Saturn

Class to model Saturn planet.

pymeeus.Saturn.ORBITAL_ELEM = [[50.077444, 1223.5110686, 0.00051908, -3e-08], [9.554909192, -2.139e-06, 4e-09, 0.0], [0.05554814, -0.000346641, -6.436e-07, 3.4e-09], [2.488879, -0.0037362, -1.519e-05, 8.7e-08], [113.665503, 0.877088, -0.00012176, -2.249e-06], [93.057237, 1.9637613, 0.00083753, 4.928e-06]]

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

pymeeus.Saturn.ORBITAL_ELEM_J2000 = [[50.077444, 1222.1138488, 0.00021004, -4.6e-08], [2.488879, 0.0025514, -4.906e-05, 1.7e-08], [113.665503, -0.2566722, -0.00018399, 4.8e-07], [93.057237, 0.5665415, 0.0005285, 4.912e-06]]

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

class pymeeus.Saturn.Saturn

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

Parameters:epoch (Epoch) – Epoch to compute Saturn 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(2125, 6, 1.0)
>>> conj = Saturn.conjunction(epoch)
>>> y, m, d = conj.get_date()
>>> print(y)
2125
>>> print(m)
8
>>> print(round(d, 4))
26.4035

static geocentric_position(epoch)

This method computes the geocentric position of Saturn (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 = Saturn.geocentric_position(epoch)
>>> print(ra.ra_str(n_dec=1))
21h 11' 41.8''
>>> print(dec.dms_str(n_dec=1))
-17d 15' 40.8''
>>> print(elon.dms_str(n_dec=1))
46d 51' 47.7''

static geometric_heliocentric_position(epoch, tofk5=True)

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

Parameters:

• epoch (Epoch) – Epoch to compute Saturn 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 = Saturn.geometric_heliocentric_position(epoch)
>>> print(round(l.to_positive(), 4))
279.5108
>>> print(round(b, 4))
0.6141
>>> print(round(r, 5))
10.06266

static magnitude(sun_dist, earth_dist, delta_U, B)

This function computes the approximate magnitude of Saturn.

Parameters:

• sun_dist (float) – Distance from Saturn to the Sun, in Astronomical Units
• earth_dist (float) – Distance from Saturn to Earth, in Astronomical Units
• delta_U (float, Angle) – Difference between the Saturnicentric longitudes of the Sun and the Earth, measured in the plane of the ring, in degrees
• B (float, Angle) – Saturnicentric latitude of the Earth refered to the plane of the ring, positive towards the north, in degrees

Returns:

Saturn’s magnitude

Return type:

float

Raises:

TypeError if input values are of wrong type.

Note

In order to obtain delta_U and B, please see method ring_parameters().

>>> sun_dist = 9.867882
>>> earth_dist = 10.464606
>>> delta_U = Angle(16.442)
>>> B = Angle(4.198)
>>> m = Saturn.magnitude(sun_dist, earth_dist, delta_U, B)
>>> print(m)
1.9

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(-6, 9, 1.0)
>>> oppo = Saturn.opposition(epoch)
>>> y, m, d = oppo.get_date()
>>> print(y)
-6
>>> print(m)
9
>>> print(round(d, 4))
14.3709

static orbital_elements_j2000(epoch)

This method computes the orbital elements of Saturn 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 = Saturn.orbital_elements_j2000(epoch)
>>> print(round(l, 6))
130.28188
>>> print(round(a, 8))
9.55490779
>>> print(round(e, 7))
0.0553209
>>> print(round(i, 6))
2.490529
>>> print(round(ome, 5))
113.49736
>>> print(round(arg, 6))
-20.068943

static orbital_elements_mean_equinox(epoch)

This method computes the orbital elements of Saturn 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 = Saturn.orbital_elements_mean_equinox(epoch)
>>> print(round(l, 6))
131.196871
>>> print(round(a, 8))
9.55490779
>>> print(round(e, 7))
0.0553209
>>> print(round(i, 6))
2.486426
>>> print(round(ome, 5))
114.23974
>>> print(round(arg, 6))
-19.896331

static passage_nodes(epoch, ascending=True)

This function computes the time of passage by the nodes (ascending or descending) of Saturn, 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 = Saturn.passage_nodes(epoch)
>>> year, month, day = time.get_date()
>>> print(year)
2034
>>> print(month)
5
>>> print(round(day, 1))
30.2
>>> print(round(r, 4))
9.0546

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(1944, 1, 1.0)
>>> e = Saturn.perihelion_aphelion(epoch)
>>> y, m, d, h, mi, s = e.get_full_date()
>>> print(y)
1944
>>> print(m)
9
>>> print(d)
8
>>> print(h)
1
>>> epoch = Epoch(2047, 1, 1.0)
>>> e = Saturn.perihelion_aphelion(epoch, perihelion=False)
>>> y, m, d, h, mi, s = e.get_full_date()
>>> print(y)
2047
>>> print(m)
7
>>> print(d)
15
>>> print(h)
0

static ring_inclination(epoch)

This function computes the inclination of the plane of Saturn’s ring, referred to the ecliptic and mean equinox of the date.

Parameters:epoch (Epoch) – Epoch to compute the ring inclination Returns:Inclination of the ring referred to the ecliptic and mean equinox of the date Return type:Angle Raises:TypeError if input value is of wrong type.

>>> epoch = Epoch(1992, 12, 16.00068)
>>> i = Saturn.ring_inclination(epoch)
>>> print(round(i, 6))
28.076131

static ring_logitude_ascending_node(epoch)

This function computes the longitude of the ascending node of the plane of Saturn’s ring, referred to the ecliptic and mean equinox of the date.

Parameters:epoch (Epoch) – Epoch to compute the ring longitude of ascending node Returns:Longitude of the ascending node of the ring, referred to the ecliptic and mean equinox of the date Return type:Angle Raises:TypeError if input value is of wrong type.

>>> epoch = Epoch(1992, 12, 16.00068)
>>> omega = Saturn.ring_logitude_ascending_node(epoch)
>>> print(round(omega, 6))
169.410243

static ring_parameters(epoch)

This function computes the parameters related to Saturn’s ring, like geocentric position angle of the semiminor axis, the size of the major and minor axes of the outer edge, etc.

Parameters:epoch (Epoch) – Epoch closest to the node passage Returns:Tuple containing:

• Saturnicentic latitude of the Earth referred to the plane of the ring (B), positive towards the north (Angle).
• Saturnicentric latitude of the Sun referred to the plane of the ring (B’), positive towards the north (Angle).
• Geocentric position angle of the northern semiminor axis of the apparent ellipse of the ring (P), measured from the north towards the east. This is also the position angle of the north pole of rotation of the planet (Angle).
• Difference between the Saturnicentric longitudes of the Sun and the Earth (delta_U), measured in the plane of the ring (Angle).
• The size of major axis of the outer edge of the outer ring (‘a’), in arcseconds (float).
• The size of minor axis of the outer edge of the outer ring (‘b’), in arcseconds (float).

Return type:tuple Raises:TypeError if input value is of wrong type.

Note

Factors by which the axes ‘a’ and ‘b’ of the outer edge of the outer ring are to be multiplied to obtain the axes of:

• Inner edge of outer ring: 0.8801
• Outer edge of inner ring: 0.8599
• Inner edge of inner ring: 0.6650
• Inner edge of dusky ring: 0.5486

>>> epoch = Epoch(1992, 12, 16.00068)
>>> B, Bprime, P, delta_U, a, b = Saturn.ring_parameters(epoch)
>>> print(round(B, 3))
16.442
>>> print(round(Bprime, 3))
14.679
>>> print(round(P, 3))
6.741
>>> print(round(delta_U, 3))
4.198
>>> print(round(a, 2))
35.87
>>> print(round(b, 2))
10.15

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(2018, 11, 1.0)
>>> sta1 = Saturn.station_longitude_1(epoch)
>>> y, m, d = sta1.get_date()
>>> print(y)
2018
>>> print(m)
4
>>> print(round(d, 4))
17.9433

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(2018, 11, 1.0)
>>> sta2 = Saturn.station_longitude_2(epoch)
>>> y, m, d = sta2.get_date()
>>> print(y)
2018
>>> print(m)
9
>>> print(round(d, 4))
6.4175

pymeeus.Saturn.VSOP87_B = [[[4330678.04, 3.60284428399, 213.299095438], [240348.303, 2.8523848939, 426.598190876], [84745.939, 0.0, 0.0], [30863.357, 3.48441504465, 220.4126424388], [34116.063, 0.57297307844, 206.1855484372], [14734.07, 2.1184659787, 639.897286314], [9916.668, 5.79003189405, 419.4846438752], [6993.564, 4.73604689179, 7.1135470008], [4807.587, 5.43305315602, 316.3918696566], [4788.392, 4.9651292742, 110.2063212194], [3432.125, 2.73255752123, 433.7117378768], [1506.129, 6.01304536144, 103.0927742186], [1060.298, 5.63099292414, 529.6909650946], [969.071, 5.20434966103, 632.7837393132], [942.05, 1.39646678088, 853.196381752], [707.645, 3.80302329547, 323.5054166574], [552.313, 5.13149109045, 202.2533951741], [399.675, 3.35891413961, 227.5261894396], [316.063, 1.99716764199, 647.0108333148], [319.38, 3.6257155098, 209.3669421749], [284.494, 4.88648481625, 224.3447957019], [314.225, 0.4651027241, 217.2312487011], [236.442, 2.13887472281, 11.0457002639], [215.354, 5.94982610103, 846.0828347512], [208.522, 2.12003893769, 415.5524906121], [178.958, 2.95361514672, 63.7358983034], [207.213, 0.73021462851, 199.0720014364], [139.14, 1.9982199094, 735.8765135318], [134.884, 5.24500819605, 742.9900605326], [140.585, 0.64417620299, 490.3340891794], [121.669, 3.11537140876, 522.5774180938], [139.24, 4.59535168021, 14.2270940016], [115.524, 3.10891547171, 216.4804891757], [114.218, 0.96261442133, 210.1177017003], [96.376, 4.48164339766, 117.3198682202], [80.593, 1.3169275015, 277.0349937414], [72.952, 3.0598848237, 536.8045120954], [69.261, 4.92378633635, 309.2783226558], [74.302, 2.8937653962, 149.5631971346], [68.04, 2.18002263974, 351.8165923087], [61.734, 0.67728106562, 1066.49547719], [56.598, 2.60963391288, 440.8252848776], [48.864, 5.78725874107, 95.9792272178], [48.243, 2.1821183743, 74.7815985673], [38.304, 5.29151303843, 1059.3819301892], [36.323, 1.63348365121, 628.8515860501], [35.055, 1.71279210041, 1052.2683831884], [34.27, 2.45740470599, 422.6660376129], [34.313, 5.97994514798, 412.3710968744], [33.787, 1.14073392951, 949.1756089698], [31.633, 4.14722153007, 437.6438911399], [36.833, 6.27769966148, 1162.4747044078], [26.98, 1.2715481681, 860.3099287528], [23.516, 2.74936525342, 838.9692877504], [23.46, 0.98962849901, 210.8514148832], [23.6, 4.11386961467, 3.9321532631], [23.631, 3.07427204313, 215.7467759928], [20.813, 3.51084686918, 330.6189636582], [19.509, 2.81857577372, 127.4717966068], [17.103, 3.89784279922, 214.2623032845], [17.635, 6.19715516746, 703.6331846174], [17.824, 2.28524493886, 388.4651552382], [20.935, 0.14356167048, 430.5303441391], [16.551, 1.66649120724, 38.1330356378], [19.1, 2.97699096081, 137.0330241624], [15.517, 4.54798410406, 956.2891559706], [17.065, 0.16611115812, 212.3358875915], [14.169, 0.48937283445, 213.3472795478], [19.027, 6.27326062836, 423.4167971383], [13.344, 2.37136126257, 429.7795846137], [12.565, 1.03178071173, 563.6312150384], [14.173, 3.57477564831, 213.2509113282], [11.374, 1.45300927024, 1368.660252845], [10.585, 6.1763342593, 200.7689224658], [10.6, 3.84358958373, 138.5174968707], [10.263, 2.17423692422, 76.2660712756], [10.072, 1.33197220789, 565.1156877467], [12.058, 0.441492427, 222.8603229936], [10.367, 1.85278552549, 350.3321196004], [8.706, 2.58144528603, 1155.361157407], [8.47, 1.97890349826, 625.6701923124], [8.518, 4.51649648578, 3.1813937377], [7.439, 4.92597321442, 212.7778305762], [7.409, 2.03506679104, 288.0806940053], [8.137, 3.98500592467, 85.8272988312], [7.985, 2.20794292064, 362.8622925726], [6.61, 6.14944028835, 417.0369633204], [7.753, 6.2366454907, 1478.8665740644], [6.318, 1.87388481013, 654.1243803156], [6.319, 1.17328438271, 1265.5674786264], [5.841, 2.35829915285, 750.1036075334], [5.808, 5.01602242794, 479.2883889155], [8.079, 0.42574715104, 554.0699874828], [6.014, 5.58952234348, 425.1137181677], [7.444, 5.41859596459, 213.8203602998], [7.567, 2.68446523795, 191.2076949102], [7.421, 4.19354269508, 9.5612275556], [5.466, 3.21737829505, 234.6397364404], [5.661, 1.4698271355, 265.9892934775], [5.851, 4.81776629912, 1.4844727083], [5.341, 3.45755372717, 203.7378678824], [4.96, 1.04628615559, 12.5301729722], [4.92, 3.85622235967, 173.9422195228], [4.883, 1.94823282939, 195.1398481733], [5.621, 0.81869581274, 52.6901980395], [5.2, 3.32827437636, 515.463871093], [4.927, 3.81806549732, 225.8292684102], [5.033, 0.10756875163, 252.6559713532], [4.416, 5.45506938037, 408.4389436113], [4.169, 1.21145214135, 1685.0521225016], [4.066, 6.24213578122, 1279.794572628], [3.972, 6.13850317719, 217.491881132], [5.398, 5.67212179194, 1375.7737998458], [3.916, 5.96105725915, 210.3783341312], [4.017, 0.99840226682, 842.1506814881], [3.899, 4.58983662507, 1272.6810256272], [3.764, 3.30663337976, 212.5483359126], [4.345, 3.1856224183, 414.0680179038], [3.565, 4.75262007127, 207.8824694666], [3.542, 2.30814954338, 1471.7530270636], [3.732, 1.61040235688, 635.9651330509], [3.709, 2.97082943086, 223.5940361765], [3.576, 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1.99006340181, 213.299095438], [632.35, 5.69778316807, 206.1855484372], [398.051, 0.0, 0.0], [187.838, 4.33779804809, 220.4126424388], [91.884, 4.84104208217, 419.4846438752], [42.369, 2.38073239056, 426.598190876], [51.548, 3.42149490328, 433.7117378768], [25.661, 4.40167213109, 227.5261894396], [20.551, 5.85313509872, 199.0720014364], [18.081, 1.99321433229, 639.897286314], [10.874, 5.37344546547, 7.1135470008], [9.59, 2.54901825866, 647.0108333148], [7.085, 3.45518372721, 316.3918696566], [6.002, 4.80055225135, 632.7837393132], [5.778, 0.01680378777, 210.1177017003], [4.881, 5.63719730884, 14.2270940016], [4.501, 1.2242441901, 853.196381752], [5.542, 3.51756747774, 440.8252848776], [3.548, 4.7129937089, 412.3710968744], [2.851, 0.62679207578, 103.0927742186], [2.173, 3.71982274459, 216.4804891757], [1.991, 6.10867071657, 217.2312487011], [1.435, 1.69177141453, 860.3099287528], [1.217, 4.30778838827, 234.6397364404], [1.157, 5.75027789902, 309.2783226558], [0.795, 5.69026441157, 117.3198682202], [0.733, 0.59842720676, 1066.49547719], [0.713, 0.21700311697, 625.6701923124], [0.773, 5.4836198199, 202.2533951741], [0.897, 2.65577866867, 654.1243803156], [0.509, 2.86079833766, 429.7795846137], [0.462, 4.17742567173, 529.6909650946], [0.39, 6.11288036049, 191.9584544356], [0.505, 4.51905764563, 323.5054166574], [0.379, 3.74436004151, 223.5940361765], [0.332, 5.4937089057, 21.3406410024], [0.377, 5.25624813434, 95.9792272178], [0.384, 4.48187414769, 330.6189636582], [0.367, 5.0319092968, 846.0828347512], [0.281, 1.14133888637, 735.8765135318], [0.245, 5.8161825325, 423.4167971383], [0.241, 1.7033512018, 522.5774180938], [0.258, 3.69110118716, 447.9388318784], [0.231, 4.15697626494, 110.2063212194], [0.305, 5.97746884029, 302.164775655], [0.284, 0.66224572127, 203.0041546995], [0.204, 1.54683820621, 209.3669421749], [0.194, 4.21193801453, 124.433415221], [0.145, 4.79689259614, 88.865680217], [0.151, 3.82010884134, 536.8045120954], [0.1, 0.03596545368, 949.1756089698], [0.097, 0.91303450276, 1073.6090241908], [0.11, 2.21197473966, 515.463871093], [0.084, 2.53842533109, 422.6660376129], [0.085, 5.11102520704, 3.9321532631], [0.077, 6.04074586787, 838.9692877504], [0.085, 1.18898817378, 728.762966531], [0.084, 4.10158366806, 224.3447957019]], [[80.384, 1.11918414679, 206.1855484372], [31.66, 3.12218745098, 213.299095438], [17.143, 2.48073200414, 220.4126424388], [11.844, 3.14159265359, 0.0], [9.005, 0.38441424927, 419.4846438752], [6.164, 1.56186379537, 433.7117378768], [4.66, 1.2823563957, 199.0720014364], [4.775, 2.63498295487, 227.5261894396], [1.487, 1.43096671616, 426.598190876], [1.424, 0.66988083613, 647.0108333148], [1.075, 6.18092274059, 639.897286314], [1.145, 1.72041928134, 440.8252848776], [0.682, 3.8484109818, 14.2270940016], [0.655, 3.49486258327, 7.1135470008], [0.456, 0.47338193402, 632.7837393132], [0.509, 0.31432285584, 412.3710968744], [0.343, 5.86413875355, 853.196381752], [0.27, 2.50125594913, 234.6397364404], [0.197, 5.39156324804, 316.3918696566], [0.236, 2.11084590211, 210.1177017003], [0.172, 6.09682874401, 860.3099287528], [0.159, 5.95049154821, 216.4804891757], [0.1, 1.98534903594, 625.6701923124], [0.112, 0.85526419268, 654.1243803156], [0.115, 5.03884718594, 117.3198682202], [0.115, 0.44589613974, 110.2063212194]], [[7.895, 2.81927558645, 206.1855484372], [1.014, 0.5118721027, 220.4126424388], [0.772, 2.99484124049, 199.0720014364], [0.967, 3.14159265359, 0.0], [0.583, 5.96456944075, 433.7117378768], [0.588, 0.78008666397, 227.5261894396], [0.445, 2.38630799074, 419.4846438752], [0.098, 5.10622131539, 647.0108333148], [0.091, 5.81659714144, 7.1135470008], [0.088, 6.17828532308, 440.8252848776], [0.089, 0.5839686453, 213.299095438]]]

This table contains Saturn’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 pages 440-442.

pymeeus.Saturn.VSOP87_L = [[[87401354.029, 0.0, 0.0], [11107659.78, 3.96205090194, 213.299095438], [1414150.958, 4.58581515873, 7.1135470008], [398379.386, 0.52112025957, 206.1855484372], [350769.223, 3.30329903015, 426.598190876], [206816.296, 0.24658366938, 103.0927742186], [79271.288, 3.8400707853, 220.4126424388], [23990.338, 4.6697693486, 110.2063212194], [16573.583, 0.43719123541, 419.4846438752], [14906.995, 5.76903283845, 316.3918696566], [15820.3, 0.9380895376, 632.7837393132], [14609.562, 1.56518573691, 3.9321532631], [13160.308, 4.44891180176, 14.2270940016], [15053.509, 2.71670027883, 639.897286314], [13005.305, 5.98119067061, 11.0457002639], [10725.066, 3.12939596466, 202.2533951741], [5863.207, 0.23657028777, 529.6909650946], [5227.771, 4.2078316238, 3.1813937377], [6126.308, 1.76328499656, 277.0349937414], [5019.658, 3.17787919533, 433.7117378768], [4592.541, 0.61976424374, 199.0720014364], [4005.862, 2.24479893937, 63.7358983034], [2953.815, 0.98280385206, 95.9792272178], [3873.696, 3.22282692566, 138.5174968707], [2461.172, 2.03163631205, 735.8765135318], [3269.49, 0.77491895787, 949.1756089698], [1758.143, 3.26580514774, 522.5774180938], [1640.183, 5.50504966218, 846.0828347512], [1391.336, 4.02331978116, 323.5054166574], [1580.641, 4.3726631412, 309.2783226558], [1123.515, 2.83726793572, 415.5524906121], [1017.258, 3.71698151814, 227.5261894396], [848.643, 3.19149825839, 209.3669421749], [1087.237, 4.18343232481, 2.4476805548], [956.752, 0.50740889886, 1265.5674786264], [789.205, 5.00745123149, 0.9632078465], [686.965, 1.74714407827, 1052.2683831884], [654.47, 1.59889331515, 0.0481841098], [748.811, 2.14398149298, 853.196381752], [633.98, 2.29889903023, 412.3710968744], [743.584, 5.25276954625, 224.3447957019], [852.677, 3.42141350697, 175.1660598002], [579.857, 3.09259007048, 74.7815985673], [624.904, 0.97046831256, 210.1177017003], [529.861, 4.44938897119, 117.3198682202], [542.643, 1.51824320514, 9.5612275556], [474.279, 5.47527185987, 742.9900605326], [448.542, 1.28990416161, 127.4717966068], [546.358, 2.12678554211, 350.3321196004], [478.054, 2.96488054338, 137.0330241624], [354.944, 3.0128648303, 838.9692877504], [451.827, 1.04436664241, 490.3340891794], [347.413, 1.53928227764, 340.7708920448], [343.475, 0.24604039134, 0.5212648618], [309.001, 3.49486734909, 216.4804891757], [322.185, 0.96137456104, 203.7378678824], [372.308, 2.27819108625, 217.2312487011], [321.543, 2.57182354537, 647.0108333148], [330.196, 0.24715617844, 1581.959348283], [249.116, 1.47010534421, 1368.660252845], [286.688, 2.37043745859, 351.8165923087], [220.225, 4.20422424873, 200.7689224658], [277.775, 0.40020408926, 211.8146227297], [204.5, 6.010822066, 265.9892934775], [207.663, 0.48349820488, 1162.4747044078], [208.655, 1.34516255304, 625.6701923124], [182.454, 5.49122292426, 2.9207613068], [226.609, 4.91003163138, 12.5301729722], [207.659, 1.283022189, 39.3568759152], [173.914, 1.86305806814, 0.7507595254], [184.69, 3.50344404958, 149.5631971346], [183.511, 0.97254952728, 4.192785694], [146.068, 6.23102544071, 195.1398481733], [164.541, 0.4400551752, 5.4166259714], [147.526, 1.53529320509, 5.6290742925], [139.666, 4.29450260069, 21.3406410024], [131.283, 4.06828961903, 10.2949407385], [117.283, 2.67920400584, 1155.361157407], [149.299, 5.73594349789, 52.6901980395], [122.373, 1.97588777199, 4.665866446], [113.747, 5.59427544714, 1059.3819301892], [102.702, 1.19748124058, 1685.0521225016], [118.156, 5.340729339, 554.0699874828], [109.275, 3.43812715686, 536.8045120954], [110.399, 0.1660402409, 1.4844727083], [124.969, 6.27737805832, 1898.3512179396], [89.949, 5.80392934702, 114.1384744825], [103.956, 2.19210363069, 88.865680217], [112.437, 1.10502663534, 191.2076949102], [106.57, 4.01156608514, 956.2891559706], [91.43, 1.8752157751, 38.1330356378], [83.791, 5.48810655641, 0.1118745846], [83.461, 2.28972767279, 628.8515860501], [96.987, 4.53666595763, 302.164775655], [100.631, 4.96513666539, 269.9214467406], [75.491, 2.18045274099, 728.762966531], [96.33, 2.8331918921, 275.5505210331], [82.363, 3.05469876064, 440.8252848776], [73.888, 5.08914205084, 1375.7737998458], [71.633, 5.1094074343, 65.2203710117], [70.409, 4.86846451411, 0.2124483211], [69.76, 3.71029022489, 14.977853527], [88.772, 3.86334563977, 278.5194664497], [68.09, 0.7341546099, 1478.8665740644], [66.501, 0.02677580336, 70.8494453042], [65.682, 2.02165559602, 142.4496501338], [75.765, 1.61410487792, 284.1485407422], [63.153, 3.49493353034, 479.2883889155], [62.539, 2.58713611532, 422.6660376129], [69.313, 3.43979731402, 515.463871093], [79.021, 4.45154941586, 35.4247226521], [63.664, 3.31749528708, 62.2514255951], [52.939, 5.51392725227, 0.2606324309], [53.011, 3.18480701697, 8.0767548473], [54.492, 2.45674090515, 22.0914005278], [50.514, 4.26749346978, 99.1606209555], [55.17, 0.9679744615, 942.062061969], [49.288, 2.38641424063, 1471.7530270636], [47.199, 2.02515248245, 312.1990839626], [61.08, 1.50295092063, 210.8514148832], [45.126, 0.93109376473, 2001.4439921582], [60.556, 2.68715551585, 388.4651552382], [43.452, 2.52602011714, 288.0806940053], [42.544, 3.81793980322, 330.6189636582], [39.915, 5.713786529, 408.4389436113], [50.145, 6.03164759907, 2214.7430875962], [45.86, 0.54229721801, 212.3358875915], [54.165, 0.78154835399, 191.9584544356], [47.016, 4.59934671151, 437.6438911399], [42.362, 1.90070070955, 430.5303441391], [39.722, 1.63259419913, 1066.49547719], [36.345, 0.84756992711, 213.3472795478], [35.468, 4.18603772925, 215.7467759928], [36.344, 3.93295730315, 213.2509113282], [38.005, 0.31313803095, 423.4167971383], [44.746, 1.12488341174, 6.1503391543], [37.902, 1.19795851115, 2.7083129857], [43.402, 1.37363944007, 563.6312150384], [43.764, 3.93043802956, 525.4981794006], [34.825, 1.01566605408, 203.0041546995], [31.755, 1.69273634405, 0.1600586944], [30.88, 6.13525703832, 417.0369633204], [36.388, 6.00586032647, 18.1592472647], [29.032, 1.19660544505, 404.5067903482], [32.812, 0.53649479713, 107.0249274817], [30.433, 0.72335287989, 222.8603229936], [32.644, 0.81204701486, 1795.258443721], [37.769, 3.69666903716, 1272.6810256272], [27.679, 1.45663979401, 7.1617311106], [27.187, 1.89731951902, 1045.1548361876], [37.699, 4.51997049537, 24.3790223882], [34.885, 4.46095761791, 214.2623032845], [32.65, 0.66372395761, 692.5874843535], [30.324, 5.30369950147, 33.9402499438], [27.48, 6.22702216249, 1.2720243872], [26.657, 4.56713198392, 7.065362891], [31.745, 5.49798599565, 56.6223513026], [28.05, 5.64447420566, 128.9562693151], [24.277, 3.93966553574, 414.0680179038], [32.017, 5.22260660455, 92.0470739547], [26.976, 0.06705123981, 205.2223405907], [22.974, 3.6581775177, 207.6700211455], [31.775, 5.59198119173, 6069.7767545534], [23.153, 2.10054506119, 1788.1448967202], [31.025, 0.37190053329, 703.6331846174], [29.376, 0.14742155778, 131.4039498699], [22.562, 5.24009182383, 212.7778305762], [26.185, 5.41311252822, 140.001969579], [25.673, 4.36038885283, 32.2433289144], [20.392, 2.8241390926, 429.7795846137], [20.659, 0.67091805084, 2317.8358618148], [24.397, 3.08740396398, 145.6310438715], [23.735, 2.54365387567, 76.2660712756], [20.157, 5.06708675157, 617.8058857862], [23.307, 3.97357729211, 483.2205421786], [22.878, 6.10452832642, 177.8743727859], [22.978, 3.20140795404, 208.633228992], [20.638, 5.22128727027, 6.592282139], [21.446, 0.72034565528, 1258.4539316256], [18.034, 6.11382719947, 210.3783341312], [22.38, 5.92299908546, 173.9422195228], [19.128, 5.77772013766, 213.8203602998], [20.871, 5.79126331864, 2531.1349572528], [19.327, 1.64147367403, 565.1156877467], [16.806, 3.27953583323, 98.8999885246], [20.833, 2.01655935909, 860.3099287528], [17.939, 3.14329498012, 831.8557407496], [15.653, 3.10137669623, 106.2741679563], [18.235, 5.22595172482, 73.297125859], [19.302, 5.9394711405, 425.1137181677], [14.514, 2.75049388379, 1.2238402774], [14.562, 5.18795088579, 305.3461693927], [14.254, 3.88079504939, 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[0.932, 5.56741549127, 647.0108333148], [0.756, 6.17716234487, 191.9584544356], [0.76, 0.69475544472, 302.164775655], [1.038, 0.23516951637, 440.8252848776], [1.007, 3.14159265359, 0.0], [0.549, 4.87733288264, 88.865680217], [0.504, 4.77955496203, 419.4846438752], [0.346, 4.31847547394, 853.196381752], [0.392, 5.69922389094, 654.1243803156], [0.242, 2.05052677361, 323.5054166574], [0.266, 1.11384528244, 234.6397364404], [0.199, 0.88505901097, 309.2783226558], [0.258, 5.10074489186, 95.9792272178], [0.166, 2.40063312194, 515.463871093], [0.155, 4.70433216164, 860.3099287528], [0.089, 1.3637107038, 412.3710968744], [0.102, 0.49450039082, 117.3198682202]]]

This table contains Saturn’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 435-440.

pymeeus.Saturn.VSOP87_R = [[[955758135.801, 0.0, 0.0], [52921382.465, 2.39226219733, 213.299095438], [1873679.934, 5.23549605091, 206.1855484372], [1464663.959, 1.64763045468, 426.598190876], [821891.059, 5.93520025371, 316.3918696566], [547506.899, 5.01532628454, 103.0927742186], [371684.449, 2.27114833428, 220.4126424388], [361778.433, 3.13904303264, 7.1135470008], [140617.548, 5.70406652991, 632.7837393132], [108974.737, 3.29313595577, 110.2063212194], [69007.015, 5.94099622447, 419.4846438752], [61053.35, 0.94037761156, 639.897286314], [48913.044, 1.55733388472, 202.2533951741], [34143.794, 0.19518550682, 277.0349937414], [32401.718, 5.47084606947, 949.1756089698], [20936.573, 0.46349163993, 735.8765135318], [20839.118, 1.5210259064, 433.7117378768], [20746.678, 5.33255667599, 199.0720014364], [15298.457, 3.05943652881, 529.6909650946], [14296.479, 2.60433537909, 323.5054166574], [11993.314, 5.98051421881, 846.0828347512], [11380.261, 1.73105746566, 522.5774180938], [12884.128, 1.64892310393, 138.5174968707], [7752.769, 5.85191318903, 95.9792272178], [9796.061, 5.20475863996, 1265.5674786264], [6465.967, 0.17733160145, 1052.2683831884], [6770.621, 3.00433479284, 14.2270940016], [5850.443, 1.45519636076, 415.5524906121], [5307.481, 0.5973753405, 63.7358983034], [4695.746, 2.14919036956, 227.5261894396], [4043.988, 1.64010323863, 209.3669421749], [3688.132, 0.7801613317, 412.3710968744], [3376.457, 3.69528478828, 224.3447957019], [2885.348, 1.38764077631, 838.9692877504], [2976.033, 5.68467931117, 210.1177017003], [3419.551, 4.94549148887, 1581.959348283], [3460.943, 1.85088802878, 175.1660598002], [3400.616, 0.55386747515, 350.3321196004], [2507.63, 3.53851863255, 742.9900605326], [2448.325, 6.18412386316, 1368.660252845], [2406.138, 2.96559220267, 117.3198682202], [2881.181, 0.17960757891, 853.196381752], [2173.959, 0.01508587396, 340.7708920448], [2024.483, 5.05411271271, 11.0457002639], [1740.254, 2.34657043464, 309.2783226558], [1861.397, 5.93361638244, 625.6701923124], [1888.436, 0.02968443389, 3.9321532631], [1610.859, 1.17302463549, 74.7815985673], [1462.631, 1.92588134017, 216.4804891757], [1474.547, 5.6767046113, 203.7378678824], [1395.109, 5.93669404929, 127.4717966068], [1781.165, 0.76314388077, 217.2312487011], [1817.186, 5.77713225779, 490.3340891794], [1472.392, 1.40064915651, 137.0330241624], [1304.089, 0.77235613966, 647.0108333148], [1149.773, 5.74021249703, 1162.4747044078], [1126.667, 4.46707803791, 265.9892934775], [1277.489, 2.98412586423, 1059.3819301892], [1207.053, 0.7528593316, 351.8165923087], [1071.399, 1.13567265104, 1155.361157407], [1020.922, 5.91233512844, 1685.0521225016], [1315.042, 5.11202572637, 211.8146227297], [1295.553, 4.69184139933, 1898.3512179396], [1099.037, 1.81765118601, 149.5631971346], [998.462, 2.63131596867, 200.7689224658], [985.869, 2.25992849742, 956.2891559706], [932.434, 3.66980793184, 554.0699874828], [664.481, 0.60297724821, 728.762966531], [659.85, 4.66635439533, 195.1398481733], [617.74, 5.62092000007, 942.062061969], [626.382, 5.9420823259, 1478.8665740644], [482.23, 1.84070179496, 479.2883889155], [487.689, 2.79373616806, 3.1813937377], [470.086, 0.8384775504, 1471.7530270636], [451.817, 5.64468459871, 2001.4439921582], [553.128, 3.41088600844, 269.9214467406], [534.397, 1.26443331367, 275.5505210331], [472.572, 1.8819858466, 515.463871093], [405.434, 1.64001413521, 536.8045120954], [517.196, 4.44310450526, 2214.7430875962], [452.848, 3.00349117198, 302.164775655], [494.34, 2.28626675074, 278.5194664497], [489.825, 5.80631420383, 191.2076949102], [427.459, 0.05741344372, 284.1485407422], [339.763, 1.40198657693, 440.8252848776], [340.627, 0.89091104306, 628.8515860501], [385.974, 1.99700402508, 1272.6810256272], [288.298, 1.12160250272, 422.6660376129], [294.444, 0.42577061903, 312.1990839626], [262.49, 0.31753439818, 1045.1548361876], [295.331, 0.67144493789, 88.865680217], [342.968, 5.85600322299, 1795.258443721], [341.117, 2.3758524725, 525.4981794006], [234.018, 4.22756813216, 114.1384744825], [223.729, 2.28129446763, 330.6189636582], [275.814, 0.47832439352, 38.1330356378], [224.592, 0.54754005675, 1788.1448967202], [303.3, 0.87946670205, 6069.7767545534], [292.103, 6.2142061192, 210.8514148832], [226.121, 0.37495223398, 142.4496501338], [277.257, 5.31917702012, 692.5874843535], [242.911, 5.37187983246, 1258.4539316256], [205.571, 0.95755250527, 288.0806940053], [207.567, 5.38126259725, 2317.8358618148], [186.835, 6.03591766061, 404.5067903482], [218.536, 5.25607043545, 212.3358875915], [222.155, 5.94588016768, 39.3568759152], [179.673, 4.41045924362, 408.4389436113], [241.44, 1.1252586811, 388.4651552382], [197.093, 3.9014194285, 52.6901980395], [236.639, 0.90802744873, 1375.7737998458], [171.915, 5.56318632797, 213.3472795478], [169.865, 2.8566755401, 99.1606209555], [214.398, 4.20253525974, 2531.1349572528], [172.01, 2.36537801012, 213.2509113282], [165.707, 2.63679789706, 215.7467759928], [230.892, 5.49463421262, 191.9584544356], [177.585, 0.38155817719, 430.5303441391], [191.514, 2.95906900704, 437.6438911399], [163.25, 3.4583251728, 617.8058857862], [162.305, 5.73050678664, 203.0041546995], [175.108, 5.71404465044, 1066.49547719], [183.041, 5.66851947172, 2111.6503133776], [150.077, 4.40663921925, 417.0369633204], [187.935, 6.07916265661, 563.6312150384], [145.127, 5.08176368814, 423.4167971383], [137.491, 5.43912787991, 222.8603229936], [172.824, 1.8492099409, 1589.0728952838], [165.478, 2.89132196119, 214.2623032845], [145.727, 1.56565192483, 831.8557407496], [176.864, 2.30323752987, 9999.986450773], [128.877, 2.55338644107, 414.0680179038], [120.093, 0.04329750542, 1361.5467058442], [143.441, 0.9981735772, 76.2660712756], [108.747, 2.09282278191, 207.6700211455], [132.106, 2.85902597898, 312.4597163935], [112.238, 0.26221759151, 2104.5367663768], [125.186, 4.78354048063, 205.2223405907], [104.427, 3.63671899047, 65.2203710117], [107.447, 3.67064138701, 212.7778305762], [108.642, 2.85492389024, 21.3406410024], [97.743, 5.12231845599, 2634.2277314714], [109.097, 1.63231061493, 208.633228992], [96.852, 4.19928280035, 305.3461693927], [96.507, 2.56002066845, 1692.1656695024], [85.829, 4.54545085982, 210.3783341312], [99.249, 5.13816222131, 1574.8458012822], [112.532, 5.03109281265, 703.6331846174], [84.023, 1.18337717265, 429.7795846137], [89.021, 5.38791571457, 107.0249274817], [110.191, 2.43656081234, 355.7487455718], [90.659, 4.20908809746, 213.8203602998], [95.885, 5.44594259071, 2428.0421830342], [94.109, 2.39786381418, 483.2205421786], [85.609, 0.03354346966, 860.3099287528], [88.796, 4.0576630675, 128.9562693151], [81.951, 1.66499731549, 62.2514255951], [91.24, 3.96942332591, 2847.5268269094], [83.961, 4.60845858022, 177.8743727859], [88.376, 3.86800515885, 140.001969579], [93.308, 0.73846639887, 831.1049812242], [91.872, 2.9497760532, 35.4247226521], [87.077, 1.33390590052, 1905.4647649404], [96.584, 4.84438390997, 131.4039498699], [71.01, 0.99334817658, 405.2575498736], [95.266, 2.51506908152, 2.4476805548], [72.514, 4.63213873657, 245.5424243524], [82.58, 1.52823217919, 145.6310438715], [76.693, 3.15240783008, 767.3690829208], [70.317, 4.0425370727, 173.9422195228], [86.015, 2.3010372727, 85.8272988312], [66.529, 4.75053522835, 70.8494453042], [65.835, 2.46869725001, 280.9671470045], [64.824, 0.09343869325, 9.5612275556], [71.557, 0.01212415296, 565.1156877467], [66.533, 1.08034871114, 339.2864193365], [63.488, 2.01740971153, 234.6397364404], [60.786, 5.12026947473, 756.3233826569], [58.123, 6.05732868566, 1677.9385755008], [64.236, 1.28586474622, 1148.2476104062], [73.124, 4.37810889148, 425.1137181677], [55.012, 3.85865703217, 342.2553647531], [57.101, 6.26689214029, 2420.9286360334], [64.09, 4.09854757476, 327.4375699205], [55.306, 1.60456896521, 543.0242872189], [57.987, 5.4726912434, 347.8844390456], [73.581, 3.72292337326, 92.0470739547], [73.76, 3.57045342615, 1.4844727083], [64.94, 2.44739629174, 267.4737661858], [54.414, 3.71479080197, 344.7030453079], [49.783, 3.93453970179, 192.6921676185], [49.537, 3.22831070579, 333.657345044], [47.539, 3.92925402178, 199.2844497575], [49.368, 4.90341763553, 217.491881132], [62.711, 4.40120079629, 214.7835681463], [46.359, 2.09430260266, 212.5483359126], [46.289, 2.6403845348, 10.2949407385], [54.335, 1.07179534996, 362.8622925726], [58.742, 2.62270940799, 225.8292684102], [48.457, 3.15166418511, 216.2198567448], [46.316, 4.8622664277, 2950.619601128], [45.97, 4.97297391881, 198.321241911], [46.678, 2.44960215701, 207.1487562837], [44.905, 1.77616995803, 223.5940361765], [44.521, 5.55987055442, 264.5048207692], [55.914, 4.29520232351, 329.7251917809], [49.643, 5.20789299388, 2744.4340526908], [58.829, 4.23073947869, 700.6642392008], [52.629, 3.7923062907, 343.2185725996], [41.532, 0.74488808688, 125.9873238985], [47.767, 2.39260015876, 207.8824694666], [56.157, 2.07214273531, 124.433415221], [43.345, 1.83707598036, 106.2741679563], [39.793, 4.00870764324, 12.5301729722], [53.882, 4.97905460628, 134.5853436076], [50.135, 5.75914508514, 320.3240229197], [44.96, 5.35721924134, 218.9281697305], [41.089, 4.92252591399, 1891.2376709388], [46.509, 2.06623129884, 2008.557539159], [42.949, 0.39856812529, 357.4456666012], [37.992, 2.06495914285, 247.2393453818], [48.733, 5.32762223699, 3127.3133312618], [34.583, 5.62555932761, 99.9113804809], [41.092, 2.4726489737, 237.6781178262], [40.763, 4.08408559215, 621.7380390493], [34.213, 0.73077393007, 750.1036075334], [33.967, 5.31264617621, 206.233732547], [36.509, 1.6882677575, 22.0914005278], [39.361, 3.4573071999, 241.6102710893], [34.796, 2.24780137629, 487.3651437628], [33.049, 4.86593901955, 209.106309744], [32.584, 2.22713131846, 319.5732633943], [39.035, 3.73870591196, 3163.918696566], [32.722, 1.06640549236, 252.6559713532], [38.671, 4.39617126814, 18.1592472647], [34.514, 1.8260750069, 380.12776796], [41.539, 0.08136234251, 210.3301500214], [33.527, 5.80475568528, 251.4321310758], [31.221, 1.96489151107, 244.318584075], [30.521, 2.26854188579, 1169.5882514086], [34.828, 5.96324553131, 217.964961884], [38.481, 4.43707551964, 160.6088973985], [35.998, 3.83262381556, 56.6223513026], [31.041, 4.89914223233, 144.1465711632], [32.342, 3.58191018804, 231.4583427027], [28.838, 5.80081031514, 1994.3304451574], [32.175, 2.13166877923, 206.1373643274], [32.643, 1.93131580544, 98.8999885246], [34.917, 5.65276617691, 497.4476361802], [28.928, 2.2165328892, 14.977853527], [31.569, 3.81846560564, 73.297125859], [32.199, 0.9981184629, 1464.6394800628], [29.153, 5.98414099408, 2737.32050569], [36.706, 4.75493516597, 348.8476468921], [28.665, 1.68732054583, 78.7137518304], [27.501, 6.12086395418, 214.0498549634], [28.795, 0.04448605904, 5.6290742925], [27.205, 0.24587543816, 313.2104759189], [32.441, 3.77921585847, 33.9402499438], [27.088, 5.2031009802, 148.0787244263], [34.956, 3.43886187587, 273.1028404783], [33.076, 2.44662095168, 969.6224780949], [27.745, 1.44598606685, 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4.97415112184, 860.3099287528], [3.22, 2.72684237392, 522.5774180938], [4.005, 1.59858435636, 405.2575498736], [3.099, 0.75235436533, 209.3669421749], [2.464, 1.19167306488, 124.433415221], [3.088, 1.32258934286, 728.762966531], [2.22, 3.28087994088, 203.0041546995], [2.127, 6.14648095022, 429.7795846137], [2.11, 0.75462855247, 295.0512286542], [2.02, 3.89394929749, 1066.49547719], [2.248, 0.49319150178, 447.9388318784], [2.18, 0.72761059998, 625.6701923124], [1.809, 0.09057839517, 942.062061969], [1.672, 1.39635398184, 224.3447957019], [1.641, 3.0246830755, 184.8449074348], [1.772, 0.81879250825, 223.5940361765], [1.902, 2.00472814984, 831.8557407496], [1.6, 5.41185167676, 824.7421937488], [1.505, 5.95520747253, 422.6660376129], [1.133, 1.11512973946, 838.9692877504], [1.19, 1.89600567803, 956.2891559706], [1.487, 2.11906469507, 529.6909650946], [1.409, 0.72254420236, 536.8045120954], [1.125, 0.89062692183, 721.6494195302], [1.301, 1.64867038984, 17.4084877393], [1.164, 5.9695798184, 195.1398481733], [0.95, 5.3608071329, 316.3918696566], [0.985, 3.05768671768, 1574.8458012822], [1.05, 1.59202481523, 735.8765135318], [0.817, 4.92838813598, 56.6223513026], [0.78, 2.72125404102, 508.3503240922], [0.969, 1.00708261792, 1045.1548361876], [0.716, 1.11042181341, 1169.5882514086]], [[128.612, 5.91282565136, 220.4126424388], [32.273, 0.69256228602, 7.1135470008], [26.698, 5.91428528629, 227.5261894396], [19.923, 0.67370653385, 14.2270940016], [20.223, 4.95136801768, 433.7117378768], [13.537, 1.45669521408, 199.0720014364], [14.097, 2.67074280191, 206.1855484372], [13.364, 4.5882699637, 426.598190876], [7.257, 4.62966127155, 213.299095438], [4.876, 3.61448275002, 639.897286314], [3.136, 4.65661021909, 191.9584544356], [2.917, 0.48665273315, 323.5054166574], [3.759, 4.89624165044, 440.8252848776], [3.303, 4.07190859545, 647.0108333148], [2.883, 3.18003019204, 419.4846438752], [2.338, 3.69553554327, 88.865680217], [1.95, 5.3272924778, 302.164775655], [2.052, 3.31663577368, 95.9792272178], [1.591, 2.67009215574, 853.196381752], [2.028, 0.56025552769, 117.3198682202], [1.56, 0.85608042681, 515.463871093], [1.678, 0.0, 0.0], [1.102, 5.98011943842, 3.1813937377], [1.285, 5.82563377753, 234.6397364404], [0.896, 5.22791858719, 216.4804891757], [1.141, 0.15741228205, 412.3710968744], [0.798, 0.37452846153, 28.4541880032], [0.837, 5.04769794123, 124.433415221]]]

This table contains Saturn’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 pages 442-445.