Neptune

Class to model Neptune planet.

class pymeeus.Neptune.Neptune

Class Neptune models that planet.

__weakref__

list of weak references to the object (if defined)

static apparent_heliocentric_position(epoch)

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

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

static conjunction(epoch)

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

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

>>> epoch = Epoch(1993, 10, 1.0)
>>> conj = Neptune.conjunction(epoch)
>>> y, m, d = conj.get_date()
>>> print(y)
1994
>>> print(m)
1
>>> print(round(d, 4))
11.3057

static geocentric_position(epoch)

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

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

>>> epoch = Epoch(1992, 12, 20.0)
>>> ra, dec, elon = Neptune.geocentric_position(epoch)
>>> print(ra.ra_str(n_dec=1))
19h 17' 14.5''
>>> print(dec.dms_str(n_dec=1))
-21d 34' 15.1''
>>> print(elon.dms_str(n_dec=1))
19d 44' 59.6''

static geometric_heliocentric_position(epoch, tofk5=True)

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

Parameters:

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

Returns:

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

Return type:

tuple

Raises:

TypeError if input values are of wrong type.

>>> epoch = Epoch(2018, 10, 27.0)
>>> l, b, r = Neptune.geometric_heliocentric_position(epoch)
>>> print(round(l.to_positive(), 4))
345.3776
>>> print(round(b, 4))
-0.9735
>>> print(round(r, 5))
29.93966

static magnitude(sun_dist, earth_dist)

This function computes the approximate magnitude of Neptune.

Parameters:

• sun_dist (float) – Distance from Neptune to Sun, in Astronomical Units
• earth_dist (float) – Distance Neptune to Earth, in Astronomical Units

Returns:

Neptune’s magnitude

Return type:

float

Raises:

TypeError if input values are of wrong type.

static opposition(epoch)

This method computes the time of the opposition closest to the given epoch.

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

>>> epoch = Epoch(1846, 8, 1)
>>> oppo = Neptune.opposition(epoch)
>>> y, m, d = oppo.get_date()
>>> print(y)
1846
>>> print(m)
8
>>> print(round(d, 4))
20.1623

static orbital_elements_j2000(epoch)

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

Parameters:epoch (Epoch) – Epoch to compute orbital elements, as an Epoch object Returns:A tuple containing the following six orbital elements: - Mean longitude of the planet (Angle) - Semimajor axis of the orbit (float, astronomical units) - eccentricity of the orbit (float) - inclination on the plane of the ecliptic (Angle) - longitude of the ascending node (Angle) - argument of the perihelion (Angle) Return type:tuple Raises:TypeError if input values are of wrong type.

>>> epoch = Epoch(2065, 6, 24.0)
>>> l, a, e, i, ome, arg = Neptune.orbital_elements_j2000(epoch)
>>> print(round(l, 6))
87.407029
>>> print(round(a, 8))
30.11038676
>>> print(round(e, 7))
0.0094597
>>> print(round(i, 6))
1.770101
>>> print(round(ome, 5))
131.74402
>>> print(round(arg, 6))
-83.6046

static orbital_elements_mean_equinox(epoch)

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

Parameters:epoch (Epoch) – Epoch to compute orbital elements, as an Epoch object Returns:A tuple containing the following six orbital elements: - Mean longitude of the planet (Angle) - Semimajor axis of the orbit (float, astronomical units) - eccentricity of the orbit (float) - inclination on the plane of the ecliptic (Angle) - longitude of the ascending node (Angle) - argument of the perihelion (Angle) Return type:tuple Raises:TypeError if input values are of wrong type.

>>> epoch = Epoch(2065, 6, 24.0)
>>> l, a, e, i, ome, arg = Neptune.orbital_elements_mean_equinox(epoch)
>>> print(round(l, 6))
88.321947
>>> print(round(a, 8))
30.11038676
>>> print(round(e, 7))
0.0094597
>>> print(round(i, 6))
1.763855
>>> print(round(ome, 5))
132.46986
>>> print(round(arg, 6))
-83.415521

pymeeus.Neptune.ORBITAL_ELEM = [[304.348665, 219.8833092, 0.00030882, 1.8e-08], [30.110386869, -1.663e-07, 6.9e-10, 0.0], [0.00945575, 6.033e-06, 0.0, -5e-11], [1.769953, -0.0093082, -7.08e-06, 2.7e-08], [131.748057, 1.1022039, 0.00025952, -6.37e-07], [48.120276, 1.4262957, 0.00038434, 2e-08]]

This table contains the parameters to compute Neptune’s orbital elements for the mean equinox of date. Based in Table 31.A, page 213

pymeeus.Neptune.ORBITAL_ELEM_J2000 = [[304.348665, 218.4862002, 5.9e-07, -2e-09], [1.769953, 0.0002256, 2.3e-07, 0.0], [131.748057, -0.0061651, -2.19e-06, -7.8e-08], [48.120276, 0.0291866, 7.61e-05, 0.0]]

This table contains the parameters to compute Neptune’s orbital elements for the standard equinox J2000.0. Based on Table 31.B, page 215

pymeeus.Neptune.VSOP87_B = [[[3088622.933, 1.44104372626, 38.1330356378], [27780.087, 5.91271882843, 76.2660712756], [27623.609, 0.0, 0.0], [15355.49, 2.52123799481, 36.6485629295], [15448.133, 3.50877080888, 39.6175083461], [1999.919, 1.50998669505, 74.7815985673], [1967.54, 4.37778195768, 1.4844727083], [1015.137, 3.21561035875, 35.1640902212], [605.767, 2.80246601405, 73.297125859], [594.878, 2.12892708114, 41.1019810544], [588.805, 3.18655882497, 2.9689454166], [401.83, 4.16883287237, 114.3991069134], [254.333, 3.27120499438, 453.424893819], [261.647, 3.76722704749, 213.299095438], [279.964, 1.68165309699, 77.7505439839], [205.59, 4.25652348864, 529.6909650946], [140.455, 3.52969556376, 137.0330241624], [98.53, 4.16774829927, 33.6796175129], [51.257, 1.95121181203, 4.4534181249], [67.971, 4.66970781659, 71.8126531507], [41.931, 5.41783694467, 111.4301614968], [41.822, 5.94832001477, 112.9146342051], [30.637, 0.93620571932, 42.5864537627], [11.084, 5.88898793049, 108.4612160802], [9.62, 0.03944255108, 70.3281804424], [9.664, 0.22455797403, 79.2350166922], [9.728, 5.30069593532, 32.1951448046], [7.386, 3.00684933642, 426.598190876], [7.087, 0.12535040656, 109.9456887885], [6.021, 6.20514068152, 115.8835796217], [6.169, 3.62098109648, 983.1158589136], [4.777, 0.75210194972, 5.9378908332], [6.391, 5.8464610106, 148.0787244263], [6.251, 2.41678769385, 152.5321425512], [4.539, 5.581820987, 175.1660598002], [5.006, 4.60815664851, 1059.3819301892], [4.289, 4.19647392821, 47.6942631934], [5.795, 5.07516716087, 415.2918581812], [4.749, 2.51605725604, 37.611770776], [4.119, 1.72779509865, 28.5718080822], [4.076, 6.00252170354, 145.1097790097], [4.429, 5.65995321659, 98.8999885246], [3.95, 2.74104636753, 350.3321196004], [4.091, 1.61787956945, 39.0962434843], [4.131, 4.40682554313, 37.1698277913], [4.71, 3.50929350767, 38.6543004996], [4.44, 4.78977105547, 38.084851528], [4.433, 1.23386935925, 38.1812197476], [3.762, 4.83940791709, 491.5579294568], [2.606, 1.20956732792, 451.9404211107], [2.537, 2.18628045751, 454.9093665273], [2.328, 5.19779918719, 72.0732855816], [2.502, 0.8598790435, 106.9767433719], [2.342, 0.81387240947, 4.192785694], [1.981, 0.46617960831, 184.7272873558], [1.963, 6.01909114576, 44.070926471], [2.18, 0.70099749844, 206.1855484372], [1.811, 0.40456996647, 40.5807161926], [1.814, 3.64699555185, 220.4126424388], [1.705, 6.13551142362, 181.7583419392], [1.855, 5.61635630213, 35.685355083], [1.595, 2.97147156093, 37.8724032069], [1.785, 2.42154818096, 388.4651552382], [1.595, 3.05266110075, 38.3936680687], [1.437, 1.48678704605, 135.5485514541], [1.387, 2.46149266117, 138.5174968707], [1.366, 1.52026779665, 68.8437077341], [1.575, 3.58964541604, 38.0211610532], [1.297, 5.06156596196, 33.9402499438], [1.487, 0.20211121607, 30.0562807905], [1.504, 5.80298577327, 46.2097904851], [1.192, 0.87275514483, 42.3258213318], [1.569, 2.43405967107, 38.2449102224], [1.207, 1.84658687853, 251.4321310758], [1.015, 0.53439848924, 129.9194771616], [0.999, 2.47463873948, 312.1990839626], [0.99, 3.41514319052, 144.1465711632], [0.963, 4.31733242907, 151.0476698429], [1.02, 0.98226686775, 143.6253063014], [0.941, 1.02993053785, 221.3758502853], [0.938, 2.43648356625, 567.8240007324], [1.111, 0.65175024456, 146.594251718], [0.777, 0.00175975222, 218.4069048687], [0.895, 0.2512386962, 30.7106720963], [0.795, 5.80519741659, 149.5631971346], [0.737, 3.40060492866, 446.3113468182], [0.719, 1.43795191278, 8.0767548473], [0.72, 0.0065100755, 460.5384408198], [0.766, 4.03399506246, 522.5774180938], [0.666, 1.39457824982, 84.3428261229], [0.584, 1.01405548136, 536.8045120954], [0.596, 0.62390100715, 35.212274331], [0.598, 5.39946724188, 41.0537969446], [0.475, 5.80072248338, 7.4223635415], [0.51, 1.3447857974, 258.0244132148], [0.458, 5.25325523118, 80.7194894005], [0.421, 3.24496387889, 416.7763308895], [0.446, 1.19167306357, 180.2738692309], [0.471, 0.92632922375, 44.7253177768], [0.387, 1.68488418788, 183.2428146475], [0.375, 0.15223869165, 255.0554677982], [0.354, 4.21526988674, 0.9632078465], [0.379, 2.16947487177, 105.4922706636], [0.341, 4.7919405168, 110.2063212194], [0.427, 5.15774894584, 31.5407534988], [0.302, 3.4570630628, 100.3844612329], [0.298, 2.26790695187, 639.897286314], [0.279, 0.25689162963, 39.5056337615], [0.32, 3.58085653166, 45.2465826386], [0.269, 5.72024180826, 36.7604375141], [0.247, 0.61040148804, 186.2117600641], [0.245, 0.64173616273, 419.4846438752], [0.235, 0.73189197665, 10213.285546211], [0.232, 0.37399822852, 490.0734567485], [0.23, 5.76570492457, 12.5301729722], [0.24, 4.13447692727, 0.5212648618], [0.279, 1.62614865256, 294.6729761443], [0.238, 2.1852891655, 219.891377577], [0.262, 3.08384135298, 6.592282139], [0.217, 2.93214905312, 27.0873353739], [0.217, 4.69210602828, 406.1031376411], [0.219, 1.3521271256, 216.9224321604], [0.2, 2.35215465744, 605.9570363702], [0.232, 3.92583619589, 1512.8068240082], [0.223, 5.52392277606, 187.6962327724], [0.19, 0.29169556516, 291.7040307277], [0.236, 3.12464145036, 563.6312150384], [0.193, 0.53675942386, 60.7669528868], [0.215, 3.78391259001, 103.0927742186], [0.172, 5.63262770743, 7.1135470008], [0.164, 4.14700645532, 77.2292791221], [0.162, 0.72021213236, 11.0457002639], [0.16, 4.23490438166, 487.3651437628], [0.191, 0.37651439206, 31.019488637], [0.157, 1.02419759383, 6283.0758499914], [0.157, 4.42530429545, 6206.8097787158], [0.178, 6.24797160202, 316.3918696566], [0.161, 5.65988283675, 343.2185725996], [0.153, 5.58405022784, 252.0865223816], [0.189, 4.8079103997, 641.1211265914], [0.166, 5.50438043692, 662.531203563], [0.146, 5.08949604858, 286.596221297], [0.145, 2.13015521881, 2042.4977891028], [0.156, 2.19452173251, 274.0660483248], [0.148, 4.85696640135, 442.7517005706], [0.187, 4.96121139073, 1589.0728952838], [0.155, 2.28260574227, 142.1408335931], [0.134, 1.29277093566, 456.3938392356], [0.126, 5.59769497652, 179.3588454942], [0.146, 2.53359213478, 256.5399405065], [0.14, 1.57962199954, 75.7448064138], [0.123, 0.05442220184, 944.9828232758], [0.122, 1.90676379802, 418.2608035978], [0.154, 1.86865302773, 331.3215390738], [0.144, 5.52229258454, 14.0146456805], [0.138, 2.80728175526, 82.8583534146], [0.107, 0.66995358132, 190.665178189], [0.114, 1.4889498028, 253.5709950899], [0.11, 5.32587573069, 240.125798381], [0.105, 0.65548440578, 173.6815870919], [0.102, 2.58735617801, 450.4559484024], [0.098, 0.44044795266, 328.3525936572], [0.101, 4.71267656829, 117.36805233], [0.094, 0.54938580474, 293.188503436], [0.095, 2.17636214523, 101.8689339412], [0.093, 0.63687810471, 377.1588225434], [0.091, 5.84828809934, 10137.0194749354], [0.089, 1.02830167997, 1021.2488945514], [0.094, 1.79320597168, 493.0424021651], [0.08, 1.58140274465, 69.1525242748], [0.075, 0.23453373368, 63.7358983034], [0.071, 1.5196198969, 488.5889840402]], [[227279.214, 3.8079308987, 38.1330356378], [1803.12, 1.97576485377, 76.2660712756], [1385.733, 4.82555548018, 36.6485629295], [1433.3, 3.14159265359, 0.0], [1073.298, 6.08054240712, 39.6175083461], [147.903, 3.85766231348, 74.7815985673], [136.448, 0.47764957338, 1.4844727083], [70.285, 6.18782052139, 35.1640902212], [51.899, 5.05221791891, 73.297125859], [37.273, 4.89476629246, 41.1019810544], [42.568, 0.30721737205, 114.3991069134], [37.104, 5.75999349109, 2.9689454166], [26.399, 5.21566335936, 213.299095438], [16.949, 4.26463671859, 77.7505439839], [18.747, 0.90426522185, 453.424893819], [12.951, 6.17709713139, 529.6909650946], [10.502, 1.20336443465, 137.0330241624], [4.416, 1.25478204684, 111.4301614968], [4.383, 6.14147099615, 71.8126531507], [3.694, 0.94837702528, 33.6796175129], [2.957, 4.7753287121, 4.4534181249], [2.698, 1.92435531119, 112.9146342051], [1.989, 3.96637567224, 42.5864537627], [1.15, 4.30568700024, 37.611770776], [0.871, 4.81775882249, 152.5321425512], [0.944, 2.2177777205, 109.9456887885], [0.936, 1.1705498394, 148.0787244263], [0.925, 2.40329074, 206.1855484372], [0.69, 1.57381082857, 38.6543004996], [0.624, 2.79466003645, 79.2350166922], [0.726, 4.13829519132, 28.5718080822], [0.64, 2.46161252327, 115.8835796217], [0.531, 2.969915305, 98.8999885246], [0.537, 1.95986772922, 220.4126424388], [0.539, 2.06690307827, 40.5807161926], [0.716, 0.5578184701, 350.3321196004], [0.563, 1.84072805158, 983.1158589136], [0.533, 1.3478767794, 47.6942631934], [0.566, 1.80111775954, 175.1660598002], [0.449, 1.62191691011, 144.1465711632], [0.371, 2.74239666472, 415.2918581812], [0.381, 6.11910193382, 426.598190876], [0.366, 2.3975258536, 129.9194771616], [0.456, 3.19611413854, 108.4612160802], [0.327, 3.62341506247, 38.1812197476], [0.328, 0.89613145346, 38.084851528], [0.341, 3.8726546907, 35.685355083], [0.331, 4.48858774501, 460.5384408198], [0.414, 1.03543720726, 70.3281804424], [0.31, 0.51297445145, 37.1698277913], [0.287, 2.183516518, 491.5579294568], [0.274, 6.11504724934, 522.5774180938], [0.281, 3.81657117512, 5.9378908332], [0.298, 4.00532631258, 39.0962434843], [0.265, 5.26569823181, 446.3113468182], [0.319, 1.34097217817, 184.7272873558], [0.203, 6.02944475303, 149.5631971346], [0.205, 5.5393573202, 536.8045120954], [0.226, 6.17710997862, 454.9093665273], [0.186, 3.24302117645, 4.192785694], [0.179, 4.91458426239, 451.9404211107], [0.198, 2.3077585288, 146.594251718], [0.166, 1.16793600058, 72.0732855816], [0.147, 2.10574339673, 44.070926471], [0.123, 1.98250467171, 46.2097904851], [0.159, 3.46955908364, 145.1097790097], [0.116, 5.8897111359, 38.0211610532], [0.115, 4.73412534395, 38.2449102224], [0.125, 3.42713474801, 251.4321310758], [0.128, 1.51108932026, 221.3758502853], [0.127, 0.17176461812, 138.5174968707], [0.124, 5.85160407534, 1059.3819301892], [0.091, 2.38273591235, 30.0562807905], [0.118, 5.27114846878, 37.8724032069], [0.117, 5.35267669439, 38.3936680687], [0.099, 5.19920708255, 135.5485514541], [0.114, 4.37452353441, 388.4651552382], [0.093, 4.64183693718, 106.9767433719], [0.084, 1.35269684746, 33.9402499438], [0.111, 3.5622646377, 181.7583419392], [0.082, 3.18401661435, 42.3258213318], [0.084, 5.51669920239, 8.0767548473]], [[9690.766, 5.57123750291, 38.1330356378], [78.815, 3.62705474219, 76.2660712756], [71.523, 0.4547668858, 36.6485629295], [58.646, 3.14159265359, 0.0], [29.915, 1.60671721861, 39.6175083461], [6.472, 5.60736756575, 74.7815985673], [5.8, 2.25341847151, 1.4844727083], [4.309, 1.68126737666, 35.1640902212], [3.502, 2.39142672984, 114.3991069134], [2.649, 0.65061457644, 73.297125859], [1.518, 0.37600329684, 213.299095438], [1.223, 1.2311604303, 2.9689454166], [0.766, 5.45279753249, 453.424893819], [0.779, 2.07081431472, 529.6909650946], [0.496, 0.26552533921, 41.1019810544], [0.469, 5.87866293959, 77.7505439839], [0.482, 5.63056237954, 137.0330241624], [0.345, 1.80085651594, 71.8126531507], [0.274, 2.86650141006, 33.6796175129], [0.158, 4.63868656467, 206.1855484372], [0.166, 1.24877330835, 220.4126424388], [0.153, 2.87376446497, 111.4301614968], [0.116, 3.63838544843, 112.9146342051], [0.085, 0.43712705655, 4.4534181249], [0.104, 6.12597614674, 144.1465711632]], [[273.423, 1.01688979072, 38.1330356378], [2.274, 2.36805657126, 36.6485629295], [2.029, 5.33364321342, 76.2660712756], [2.393, 0.0, 0.0], [0.538, 3.21934211365, 39.6175083461], [0.242, 4.52650721578, 114.3991069134], [0.185, 1.04913770083, 74.7815985673], [0.155, 3.62376309338, 35.1640902212], [0.157, 3.9419536961, 1.4844727083]], [[5.728, 2.66872693322, 38.1330356378]], [[0.113, 4.70646877989, 38.1330356378]]]

This table contains Neptune’s periodic terms (all of them) from the planetary theory VSOP87 for the heliocentric latitude at the equinox of date (taken from the ‘D’ solution). In Meeus’ book a shortened version can be found in page 453.

pymeeus.Neptune.VSOP87_L = [[[531188633.047, 0.0, 0.0], [1798475.509, 2.9010127305, 38.1330356378], [1019727.662, 0.4858092366, 1.4844727083], [124531.845, 4.83008090682, 36.6485629295], [42064.45, 5.41054991607, 2.9689454166], [37714.589, 6.09221834946, 35.1640902212], [33784.734, 1.24488865578, 76.2660712756], [16482.741, 7.729261e-05, 491.5579294568], [9198.582, 4.93747059924, 39.6175083461], [8994.249, 0.27462142569, 175.1660598002], [4216.235, 1.98711914364, 73.297125859], [3364.818, 1.03590121818, 33.6796175129], [2284.8, 4.20606932559, 4.4534181249], [1433.512, 2.78340432711, 74.7815985673], [900.24, 2.07606702418, 109.9456887885], [744.996, 3.19032530145, 71.8126531507], [506.206, 5.74785370252, 114.3991069134], [399.552, 0.34972342569, 1021.2488945514], [345.195, 3.46186210169, 41.1019810544], [306.338, 0.49684039897, 0.5212648618], [287.322, 4.50523446022, 0.0481841098], [323.004, 2.24815188609, 32.1951448046], [340.323, 3.30369900416, 77.7505439839], [266.605, 4.88932609483, 0.9632078465], [227.079, 1.79713054538, 453.424893819], [244.722, 1.24693337933, 9.5612275556], [232.887, 2.50459795017, 137.0330241624], [282.17, 2.24565579693, 146.594251718], [251.941, 5.78166597292, 388.4651552382], [150.18, 2.99706110414, 5.9378908332], [170.404, 3.3239063065, 108.4612160802], [151.401, 2.1915309428, 33.9402499438], [148.295, 0.85948986145, 111.4301614968], [118.672, 3.67706204305, 2.4476805548], [101.821, 5.70539236951, 0.1118745846], [97.873, 2.80518260528, 8.0767548473], [103.054, 4.40441222, 70.3281804424], [103.305, 0.04078966679, 0.2606324309], [109.3, 2.41599378049, 183.2428146475], [73.938, 1.32805041516, 529.6909650946], [77.725, 4.16446516424, 4.192785694], [86.379, 4.22834506045, 490.0734567485], [81.536, 5.19908046216, 493.0424021651], [71.503, 5.29530386579, 350.3321196004], [64.418, 3.5454101605, 168.0525127994], [62.57, 0.15028731465, 182.279606801], [58.488, 3.50106873945, 145.1097790097], [48.276, 1.11259925628, 112.9146342051], [47.229, 4.57373229818, 46.2097904851], [39.124, 1.6656935605, 213.299095438], [47.728, 0.12906212461, 484.444382456], [46.858, 3.01699530327, 498.6714764576], [38.659, 2.38685706479, 2.9207613068], [47.046, 4.498446604, 173.6815870919], [47.565, 2.58404814824, 219.891377577], [44.714, 5.47302733614, 176.6505325085], [32.279, 3.4575915122, 30.7106720963], [28.249, 4.13282446716, 6.592282139], [24.433, 4.55736848232, 106.9767433719], [24.661, 3.67822620786, 181.7583419392], [24.505, 1.55095867965, 7.1135470008], [21.848, 1.04366818343, 39.0962434843], [16.936, 6.10896452834, 44.7253177768], [22.169, 2.74932970271, 256.5399405065], [16.614, 4.98188930613, 37.611770776], [17.728, 3.55049134167, 1.3725981237], [17.347, 2.1406923488, 42.5864537627], [14.953, 3.36405649131, 98.8999885246], [14.566, 0.69857991985, 1550.939859646], [15.676, 6.22010212025, 454.9093665273], [13.243, 5.61712542227, 68.8437077341], [14.837, 3.52557245517, 25.6028626656], [12.757, 0.04509743861, 11.0457002639], [11.988, 4.81687553351, 24.1183899573], [11.06, 1.78958277553, 7.4223635415], [12.108, 1.87022663714, 79.2350166922], [11.698, 0.49005698002, 1.5963472929], [10.459, 2.38743199893, 381.3516082374], [11.681, 3.85151357766, 218.4069048687], [8.744, 0.1416856861, 148.0787244263], [9.196, 1.00274090619, 72.0732855816], [11.343, 0.81432278263, 525.4981794006], [10.097, 5.03383557061, 601.7642506762], [8.035, 1.7768572301, 0.2124483211], [8.382, 3.07534786987, 1.2720243872], [10.803, 2.92081211459, 293.188503436], [7.666, 1.52223325105, 115.8835796217], [7.531, 5.37537256533, 5.1078094307], [8.691, 4.74352784364, 143.6253063014], [10.183, 1.15395455831, 6244.9428143536], [8.283, 0.35956716764, 138.5174968707], [9.544, 4.02452832984, 152.5321425512], [7.274, 4.10937535938, 251.4321310758], [7.465, 1.72131945843, 31.019488637], [6.902, 4.62452068308, 2.7083129857], [7.094, 5.11528393609, 312.1990839626], [7.929, 2.10765101655, 27.0873353739], [6.156, 3.50746507109, 28.5718080822], [7.134, 2.05292376023, 278.2588340188], [8.193, 2.58588219154, 141.2258098564], [5.499, 2.09250039025, 1.6969210294], [5.279, 4.09390686798, 983.1158589136], [6.947, 3.48041784595, 415.2918581812], [5.916, 0.68957324226, 62.2514255951], [5.925, 4.0250459262, 255.0554677982], [4.606, 1.17779101436, 43.2408450685], [5.357, 3.63061058987, 5.4166259714], [5.918, 2.57693824084, 10175.1525105732], [5.482, 3.0797973728, 329.8370663655], [3.956, 5.00418696742, 184.7272873558], [5.408, 3.31313295602, 528.2064923863], [4.767, 4.91981150665, 456.3938392356], [3.77, 1.57277409442, 32.7164096664], [3.924, 4.92763242635, 180.2738692309], [3.707, 4.82965453201, 221.3758502853], [3.802, 4.96279204998, 594.6507036754], [4.014, 1.6390516403, 40.5807161926], [3.061, 0.39713858313, 1.4362885985], [3.261, 4.65478978469, 29.226199388], [3.474, 5.65891305944, 395.578702239], [2.918, 5.91079083895, 1.2238402774], [3.649, 3.88114678609, 494.5268748734], [3.225, 5.57423738665, 1014.1353475506], [2.845, 0.56009386585, 144.1465711632], [2.848, 0.55423029727, 567.8240007324], [3.44, 1.70887250883, 12.5301729722], [3.267, 5.6328779982, 488.5889840402], [3.107, 5.79335949207, 105.4922706636], [2.712, 2.43726364359, 60.7669528868], [3.202, 2.21483496593, 41.0537969446], [3.134, 4.69665220513, 82.8583534146], [3.59, 5.69939670162, 1124.34166877], [2.967, 0.54448940101, 135.5485514541], [3.211, 4.19927605853, 291.7040307277], [2.899, 5.99669788291, 22.633917249], [3.143, 2.93495725805, 31.2319369581], [2.729, 4.62707721219, 5.6290742925], [2.513, 5.60391563025, 19.1224551112], [2.69, 5.32070128202, 2.0057375701], [2.63, 6.00855841124, 37.1698277913], [2.296, 6.06934502789, 451.9404211107], [2.858, 4.88677262419, 258.0244132148], [2.879, 5.12239168488, 38.6543004996], [2.27, 2.08634524182, 30.0562807905], [2.301, 3.35951602914, 1028.3624415522], [3.001, 3.59143817947, 211.8146227297], [2.237, 0.3845555347, 3.6233367224], [2.901, 3.24755614136, 366.485629295], [2.592, 1.36262641469, 35.4247226521], [2.418, 4.93467056526, 47.6942631934], [2.089, 5.79838063413, 4.665866446], [2.586, 2.69392971321, 38.1812197476], [1.913, 5.53560681085, 149.5631971346], [1.971, 6.00790964671, 34.2008823747], [2.586, 6.24984047544, 38.084851528], [2.098, 4.57819744766, 1019.7644218431], [1.869, 3.85907708723, 911.042573332], [2.486, 5.21235809332, 140.001969579], [1.795, 1.68012868451, 1059.3819301892], [2.326, 2.82664069146, 807.9497991134], [1.984, 5.54763522932, 1022.7333672597], [1.919, 5.10717766499, 216.9224321604], [2.004, 5.47811228948, 63.7358983034], [2.021, 4.15631916516, 178.1350052168], [1.76, 6.00927149342, 172.1971143836], [2.14, 2.65037925793, 700.6642392008], [1.988, 3.3585027278, 186.2117600641], [1.956, 5.01527508588, 294.6729761443], [1.966, 4.07957525462, 20.6069278195], [1.637, 0.53823942149, 67.3592350258], [1.54, 2.62327849119, 41.7563723602], [1.81, 5.81430038477, 129.9194771616], [1.776, 4.37047808449, 328.3525936572], [1.46, 2.63664516309, 2.857070832], [1.388, 2.10598045632, 3.9321532631], [1.352, 0.55618245459, 0.6543913058], [1.668, 2.77543377384, 16.1535096946], [1.338, 0.37643611305, 14.0146456805], [1.218, 0.7345643475, 426.598190876], [1.531, 4.54891769768, 526.722019678], [1.61, 3.40993944436, 403.1341922245], [1.361, 4.48227243414, 17.6379824029], [1.589, 5.59323020112, 3302.479391062], [1.132, 5.6452072536, 151.0476698429], [1.357, 4.0639903143, 26.826702943], [1.494, 4.98692049495, 666.723989257], [1.077, 4.3091147025, 0.6331394464], [1.042, 6.02756893581, 106.0135355254], [1.06, 0.74679491358, 487.3651437628], [1.31, 3.7852638093, 386.9806825299], [1.342, 4.52685061062, 563.6312150384], [0.986, 0.00600924269, 81.3738807063], [1.232, 5.17443930901, 331.3215390738], [0.929, 4.51267465978, 38.3936680687], [0.956, 3.5044779102, 64.9597385808], [0.929, 4.43109514438, 37.8724032069], [0.926, 6.09803297747, 4.1446015842], [0.972, 0.59038366513, 8.9068362498], [1.246, 4.69840351226, 389.9496279465], [1.009, 5.98451242784, 142.1408335931], [1.02, 0.832338923, 39.3568759152], [1.013, 0.37845630298, 36.9091953604], [0.94, 2.42688145966, 343.2185725996], [0.974, 5.23958752786, 253.5709950899], [0.964, 5.09748190218, 357.4456666012], [0.835, 1.4556862667, 35.212274331], [1.077, 0.71409061316, 44.070926471], [1.083, 2.27578897621, 6.9010986797], [0.938, 5.03471583911, 69.3649725959], [1.078, 1.20253141912, 35.685355083], [1.027, 0.18243183397, 84.3428261229], [0.764, 4.62720907712, 0.8300814025], [1.013, 0.42234855022, 32.4557772355], [0.939, 4.50445799766, 365.0011565867], [0.756, 0.82872484717, 17.5261078183], [0.916, 3.89409205418, 38.2449102224], [0.736, 4.78125743795, 5.3684418616], [0.762, 0.0189733713, 189.3931538018], [0.738, 2.31770478416, 42.3258213318], [0.86, 4.82440483506, 210.3301500214], [0.888, 3.20360339895, 348.8476468921], [0.916, 5.04967792934, 38.0211610532], [0.638, 0.63267396269, 244.318584075], [0.636, 1.02615137352, 2080.6308247406], [0.774, 5.44432678139, 367.9701020033], [0.644, 1.94044989547, 446.3113468182], [0.631, 4.82928491724, 460.5384408198], [0.855, 3.57592750113, 439.782755154], [0.678, 4.48687912809, 351.8165923087], [0.724, 4.8914160928, 119.5069163441], [0.594, 0.59315717529, 491.036664595], [0.655, 1.99014093, 19.0105805266], [0.58, 2.57189536188, 492.0791943186], [0.694, 0.08328521209, 5.6772584023], [0.733, 5.81485239057, 29.7474642498], [0.666, 3.42196897591, 179.0982130633], [0.678, 0.29428615814, 171.2339065371], [0.635, 2.13805182663, 164.1203595363], [0.623, 5.6145494038, 285.3723810196], [0.529, 1.88063108785, 416.7763308895], [0.529, 5.1325078803, 697.743477894], [0.5, 1.49548514415, 704.8570248948], [0.487, 4.97772067947, 274.0660483248], [0.666, 6.26456825266, 1474.6737883704], [0.532, 0.25784352716, 477.3308354552], [0.557, 0.71378452161, 80.7194894005], [0.556, 2.60791360513, 418.2608035978], [0.584, 4.29064541383, 16.6747745564], [0.524, 5.4275939228, 290.2195580194], [0.524, 0.29054995359, 247.2393453818], [0.541, 4.36400580938, 815.0633461142], [0.526, 1.66512720297, 97.4155158163], [0.497, 4.72640318293, 401.6497195162], [0.432, 2.98481475894, 100.3844612329], [0.382, 0.28067758468, 8.385571388], [0.424, 6.16774845481, 178.7893965226], [0.484, 0.01535318279, 738.7972748386], [0.518, 4.4891659141, 875.830299001], [0.506, 5.38611121207, 404.6186649328], [0.396, 4.62747640832, 6.1503391543], [0.466, 0.23340415764, 120.9913890524], [0.409, 3.08849480895, 59.2824801785], [0.47, 5.01853200224, 313.6835566709], [0.442, 3.68919475089, 457.8783119439], [0.384, 3.69499925394, 160.9389657986], [0.364, 0.76192181046, 104.0077979553], [0.416, 0.26652109651, 103.0927742186], [0.401, 4.06530055968, 14.6690369863], [0.454, 3.72767803715, 476.4313180835], [0.434, 0.335338022, 984.6003316219], [0.34, 0.99915726716, 31.5407534988], [0.42, 3.65147769268, 20.4950532349], [0.334, 0.35121412008, 1227.4344429886], [0.323, 5.45836731979, 918.1561203328], [0.407, 4.19457842203, 309.7995875176], [0.381, 0.0136485696, 495.4900827199], [0.334, 4.05924071124, 8.3373872782], [0.38, 3.17063415023, 487.6257761937], [0.309, 0.48352303405, 118.0224436358], [0.38, 2.70238752925, 134.1122628556], [0.362, 4.8898581061, 438.2982824457], [0.327, 2.91090790412, 505.7850234584], [0.308, 0.96082817124, 21.1494445407], [0.288, 1.48123872077, 220.4126424388], [0.293, 2.56582281789, 662.531203563], [0.331, 4.37715965811, 180.7951340927], [0.326, 2.46104924164, 169.5369855077], [0.289, 2.63591886391, 55.7710180407], [0.288, 5.02487283285, 1440.7335384266], [0.344, 1.4893099727, 166.5680400911], [0.266, 0.63672427386, 79.1868325824], [0.268, 5.02354540478, 377.4194549743], [0.308, 1.50185265748, 77.2292791221], [0.324, 5.30240189273, 457.617679513], [0.265, 1.087366328, 450.4559484024], [0.264, 0.83337660655, 488.3765357191], [0.29, 1.80003152563, 101.8689339412], [0.262, 2.3039000336, 494.7393231945], [0.325, 5.52669889053, 441.2672278623], [0.254, 0.02963623277, 117.36805233], [0.3, 0.1743570554, 252.9166037841], [0.315, 5.3488501304, 183.7640795093], [0.313, 5.45945846595, 13.4933808187], [0.306, 5.23085809622, 45.2465826386], [0.237, 0.32676889138, 208.8456773131], [0.263, 2.66670785888, 464.7312265138], [0.234, 1.82700149824, 52175.8062831484], [0.275, 5.04385701142, 156.1554792736], [0.265, 5.64967127743, 326.8681209489], [0.247, 1.74540930625, 65.8747623175], [0.269, 6.09827783249, 1654.0326338646], [0.229, 2.25832077914, 190.665178189], [0.294, 5.45249564193, 206.1855484372], [0.238, 1.55647021369, 79.889407998], [0.23, 6.13158632762, 178.3474535379], [0.274, 4.10829870815, 518.3846323998], [0.225, 3.86300359251, 171.9846660625], [0.228, 2.48511565618, 12566.1516999828], [0.272, 5.61149862463, 148.3393568572], [0.214, 1.45987216039, 522.5774180938], [0.211, 4.04791980901, 6205.3253060075], [0.266, 0.99036038827, 209.106309744], [0.23, 0.5404995153, 532.6117264014], [0.226, 3.8415296162, 283.6272758804], [0.243, 5.32730346969, 485.9288551643], [0.209, 4.35051470487, 536.8045120954], [0.232, 3.01948719112, 10.9338256793], [0.264, 5.70536379124, 490.3340891794], [0.28, 3.99993658196, 674.8007441043], [0.246, 0.37698964335, 157.6399519819], [0.219, 5.67679857772, 52099.5402118728], [0.251, 1.52353965506, 6.8529145699], [0.203, 5.44328656642, 145.6310438715], [0.238, 0.96169723853, 497.1870037493], [0.219, 4.52300776062, 1615.8995982268], [0.275, 2.37619210741, 2118.7638603784], [0.258, 5.1244814878, 608.877797677], [0.26, 3.88543008475, 513.079881013], [0.191, 3.72574595369, 65.2203710117], [0.211, 0.06484535455, 215.4379594521], [0.236, 3.95835282821, 141.4864422873], [0.189, 5.28135043909, 377.1588225434], [0.243, 4.35559878377, 482.9599097477], [0.243, 6.06808644973, 154.0166152595], [0.249, 1.57215637373, 14.2270940016], [0.238, 1.93340192445, 500.1559491659], [0.209, 5.02893682321, 364.559213602], [0.227, 5.7298429854, 1543.8263126452], [0.217, 2.45036922991, 187.1749679106], [0.181, 1.65699502247, 1627.2059309216], [0.214, 1.60213179145, 11.3063326948], [0.203, 0.74638490279, 14.5571624017], [0.192, 3.17719161639, 343.4792050305], [0.177, 1.50027795761, 9.449352971], [0.177, 0.03038098292, 165.6048322446], [0.176, 4.64462444674, 315.1680293792], [0.208, 2.65835778368, 496.0113475817], [0.174, 2.76155855705, 49.1787359017], [0.196, 1.95549714182, 335.7749571987], [0.2, 4.16839394758, 285.1117485887], [0.199, 0.06168021293, 73.5577582899], [0.188, 6.17288913873, 535.3200393871], [0.215, 1.92414563346, 552.6973893591], [0.166, 5.4903813969, 10135.5350022271], [0.192, 0.9697343412, 304.2342036999], [0.209, 5.34065233845, 13.642138665], [0.203, 5.11234865419, 324.7292569348], [0.177, 3.5068084179, 207.3612046048], [0.174, 1.95010708561, 319.3126309634], [0.187, 5.57685931698, 266.1011680621], [0.181, 1.43525075751, 279.7433067271], [0.165, 4.00537112057, 493.5636670269], [0.191, 1.68313683465, 563.3705826075], [0.173, 3.93200456456, 238.9019581036], [0.161, 5.96143146317, 36.1272980677], [0.194, 2.3766423145, 944.9828232758], [0.165, 0.97421918976, 556.5176680376], [0.189, 1.11279570541, 1127.2624300768], [0.172, 0.75085513952, 267.5856407704], [0.193, 2.12636756833, 20350.3050211464], [0.181, 2.1081456208, 113.8778420516], [0.194, 1.13504964219, 57.255490749], [0.181, 6.23699820519, 355.9611938929], [0.198, 5.68125942959, 6280.1069045748], [0.173, 5.15083799917, 474.9468453752], [0.151, 1.66981962338, 116.5379709275], [0.15, 5.42593657173, 526.9826521089], [0.205, 4.16096717573, 711.4493070338], [0.177, 3.49360697678, 421.2297490144], [0.168, 0.52839230204, 487.1045113319], [0.16, 4.77712663799, 524.0137066923], [0.145, 2.81448128781, 1512.8068240082], [0.146, 4.9957011266, 142.6620984549], [0.188, 0.8210416155, 10210.3166007944], [0.145, 4.96888131586, 1189.3014073508], [0.181, 2.9970479059, 75.7448064138], [0.176, 0.41626373842, 222.8603229936], [0.137, 2.96534226337, 6206.8097787158], [0.138, 1.22260849471, 187.6962327724], [0.128, 2.53394068407, 276.7743613105], [0.13, 3.04810765699, 310.7146112543], [0.122, 3.01323006886, 70.8494453042], [0.111, 0.77449448649, 179.3588454942], [0.141, 0.18423889807, 131.4039498699], [0.126, 5.77648809669, 525.2375469697], [0.124, 2.93225731024, 179.6194779251], [0.111, 6.18471578216, 981.6313862053], [0.141, 2.63342951123, 381.6122406683], [0.11, 5.25053027081, 986.0848043302], [0.096, 3.86591534559, 240.125798381], [0.12, 3.78755085035, 1057.8974574809], [0.093, 4.54014016637, 36.6967470393], [0.109, 1.533275859, 419.7452763061], [0.094, 4.21870300178, 1024.217839968], [0.109, 2.15905156247, 289.5651667136], [0.104, 0.20665642552, 564.8550553158], [0.081, 1.89134135215, 36.6003788197], [0.08, 4.38832594589, 10137.0194749354], [0.08, 1.73940577376, 39.5056337615], [0.084, 0.81316746605, 170.7126416753], [0.09, 0.60145818457, 36.7604375141], [0.074, 4.92511651321, 1549.4553869377], [0.072, 5.06852406179, 249.9476583675]], [[3837687716.731, 0.0, 0.0], [16604.187, 4.86319129565, 1.4844727083], [15807.148, 2.27923488532, 38.1330356378], [3334.701, 3.6819967602, 76.2660712756], [1305.84, 3.67320813491, 2.9689454166], [604.832, 1.50477747549, 35.1640902212], [178.623, 3.45318524147, 39.6175083461], [106.537, 2.45126138334, 4.4534181249], [105.747, 2.7547932655, 33.6796175129], [72.684, 5.48724732699, 36.6485629295], [57.069, 5.2164980497, 0.5212648618], [57.355, 1.85767603384, 114.3991069134], [35.368, 4.51676827545, 74.7815985673], [32.216, 5.9041148968, 77.7505439839], [29.871, 3.67043294114, 388.4651552382], [28.866, 5.16877529164, 9.5612275556], [28.742, 5.16732589024, 2.4476805548], [25.507, 5.24526281928, 168.0525127994], [24.869, 4.7319306781, 182.279606801], [20.205, 5.78945415677, 1021.2488945514], [19.022, 1.82981144269, 484.444382456], [18.661, 1.31606255521, 498.6714764576], [15.063, 4.9500389376, 137.0330241624], [15.094, 3.9870525494, 32.1951448046], [10.72, 2.44148149225, 4.192785694], [11.725, 4.89255650674, 71.8126531507], [9.581, 1.23188039594, 5.9378908332], [9.606, 1.88534821556, 41.1019810544], [8.968, 0.01758559103, 8.0767548473], [9.882, 6.08165628679, 7.1135470008], [7.632, 5.51307048241, 73.297125859], [6.992, 0.61688864282, 2.9207613068], [5.543, 2.24141557794, 46.2097904851], [4.845, 3.7105582375, 112.9146342051], [3.7, 5.25713252333, 111.4301614968], [3.233, 6.10303038418, 70.3281804424], [2.939, 4.86520586648, 98.8999885246], [2.403, 2.90637675099, 601.7642506762], [2.398, 1.04343654629, 6.592282139], [2.784, 4.95821114677, 108.4612160802], [2.894, 4.20148844767, 381.3516082374], [2.111, 5.93089610785, 25.6028626656], [2.075, 5.20632201951, 30.7106720963], [2.126, 0.54976393136, 41.0537969446], [2.235, 2.38045158073, 453.424893819], [1.859, 0.89409373259, 24.1183899573], [2.018, 3.42245274178, 31.019488637], [1.7, 3.91715254287, 11.0457002639], [1.776, 3.86571077241, 395.578702239], [1.644, 0.15855999051, 152.5321425512], [1.646, 3.34591387314, 44.7253177768], [1.876, 2.59784179105, 33.9402499438], [1.614, 0.42137145545, 175.1660598002], [1.468, 6.12983933526, 1550.939859646], [1.408, 6.13722948564, 490.0734567485], [1.207, 0.59525736062, 312.1990839626], [1.336, 3.28611928206, 493.0424021651], [1.176, 5.87266726996, 5.4166259714], [1.517, 3.12967210501, 491.5579294568], [1.053, 4.6037551683, 79.2350166922], [1.037, 4.89007314395, 1.2720243872], [1.034, 5.93741289103, 32.7164096664], [1.038, 1.13470380744, 1014.1353475506], [1.002, 1.85850922283, 5.1078094307], [0.983, 0.05345050384, 7.4223635415], [0.998, 1.73689827444, 1028.3624415522], [1.193, 4.63176675581, 60.7669528868], [0.94, 3.09103721222, 62.2514255951], [0.994, 4.11489180313, 4.665866446], [0.89, 0.87049255398, 31.2319369581], [0.852, 5.35508394316, 144.1465711632], [0.922, 5.12373360511, 145.1097790097], [0.789, 0.37496785039, 26.826702943], [0.828, 4.060351946, 115.8835796217], [0.711, 3.14189997439, 278.2588340188], [0.727, 1.39718382835, 213.299095438], [0.781, 0.10946327923, 173.6815870919], [0.793, 6.13086312116, 567.8240007324], [0.669, 4.50554989443, 27.0873353739], [0.825, 1.35568908148, 129.9194771616], [0.738, 3.5676601896, 176.6505325085], [0.714, 6.24797992301, 106.9767433719], [0.654, 1.13177751192, 68.8437077341], [0.624, 0.01567750666, 28.5718080822], [0.608, 4.60180625368, 189.3931538018], [0.595, 0.00857468445, 42.5864537627], [0.53, 5.61201247153, 12.5301729722], [0.521, 1.02371768017, 415.2918581812], [0.639, 0.68930265745, 529.6909650946], [0.526, 3.02138731705, 5.6290742925], [0.456, 4.44331571392, 43.2408450685], [0.524, 3.43316448349, 38.6543004996], [0.436, 2.41630174435, 82.8583534146], [0.424, 1.95736011325, 477.3308354552], [0.443, 3.39350946329, 357.4456666012], [0.383, 1.90232196422, 22.633917249], [0.479, 5.55141744216, 37.611770776], [0.462, 3.80436154644, 343.2185725996], [0.384, 5.60377408953, 594.6507036754], [0.369, 4.45577410338, 6.9010986797], [0.358, 3.69126616347, 3.9321532631], [0.352, 3.10952926034, 135.5485514541], [0.368, 3.53577440355, 40.5807161926], [0.424, 5.27159202779, 181.7583419392], [0.361, 0.29018303419, 72.0732855816], [0.39, 5.49512204296, 350.3321196004], [0.378, 2.74122401337, 488.3765357191], [0.372, 0.39980033572, 494.7393231945], [0.353, 1.10614174053, 20.6069278195], [0.296, 0.86351261285, 149.5631971346], [0.307, 5.39420288683, 160.9389657986], [0.395, 1.93577214824, 10137.0194749354], [0.288, 2.28755739359, 47.6942631934], [0.295, 2.4873753724, 19.1224551112], [0.29, 0.18636083306, 143.6253063014], [0.266, 3.09977370364, 69.3649725959], [0.266, 1.21002824826, 505.7850234584], [0.252, 3.12745026026, 460.5384408198], [0.328, 0.50849285663, 6206.8097787158], [0.257, 3.64119914774, 446.3113468182], [0.239, 5.54080102299, 911.042573332], [0.265, 0.62702473701, 253.5709950899], [0.287, 2.44403568436, 16.6747745564], [0.231, 2.47026250085, 454.9093665273], [0.23, 3.24571542922, 1066.49547719], [0.282, 1.48595620175, 983.1158589136], [0.212, 5.41931177641, 64.9597385808], [0.213, 1.64175339637, 1089.129394439], [0.238, 2.69801319489, 882.9438460018], [0.21, 4.53976756699, 1093.322180133], [0.22, 2.30038816175, 1052.2683831884], [0.256, 0.4207359846, 23.9059416362], [0.216, 5.4422591887, 39.0962434843], [0.201, 2.58746514605, 119.5069163441], [0.224, 4.43751392203, 639.897286314], [0.186, 2.50651218075, 487.3651437628], [0.189, 4.05785534221, 120.9913890524], [0.184, 2.24245977278, 815.0633461142], [0.202, 3.43517732411, 45.2465826386], [0.175, 4.49165234532, 171.2339065371], [0.171, 5.50633466316, 179.0982130633], [0.2, 6.12663205401, 14.2270940016], [0.173, 2.61090344107, 389.9496279465], [0.167, 3.94754384833, 77.2292791221], [0.166, 3.41009128748, 81.3738807063], [0.163, 3.88198848446, 556.5176680376], [0.164, 1.49614763046, 63.7358983034], [0.176, 3.86129425367, 148.3393568572], [0.161, 2.22215642318, 574.9375477332], [0.171, 0.66899426684, 179.3106613844], [0.161, 1.21480182441, 1024.4302882891], [0.155, 3.25842414799, 10251.4185818488], [0.183, 5.45168150656, 218.4069048687], [0.152, 3.35145509017, 285.3723810196], [0.152, 0.42398786475, 274.0660483248], [0.146, 5.70714579127, 419.4846438752], [0.156, 0.6432152487, 1029.8469142605], [0.147, 4.3095893074, 157.6399519819], [0.147, 1.8068917751, 377.4194549743], [0.14, 1.49826604627, 386.9806825299], [0.137, 2.14480243915, 563.6312150384], [0.127, 3.9872659971, 84.3428261229], [0.134, 4.16039455079, 169.5369855077], [0.121, 0.29300927469, 206.1855484372], [0.129, 2.6762505701, 180.7951340927], [0.134, 3.18868986487, 166.5680400911], [0.135, 5.0751756178, 426.598190876], [0.136, 1.8167245174, 151.0476698429], [0.129, 3.64795525602, 183.7640795093], [0.116, 6.06435563172, 220.4126424388], [0.123, 4.46641157829, 1022.7333672597], [0.112, 4.34485256988, 138.5174968707], [0.116, 5.58946529961, 35.685355083], [0.108, 1.03796693383, 488.5889840402], [0.108, 2.1037848588, 494.5268748734], [0.106, 0.87068583107, 1059.3819301892], [0.097, 0.74486741478, 485.9288551643], [0.095, 5.54259914856, 497.1870037493], [0.085, 3.16062141266, 522.5774180938], [0.097, 6.05634803604, 482.9599097477], [0.095, 0.2311185273, 500.1559491659], [0.084, 2.64687252518, 536.8045120954], [0.074, 3.90678924318, 1019.7644218431]], [[53892.649, 0.0, 0.0], [281.251, 1.19084538887, 38.1330356378], [295.693, 1.85520292248, 1.4844727083], [270.19, 5.72143228148, 76.2660712756], [23.023, 1.21035596452, 2.9689454166], [7.333, 0.5403330683, 2.4476805548], [9.057, 4.42544992035, 35.1640902212], [5.223, 0.67427930044, 168.0525127994], [5.201, 3.02338671812, 182.279606801], [4.288, 3.84351844003, 114.3991069134], [3.925, 3.53214557374, 484.444382456], [3.741, 5.90238217874, 498.6714764576], [2.966, 0.31002477611, 4.4534181249], [3.415, 0.55971639038, 74.7815985673], [3.255, 1.84921884906, 175.1660598002], [2.157, 1.89135758747, 388.4651552382], [2.211, 4.3799709224, 7.1135470008], [1.847, 3.48574435762, 9.5612275556], [2.451, 4.68586840176, 491.5579294568], [1.844, 5.12281562096, 33.6796175129], [2.204, 1.69321574906, 77.7505439839], [1.652, 2.55859494053, 36.6485629295], [1.309, 4.52400192922, 1021.2488945514], [1.124, 0.38710602242, 137.0330241624], [0.664, 0.88101734307, 4.192785694], [0.497, 2.24615784762, 395.578702239], [0.512, 6.22609200672, 381.3516082374], [0.582, 5.25716719826, 31.019488637], [0.446, 0.36647221351, 98.8999885246], [0.383, 5.48585528762, 5.9378908332], [0.375, 4.61250246774, 8.0767548473], [0.354, 1.30783918287, 601.7642506762], [0.259, 5.66033623678, 112.9146342051], [0.247, 2.89695614593, 189.3931538018], [0.245, 4.26572913391, 220.4126424388], [0.2, 0.52604535784, 64.9597385808], [0.191, 4.88786653062, 39.6175083461], [0.233, 3.16423779113, 41.1019810544], [0.248, 5.85877831382, 1059.3819301892], [0.194, 2.37949641473, 73.297125859], [0.227, 0.20028518978, 60.7669528868], [0.184, 3.01962045713, 1014.1353475506], [0.19, 5.57500985081, 343.2185725996], [0.172, 3.66036463613, 477.3308354552], [0.172, 0.59550457102, 46.2097904851], [0.182, 1.92429384025, 183.7640795093], [0.171, 1.61368476689, 357.4456666012], [0.173, 6.23717119485, 493.0424021651], [0.217, 1.46218158211, 71.8126531507], [0.178, 0.34928799031, 1028.3624415522], [0.169, 4.91086673212, 166.5680400911], [0.157, 5.89200571154, 169.5369855077], [0.182, 2.33457064554, 152.5321425512], [0.151, 3.81621340568, 146.594251718], [0.136, 2.75150881988, 144.1465711632], [0.104, 6.03262825314, 529.6909650946], [0.076, 0.20932812381, 453.424893819]], [[31.254, 0.0, 0.0], [12.461, 6.04431418812, 1.4844727083], [14.541, 1.35337075856, 76.2660712756], [11.547, 6.11257808366, 38.1330356378], [1.351, 4.93951495175, 2.9689454166], [0.741, 2.35936954597, 168.0525127994], [0.715, 1.27409542804, 182.279606801], [0.537, 5.23632185196, 484.444382456], [0.523, 4.16769839601, 498.6714764576], [0.664, 0.55871435877, 31.019488637], [0.301, 2.69253200796, 7.1135470008], [0.194, 2.05904114139, 137.0330241624], [0.206, 2.51012178002, 74.7815985673], [0.16, 5.63111039032, 114.3991069134], [0.149, 3.09327713923, 35.1640902212]], [[113.998, 3.14159265359, 0.0], [0.605, 3.18211885677, 76.2660712756]], [[0.874, 3.14159265359, 0.0]]]

This table contains Neptune’s periodic terms (all of them) from the planetary theory VSOP87 for the heliocentric longitude at the equinox of date (taken from the ‘D’ solution). In Meeus’ book a shortened version can be found in pages 452-453.

pymeeus.Neptune.VSOP87_R = [[[3007013206.102, 0.0, 0.0], [27062259.49, 1.3299945893, 38.1330356378], [1691764.281, 3.25186138896, 36.6485629295], [807830.737, 5.18592836167, 1.4844727083], [537760.613, 4.52113902845, 35.1640902212], [495725.642, 1.57105654815, 491.5579294568], [274571.97, 1.84552256801, 175.1660598002], [135134.095, 3.37220607384, 39.6175083461], [121801.825, 5.79754444303, 76.2660712756], [100895.397, 0.37702748681, 73.297125859], [69791.722, 3.79617226928, 2.9689454166], [46687.838, 5.74937810094, 33.6796175129], [24593.778, 0.50801728204, 109.9456887885], [16939.242, 1.59422166991, 71.8126531507], [14229.686, 1.07786112902, 74.7815985673], [12011.825, 1.92062131635, 1021.2488945514], [8394.731, 0.67816895547, 146.594251718], [7571.8, 1.07149263431, 388.4651552382], [5720.852, 2.59059512267, 4.4534181249], [4839.672, 1.9068599107, 41.1019810544], [4483.492, 2.90573457534, 529.6909650946], [4270.202, 3.41343865825, 453.424893819], [4353.79, 0.6798566237, 32.1951448046], [4420.804, 1.74993796503, 108.4612160802], [2881.063, 1.98600105123, 137.0330241624], [2635.535, 3.09755943422, 213.299095438], [3380.93, 0.84810683275, 183.2428146475], [2878.942, 3.67415901855, 350.3321196004], [2306.293, 2.80962935724, 70.3281804424], [2530.149, 5.79839567009, 490.0734567485], [2523.132, 0.48630800015, 493.0424021651], [2087.303, 0.61858378281, 33.9402499438], [1976.522, 5.1170304456, 168.0525127994], [1905.254, 1.72186472126, 182.279606801], [1654.039, 1.92782545887, 145.1097790097], [1435.072, 1.70005157785, 484.444382456], [1403.029, 4.58914203187, 498.6714764576], [1499.193, 1.01623299513, 219.891377577], [1398.86, 0.7622031762, 176.6505325085], [1403.377, 6.07659416908, 173.6815870919], [1128.56, 5.96661179805, 9.5612275556], [1228.304, 1.59881465324, 77.7505439839], [835.414, 3.97066884218, 114.3991069134], [811.186, 3.0025888087, 46.2097904851], [731.925, 2.10447054189, 181.7583419392], [615.781, 2.97874625677, 106.9767433719], [704.778, 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4.62301099402, 1024.217839968], [4.536, 2.45860473853, 496.0113475817], [4.398, 5.65312496227, 3.9321532631], [4.287, 0.66340266603, 1012.6508748423], [4.086, 0.14551174994, 385.2837615005], [4.029, 5.98399329775, 178.3474535379], [4.276, 3.6820508297, 348.8476468921], [5.257, 3.75263242432, 379.8671355291], [4.012, 0.42559540783, 104313.47953065898], [4.025, 2.40645188238, 84.3428261229], [3.957, 0.86846121055, 171.9846660625], [3.961, 3.04953080906, 1017.3167412883], [5.559, 0.77714806229, 1447.8470854274], [5.071, 2.61075526868, 1536.7127656444], [4.052, 5.00014006312, 391.6465489759], [5.182, 4.73444634983, 382.8360809457], [3.763, 4.29449373755, 313.6835566709], [4.038, 2.82857942788, 1661.1461808654], [4.067, 5.7316992896, 169.5369855077], [3.841, 1.6258092842, 0.9632078465], [3.901, 2.70874386576, 14.0146456805], [3.721, 1.20062375429, 1026.8779688439], [3.911, 3.01809123569, 100.3844612329], [3.489, 4.28865448963, 1025.1810478145], [3.714, 5.05021268365, 292.4859280204], [3.816, 3.93084933114, 39.0962434843], [3.988, 2.82832650224, 134.1122628556], [3.745, 4.24728135115, 180.7951340927], [3.836, 1.02685786071, 1018.2799491348], [3.941, 5.21895739331, 183.7640795093], [4.669, 4.38080962573, 1066.49547719], [3.78, 6.03723468132, 1022.7333672597], [3.647, 3.98130320367, 608.877797677], [3.456, 5.54052355058, 846.0828347512], [4.047, 3.71041480907, 1018.0675008137], [3.865, 4.76002199091, 166.5680400911], [3.629, 3.29053233846, 447.7958195265], [3.564, 4.36703678321, 397.0631749473], [3.304, 1.49289552229, 1505.6932770074], [3.976, 2.42476188945, 106.0135355254], [4.217, 4.21677652639, 1052.2683831884], [3.294, 0.42088065654, 22.633917249], [3.615, 3.68096122231, 494.5268748734], [3.23, 5.10786091356, 69.1525242748], [3.28, 3.62226152032, 531.1754378029], [3.337, 2.7250287632, 481.4754370394], [3.187, 0.08677634706, 399.5108555021], [3.389, 1.79454271219, 1519.920371009], [3.179, 3.40418030121, 423.6292454594], [3.154, 3.69356460843, 470.2172884544], [3.706, 2.79048710497, 462.0229135281], [3.136, 4.38015969606, 385.4962098216], [3.122, 0.48346644637, 79.1868325824], [3.392, 0.48037804731, 521.0929453855], [3.465, 0.93152295589, 2183.7235989592], [3.735, 0.98809808606, 487.4133278726], [3.998, 3.38773325131, 6283.0758499914], [2.998, 2.61728063127, 487.6257761937], [3.295, 2.53821501556, 4.665866446], [2.964, 3.66274645375, 495.4900827199], [3.901, 1.65463523144, 210.3301500214], [2.95, 1.99904237956, 872.9095376942], [2.948, 2.90769224206, 391.4341006548], [2.971, 0.31626092637, 5.1078094307], [3.085, 0.95725590904, 109.9456887885], [2.995, 3.34433305798, 394.0942295307], [3.126, 5.89472116854, 105.4922706636], [3.904, 3.01022809543, 556.5176680376], [3.388, 6.24936444215, 535.3200393871], [2.93, 6.15005257333, 164.1203595363], [3.267, 4.19718045293, 518.3846323998], [3.946, 2.8884275967, 151.260118164], [3.076, 6.04134449219, 142.1408335931], [2.823, 0.60712626756, 214.7835681463], [2.917, 2.74502617182, 138.5174968707], [3.347, 6.09373507569, 6246.4272870619], [3.659, 5.12211619716, 79.2350166922], [3.01, 0.24656411754, 91.7864415238], [2.861, 6.17465663902, 422.405405182], [2.989, 2.31620917965, 485.9288551643], [3.088, 2.29186342974, 110.2063212194], [3.03, 3.698661491, 532.6117264014], [3.02, 2.36422658177, 290.2195580194], [3.17, 1.23078934548, 10176.6369832815], [2.652, 3.35836234807, 148.0787244263], [2.673, 6.03366372927, 196.5067008026], [2.63, 0.46957619348, 1970.4245035212], [2.599, 4.86022081674, 439.1977998174], [2.878, 2.61946597178, 488.5889840402], [2.72, 1.71836225398, 364.559213602], [3.333, 3.25126857354, 30.0562807905], [3.053, 2.49346960035, 6243.4583416453], [3.062, 6.23776299963, 419.4846438752], [2.786, 0.83078219939, 497.1870037493], [2.834, 3.52926079424, 457.8783119439], [2.932, 1.80245810977, 500.1559491659], [3.03, 5.10152500393, 367.9701020033], [2.956, 5.76230870725, 986.0848043302], [3.116, 2.20042242739, 495.702531041], [2.554, 0.65945973992, 67.3592350258], [2.901, 3.91891656185, 10173.6680378649], [2.84, 1.34453183591, 482.9599097477], [2.458, 1.20012815574, 489.110248902], [2.556, 3.86921927085, 487.1045113319], [2.614, 1.51881085312, 463.5073862364], [2.386, 4.58400538443, 615.9913446778], [2.438, 5.19827220476, 501.1191570124], [2.537, 1.64802783144, 519.6084726772], [2.444, 3.87859489652, 185.2485522176], [2.795, 4.0426575258, 255.0554677982], [2.895, 3.26202698812, 1646.9190868638], [2.225, 5.75197574692, 605.9570363702], [2.324, 3.99503920129, 481.2629887183], [2.962, 1.74151265966, 2080.6308247406], [2.621, 1.74442251671, 35.212274331]], [[4247.412, 5.89910679117, 38.1330356378], [217.57, 0.3458182908, 1.4844727083], [163.025, 2.2387294713, 168.0525127994], [156.285, 4.59414467342, 182.279606801], [117.94, 5.10295026024, 484.444382456], [112.429, 1.19000583596, 498.6714764576], [127.141, 2.84786298079, 35.1640902212], [99.467, 3.41578558739, 175.1660598002], [64.814, 3.4621406484, 388.4651552382], [77.286, 0.01659281785, 491.5579294568], [49.509, 4.06995509133, 76.2660712756], [39.33, 6.09521855958, 1021.2488945514], [36.45, 5.17130059988, 137.0330241624], [37.08, 5.97288967681, 2.9689454166], [30.484, 3.58259801313, 33.6796175129], [21.099, 0.76843555176, 36.6485629295], [13.886, 3.59248623971, 395.578702239], [13.117, 5.09263515697, 98.8999885246], [11.379, 1.18060018898, 381.3516082374], [9.132, 2.34787658568, 601.7642506762], [8.527, 5.25134685897, 2.4476805548], [8.136, 4.96270726986, 4.4534181249], [7.417, 4.46775409796, 189.3931538018], [7.225, 1.92287508629, 9.5612275556], [7.289, 1.6551952578, 1028.3624415522], [8.076, 5.84268048311, 220.4126424388], [9.654, 0.0, 0.0], [6.554, 0.69397520733, 144.1465711632], [7.782, 1.14341656235, 1059.3819301892], [5.665, 6.25378258571, 74.7815985673], [5.628, 5.23383764266, 46.2097904851], [5.523, 4.59041448911, 1014.1353475506], [5.177, 5.23116646157, 477.3308354552], [5.503, 3.49522319102, 183.7640795093], [4.878, 3.52934357721, 39.6175083461], [4.787, 2.08260524745, 41.1019810544], [5.055, 0.19949888617, 166.5680400911], [4.751, 1.1805494827, 169.5369855077], [4.747, 1.50608965076, 73.297125859], [6.113, 6.18326155595, 71.8126531507], [4.606, 3.91970908886, 587.5371566746], [5.756, 2.23667359233, 176.6505325085], [4.536, 2.84337336954, 7.1135470008], [4.338, 0.51553847388, 446.3113468182], [3.891, 0.26338839265, 1550.939859646], [4.465, 3.01487041298, 129.9194771616], [3.727, 2.37977930658, 160.9389657986], [3.84, 3.7929038188, 111.4301614968], [4.142, 1.70293820961, 983.1158589136], [3.296, 1.07748822909, 505.7850234584], [4.008, 0.30663868827, 494.7393231945], [3.974, 5.9735178384, 488.3765357191], [3.925, 4.85736421123, 60.7669528868], [2.966, 2.01608546009, 822.176893115], [3.972, 1.07780371834, 374.2380612366], [3.843, 5.23002047199, 350.3321196004], [2.848, 6.17799253802, 704.8570248948], [3.527, 0.79317138165, 274.0660483248], [2.828, 1.32275775835, 386.9806825299], [2.773, 5.37132330836, 251.4321310758], [3.113, 5.1262228869, 426.598190876], [3.344, 5.61433537548, 1124.34166877], [2.597, 0.67759426519, 312.1990839626], [2.581, 3.55847612121, 567.8240007324], [2.578, 1.45603792456, 1035.475988553], [2.541, 5.19427579702, 1227.4344429886], [2.51, 4.12148891512, 171.2339065371], [2.511, 2.71606957319, 179.0982130633], [2.342, 0.96469916587, 1019.7644218431], [2.5, 0.7028227603, 707.7777862016], [2.48, 4.59623030219, 693.5506922], [2.253, 0.74334306011, 976.0023119128]], [[166.297, 4.55243893489, 38.1330356378], [22.38, 3.94830879358, 168.0525127994], [21.348, 2.86296778794, 182.279606801], [16.233, 0.54226725872, 484.444382456], [15.623, 5.75702251906, 498.6714764576], [11.867, 4.4028019271, 1.4844727083], [6.448, 5.19003066847, 31.019488637], [3.655, 5.91335292846, 1007.0218005498], [3.681, 1.62865545676, 388.4651552382], [3.198, 0.70197118575, 1558.0534066468], [3.243, 1.8803566598, 522.5774180938], [3.269, 2.94301808574, 76.2660712756], [2.688, 1.87062743473, 402.6922492398], [3.246, 0.79381356193, 536.8045120954], [2.65, 5.76858449026, 343.2185725996], [2.644, 4.64542905401, 500.1559491659], [2.541, 4.79217120822, 482.9599097477], [2.523, 1.7286988978, 395.578702239], [2.69, 2.21096415618, 446.3113468182], [2.355, 5.77381398401, 485.9288551643], [2.874, 6.1964334054, 815.0633461142], [2.278, 3.66579603119, 497.1870037493]], [[4.227, 2.40375758563, 477.3308354552], [4.333, 0.10459484545, 395.578702239], [3.545, 4.78431259422, 1028.3624415522], [3.154, 3.88192942366, 505.7850234584], [3.016, 1.03609346831, 189.3931538018], [2.294, 1.10879658603, 182.279606801], [2.295, 5.67776133184, 168.0525127994]]]

This table contains Neptune’s periodic terms (all of them) from the planetary theory VSOP87 for the radius vector at the equinox of date (taken from the ‘D’ solution). In Meeus’ book a shortened version can be found in page 454.