346, 104, 2.922, 134.585, 104, 1.816, 72.334, 104, 2.576, 191.208, 100, 4.941, 120.358, 97, 3.81, 152.53, 95, 4.03, 82.86, 94, 5.02, 51.21, 93, 3.09, 77.23, 86, 0.53, 145.11, 85, 0.62, 116.43, 85, 5.72, 68.84, 85, 5.56, 344.70, 78, 1.64, 479.29, 77, 0.08, 45.58, 76, 4.20, 73.82, 76, 3.79, 75.74, 72, 4.31, 565.12, 72, 3.71, 408.44, 72, 3.94, 153.50, 71, 2.38, 60.77, 65, 1.56, 106.98, 64, 1.94, 41.64, 63, 4.19, 184.73, 62, 3.24, 422.67, 62, 4.39, 453.42, 62, 3.90, 4.45, 60, 0.60, 74.89, 59, 1.56, 456.39, 58, 5.33, 220.41, 57, 0.84, 146.59, 55, 1.60, 14.98, 54, 3.73, 7.11, 53, 4.45, 426.60, 53, 5.20, 358.93, 53, 3.50, 125.99, 52, 6.09, 404.51, 52, 1.76, 8.08, 51, 0.37, 206.19, 51, 0.53, 490.33, 49, 5.85, 112.91, 49, 4.26, 5.42, 49, 0.94, 99.16, 49, 3.63, 81.00, 48, 1.97, 288.08, 46, 5.35, 152.74, 44, 3.04, 20.61, 43, 1.26, 1514.29, 42, 0.05, 128.96, 42, 2.51, 24.38, 41, 2.34, 277.03, 40, 5.10, 35.42, 39, 5.49, 200.77, 39, 0.74, 347.88, 39, 4.95, 92.94, 38, 2.06, 333.66, 38, 3.62, 173.94, 36, 3.73, 96.87, 34, 3.68, 66.92, 33, 6.26, 1059.38, 33, 1.38, 74.67, 32, 4.38, 221.38, 32, 0.54, 203.74, 31, 0.80, 373.01, 31, 2.05, 230.56, 31, 2.54, 977.49, 30, 0.71, 109.95, 30, 0.19, 387.24, 29, 5.43, 58.11, 29, 3.11, 991.71, 28, 4.77, 415.55, 28, 0.37, 80.20, 27, 2.15, 140.00, 27, 2.03, 536.80, 27, 1.36, 0.96, 26, 4.53, 454.91, 26, 3.47, 144.15, 26, 5.43, 546.96, 26, 2.57, 522.58, 25, 1.80, 143.63, 25, 5.12, 81.37, 25, 0.55, 181.76, 25, 3.04, 14.01, 24, 3.30, 617.81, 24, 2.20, 628.85, 24, 5.67, 443.86, 24, 5.60, 32.20, 24, 4.95, 561.18, 24, 0.66, 46.21, 23, 3.81, 55.14, 23, 5.85, 297.64, 22, 4.82, 135.55, 22, 4.62, 391.17, 22, 4.59, 241.61, 22, 1.23, 41.10, 21, 5.27, 159.12, 21, 4.19, 329.73, 21, 0.24, 465.96, 21, 0.91, 76.48, 20, 3.16, 186.21, 20, 0.66, 66.70, 20, 1.30, 518.65, 20, 4.91, 909.82,
22440, 0.69953, 74.78160, 4727, 1.6990, 63.7359, 1682, 4.6483, 70.8494, 1650, 3.0966, 11.0457, 1434, 3.5212, 149.5632, 770, 0.000, 0.000, 500, 6.172, 76.266, 461, 0.767, 3.932, 390, 4.496, 56.622, 390, 5.527, 85.827, 292, 0.204, 52.690, 287, 3.534, 73.297, 273, 3.847, 138.517, 220, 1.964, 131.404, 216, 0.848, 77.963, 205, 3.248, 78.714, 149, 4.898, 127.472, 129, 2.081, 3.181, 117, 4.934, 447.796, 114, 4.787, 145.631, 113, 1.014, 462.023, 104, 3.586, 71.600, 99, 6.16, 224.34, 91, 0.68, 18.16, 89, 0.23, 202.25, 88, 2.93, 62.25, 71, 6.10, 454.91, 64, 3.39, 1.48, 64, 3.96, 67.67, 62, 3.30, 351.82, 59, 5.56, 9.56, 58, 4.91, 22.09, 51, 3.87, 65.22, 49, 3.75, 269.92, 44, 5.90, 71.81, 44, 1.93, 59.80, 42, 6.14, 284.15, 42, 2.62, 151.05, 42, 2.09, 12.53, 37, 5.91, 984.60, 36, 5.40, 77.75, 31, 4.59, 148.08, 31, 2.27, 195.14, 28, 4.58, 77.23, 28, 4.91, 277.03, 27, 3.53, 209.37, 26, 0.66, 120.36, 24, 5.87, 69.36, 23, 1.04, 84.34, 23, 1.71, 160.61, 21, 2.20, 45.58, 20, 2.32, 2.45, 17, 4.37, 54.17, 17, 4.78, 213.30, 17, 1.86, 340.77, 16, 0.40, 265.99, 16, 3.65, 152.74, 15, 5.44, 408.44, 14, 3.39, 358.93, 13, 1.53, 422.67, 13, 5.25, 137.03, 13, 1.26, 134.59, 13, 4.43, 87.31, 13, 3.03, 92.94, 12, 1.33, 51.21, 12, 3.24, 116.43, 12, 5.10, 191.21, 12, 4.66, 41.64, 12, 3.73, 220.41, 12, 4.17, 60.55, 11, 2.03, 7.11, 11, 1.08, 72.33, 10, 1.19, 344.70, 10, 0.33, 70.33, 10, 5.97, 35.16, 10, 3.06, 2.97, 10, 0.39, 415.55, 9, 2.44, 565.12, 9, 6.05, 146.38, 9, 5.19, 225.83, 9, 6.01, 5.42, 9, 5.82, 153.50, 9, 5.25, 347.88, 8, 3.91, 333.66, 8, 4.49, 70.12, 8, 3.72, 14.98, 8, 2.27, 299.13, 8, 2.26, 206.19, 8, 5.72, 55.14, 8, 0.90, 222.86, 7, 1.51, 991.71, 7, 1.18, 96.87,
1164, 4.7345, 74.7816, 212, 3.343, 63.736, 196, 2.980, 70.849, 105, 0.958, 11.046, 73, 1.00, 149.56, 72, 0.03, 56.62, 55, 2.59, 3.93, 36, 5.65, 77.96, 34, 3.82, 76.27, 32, 3.60, 131.40, 30, 3.44, 85.83, 28, 0.43, 3.18, 27, 2.55, 52.69, 25, 5.14, 78.71, 19, 5.13, 18.16, 18, 0.00, 0.00, 16, 5.20, 71.60, 16, 0.37, 447.80, 15, 2.97, 145.63, 15, 5.57, 462.02, 15, 3.86, 73.30, 11, 6.03, 138.52, 11, 3.58, 224.34, 8, 2.62, 22.09, 8, 0.30, 127.47, 8, 1.45, 1.48, 7, 5.44, 269.92, 7, 0.01, 151.05, 6, 4.37, 284.15, 6, 4.23, 373.01, 5, 4.16, 195.14, 5, 0.78, 62.25, 5, 1.84, 202.25, 5, 2.78, 120.36, 4, 3.96, 9.56, 4, 1.84, 72.33, 4, 1.86, 152.74, 4, 1.89, 209.37, 4, 1.05, 92.94, 4, 2.00, 65.22, 4, 1.17, 153.50, 4, 3.93, 124.29, 3, 1.54, 148.08, 3, 1.41, 351.82, 3, 2.99, 387.24, 3, 5.84, 160.61, 3, 6.04, 12.53, 3, 0.79, 572.23, 3, 5.65, 134.59, 3, 2.77, 213.30, 3, 1.99, 450.98,
53, 3.01, 74.78, 10, 1.91, 56.62, 7, 5.09, 11.05, 7, 5.43, 149.56, 4, 5.23, 131.40, 3, 1.30, 85.83, 3, 3.14, 0.00, 3, 0.44, 63.74, 2, 6.21, 358.93, 2, 0.92, 145.63, 2, 2.23, 440.68 ]

# Neptun: 1", 30e-6 AE
p7 = [100000000,
20, 188, 260, 281, 293, 299, 302, 359, 404, 419, 422, 425, 425, 638, 701, 743, 746, 746, 746,
531188633, 0.000000000, 0.000000000, 1798476, 2.9010127, 38.1330356, 1019728, 0.4858092, 1.4844727, 124532, 4.830081, 36.648563, 42064, 5.41055, 2.96895, 37715, 6.09222, 35.16409, 33785, 1.24489, 76.26607, 16483, 0.00008, 491.55793, 9199, 4.9375, 39.6175, 8994, 0.2746, 175.1661, 4216, 1.9871, 73.2971, 3365, 1.0359, 33.6796, 2285, 4.2061, 4.4534, 1434, 2.7834, 74.7816, 900, 2.076, 109.946, 745, 3.190, 71.813, 506, 5.748, 114.399, 400, 0.350, 1021.249, 345, 3.462, 41.102, 340, 3.304, 77.751, 323, 2.248, 32.195, 306, 0.497, 0.521, 287, 4.505, 0.048, 282, 2.246, 146.594, 267, 4.889, 0.963, 252, 5.782, 388.465, 245, 1.247, 9.561, 233, 2.505, 137.033, 227, 1.797, 453.425, 170, 3.324, 108.461, 151, 2.192, 33.940, 150, 2.997, 5.938, 148, 0.859, 111.430, 119, 3.677, 2.448, 109, 2.416, 183.243, 103, 0.041, 0.261, 103, 4.404, 70.328, 102, 5.705, 0.112, 98, 2.81, 8.08, 86, 4.23, 490.07, 82, 5.20, 493.04, 78, 4.16, 4.19, 74, 1.33, 529.69, 72, 5.30, 350.33, 64, 3.55, 168.05, 63, 0.15, 182.28, 58, 3.50, 145.11, 48, 1.11, 112.91, 48, 0.13, 484.44, 48, 2.58, 219.89, 47, 4.57, 46.21, 47, 4.50, 173.68, 47, 3.02, 498.67, 45, 5.47, 176.65, 39, 1.67, 213.30, 39, 2.39, 2.92,
3837687717, 0.0000000000, 0.0000000000, 16604, 4.86319, 1.48447, 15807, 2.27923, 38.13304, 3335, 3.6820, 76.2661, 1306, 3.6732, 2.9689, 605, 1.505, 35.164, 179, 3.453, 39.618, 107, 2.451, 4.453, 106, 2.755, 33.680, 73, 5.49, 36.65, 57, 1.86, 114.40, 57, 5.22, 0.52, 35, 4.52, 74.78, 32, 5.90, 77.75, 30, 3.67, 388.47, 29, 5.17, 9.56, 29, 5.17, 2.45, 26, 5.25, 168.05, 25, 4.73, 182.28, 20, 5.79, 1021.25, 19, 1.83, 484.44, 19, 1.32, 498.67, 15, 3.99, 32.20, 15, 4.95, 137.03,
53893, 0.00000, 0.00000, 296, 1.855, 1.484, 281, 1.191, 38.133, 270, 5.721, 76.266, 23, 1.21, 2.97, 9, 4.43, 35.16, 7, 0.54, 2.45,
31, 0.00, 0.00, 15, 1.35, 76.27, 12, 6.04, 1.48, 12, 6.11, 38.13,
114, 3.142, 0.000, 1, 3.18, 76.27,
1, 3.14, 0.00,
3088623, 1.4410437, 38.1330356, 27780, 5.91272, 76.26607, 27624, 0.00000, 0.00000, 15448, 3.50877, 39.61751, 15355, 2.52124, 36.64856, 2000, 1.5100, 74.7816, 1968, 4.3778, 1.4845, 1015, 3.2156, 35.1641, 606, 2.802, 73.297, 595, 2.129, 41.102, 589, 3.187, 2.969, 402, 4.169, 114.399, 280, 1.682, 77.751, 262, 3.767, 213.299, 254, 3.271, 453.425, 206, 4.257, 529.691, 140, 3.530, 137.033, 99, 4.17, 33.68, 68, 4.67, 71.81,
227279, 3.807931, 38.133036, 1803, 1.9758, 76.2661, 1433, 3.1416, 0.0000, 1386, 4.8256, 36.6486, 1073, 6.0805, 39.6175, 148, 3.858, 74.782, 136, 0.478, 1.484, 70, 6.19, 35.16, 52, 5.05, 73.30, 43, 0.31, 114.40, 37, 4.89, 41.10, 37, 5.76, 2.97, 26, 5.22, 213.30, 19, 0.90, 453.42, 17, 4.26, 77.75,
9691, 5.5712, 38.1330, 79, 3.63, 76.27, 72, 0.45, 36.65, 59, 3.14, 0.00, 30, 1.61, 39.62,
273, 1.017, 38.133,
6, 2.67, 38.13,
3007013206, 0.0000000000, 0.0000000000, 27062259, 1.32999459, 38.13303564, 1691764, 3.2518614, 36.6485629, 807831, 5.185928, 1.484473, 537761, 4.521139, 35.164090, 495726, 1.571057, 491.557929, 274572, 1.845523, 175.166060, 135134, 3.372206, 39.617508, 121802, 5.797544, 76.266071, 100895, 0.377027, 73.297126, 69792, 3.79617, 2.96895, 46688, 5.74938, 33.67962, 24594, 0.50802, 109.94569, 16939, 1.59422, 71.81265, 14230, 1.07786, 74.78160, 12012, 1.92062, 1021.24889, 8395, 0.6782, 146.5943, 7572, 1.0715, 388.4652, 5721, 2.5906, 4.4534, 4840, 1.9069, 41.1020, 4483, 2.9057, 529.6910, 4421, 1.7499, 108.4612, 4354, 0.6799, 32.1951, 4270, 3.4134, 453.4249, 3381, 0.8481, 183.2428, 2881, 1.9860, 137.0330, 2879, 3.6742, 350.3321, 2636, 3.0976, 213.2991, 2530, 5.7984, 490.0735, 2523, 0.4863, 493.0424, 2306, 2.8096, 70.3282, 2087, 0.6186, 33.9402, 1977, 5.1170, 168.0525, 1905, 1.7219, 182.2796, 1654, 1.9278, 145.1098, 1499, 1.0162, 219.8914, 1435, 1.7001, 484.4444, 1403, 6.0766, 173.6816, 1403, 4.5891, 498.6715, 1399, 0.7622, 176.6505, 1228, 1.5988, 77.7505, 1129, 5.9666, 9.5612, 835, 3.971, 114.399, 811, 3.003, 46.210, 732, 2.104, 181.758, 705, 1.187, 256.540, 616, 2.979, 106.977, 530, 4.241, 111.430, 502, 1.387, 5.938, 437, 2.270, 1550.940, 422, 5.532, 525.498, 421, 1.891, 30.711, 400, 1.256, 8.077, 382, 3.300, 983.116, 355, 2.278, 218.407, 345, 1.359, 293.189, 333, 5.751, 39.096, 321, 1.506, 454.909, 314, 3.959, 381.352, 309, 2.855, 72.073, 307, 0.320, 601.764, 306, 2.725, 6244.943, 294, 4.891, 528.206, 292, 4.024, 68.844, 281, 4.542, 44.725, 280, 1.541, 98.900, 268, 5.133, 112.915, 251, 3.540, 312.199, 248, 3.411, 37.612, 246, 1.015, 141.226, 240, 3.164, 143.625,
236339, 0.704980, 38.133036, 13220, 3.32015, 1.48447, 8622, 6.2163, 35.1641, 2702, 1.8814, 39.6175, 2155, 2.0943, 2.9689, 2153, 5.1687, 76.2661, 1603, 0.0000, 0.0000, 1464, 1.1842, 33.6796, 1136, 3.9189, 36.6486, 898, 5.241, 388.465, 790, 0.533, 168.053, 760, 0.021, 182.280, 607, 1.077, 1021.249, 572, 3.401, 484.444, 561, 2.887, 498.671, 490, 3.468, 137.033, 271, 3.274, 71.813, 264, 0.862, 4.453, 204, 2.418, 32.195, 155, 0.365, 41.102, 133, 3.602, 9.561,
4247, 5.8991, 38.1330, 218, 0.346, 1.484, 163, 2.239, 168.053, 156, 4.594, 182.280, 127, 2.848, 35.164, 118, 5.103, 484.444, 112, 1.190, 498.671, 99, 3.42, 175.17, 77, 0.02, 491.56, 65, 3.46, 388.47, 50, 4.07, 76.27, 39, 6.10, 1021.25, 37, 5.97, 2.97, 36, 5.17, 137.03,
166, 4.552, 38.133 ]

allePlaneten = [p0, p1, p2, p3, p4, p5, p6, p7 ]


def berechneHeliozentrisch(planet, JD) :
        f = allePlaneten[planet]
        # f=p0[];
        # Indextabelle auslesen nach ix
        z = 0
        faktor = f[z]; z=z+1
        ix=[0 for i in range(0,18)]
        pos = int(f[z]); z=z+1
        for i in range(0,18):
                anz = int(f[z] - pos)
                pos = int(f[z])
                z=z+1
                if ((anz % 3) != 0):
                        print("Index muss durch 3 teilbar sein. Sollte nicht vorkommen")
                ix[i] = int(anz / 3)
        
        tau = (JD - 2451545) / 365250.0
        LBR=[0 for i in range(0,18)] # L0-L5, B0-B5, R0-R5 in einer Tabelle
        for j in range(0,18):
                lbr = 0
                for i in range (0, ix[j]):
                        A = f[z]; z=z+1
                        B = f[z]; z=z+1
                        C = f[z]; z=z+1
                        lbr += A * cos(B + C * tau)
                LBR[j] = lbr
        l = 0; b = 0; r = 0
        for i in range(5,-1,-1):
                l = tau * l + LBR[i]
                b = tau * b + LBR[i + 6]
                r = tau * r + LBR[i + 12]
        l = l / faktor
        b = b / faktor
        r = r / faktor
        # Rückgabe im Gradmaß
        x = r * cos(l) * cos(b)
        y = r * sin(l) * cos(b)
        z = r * sin(b)
        l = 180 * l / pi
        b = 180 * b / pi
        l = to360(l)
        if (l < 0): l = l + 360
        b = to360(b)
        return x, y, z, l, b, r


def JD02JD(JD0, JD, alpha, delta) :
        alpha = alpha * 15 # in Grad
        T = (JD0 - 2451545.0) / 36525.0
        t = (JD - JD0) / 36525.0
        zeta = (2306.2181 + 1.39656 * T - 0.000139 * T * T) * t\
                + (0.30188 - 0.000344 * T) * t * t + 0.017998 * t * t * t
        z = (2306.2181 + 1.39656 * T - 0.000139 * T * T) * t\
                + (1.09468 + 0.000066 * T) * t * t + 0.018203 * t * t * t
        theta = (2004.3109 - 0.85330 * T - 0.000217 * T * T) * t\
                - (0.42665 + 0.000217 * T) * t * t - 0.041833 * t * t * t
        zeta = zeta / 3600.0
        z = z / 3600.0
        theta = theta / 3600
        A = Cos(delta) * Sin(alpha + zeta)
        B = Cos(theta) * Cos(delta) * Cos(alpha + zeta) - Sin(theta) * Sin(delta)
        C = Sin(theta) * Cos(delta) * Cos(alpha + zeta) + Cos(theta) * Sin(delta)
        alpZ = Atan2(A, B)
        alpha = alpZ + z
        alpha = alpha / 15
        delta = Asin(C) # in h
        return alpha, delta

def sternzeit(JD): # Meeus Kap. 12
	# einfache Methode, welche die Zahlengenauigkeit belastet
	T = (JD - 2451545.0) / 36525.0
	theta0 = 280.46061837 + 360.98564736629 * (JD - 2451545.0) + 0.000387933 * T * T - T * T * T / 39710000.0
	theta0 = To360(theta0)
	return theta0 / 15


def berechneGeozentrisch(pnr, JD, epoche2000) :
        slng, slat, sdist, sx, sy, sz = sunNewcomb(JD)
        x, y, z, l, b, r = berechneHeliozentrisch(pnr, JD)
        # Berechnung der Lichtlaufzeit, dazu Sonnenort berechnen
        Delta = sqrt(sq(x + sx) + sq(y + sy) + sq(z + sz))
        tau = 0.0057755183 * Delta
        # scheinbarer Planetenort
        x, y, z, l, b, r = berechneHeliozentrisch(pnr, JD - tau)
        # Abstand aktualisieren
        Delta = sqrt(sq(x + sx) + sq(y + sy) + sq(z + sz))
        # geozentrische Koordinaten
        Lambda = Atan2(y + sy, x + sx)
        if (Lambda < 0): Lambda += 360
        beta = Asin((z + sz) / Delta)
        # Umrechnen in R.A, Deklination über Schiefe der Ekliptik
        T = (JD - 2451545) / 36525.0
        eps = 23 + 26 / 60.0 + 21.448 / 3600
        eps = eps + (-46.8150 * T - 0.00059 * T * T + 0.001813 * T * T * T) / 3600
        alp = Atan2(Sin(Lambda) * Cos(eps) - Tan(beta) * Sin(eps), Cos(Lambda))
        alp = alp / 15
        if (alp < 0):
                alp += 24
        delta = Asin(Sin(beta) * Cos(eps) + Cos(beta) * Sin(eps) * Sin(Lambda))
        # hiermit zurückkehren, wenn man die Epoche des Datums gewünscht ist
        alpha = alp
        if (epoche2000==0):
                return alpha, delta, Delta
        # oder weiterrechnen für Epochentransformation Kap.21 
        alpha, delta = JD02JD(JD, 2451545.0, alpha, delta)
        if (alpha < 0): alpha += 24
        return alpha, delta, Delta

def berechneTopozentrisch(JD, alpha, delta, Delta, phi, L, h):
	# Kugelform und Höhe, Meeus Kap 11
	a = 6378140 # Erdradius am Äquator
	b = 6356755 # Erdradius zu den Polen
	u = Atan(b / a * Tan(phi))
	rhoSinPhiS = b / a * Sin(u) + h / a * Sin(phi)
	rhoCosPhiS = Cos(u) + h / a * Cos(phi)
	sinPi = Sin(8.794 / 3600) / Delta
	H = sternzeit(JD) - L - alpha
	H = To360(H * 15)
	y = -rhoCosPhiS * sinPi * Sin(H)
	x = Cos(delta) - rhoCosPhiS * sinPi * Cos(H)
	da = Atan2(y, x)
	alphaT = alpha + da / 15 # alpha ist in hms
	y = (Sin(delta) - rhoSinPhiS * sinPi) * Cos(da)
	x = Cos(delta) - rhoCosPhiS * sinPi * Cos(H)
	deltaT = Atan2(y, x)
	return alphaT, deltaT