Mars

Class to model Mars planet.

class pymeeus.Mars.Mars

Class Mars 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 Mars for a given epoch, using the VSOP87 theory.

Parameters:epoch (Epoch) – Epoch to compute Mars 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 = Mars.conjunction(epoch)
>>> y, m, d = conj.get_date()
>>> print(y)
1993
>>> print(m)
12
>>> print(round(d, 4))
27.0898

static geocentric_position(epoch)

This method computes the geocentric position of Mars (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 = Mars.geocentric_position(epoch)
>>> print(ra.ra_str(n_dec=1))
7h 48' 35.4''
>>> print(dec.dms_str(n_dec=1))
24d 35' 33.9''
>>> print(elon.dms_str(n_dec=1))
153d 35' 1.6''

static geometric_heliocentric_position(epoch, tofk5=True)

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

Parameters:

• epoch (Epoch) – Epoch to compute Mars 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 = Mars.geometric_heliocentric_position(epoch)
>>> print(round(l.to_positive(), 4))
2.0015
>>> print(round(b, 4))
-1.3683
>>> print(round(r, 5))
1.39306

static magnitude(sun_dist, earth_dist, phase_angle)

This function computes the approximate magnitude of Mars.

Parameters:

• sun_dist (float) – Distance from Mars to the Sun, in Astronomical Units
• earth_dist (float) – Distance from Mars to Earth, in Astronomical Units
• phase_angle (float, Angle) – Mars phase angle

Returns:

Mars’ 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(2729, 10, 1.0)
>>> oppo = Mars.opposition(epoch)
>>> y, m, d = oppo.get_date()
>>> print(y)
2729
>>> print(m)
9
>>> print(round(d, 4))
9.1412

static orbital_elements_j2000(epoch)

This method computes the orbital elements of Mars 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 = Mars.orbital_elements_j2000(epoch)
>>> print(round(l, 6))
287.94027
>>> print(round(a, 8))
1.52367934
>>> print(round(e, 7))
0.0934599
>>> print(round(i, 6))
1.844381
>>> print(round(ome, 5))
49.36464
>>> print(round(arg, 6))
286.98617

static orbital_elements_mean_equinox(epoch)

This method computes the orbital elements of Mars 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 = Mars.orbital_elements_mean_equinox(epoch)
>>> print(round(l, 6))
288.855211
>>> print(round(a, 8))
1.52367934
>>> print(round(e, 7))
0.0934599
>>> print(round(i, 6))
1.849338
>>> print(round(ome, 5))
50.06365
>>> print(round(arg, 6))
287.202108

static passage_nodes(epoch, ascending=True)

This function computes the time of passage by the nodes (ascending or descending) of Mars, nearest to the given epoch.

Parameters:

• epoch (Epoch) – Epoch closest to the node passage
• ascending (bool) – Whether the time of passage by the ascending (True) or descending (False) node will be computed

Returns:

Tuple containing: - Time of passage through the node (Epoch) - Radius vector when passing through the node (in AU, float)

Return type:

tuple

Raises:

TypeError if input values are of wrong type.

>>> epoch = Epoch(2019, 1, 1)
>>> time, r = Mars.passage_nodes(epoch)
>>> year, month, day = time.get_date()
>>> print(year)
2019
>>> print(month)
1
>>> print(round(day, 1))
15.2
>>> print(round(r, 4))
1.4709

static perihelion_aphelion(epoch, perihelion=True)

This method computes the time of Perihelion (or Aphelion) closer to a given epoch.

Parameters:

• epoch (Epoch) – Epoch close to the desired Perihelion (or Aphelion)
• peihelion – If True, the epoch of the closest Perihelion is computed, if False, the epoch of the closest Aphelion is found.

Returns:

The epoch of the desired Perihelion (or Aphelion)

Return type:

Epoch

Raises:

TypeError if input values are of wrong type.

>>> epoch = Epoch(2019, 2, 23.0)
>>> e = Mars.perihelion_aphelion(epoch)
>>> y, m, d, h, mi, s = e.get_full_date()
>>> print(y)
2018
>>> print(m)
9
>>> print(d)
16
>>> print(h)
12
>>> epoch = Epoch(2032, 1, 1.0)
>>> e = Mars.perihelion_aphelion(epoch, perihelion=False)
>>> y, m, d, h, mi, s = e.get_full_date()
>>> print(y)
2032
>>> print(m)
10
>>> print(d)
24
>>> print(h)
22

static station_longitude_1(epoch)

This method computes the time of the 1st station in longitude (i.e. when the planet is stationary and begins to move westward - retrograde - among the starts) closest to the given epoch.

Parameters:epoch (Epoch) – Epoch close to the desired opposition Returns:Time when the 1st station in longitude 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(1997, 3, 1.0)
>>> sta1 = Mars.station_longitude_1(epoch)
>>> y, m, d = sta1.get_date()
>>> print(y)
1997
>>> print(m)
2
>>> print(round(d, 4))
6.033

static station_longitude_2(epoch)

This method computes the time of the 2nd station in longitude (i.e. when the planet is stationary and begins to move eastward - prograde - among the starts) closest to the given epoch.

Parameters:epoch (Epoch) – Epoch close to the desired opposition Returns:Time when the 2nd station in longitude 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(1997, 3, 1.0)
>>> sta2 = Mars.station_longitude_2(epoch)
>>> y, m, d = sta2.get_date()
>>> print(y)
1997
>>> print(m)
4
>>> print(round(d, 4))
27.7553

pymeeus.Mars.ORBITAL_ELEM = [[355.433, 19141.6964471, 0.00031052, 1.6e-08], [1.523679342, 0.0, 0.0, 0.0], [0.09340065, 9.0484e-05, -8.06e-08, -2.5e-10], [1.849726, -0.0006011, 1.276e-05, -7e-09], [49.558093, 0.7720959, 1.557e-05, 2.267e-06], [336.060234, 1.8410449, 0.00013477, 5.36e-07]]

This table contains the parameters to compute Mars’ orbital elements for the mean equinox of date. Based in Table 31.A, page 212

pymeeus.Mars.ORBITAL_ELEM_J2000 = [[355.433, 19140.2993039, 2.62e-06, -3e-09], [1.849726, -0.0081477, -2.255e-05, -2.9e-08], [49.558093, -0.295025, -0.00064048, -1.964e-06], [336.060234, 0.4439016, -0.00017313, 5.18e-07]]

This table contains the parameters to compute Mars’ orbital elements for the standard equinox J2000.0. Based on Table 31.B, page 214

pymeeus.Mars.VSOP87_B = [[[3197134.986, 3.76832042432, 3340.6124266998], [298033.234, 4.10616996243, 6681.2248533996], [289104.742, 0.0, 0.0], [31365.538, 4.44651052853, 10021.8372800994], [3484.1, 4.78812547889, 13362.4497067992], [442.999, 5.65233015876, 3337.0893083508], [443.401, 5.02642620491, 3344.1355450488], [399.109, 5.130568147, 16703.062133499], [292.506, 3.79290644595, 2281.2304965106], [181.982, 6.13648011704, 6151.533888305], [163.159, 4.26399626634, 529.6909650946], [159.678, 2.23194610246, 1059.3819301892], [139.323, 2.41796344238, 8962.4553499102], [149.297, 2.16501209917, 5621.8429232104], [142.686, 1.1821501611, 3340.5951730476], [142.685, 3.2129218082, 3340.629680352], [82.544, 5.36667872319, 6684.7479717486], [73.64, 5.09187524843, 398.1490034082], [72.66, 5.53775710437, 6283.0758499914], [86.377, 5.74429648412, 3738.761430108], [83.276, 5.98866315739, 6677.7017350506], [60.116, 3.67960808826, 796.2980068164], [63.111, 0.73049113369, 5884.9268465832], [62.338, 4.85071999184, 2942.4634232916], [46.951, 5.54339723804, 3340.545116397], [46.953, 5.13486627234, 3340.6797370026], [46.63, 5.47361665459, 20043.6745601988], [45.588, 2.13262507507, 2810.9214616052], [41.269, 0.20003189001, 9492.1463150048], [47.199, 4.52184736343, 3149.1641605882], [38.54, 4.08008443274, 4136.9104335162], [33.069, 4.06581918329, 1751.539531416], [29.694, 5.92218297386, 3532.0606928114], [32.736, 2.62071056958, 2914.0142358238], [29.521, 2.75342566734, 12303.06777661], [28.169, 2.06282533993, 5486.777843175], [28.618, 4.94710527914, 3870.3033917944], [26.603, 3.5508584402, 6681.2421070518], [26.603, 1.52008675291, 6681.2075997474], [23.336, 2.27624532707, 1589.0728952838], [26.052, 2.60064548916, 4399.994356889], [22.637, 2.27507466406, 1194.4470102246], [18.887, 6.04416196149, 7079.3738568078], [14.846, 3.41358603159, 5088.6288397668], [19.947, 2.67365368471, 8432.7643848156], [14.682, 5.89211938785, 9623.6882766912], [14.152, 2.42512744356, 3333.498879699], [13.31, 2.62839773036, 426.598190876], [14.008, 1.67425558329, 6254.6266625236], [15.104, 2.81013535571, 3496.032826134], [13.011, 5.70759434129, 10025.3603984484], [12.08, 1.51804981987, 3185.1920272656], [13.183, 0.04521207632, 10018.3141617504], [11.554, 5.5741897182, 191.4482661116], [11.196, 0.55829576311, 5092.1519581158], [11.53, 2.13314819584, 11773.3768115154], [10.435, 5.72414012635, 6467.9257579616], [9.846, 0.86942245495, 1592.5960136328], [9.761, 1.0934228866, 2544.3144198834], [8.754, 5.47281660412, 6681.2921637024], [8.937, 4.8379038561, 6489.776587288], [8.652, 4.72118876809, 213.299095438], [8.797, 2.86597575792, 3341.592747768], [8.384, 2.65895230037, 4535.0594369244], [8.213, 4.8260813471, 3553.9115221378], [8.799, 1.52910882795, 3339.6321056316], [8.103, 1.00994045172, 9225.539273283], [8.754, 5.88131160438, 6681.1575430968], [7.209, 4.41679446871, 7477.522860216], [8.56, 4.79003986337, 4690.4798363586], [6.087, 1.89071507516, 9595.2390892234], [6.974, 0.53246284561, 12832.7587417046], [5.584, 6.18909308524, 4292.3308329504], [5.038, 6.06393121994, 7210.9158184942], [5.126, 0.11856805, 4562.4609930212], [4.863, 1.33051301524, 3894.1818295422], [5.592, 3.97792577165, 3127.3133312618], [4.965, 5.74589127183, 1990.745017041], [5.53, 5.81711987294, 23384.2869868986], [4.184, 3.88899446923, 10021.8545337516], [4.184, 1.8582188554, 10021.8200264472], [4.685, 1.11750235736, 3319.8370312074], [3.954, 2.65573703692, 4929.6853219836], [5.174, 3.62343554596, 2700.7151403858], [4.639, 6.14089337232, 7.1135470008], [4.686, 3.27731664264, 3361.3878221922], [4.999, 3.09121636067, 15643.6802033098], [3.919, 2.96552252075, 7740.6067835888], [3.361, 1.85016770821, 2957.7158944766], [4.246, 4.1963927863, 2146.1654164752], [4.101, 6.22532797325, 10213.285546211], [3.124, 0.08536218671, 10419.9862835076], [3.079, 2.41163389513, 3344.2028553516], [3.093, 1.98041729732, 3337.021998048], [3.044, 4.38894419912, 1221.8485663214], [2.879, 2.93292197885, 2787.0430238574], [3.372, 4.45558202843, 6674.1113063988], [2.51, 4.06249795775, 6872.6731195112], [2.616, 1.23659420897, 4933.2084403326], [3.011, 4.33965766608, 2388.8940204492], [3.094, 2.40385309455, 2118.7638603784], [2.516, 2.30275910483, 3723.508958923], [2.192, 1.688775987, 639.897286314], [2.157, 6.07600403318, 9808.5381846614], [2.686, 2.38172448359, 15113.9892382152], [2.156, 2.87771528495, 6041.3275670856], [2.495, 3.87395320804, 7903.073419721], [2.253, 0.47469626036, 3475.6775067352], [2.443, 3.02632351975, 3767.2106175758], [1.937, 0.38000997629, 13358.9265884502], [2.213, 3.9198232636, 3205.5473466644], [2.385, 6.23883456815, 12964.300703391], [1.806, 2.38408432339, 11243.6858464208], [2.265, 1.8577388518, 6525.8044539654], [1.642, 1.86812936557, 6680.2445323314], [1.616, 3.39954231101, 8429.2412664666], [1.646, 0.73261192032, 2274.1169495098], [1.91, 6.04319894051, 13365.9728251482], [1.492, 2.9936092905, 7875.6718636242], [1.567, 1.76860259924, 382.8965322232], [1.459, 1.40571286543, 14584.2982731206], [1.527, 5.79343536555, 6894.5239488376], [1.409, 5.17099876287, 9830.3890139878], [1.665, 3.60183854165, 2288.3440435114], [1.616, 2.1944777548, 8827.3902698748], [1.746, 0.10485504333, 3583.3410306738], [1.637, 3.20410489018, 6682.2051744678], [1.269, 2.02253791623, 155.4203994342], [1.507, 5.80795976424, 1748.016413067], [1.296, 2.92899986522, 9381.9399937854], [1.291, 2.98932404463, 6836.6452528338], [1.377, 5.8098082145, 10021.9045904022], [1.357, 0.32856318286, 4032.7700279266], [1.377, 6.21830533138, 10021.7699697966], [1.227, 2.20421067322, 12935.8515159232], [1.08, 4.75502761725, 10818.1352869158], [1.016, 1.33950348904, 12566.1516999828], [1.083, 0.87622049125, 16173.3711684044], [0.957, 5.29505019432, 1066.49547719], [1.035, 2.44286811558, 1052.2683831884], [1.153, 4.73786864168, 8031.0922630584], [1.042, 1.73541825729, 3369.0616141676], [0.899, 1.87265511538, 3077.528503327], [0.892, 2.51347636401, 3603.6963500726], [0.904, 0.27361540197, 3325.3599555148], [0.883, 5.4653793674, 5614.7293762096], [0.949, 0.04595688771, 7064.1213856228], [0.872, 3.61205859852, 6702.000248892], [0.842, 5.61713543212, 8955.3418029094], [0.842, 0.57536275896, 3191.0492295652], [0.904, 4.11832249537, 3355.8648978848], [1.044, 2.6588954211, 3312.163239232], [0.807, 2.2644325982, 8969.568896911], [1.046, 6.11317298058, 5331.3574437408], [0.933, 0.82551054416, 3503.079062832], [0.946, 1.92368414869, 5628.9564702112], [0.978, 4.55697167317, 3097.88382272579], [0.846, 4.65096242323, 6438.4962494256], [0.901, 1.46788821922, 6660.4494579072], [0.739, 4.97716008834, 10014.7237330986], [0.762, 3.42576079312, 18984.2926300096], [0.934, 0.35014113954, 3264.3463554242], [0.894, 0.34991139502, 10551.528245194], [0.665, 6.05561837558, 7632.9432596502], [0.605, 4.68480399923, 5729.506447149], [0.593, 2.97207045977, 3178.1457905676], [0.617, 2.19529512598, 13362.432453147], [0.579, 3.32303439858, 11081.2192102886], [0.579, 2.31217959727, 6677.6344247478], [0.572, 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[0.744, 0.50445805257, 6681.2248533996], [0.148, 1.05056602649, 10021.8372800994], [0.102, 2.66185835593, 3496.032826134], [0.053, 5.27888218929, 3337.0893083508], [0.022, 4.09971603267, 3097.88382272579], [0.023, 1.7242234213, 3185.1920272656], [0.013, 5.41704779112, 16703.062133499], [0.013, 2.06957065662, 13362.4497067992], [0.01, 0.959895956, 3894.1818295422]], [[0.457, 4.86794125358, 3340.6124266998], [0.053, 5.30547050586, 6681.2248533996], [0.012, 5.75114070583, 10021.8372800994], [0.013, 4.17736925293, 3496.032826134], [0.007, 0.0, 0.0]]]

This table contains Mars’ periodic terms (all of them) from the planetary theory VSOP87 for the heliocentric latitude at the equinox of date (taken from the ‘D’ solution). In Meeus’ book a shortened version can be found in pages 424-425.

pymeeus.Mars.VSOP87_L = [[[620347711.583, 0.0, 0.0], [18656368.1, 5.05037100303, 3340.6124266998], [1108216.792, 5.40099836958, 6681.2248533996], [91798.394, 5.75478745111, 10021.8372800994], [27744.987, 5.97049512942, 3.523118349], [10610.23, 2.93958524973, 2281.2304965106], [12315.897, 0.84956081238, 2810.9214616052], [8926.772, 4.15697845939, 0.0172536522], [8715.688, 6.11005159792, 13362.4497067992], [6797.552, 0.36462243626, 398.1490034082], [7774.867, 3.33968655074, 5621.8429232104], [3575.079, 1.66186540141, 2544.3144198834], [4161.101, 0.2281497533, 2942.4634232916], [3075.25, 0.85696597082, 191.4482661116], [2628.122, 0.6480614357, 3337.0893083508], [2937.543, 6.07893711408, 0.0673103028], [2389.42, 5.03896401349, 796.2980068164], [2579.842, 0.02996706197, 3344.1355450488], [1528.14, 1.14979306228, 6151.533888305], [1798.808, 0.65634026844, 529.6909650946], [1264.356, 3.62275092231, 5092.1519581158], [1286.232, 3.06795924626, 2146.1654164752], [1546.408, 2.91579633392, 1751.539531416], [1024.907, 3.69334293555, 8962.4553499102], [891.567, 0.1829389909, 16703.062133499], [858.76, 2.40093704204, 2914.0142358238], [832.718, 2.46418591282, 3340.5951730476], [832.724, 4.49495753458, 3340.629680352], [712.899, 3.66336014788, 1059.3819301892], [748.724, 3.82248399468, 155.4203994342], [723.863, 0.67497565801, 3738.761430108], [635.557, 2.92182704275, 8432.7643848156], [655.163, 0.48864075176, 3127.3133312618], [550.472, 3.81001205408, 0.9803210682], [552.746, 4.47478863016, 1748.016413067], [425.972, 0.55365138172, 6283.0758499914], [415.132, 0.49662314774, 213.299095438], [472.164, 3.6254781941, 1194.4470102246], [306.552, 0.38052862973, 6684.7479717486], [312.141, 0.99853322843, 6677.7017350506], [293.199, 4.22131277914, 20.7753954924], [302.377, 4.48618150321, 3532.0606928114], [274.028, 0.54222141841, 3340.545116397], [281.073, 5.88163372945, 1349.8674096588], [231.185, 1.28240685294, 3870.3033917944], [283.6, 5.76885494123, 3149.1641605882], [236.114, 5.75504515576, 3333.498879699], [274.035, 0.13372501211, 3340.6797370026], [299.396, 2.78323705697, 6254.6266625236], [204.161, 2.82133266185, 1221.8485663214], [238.857, 5.37155471672, 4136.9104335162], [188.639, 1.49103016486, 9492.1463150048], [221.225, 3.50466672203, 382.8965322232], [179.196, 1.00561112574, 951.7184062506], [172.11, 0.43943041719, 5486.777843175], [193.126, 3.35715137745, 3.5904286518], [144.305, 1.41874193418, 135.0650800354], [160.011, 3.94854735192, 4562.4609930212], [174.068, 2.41360332576, 553.5694028424], [130.993, 4.04491720264, 12303.06777661], [138.245, 4.30145176915, 7.1135470008], [128.062, 1.80665643332, 5088.6288397668], [139.897, 3.32592516164, 2700.7151403858], [128.102, 2.20806651008, 1592.5960136328], [116.945, 3.12805282207, 7903.073419721], [110.375, 1.05195079687, 242.728603974], [113.486, 3.70070798123, 1589.0728952838], [100.09, 3.24343740861, 11773.3768115154], [95.592, 0.53954181149, 20043.6745601988], [98.947, 4.8455829474, 6681.2421070518], [104.541, 0.78535382076, 8827.3902698748], [84.187, 3.9897072073, 4399.994356889], [86.931, 2.20186740523, 11243.6858464208], [71.437, 2.80307550016, 3185.1920272656], [72.091, 5.84672102525, 5884.9268465832], [73.476, 2.18428012567, 8429.2412664666], [98.946, 2.81481140371, 6681.2075997474], [68.414, 2.73834914412, 2288.3440435114], [86.751, 1.02092221563, 7079.3738568078], [65.32, 2.68118597578, 28.4491874678], [83.749, 3.2025613099, 4690.4798363586], [75.034, 0.76643418252, 6467.9257579616], [68.984, 3.76399731788, 6041.3275670856], [66.706, 0.73630620766, 3723.508958923], [63.314, 4.5277147047, 426.598190876], [61.683, 6.16831509419, 2274.1169495098], [52.256, 0.89941531307, 9623.6882766912], [55.488, 4.6062546702, 4292.3308329504], [51.332, 4.14823636534, 3341.592747768], [56.629, 5.06250410206, 15.252471185], [63.376, 0.91296240798, 3553.9115221378], [45.829, 0.78784235062, 1990.745017041], [48.542, 3.95670418719, 4535.0594369244], [41.223, 6.02019329922, 3894.1818295422], [41.939, 3.58326425115, 8031.0922630584], [56.396, 1.68727150304, 6872.6731195112], [55.909, 3.46260833495, 263.0839233728], [51.678, 2.81307492682, 3339.6321056316], [40.671, 3.13832621829, 9595.2390892234], [38.107, 0.7340194632, 10025.3603984484], [39.495, 5.6322539216, 3097.88382272579], [44.174, 3.19529736702, 5628.9564702112], [36.716, 2.63720775102, 692.1576012268], [45.905, 0.28718981497, 5614.7293762096], [38.352, 5.82880707426, 3191.0492295652], [38.206, 2.34835984063, 162.4666361322], [32.562, 0.48400659333, 6681.2921637024], [37.135, 0.68508150774, 2818.035008606], [31.168, 3.98160912982, 20.3553193988], [32.561, 0.89250316888, 6681.1575430968], [37.752, 4.15482955299, 2803.8079146044], [33.626, 6.11992401052, 6489.776587288], [29.007, 2.42707385674, 3319.8370312074], [38.79, 1.35198498795, 10018.3141617504], [33.148, 1.14023770004, 5.5229243074], [27.584, 1.59691203058, 7210.9158184942], [28.686, 5.72055456734, 7477.522860216], [34.031, 2.59544082509, 11769.8536931664], [25.38, 0.52093116112, 10.6366653498], [26.357, 1.34532646574, 3496.032826134], [24.554, 4.00323183088, 11371.7046897582], [25.637, 0.2496352342, 522.5774180938], [27.278, 4.55645328122, 3361.3878221922], [23.764, 1.84058377256, 12832.7587417046], [22.816, 3.52628212106, 1648.4467571974], [22.274, 0.72106133721, 266.6070417218], [21.202, 3.11824472284, 2957.7158944766], [20.158, 3.67131504946, 1758.6530784168], [21.53, 6.15388757177, 3264.3463554242], [20.093, 1.08247416065, 7064.1213856228], [21.343, 4.28218757863, 4032.7700279266], [27.54, 6.08389942337, 6674.1113063988], [19.849, 2.37668920745, 10713.9948813262], [25.512, 3.43242352804, 3443.7052009184], [22.542, 5.64861703438, 2388.8940204492], [24.378, 0.96994696413, 632.7837393132], [23.079, 4.74990214223, 3347.7259737006], [17.709, 3.69742343974, 3344.2028553516], [22.662, 3.95446324417, 4989.0591838972], [22.604, 5.24082917494, 3205.5473466644], [16.811, 5.48619684111, 3.881335358], [18.422, 4.22535881468, 2787.0430238574], [22.737, 4.98520896596, 7632.9432596502], [16.648, 2.52823633184, 14584.2982731206], [20.963, 4.27878216453, 5099.2655051166], [16.042, 1.76786752521, 3475.6775067352], [15.816, 3.13240869691, 59.3738619136], [18.113, 3.25756020453, 3337.021998048], [19.295, 3.23911854642, 7.046236698], [16.772, 4.3973150711, 15643.6802033098], [17.555, 4.09197396097, 74.7815985673], [13.704, 2.5411701816, 4933.2084403326], [16.011, 1.54669633224, 14054.607308026], [13.547, 4.04152185347, 4929.6853219836], [14.566, 3.45210993051, 7373.3824546264], [13.926, 5.40797129468, 10973.55568635], [14.246, 0.59808746067, 23.8784377478], [14.023, 1.44218648988, 10404.7338123226], [16.051, 3.79409950488, 2118.7638603784], [13.714, 3.59050634457, 15113.9892382152], [18.038, 4.25391532, 2487.4160449478], [15.846, 0.56901288692, 103.0927742186], [13.403, 5.16920432994, 10213.285546211], [16.069, 2.36895958451, 3265.8308281325], [12.773, 0.10483085657, 7234.794256242], [12.199, 1.73079687044, 36.0278666774], [12.283, 5.19940030635, 10021.8545337516], [11.945, 5.47997890162, 2921.1277828246], [11.89, 4.76593905835, 5828.0284716476], [12.283, 3.16862882612, 10021.8200264472], [13.274, 6.1780690534, 1744.4259844152], [11.777, 5.727315509, 0.42007609361], [12.34, 2.52146766331, 2906.900688823], [14.458, 4.38010658432, 316.3918696566], [10.639, 3.45016942919, 639.897286314], [10.925, 0.60397688999, 5085.038411115], [10.645, 5.47696728127, 419.4846438752], [10.797, 1.37191539718, 10419.9862835076], [10.565, 1.09061610786, 12168.0026965746], [9.578, 4.89489266197, 3230.4061054804], [9.808, 5.83632873998, 14314.1681130498], [9.72, 6.28282606427, 9225.539273283], [9.146, 1.10220667397, 9808.5381846614], [12.733, 1.79883375851, 13745.3462390224], [9.779, 3.60056884868, 206.1855484372], [12.156, 4.42295240981, 14712.317116458], [8.801, 3.97218590685, 170.6728706192], [10.685, 4.33894776374, 7740.6067835888], [10.041, 1.3829466683, 3583.3410306738], [8.499, 4.29275471153, 0.4298831267], [9.882, 2.69148019691, 36.6053653042], [10.585, 0.89641284928, 23384.2869868986], [8.478, 2.86886131803, 9381.9399937854], [9.56, 4.33382353581, 131.5419616864], [8.433, 3.1523973397, 6525.8044539654], [7.517, 1.24476310635, 6894.5239488376], [6.753, 1.58869332894, 6836.6452528338], [6.666, 4.38910103043, 66.4874089144], [6.697, 5.77315870484, 5202.3582793352], [6.188, 1.5784796785, 3325.3599555148], [8.392, 2.90734956761, 43.718912305], [6.427, 6.03333185624, 574.3447983348], [6.296, 0.06976040737, 1964.838626854], [6.144, 5.43713363624, 1861.7458526354], [8.18, 0.43967386003, 2707.8286873866], [6.532, 1.24907069366, 12964.300703391], [7.341, 4.95693808975, 3767.2106175758], [6.134, 3.16322441707, 6680.2445323314], [5.937, 4.22752447794, 4459.3682188026], [5.848, 4.30379700916, 7875.6718636242], [5.895, 0.77226207039, 2699.7348193176], [5.962, 3.01318151415, 3369.0616141676], [6.307, 1.77830983983, 2178.137722292], [6.103, 4.49866000852, 6682.2051744678], [5.77, 0.96127853878, 13916.0191096416], [5.725, 4.93042706875, 2384.3232707292], [7.576, 6.16308742022, 6531.661656265], [7.285, 0.52756973131, 10575.4066829418], [5.212, 3.48999909365, 12935.8515159232], [5.266, 4.51201042373, 6144.4203413042], [6.632, 3.48100908925, 1118.7557921028], [5.182, 3.25459432228, 2391.43681773], [5.214, 0.01023839897, 533.2140834436], [5.436, 6.18510045571, 8425.6508378148], [5.491, 3.42235890731, 3134.4268782626], [5.773, 3.55190490896, 8969.568896911], [5.093, 0.60873962999, 8955.3418029094], [4.798, 4.63144694279, 4569.574540022], [5.773, 5.92316959013, 640.8776073822], [5.661, 0.75892958537, 3120.199784261], [4.912, 1.70762118141, 13358.9265884502], [5.438, 4.29256867866, 3503.079062832], [4.631, 3.34058594066, 3116.2676309979], [5.823, 2.39009621568, 3302.479391062], [5.095, 1.12497131307, 5331.3574437408], [4.409, 1.3870873295, 17256.6315363414], [4.193, 0.19116539271, 9830.3890139878], [4.164, 0.43798301495, 1066.49547719], [4.22, 1.69427060019, 13524.9163429314], [5.192, 3.63500646439, 536.8045120954], [5.664, 0.50446281443, 5305.4510535538], [5.264, 5.40031180025, 3355.8648978848], [5.403, 5.96867227489, 3074.005384978], [4.046, 0.83826342101, 10021.9045904022], [4.153, 3.14497570817, 8439.8779318164], [4.82, 1.09025983917, 13365.9728251482], [4.906, 3.73078406569, 1228.9621133222], [4.576, 0.99344843456, 6158.6474353058], [4.211, 3.87091723842, 3312.163239232], [4.917, 6.25051681717, 17654.7805397496], [3.597, 6.07298181151, 10818.1352869158], [3.547, 1.87663674277, 17395.2197347258], [3.734, 1.37011069213, 3973.396166013], [4.422, 2.89974680697, 6247.5131155228], [3.975, 4.03441621102, 1052.2683831884], [4.466, 4.59188422424, 5518.7501489918], [3.445, 4.26610076208, 3178.1457905676], [3.607, 4.24527056399, 8329.671610597], [3.511, 1.95133364438, 10177.2576795336], [3.3, 0.68865737747, 149.5631971346], [3.235, 3.90171358031, 27.4015560968], [3.946, 5.81982010903, 6261.7402095244], [3.387, 0.14377701728, 10014.7237330986], 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[0.013, 1.38424462832, 3340.6797370026], [0.012, 3.28248484262, 8671.9698704406], [0.014, 0.23027665815, 3767.2106175758]], [[113.969, 3.14159265359, 0.0], [28.725, 5.63662412043, 6681.2248533996], [24.447, 5.13868481454, 3340.6124266998], [11.187, 6.03161074431, 10021.8372800994], [3.19, 3.56267988299, 155.4203994342], [3.252, 0.13228350651, 13362.4497067992], [0.787, 0.49340783377, 16703.062133499], [0.776, 1.31734531594, 242.728603974], [0.494, 3.06356214498, 3185.1920272656], [0.374, 2.15785846355, 553.5694028424], [0.331, 6.23159792887, 3.523118349], [0.197, 0.44350153983, 3344.1355450488], [0.181, 0.81531283571, 20043.6745601988], [0.168, 3.73509781785, 3496.032826134], [0.086, 0.79259553758, 6684.7479717486], [0.115, 1.66898531261, 3583.3410306738], [0.092, 3.40530361815, 6525.8044539654], [0.064, 4.47443580658, 2787.0430238574], [0.045, 5.17216217058, 3097.88382272579], [0.041, 1.21875027733, 23384.2869868986], [0.036, 5.53975653407, 3149.1641605882], [0.039, 5.40966345885, 4136.9104335162], [0.028, 4.85378781404, 6127.6554505572], [0.027, 0.42811091036, 3738.761430108], [0.032, 1.22337093927, 10025.3603984484], [0.025, 1.56348878811, 26724.8994135984], [0.029, 2.40178626971, 3894.1818295422], [0.023, 4.16371253947, 3341.592747768], [0.022, 5.98429191667, 7477.522860216], [0.019, 2.03228980685, 6923.9534573736], [0.02, 3.79275573433, 9866.4168806652], [0.021, 4.27532111122, 6836.6452528338], [0.015, 1.56315497374, 13365.9728251482], [0.011, 1.33261955275, 2281.2304965106], [0.009, 6.15390464542, 6489.776587288], [0.007, 4.23894194106, 4535.0594369244]], [[0.71, 4.04089996521, 6681.2248533996], [0.868, 3.14159265359, 0.0], [0.51, 4.49214901625, 10021.8372800994], [0.357, 5.07435505061, 155.4203994342], [0.223, 3.51351884241, 3340.6124266998], [0.199, 4.85313666795, 13362.4497067992], [0.1, 6.09089356066, 242.728603974], [0.069, 5.19017483537, 16703.062133499], [0.064, 1.55783055571, 3185.1920272656], [0.035, 3.68246171643, 553.5694028424], [0.025, 5.22079788019, 3496.032826134], [0.024, 0.17861991485, 3583.3410306738], [0.019, 5.5918471446, 20043.6745601988], [0.014, 5.95565787085, 23384.2869868986], [0.012, 1.93859256739, 6525.8044539654]]]

This table contains Mars’ 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 421-424.

pymeeus.Mars.VSOP87_R = [[[153033488.276, 0.0, 0.0], [14184953.153, 3.47971283519, 3340.6124266998], [660776.357, 3.81783442097, 6681.2248533996], [46179.117, 4.15595316284, 10021.8372800994], [8109.738, 5.55958460165, 2810.9214616052], [7485.315, 1.77238998069, 5621.8429232104], [5523.193, 1.3643631888, 2281.2304965106], [3825.16, 4.49407182408, 13362.4497067992], [2306.539, 0.09081742493, 2544.3144198834], [1999.399, 5.36059605227, 3337.0893083508], [2484.385, 4.92545577893, 2942.4634232916], [1960.198, 4.74249386323, 3344.1355450488], [1167.115, 2.11261501155, 5092.1519581158], [1102.828, 5.0090826416, 398.1490034082], [899.077, 4.40790433994, 529.6909650946], [992.252, 5.83862401067, 6151.533888305], [807.348, 2.10216647104, 1059.3819301892], [797.91, 3.44839026172, 796.2980068164], [740.98, 1.49906336892, 2146.1654164752], [692.34, 2.13378814785, 8962.4553499102], [633.144, 0.89353285018, 3340.5951730476], [725.583, 1.24516913473, 8432.7643848156], [633.14, 2.92430448169, 3340.629680352], [574.352, 0.82896196337, 2914.0142358238], [526.187, 5.38292276228, 3738.761430108], [629.976, 1.28738135858, 1751.539531416], [472.776, 5.19850457873, 3127.3133312618], [348.095, 4.83219198908, 16703.062133499], [283.702, 2.90692294913, 3532.0606928114], [279.552, 5.25749247548, 6283.0758499914], [233.827, 5.10546492529, 5486.777843175], [219.428, 5.58340248784, 191.4482661116], [269.891, 3.76394728622, 5884.9268465832], [208.333, 5.25476080773, 3340.545116397], [275.224, 2.90818883832, 1748.016413067], [275.501, 1.21767967781, 6254.6266625236], [239.133, 2.03669896238, 1194.4470102246], [223.19, 4.19861593779, 3149.1641605882], [182.686, 5.08062683355, 6684.7479717486], [186.213, 5.69871555748, 6677.7017350506], [175.995, 5.95341786369, 3870.3033917944], [178.613, 4.18423025538, 3333.498879699], [208.336, 4.84626442122, 3340.6797370026], [228.128, 3.2552902062, 6872.6731195112], [144.286, 0.21296012258, 5088.6288397668], [163.534, 3.79889068111, 4136.9104335162], [133.12, 1.5391010671, 7903.073419721], [141.759, 2.47790321309, 4562.4609930212], [114.941, 4.31745088059, 1349.8674096588], [118.781, 2.12178071222, 1589.0728952838], [102.096, 6.18138550087, 9492.1463150048], [128.555, 5.49883294915, 8827.3902698748], [111.538, 0.55339169625, 11243.6858464208], [82.498, 1.6222704459, 11773.3768115154], [83.212, 0.61553380568, 8429.2412664666], [84.47, 0.6227459311, 1592.5960136328], [86.659, 1.74988330093, 2700.7151403858], [71.826, 2.47489899385, 12303.06777661], [85.312, 1.61621097912, 4690.4798363586], [63.641, 2.67334126661, 426.598190876], [68.599, 2.40197828418, 4399.994356889], [58.559, 4.72052787516, 213.299095438], [62.015, 1.10065866221, 1221.8485663214], [66.509, 2.21307705185, 6041.3275670856], [55.811, 1.23288325946, 3185.1920272656], [54.989, 5.72691385306, 951.7184062506], [52.418, 3.02366828926, 4292.3308329504], [55.686, 5.44686699242, 3723.508958923], [58.959, 3.26242666052, 6681.2421070518], [44.629, 2.0147364039, 8031.0922630584], [58.959, 1.23165502899, 6681.2075997474], [42.444, 2.26551590902, 155.4203994342], [38.956, 2.57760416009, 3341.592747768], [51.561, 5.72326937712, 7079.3738568078], [48.939, 5.61614696751, 3553.9115221378], [45.414, 5.43290921705, 6467.9257579616], [36.435, 4.43921812388, 3894.1818295422], [35.98, 1.15966567007, 2288.3440435114], [35.265, 5.49029710802, 1990.745017041], [42.191, 1.6325374276, 5628.9564702112], [44.292, 5.0034136685, 5614.7293762096], [33.623, 5.17029029766, 20043.6745601988], [43.256, 1.03732072925, 11769.8536931664], [39.237, 1.24237122859, 3339.6321056316], [31.943, 4.59258406791, 2274.1169495098], [30.345, 2.4417767013, 11371.7046897582], [32.259, 2.38215172582, 4535.0594369244], [31.87, 4.37521442752, 3.523118349], [29.35, 4.06034813442, 3097.88382272579], [31.972, 1.93970478412, 382.8965322232], [26.166, 5.58466944895, 9623.6882766912], [27.904, 4.25805969214, 3191.0492295652], [33.065, 0.85467740581, 553.5694028424], [27.543, 1.57668567401, 9595.2390892234], [25.159, 0.81355213242, 10713.9948813262], [22.07, 0.85747723964, 3319.8370312074], [24.772, 5.38970742761, 2818.035008606], [23.359, 6.01453778225, 3496.032826134], [24.732, 2.58034797703, 2803.8079146044], [19.365, 5.18528750472, 6681.2921637024], [19.122, 5.41968559451, 10025.3603984484], [19.364, 5.59378382138, 6681.1575430968], [18.33, 5.7956732424, 7064.1213856228], [18.193, 5.61307426173, 7.1135470008], [20.392, 4.53637816869, 6489.776587288], [21.26, 6.19160142215, 14054.607308026], [17.094, 1.55004739305, 2957.7158944766], [22.791, 3.41709388606, 7632.9432596502], [20.585, 2.98697279083, 3361.3878221922], [18.005, 2.81431094394, 4032.7700279266], [17.049, 6.15528099726, 10404.7338123226], [16.488, 3.84534700818, 10973.55568635], [16.052, 0.92823508003, 14584.2982731206], [21.027, 2.38474290907, 4989.0591838972], [16.267, 1.92321585819, 7373.3824546264], [16.291, 6.28233085307, 7210.9158184942], [18.585, 4.07325116588, 2388.8940204492], [15.977, 4.58368417141, 3264.3463554242], [19.913, 2.7351844595, 5099.2655051166], [19.661, 1.86285979, 3443.7052009184], [16.5, 4.14061745086, 7477.522860216], [19.495, 6.03778234182, 10018.3141617504], [15.104, 2.65433427561, 2787.0430238574], [19.099, 0.22623441108, 13745.3462390224], [17.163, 3.18825562972, 3347.7259737006], [13.423, 2.12818658793, 3344.2028553516], [15.41, 2.2077350796, 2118.7638603784], [17.238, 3.67067776368, 3205.5473466644], [13.113, 4.27490214998, 14314.1681130498], [16.451, 2.86641622696, 14712.317116458], [13.734, 1.68629769646, 3337.021998048], [16.659, 4.52130808861, 6674.1113063988], [11.83, 0.19684525299, 3475.6775067352], [11.767, 3.22897247987, 5828.0284716476], [11.886, 4.82057654742, 7234.794256242], [10.609, 1.73997337551, 639.897286314], [11.154, 0.23859830185, 12832.7587417046], [11.03, 0.4454170644, 10213.285546211], [10.24, 5.74758340632, 242.728603974], [10.051, 2.45102946726, 4929.6853219836], [10.061, 0.78907665448, 9381.9399937854], [10.065, 5.37506605762, 5085.038411115], [11.902, 0.79897698904, 3265.8308281325], [8.99, 0.96463418322, 4933.2084403326], [8.97, 4.18326774405, 9225.539273283], [8.982, 1.98501418026, 15113.9892382152], [8.324, 1.93694866513, 1648.4467571974], [7.833, 2.04997447879, 1758.6530784168], [7.957, 3.92331072722, 2921.1277828246], [10.224, 2.66497189021, 2487.4160449478], [8.277, 0.94860765546, 2906.900688823], [7.371, 0.84378341481, 692.1576012268], [7.545, 5.68031160782, 13916.0191096416], [7.912, 2.81294761885, 15643.6802033098], [6.958, 3.32193127272, 3230.4061054804], [7.426, 6.09656283295, 3583.3410306738], [6.402, 4.19806996774, 5202.3582793352], [6.529, 6.1192925271, 135.0650800354], [6.13, 0.00117252232, 6836.6452528338], [6.226, 6.10683955669, 17256.6315363414], [8.193, 5.24811458833, 10575.4066829418], [6.168, 3.60069207439, 10021.8545337516], [6.169, 1.56992114335, 10021.8200264472], [5.671, 0.1365030666, 13524.9163429314], [6.257, 4.50450768937, 8425.6508378148], [5.249, 2.70122358603, 4459.3682188026], [6.479, 2.74267498287, 7740.6067835888], [5.53, 6.06408145092, 10419.9862835076], [5.536, 5.74996063243, 12168.0026965746], [6.826, 4.69327545839, 17654.7805397496], [5.005, 4.68382632238, 522.5774180938], [6.328, 3.31896726895, 3767.2106175758], [4.734, 0.00755678425, 3325.3599555148], [5.032, 2.33696685608, 1052.2683831884], [4.661, 5.15051711401, 1066.49547719], [4.724, 5.77956037309, 9808.5381846614], [5.136, 1.57259709878, 6525.8044539654], [4.522, 1.44218620352, 3369.0616141676], [6.189, 4.58996159356, 6531.661656265], [6.205, 4.48164856516, 22747.2907148744], [5.329, 4.55145599182, 1744.4259844152], [4.511, 5.94511266539, 6894.5239488376], [4.33, 3.10901365758, 4569.574540022], [5.366, 5.08043436437, 2707.8286873866], [5.134, 1.28568358496, 8439.8779318164], [4.127, 5.48538052912, 2699.7348193176], [5.394, 5.21695066244, 5305.4510535538], [4.449, 5.56764082611, 16865.5287696312], [3.898, 1.4878243479, 9168.6408983474], [3.863, 1.2305080393, 16858.4825329332], [3.766, 0.27090392616, 17395.2197347258], [4.683, 3.05668892586, 5518.7501489918], [4.258, 2.7909014579, 3503.079062832], [3.864, 0.37957291785, 10177.2576795336], [3.992, 1.8442476803, 3134.4268782626], [3.643, 2.95318600206, 6144.4203413042], [3.654, 1.58063207414, 6680.2445323314], [3.931, 1.98436570971, 8969.568896911], [3.35, 2.72637081667, 7875.6718636242], [3.623, 2.91544991631, 6682.2051744678], [4.392, 0.81931997702, 3302.479391062], [4.062, 5.46935175827, 3120.199784261], [3.319, 1.77193665786, 3116.2676309979], [3.51, 1.18027333874, 10184.3039162316], [4.008, 1.33675167812, 6247.5131155228], [3.603, 0.15469852619, 2178.137722292], [3.313, 3.12853663982, 17277.4069318338], [4.138, 4.39568891039, 3074.005384978], [3.201, 3.36492925275, 2384.3232707292], [3.991, 3.8286783691, 3355.8648978848], [4.205, 1.9053227917, 263.0839233728], [3.743, 4.25458024187, 6261.7402095244], [3.111, 1.65445053349, 20199.094959633], [3.634, 5.55063049451, 632.7837393132], [2.892, 1.915149207, 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[[0.476, 2.47617204701, 6681.2248533996], [0.268, 2.91510547706, 10021.8372800994], [0.115, 1.76888962311, 3340.6124266998], [0.096, 3.31378377179, 13362.4497067992], [0.048, 6.27457828287, 3185.1920272656], [0.027, 3.69380877066, 16703.062133499], [0.013, 3.72005807206, 3496.032826134], [0.012, 4.88179002689, 3583.3410306738], [0.012, 3.14159265359, 0.0]]]

This table contains Mars’ periodic terms (all of them) from the planetary theory VSOP87 for the radius vector at the equinox of date (taken from the ‘D’ solution). In Meeus’ book a shortened version can be found in pages 425-426.