Earth

Class to model Earth’s globe.

class pymeeus.Earth.Earth(ellipsoid=Ellipsoid(6378137.0, 0.00335281066475, 7.292115e-05))

Class Earth models the figure of the Earth surface and, with the help of a configurable reference ellipsoid, provides a set of handy method to compute different parameters, like the distance between two points on the surface.

Please note that here we depart a little bit from Meeus’ book because the Earth class uses the World Geodetic System 1984 (WGS84) as the default reference ellipsoid, instead of the International Astronomical Union 1974, which Meeus uses. This change is done because WGS84 is regarded as more modern.

__init__(ellipsoid=Ellipsoid(6378137.0, 0.00335281066475, 7.292115e-05))

Earth constructor.

It takes a reference ellipsoid as input. If not provided, the ellipsoid used is the WGS84 by default.

Parameters:ellipsoid – Reference ellipsoid to be used. WGS84 by default. Returns:Earth object. Return type:Earth Raises:TypeError if input value is of wrong type.

__repr__()

Method providing the ‘official’ string representation of the object. It provides a valid expression that could be used to recreate the object.

Returns:As string with a valid expression to recreate the object Return type:string

__str__()

Method used when trying to print the Earth object. It essentially returns the corresponting ‘__str__()’ method from the reference ellipsoid being used.

Returns:Semi-major equatorial radius, flattening and angular velocity of the current reference ellipsoid, as a string. Return type:string

>>> e = Earth()
>>> s = str(e)
>>> v = s.split(':')
>>> print(v[0] + '|' + str(round(float(v[1]), 14)) + '|' + v[2] )
6378137.0|0.00335281066475|7.292115e-05

__weakref__

list of weak references to the object (if defined)

static apparent_heliocentric_position(epoch, nutation=True)

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

Parameters:

• epoch (Epoch) – Epoch to compute Earth position, as an Epoch object
• nutation (bool) – Whether the nutation correction will be applied

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(1992, 10, 13.0)
>>> lon, lat, r = Earth.apparent_heliocentric_position(epoch)
>>> print(round(lon.to_positive(), 6))
19.905986
>>> print(lat.dms_str(n_dec=3))
-0.721''
>>> print(round(r, 8))
0.99760852

distance(lon1, lat1, lon2, lat2)

This method computes the distance between two points on the Earth’s surface using the method from H. Andoyer.

Note

We will consider that positions ‘East’ and ‘South’ are negative.

Parameters:

• lon1 (int, float, Angle) – Longitude of the first point, in degrees
• lat1 (int, float, Angle) – Geodetical or geographical latitude of the first point, in degrees
• lon2 (int, float, Angle) – Longitude of the second point, in degrees
• lat2 (int, float, Angle) – Geodetical or geographical latitude of the second point, in degrees

Returns:

Tuple with distance between the two points along Earth’s surface, and approximate error, in meters

Return type:

tuple

Raises:

TypeError if input values are of wrong type.

>>> e = Earth(ellipsoid=IAU76)
>>> lon1 = Angle(-2, 20, 14.0)
>>> lat1 = Angle(48, 50, 11.0)
>>> lon2 = Angle(77, 3, 56.0)
>>> lat2 = Angle(38, 55, 17.0)
>>> dist, error = e.distance(lon1, lat1, lon2, lat2)
>>> round(dist, 0)
6181628.0
>>> error
69.0
>>> lon1 = Angle(-2.09)
>>> lat1 = Angle(41.3)
>>> lon2 = Angle(73.99)
>>> lat2 = Angle(40.75)
>>> dist, error = e.distance(lon1, lat1, lon2, lat2)
>>> round(dist, 0)
6176760.0
>>> error
69.0

static geometric_heliocentric_position(epoch, tofk5=True)

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

Parameters:

• epoch (Epoch) – Epoch to compute Earth 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(1992, 10, 13.0)
>>> l, b, r = Earth.geometric_heliocentric_position(epoch, tofk5=False)
>>> print(round(l.to_positive(), 6))
19.907297
>>> print(b.dms_str(n_dec=3))
-0.744''
>>> print(round(r, 8))
0.99760852

static geometric_heliocentric_position_j2000(epoch, tofk5=True)

This method computes the geometric heliocentric position of the Earth for a given epoch, using the VSOP87 theory, referred to the equinox J2000.0.

Parameters:

• epoch (Epoch) – Epoch to compute Earth 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.

linear_velocity(latitude)

Method to compute the linear velocity of a point at latitude, due to the rotation of the Earth.

Parameters:latitude (int, float, Angle) – Geodetical or geographical latitude of the observer, in degrees Returns:Linear velocity of a point at latitude, in meters per second Return type:float Raises:TypeError if input value is of wrong type.

>>> e = Earth(ellipsoid=IAU76)
>>> round(e.linear_velocity(42.0), 2)
346.16

static orbital_elements_j2000(epoch)

This method computes the orbital elements of Earth 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 = Earth.orbital_elements_j2000(epoch)
>>> print(round(l, 6))
271.801199
>>> print(round(a, 8))
1.00000102
>>> print(round(e, 7))
0.0166811
>>> print(round(i, 6))
0.008544
>>> print(round(ome, 5))
174.71534
>>> print(round(arg, 6))
-71.566717

static orbital_elements_mean_equinox(epoch)

This method computes the orbital elements of Earth 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 = Earth.orbital_elements_mean_equinox(epoch)
>>> print(round(l, 6))
272.716028
>>> print(round(a, 8))
1.00000102
>>> print(round(e, 7))
0.0166811
>>> print(round(i, 6))
0.0
>>> print(round(ome, 5))
174.71534
>>> print(round(arg, 6))
-70.651889

static parallax_correction(right_ascension, declination, latitude, distance, hour_angle, height=0.0)

This function computes the parallaxes in right ascension and declination in order to obtain the topocentric values.

Parameters:

• right_ascension (Angle) – Geocentric right ascension, as an Angle object
• declination (Angle) – Geocentric declination, as an Angle object
• latitude (Angle) – Latitude of the observation point
• distance (float) – Distance from the celestial object to the Earth, in Astronomical Units
• hour_angle (Angle) – Geocentric hour angle of the celestial object, as an Angle
• heigth – Height of observation point above sea level, in meters

Returns:

Tuple containing the topocentric right ascension and declination

Return type:

tuple

Raises:

TypeError if input values are of wrong type.

>>> right_ascension = Angle(22, 38, 7.25, ra=True)
>>> declination = Angle(-15, 46, 15.9)
>>> latitude = Angle(33, 21, 22)
>>> distance = 0.37276
>>> hour_angle = Angle(288.7958)
>>> topo_ra, topo_dec = Earth.parallax_correction(right_ascension,                                                           declination,                                                           latitude, distance,                                                           hour_angle)
>>> print(topo_ra.ra_str(n_dec=2))
22h 38' 8.54''
>>> print(topo_dec.dms_str(n_dec=1))
-15d 46' 30.0''

static parallax_ecliptical(longitude, latitude, semidiameter, obs_lat, obliquity, sidereal_time, distance, height=0.0)

This function computes the topocentric coordinates of a celestial body (Moon or planet) directly from its geocentric values in ecliptical coordinates.

Parameters:

• longitude (Angle) – Geocentric ecliptical longitude as an Angle
• latitude (Angle) – Geocentric ecliptical latitude as an Angle
• semidiameter (Angle) – Geocentric semidiameter as an Angle
• obs_lat (Angle) – Latitude of the observation point
• obliquity (Angle) – Obliquity of the eliptic, as an Angle
• sidereal_time (Angle) – Local sidereal time, as an Angle
• distance (float) – Distance from the celestial object to the Earth, in Astronomical Units
• heigth – Height of observation point above sea level, in meters

Returns:

Tuple containing the topocentric longitude, latitude and semidiameter

Return type:

tuple

Raises:

TypeError if input values are of wrong type.

>>> longitude = Angle(181, 46, 22.5)
>>> latitude = Angle(2, 17, 26.2)
>>> semidiameter = Angle(0, 16, 15.5)
>>> obs_lat = Angle(50, 5, 7.8)
>>> obliquity = Angle(23, 28, 0.8)
>>> sidereal_time = Angle(209, 46, 7.9)
>>> distance = 0.0024650163
>>> topo_lon, topo_lat, topo_diam =                 Earth.parallax_ecliptical(longitude, latitude, semidiameter,                                           obs_lat, obliquity, sidereal_time,                                           distance)
>>> print(topo_lon.dms_str(n_dec=1))
181d 48' 5.0''
>>> print(topo_lat.dms_str(n_dec=1))
1d 29' 7.1''
>>> print(topo_diam.dms_str(n_dec=1))
16' 25.5''

static passage_nodes(epoch, ascending=True)

This function computes the time of passage by the nodes (ascending or descending) of Earth, 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 = Earth.passage_nodes(epoch)
>>> year, month, day = time.get_date()
>>> print(year)
2019
>>> print(month)
3
>>> print(round(day, 1))
15.0
>>> print(round(r, 4))
0.9945

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(1989, 11, 20.0)
>>> e = Earth.perihelion_aphelion(epoch)
>>> y, m, d, h, mi, s = e.get_full_date()
>>> print(y)
1990
>>> print(m)
1
>>> print(d)
4
>>> print(h)
17
>>> epoch = Epoch(2000, 4, 1.0)
>>> e = Earth.perihelion_aphelion(epoch, perihelion=False)
>>> y, m, d, h, mi, s = e.get_full_date()
>>> print(y)
2000
>>> print(m)
7
>>> print(d)
3
>>> print(h)
23
>>> print(mi)
51
>>> epoch = Epoch(2003, 3, 10.0)
>>> e = Earth.perihelion_aphelion(epoch)
>>> y, m, d, h, mi, s = e.get_full_date()
>>> print(y)
2003
>>> print(m)
1
>>> print(d)
4
>>> print(h)
5
>>> print(mi)
1
>>> epoch = Epoch(2009, 5, 1.0)
>>> e = Earth.perihelion_aphelion(epoch, perihelion=False)
>>> y, m, d, h, mi, s = e.get_full_date()
>>> print(y)
2009
>>> print(m)
7
>>> print(d)
4
>>> print(h)
1
>>> print(mi)
41

rho(latitude)

Method to compute the rho term, which is the observer distance to the center of the Earth, when the observer is at sea level. In this case, the Earth’s equatorial radius is taken as unity.

Parameters:latitude (int, float, Angle) – Geodetical or geographical latitude of the observer, in degrees Returns:Rho: Distance to the center of the Earth from sea level. It is a ratio with respect to Earth equatorial radius. Return type:float Raises:TypeError if input value is of wrong type.

>>> e = Earth(ellipsoid=IAU76)
>>> round(e.rho(0.0), 1)
1.0

rho_cosphi(latitude, height)

Method to compute the rho*cos(phi’) term, needed in the calculation of diurnal parallaxes, eclipses and occulatitions.

Parameters:

• latitude (int, float, Angle) – Geodetical or geographical latitude of the observer, in degrees
• height (int, float) – Height of the observer above the sea level, in meters

Returns:

rho*cos(phi’) term

Return type:

float

Raises:

TypeError if input value is of wrong type.

>>> lat = Angle(33, 21, 22.0)
>>> e = Earth(ellipsoid=IAU76)
>>> round(e.rho_cosphi(lat, 1706), 6)
0.836339

rho_sinphi(latitude, height)

Method to compute the rho*sin(phi’) term, needed in the calculation of diurnal parallaxes, eclipses and occulatitions.

Parameters:

• latitude (int, float, Angle) – Geodetical or geographical latitude of the observer, in degrees
• height (int, float) – Height of the observer above the sea level, in meters

Returns:

rho*sin(phi’) term

Return type:

float

Raises:

TypeError if input value is of wrong type.

>>> lat = Angle(33, 21, 22.0)
>>> e = Earth(ellipsoid=IAU76)
>>> round(e.rho_sinphi(lat, 1706), 6)
0.546861

rm(latitude)

Method to compute the radius of curvature of the Earth’s meridian at the given latitude.

Parameters:latitude (int, float, Angle) – Geodetical or geographical latitude of the observer, in degrees Returns:Radius of curvature of the Earth’s meridian at the given latitude, in meters Return type:float Raises:TypeError if input value is of wrong type.

>>> e = Earth(ellipsoid=IAU76)
>>> round(e.rm(42.0), 1)
6364033.3

rp(latitude)

Method to compute the radius of the parallel circle at the given latitude.

Parameters:latitude (int, float, Angle) – Geodetical or geographical latitude of the observer, in degrees Returns:Radius of the parallel circle at given latitude, in meters Return type:float Raises:TypeError if input value is of wrong type.

>>> e = Earth(ellipsoid=IAU76)
>>> round(e.rp(42.0), 1)
4747001.2

set(ellipsoid)

Method used to define an Earth object.

It takes a reference ellipsoid as input. If not provided, the ellipsoid used is the WGS84 by default.

Parameters:ellipsoid – Reference ellipsoid to be used. WGS84 by default. Returns:None Return type:None Raises:TypeError if input value is of wrong type.

class pymeeus.Earth.Ellipsoid(a, f, omega)

Class Ellipsoid is useful to encapsulate the most important parameters of a given reference ellipsoid.

__init__(a, f, omega)

Ellipsoid constructor.

Parameters:

• a (float) – Semi-major or equatorial radius, in meters
• f (float) – Flattening
• omega (float) – Angular velocity of the Earth, in rad/s

__repr__()

Method providing the ‘official’ string representation of the object. It provides a valid expression that could be used to recreate the object.

Returns:As string with a valid expression to recreate the object Return type:string

>>> a = Ellipsoid(6378140.0, 0.0033528132, 7.292e-5)
>>> repr(a)
'Ellipsoid(6378140.0, 0.0033528132, 7.292e-05)'

__str__()

Method used when trying to print the object.

Returns:Semi-major equatorial radius, flattening and angular velocity as a string. Return type:string

>>> a = Ellipsoid(6378140.0, 0.0033528132, 7.292e-5)
>>> print(a)
6378140.0:0.0033528132:7.292e-05

__weakref__

list of weak references to the object (if defined)

b()

Method to return the semi-minor radius.

Returns:Semi-minor radius, in meters Return type:float

>>> a = Ellipsoid(6378140.0, 0.0033528132, 7.292e-5)
>>> round(a.b(), 3)
6356755.288

e()

Method to return the eccentricity of the Earth’s meridian.

Returns:Eccentricity of the Earth’s meridian Return type:float

>>> a = Ellipsoid(6378140.0, 0.0033528132, 7.292e-5)
>>> round(a.e(), 8)
0.08181922

pymeeus.Earth.IAU76 = Ellipsoid(6378140.0, 0.0033528131779, 7.292114992e-05)

Reference ellipsoid defined by the International Astronomic Union in 1976

pymeeus.Earth.ORBITAL_ELEM = [[100.466457, 36000.7698278, 0.00030322, 2e-08], [1.000001018, 0.0, 0.0, 0.0], [0.01670863, -4.2037e-05, -1.267e-07, 1.4e-10], [0.0, 0.0, 0.0, 0.0], [174.873176, -0.2410908, 4.262e-05, 1e-09], [102.937348, 1.7195366, 0.00045688, -1.8e-08]]

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

pymeeus.Earth.ORBITAL_ELEM_J2000 = [[100.466457, 35999.3728565, -5.68e-06, -1e-09], [0.0, 0.0130548, -9.31e-06, -3.4e-08], [174.873176, -0.2410908, 4.262e-05, 1e-09], [102.937348, 0.3225654, 0.00014799, -3.9e-08]]

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

pymeeus.Earth.VSOP87_B = [[[279.62, 3.19870156017, 84334.66158130829], [101.643, 5.42248619256, 5507.5532386674], [80.445, 3.88013204458, 5223.6939198022], [43.806, 3.70444689758, 2352.8661537718], [31.933, 4.00026369781, 1577.3435424478], [22.724, 3.9847383156, 1047.7473117547], [16.392, 3.56456119782, 5856.4776591154], [18.141, 4.98367470263, 6283.0758499914], [14.443, 3.70275614914, 9437.762934887], [14.304, 3.41117857525, 10213.285546211], [11.246, 4.8282069053, 14143.4952424306], [10.9, 2.08574562327, 6812.766815086], [9.714, 3.47303947752, 4694.0029547076], [10.367, 4.05663927946, 71092.88135493269], [8.775, 4.44016515669, 5753.3848848968], [8.366, 4.9925151218, 7084.8967811152], [6.921, 4.32559054073, 6275.9623029906], [9.145, 1.14182646613, 6620.8901131878], [7.194, 3.60193205752, 529.6909650946], [7.698, 5.55425745881, 167621.5758508619], [5.285, 2.48446991566, 4705.7323075436], [5.208, 6.24992674537, 18073.7049386502], [4.529, 2.33827747356, 6309.3741697912], [5.579, 4.41023653738, 7860.4193924392], [4.743, 0.70995680136, 5884.9268465832], [4.301, 1.10255777773, 6681.2248533996], [3.849, 1.82229412531, 5486.777843175], [4.093, 5.11700141207, 13367.9726311066], [3.681, 0.43793170356, 3154.6870848956], [3.42, 5.42034800952, 6069.7767545534], [3.617, 6.04641937526, 3930.2096962196], [3.67, 4.58210192227, 12194.0329146209], [2.918, 1.95463881126, 10977.078804699], [2.797, 5.61259275048, 11790.6290886588], [2.502, 0.60499729367, 6496.3749454294], [2.319, 5.01648216014, 1059.3819301892], [2.684, 1.39470396488, 22003.9146348698], [2.428, 3.24183056052, 78051.5857313169], [2.12, 4.30691000285, 5643.1785636774], [2.257, 3.15557225618, 90617.7374312997], [1.813, 3.75574218285, 3340.6124266998], [2.226, 2.79699346659, 12036.4607348882], [1.888, 0.86991545823, 8635.9420037632], [1.517, 1.95852055701, 398.1490034082], [1.581, 3.19976230948, 5088.6288397668], [1.421, 6.25530883827, 2544.3144198834], [1.595, 0.25619915135, 17298.1823273262], [1.391, 4.69964175561, 7058.5984613154], [1.478, 2.81808207569, 25934.1243310894], [1.481, 3.65823554806, 11506.7697697936], [1.693, 4.95689385293, 156475.2902479957], [1.183, 1.29343061246, 775.522611324], [1.114, 2.37889311846, 3738.761430108], [0.994, 4.30088900425, 9225.539273283], [0.924, 3.06451026812, 4164.311989613], [0.867, 0.55606931068, 8429.2412664666], [0.988, 5.97286104208, 7079.3738568078], [0.824, 1.50984806173, 10447.3878396044], [0.915, 0.12635654592, 11015.1064773348], [0.742, 1.99159139281, 26087.9031415742], [1.039, 3.14159265359, 0.0], [0.85, 4.24120016095, 29864.334027309], [0.755, 2.8963187332, 4732.0306273434], [0.714, 1.37548118603, 2146.1654164752], [0.708, 1.91406542362, 8031.0922630584], [0.746, 0.57893808616, 796.2980068164], [0.802, 5.1233913723, 2942.4634232916], [0.751, 1.67479850166, 21228.3920235458], [0.602, 4.09976538826, 64809.80550494129], [0.594, 3.49580704962, 16496.3613962024], [0.592, 4.59481504319, 4690.4798363586], [0.53, 5.739792952, 8827.3902698748], [0.503, 5.66433137112, 33794.5437235286], [0.483, 1.57106522411, 801.8209311238], [0.438, 0.06707733767, 3128.3887650958], [0.423, 2.86944595927, 12566.1516999828], [0.504, 3.2620766916, 7632.9432596502], [0.552, 1.02926440457, 239762.20451754928], [0.427, 3.6743437821, 213.299095438], [0.404, 1.46193297142, 15720.8387848784], [0.503, 4.85802444134, 6290.1893969922], [0.417, 0.81920713533, 5216.5803728014], [0.365, 0.01002966162, 12168.0026965746], [0.363, 1.28376436579, 6206.8097787158], [0.353, 4.7005913311, 7234.794256242], [0.415, 0.96862624175, 4136.9104335162], [0.387, 3.09145061418, 25158.6017197654], [0.373, 2.65119262792, 7342.4577801806], [0.361, 2.97762937739, 9623.6882766912], [0.418, 3.75759994446, 5230.807466803], [0.396, 1.22507712354, 6438.4962494256], [0.322, 1.21162178805, 8662.240323563], [0.284, 5.64170320068, 1589.0728952838], [0.379, 1.72248432748, 14945.3161735544], [0.32, 3.94161159962, 7330.8231617461], [0.313, 5.47602376446, 1194.4470102246], [0.292, 1.38971327603, 11769.8536931664], [0.305, 0.80429352049, 37724.7534197482], [0.257, 5.81382809757, 426.598190876], [0.265, 6.10358507671, 6836.6452528338], [0.25, 4.56452895547, 7477.522860216], [0.266, 2.62926282354, 7238.6755916], [0.263, 6.22089501237, 6133.5126528568], [0.306, 2.79682380531, 1748.016413067], [0.236, 2.46093023714, 11371.7046897582], [0.316, 1.62662805006, 250908.4901204155], [0.216, 3.68721275185, 5849.3641121146], [0.23, 0.36165162947, 5863.5912061162], [0.233, 5.03509933858, 20426.571092422], [0.2, 5.86073159059, 4535.0594369244], [0.277, 4.65400292395, 82239.1669577989], [0.209, 3.72323200804, 10973.55568635], [0.199, 5.05186622555, 5429.8794682394], [0.256, 2.4092327977, 19651.048481098], [0.21, 4.50691909144, 29088.811415985], [0.181, 6.00294783127, 4292.3308329504], [0.249, 0.12900984422, 154379.7956244863], [0.209, 3.87759458598, 17789.845619785], [0.225, 3.18339652605, 18875.525869774], [0.191, 4.53897489299, 18477.1087646123], [0.172, 2.09694183014, 13095.8426650774], [0.182, 3.161079435, 16730.4636895958], [0.188, 2.22746128596, 41654.9631159678], [0.164, 5.18686275017, 5481.2549188676], [0.16, 2.49298855159, 12592.4500197826], [0.155, 1.5959543823, 10021.8372800994], [0.135, 0.21349051064, 10988.808157535], [0.178, 3.8037517797, 23581.2581773176], [0.123, 1.66800739151, 15110.4661198662], [0.122, 2.72678272244, 18849.2275499742], [0.126, 1.1767551291, 14919.0178537546], [0.142, 3.95053441332, 337.8142631964], [0.116, 6.06340906229, 6709.6740408674], [0.137, 3.52143246757, 12139.5535091068], [0.136, 2.92179113542, 32217.2001810808], [0.11, 3.51203379263, 18052.9295431578], [0.147, 4.63371971408, 22805.7355659936], [0.108, 5.45280814878, 7.1135470008], [0.148, 0.65447253687, 95480.9471841745], [0.119, 5.92110458985, 33019.0211122046], [0.11, 5.34824206306, 639.897286314], [0.106, 3.71081682629, 14314.1681130498], [0.139, 6.17607198418, 24356.7807886416], [0.118, 5.5973871267, 161338.5000008705], [0.117, 3.6506527164, 45585.1728121874], [0.127, 4.74596574209, 49515.382508407], [0.12, 1.04211499785, 6915.8595893046], [0.12, 5.60638811846, 5650.2921106782], [0.115, 3.10668213289, 14712.317116458], [0.099, 0.69018940049, 12779.4507954208], [0.097, 1.07908724794, 9917.6968745098], [0.093, 2.62295197319, 17260.1546546904], [0.099, 4.45774681732, 4933.2084403326], [0.123, 1.37488922089, 28286.9904848612], [0.121, 5.19767249813, 27511.4678735372], [0.105, 0.87192267806, 77375.95720492408], [0.087, 3.9363781295, 17654.7805397496], [0.122, 2.2395606868, 83997.09113559539], [0.087, 4.18201600952, 22779.4372461938], [0.104, 4.59580877295, 1349.8674096588], [0.102, 2.83545248411, 12352.8526045448], [0.102, 3.97386522171, 10818.1352869158], [0.101, 4.32892825857, 36147.4098773004], [0.094, 5.00001709261, 150192.2143980043], [0.077, 3.97199369296, 1592.5960136328], [0.1, 6.07733097102, 26735.9452622132], [0.086, 5.2602963825, 28313.288804661], [0.093, 4.31900620254, 44809.6502008634], [0.076, 6.22743405935, 13521.7514415914], [0.072, 1.55820597747, 6256.7775301916], [0.082, 4.95202664555, 10575.4066829418], [0.082, 1.69647647075, 1990.745017041], [0.075, 2.29836095644, 3634.6210245184], [0.075, 2.66367876557, 16200.7727245012], [0.087, 0.26630214764, 31441.6775697568], [0.077, 2.25530954137, 5235.3285382367], [0.076, 1.09869730846, 12903.9659631792], [0.058, 4.28246138307, 12559.038152982], [0.064, 5.51112830114, 173904.65170085328], [0.056, 2.60133794851, 73188.3759784421], [0.055, 5.81483150022, 143233.51002162008], [0.054, 3.38482031504, 323049.11878710287], [0.039, 3.28500401343, 71768.50988132549], [0.039, 3.1123991069, 96900.81328129109]], [[9.03, 3.8972906189, 5507.5532386674], [6.177, 1.73038850355, 5223.6939198022], [3.8, 5.24404145734, 2352.8661537718], [2.834, 2.4734503745, 1577.3435424478], [1.817, 0.41874743765, 6283.0758499914], [1.499, 1.83320979291, 5856.4776591154], [1.466, 5.69401926017, 5753.3848848968], [1.301, 2.18890066314, 9437.762934887], [1.233, 4.95222451476, 10213.285546211], [1.021, 0.12866660208, 7860.4193924392], [0.982, 0.09005453285, 14143.4952424306], [0.865, 1.73949953555, 3930.2096962196], [0.581, 2.26949174067, 5884.9268465832], [0.524, 5.65662503159, 529.6909650946], [0.473, 6.22750969242, 6309.3741697912], [0.451, 1.53288619213, 18073.7049386502], [0.364, 3.61614477374, 13367.9726311066], [0.372, 3.2247072132, 6275.9623029906], [0.268, 2.34341267879, 11790.6290886588], [0.322, 0.94084045832, 6069.7767545534], [0.232, 0.26781182579, 7058.5984613154], [0.216, 6.05952221329, 10977.078804699], [0.232, 2.93325646109, 22003.9146348698], [0.204, 3.86264841382, 6496.3749454294], [0.202, 2.81892511133, 15720.8387848784], [0.185, 4.93512381859, 12036.4607348882], [0.22, 3.99305643742, 6812.766815086], [0.166, 1.74970002999, 11506.7697697936], [0.212, 1.57166285369, 4694.0029547076], [0.157, 1.08259734788, 5643.1785636774], [0.154, 5.99434678412, 5486.777843175], [0.144, 5.23285656085, 78051.5857313169], [0.144, 1.16454655948, 90617.7374312997], [0.137, 2.67760436027, 6290.1893969922], [0.18, 2.06509026215, 7084.8967811152], [0.121, 5.90212574947, 9225.539273283], [0.15, 2.00175038718, 5230.807466803], [0.149, 5.06157254516, 17298.1823273262], [0.118, 5.39979058038, 3340.6124266998], [0.161, 3.32421999691, 6283.3196674749], [0.121, 4.36722193162, 19651.048481098], [0.116, 5.83462858507, 4705.7323075436], [0.128, 4.35489873365, 25934.1243310894], [0.143, 0.0, 0.0], [0.109, 2.52157834166, 6438.4962494256], [0.099, 2.70727488041, 5216.5803728014], [0.103, 0.93782340879, 8827.3902698748], [0.082, 4.2921468039, 8635.9420037632], [0.079, 2.24085737326, 1059.3819301892], [0.097, 5.50959692365, 29864.334027309], [0.072, 0.21891639822, 21228.3920235458], [0.071, 2.86755026812, 6681.2248533996], [0.074, 2.20184828895, 37724.7534197482], [0.063, 4.45586625948, 7079.3738568078], [0.061, 0.63918772258, 33794.5437235286], [0.047, 2.09070235724, 3128.3887650958], [0.047, 3.325438433, 26087.9031415742], [0.049, 1.60680905005, 6702.5604938666], [0.057, 0.11215813438, 29088.811415985], [0.056, 5.47982934911, 775.522611324], [0.05, 1.89396788463, 12139.5535091068], [0.047, 2.9721490724, 20426.571092422], [0.041, 5.5532939489, 11015.1064773348], [0.041, 5.91861144924, 23581.2581773176], [0.045, 4.95273290181, 5863.5912061162], [0.05, 3.62740835096, 41654.9631159678], [0.037, 6.09033460601, 64809.80550494129], [0.037, 5.86153655431, 12566.1516999828], [0.046, 1.65798680284, 25158.6017197654], [0.038, 2.00673650251, 426.598190876], [0.036, 6.24373396652, 6283.14316029419], [0.036, 0.40465162918, 6283.0085396886], [0.032, 6.03707103538, 2942.4634232916], [0.041, 4.86809570283, 1592.5960136328], [0.028, 4.38359423735, 7632.9432596502], [0.028, 6.03334294232, 17789.845619785], [0.026, 3.88971333608, 5331.3574437408], [0.026, 5.94932724051, 16496.3613962024], [0.031, 1.44666331503, 16730.4636895958], [0.026, 6.26376705837, 23543.23050468179], [0.033, 0.93797239147, 213.299095438], [0.026, 3.71858432944, 13095.8426650774], [0.027, 0.60565274405, 10988.808157535], [0.023, 4.4438898555, 18849.2275499742], [0.028, 1.53862289477, 6279.4854213396], [0.028, 1.96831814872, 6286.6662786432], [0.028, 5.78094918529, 15110.4661198662], [0.026, 2.48165809843, 5729.506447149], [0.02, 3.85655029499, 9623.6882766912], [0.021, 5.83006047147, 7234.794256242], [0.021, 0.69628570421, 398.1490034082], [0.022, 5.02222806555, 6127.6554505572], [0.02, 3.4761126529, 6148.010769956], [0.02, 0.90769829044, 5481.2549188676], [0.02, 0.03081589303, 6418.1409300268], [0.02, 3.74220084927, 1589.0728952838], [0.021, 4.00149269576, 3154.6870848956], [0.018, 1.58348238359, 2118.7638603784], [0.019, 0.85407021371, 14712.317116458]], [[1.662, 1.62703209173, 84334.66158130829], [0.492, 2.41382223971, 1047.7473117547], [0.344, 2.24353004539, 5507.5532386674], [0.258, 6.00906896311, 5223.6939198022], [0.131, 0.9544734524, 6283.0758499914], [0.086, 1.67530247303, 7860.4193924392], [0.09, 0.97606804452, 1577.3435424478], [0.09, 0.37899871725, 2352.8661537718], [0.089, 6.25807507963, 10213.285546211], [0.075, 0.84213523741, 167621.5758508619], [0.052, 1.70501566089, 14143.4952424306], [0.057, 6.15295833679, 12194.0329146209], [0.051, 1.2761601674, 5753.3848848968], [0.051, 5.37229738682, 6812.766815086], [0.034, 1.73672994279, 7058.5984613154], [0.038, 2.77761031485, 10988.808157535], [0.046, 3.38617099014, 156475.2902479957], [0.021, 1.95248349228, 8827.3902698748], [0.018, 3.33419222028, 8429.2412664666], [0.019, 4.32945160287, 17789.845619785], [0.017, 0.66191210656, 6283.0085396886], [0.018, 3.74885333072, 11769.8536931664], [0.017, 4.23058370776, 10977.078804699], [0.017, 1.78116162721, 5486.777843175], [0.021, 1.36972913918, 12036.4607348882], [0.017, 2.79601092529, 796.2980068164], [0.015, 0.4308784885, 11790.6290886588], [0.017, 1.35132152761, 78051.5857313169], [0.015, 1.17032155085, 213.299095438], [0.018, 2.85221514199, 5088.6288397668], [0.017, 0.21780913672, 6283.14316029419], [0.013, 1.21201504386, 25132.3033999656], [0.012, 1.12953712197, 90617.7374312997], [0.012, 5.13714452592, 7079.3738568078], [0.013, 3.79842135217, 4933.2084403326], [0.012, 4.89407978213, 3738.761430108], [0.015, 6.05682328852, 398.1490034082], [0.014, 4.81029291856, 4694.0029547076], [0.011, 0.61684523405, 3128.3887650958], [0.011, 5.328765385, 6040.3472460174], [0.014, 5.27227350286, 4535.0594369244], [0.011, 2.39292099451, 5331.3574437408], [0.01, 4.4529653271, 6525.8044539654], [0.014, 4.66400985037, 8031.0922630584], [0.01, 3.22472385926, 9437.762934887], [0.011, 3.80913404437, 801.8209311238], [0.01, 5.15032130575, 11371.7046897582], [0.013, 0.98720797401, 5729.506447149], [0.009, 5.94191743597, 7632.9432596502]], [[0.011, 0.23877262399, 7860.4193924392], [0.009, 1.16069982609, 5507.5532386674], [0.008, 1.65357552925, 5884.9268465832], [0.008, 2.86720038197, 7058.5984613154], [0.007, 3.04818741666, 5486.777843175], [0.007, 2.59437103785, 529.6909650946], [0.008, 4.02863090524, 6256.7775301916], [0.008, 2.42003508927, 5753.3848848968], [0.006, 0.84181087594, 6275.9623029906], [0.006, 5.40160929468, 1577.3435424478], [0.007, 2.73399865247, 6309.3741697912]], [[0.004, 0.79662198849, 6438.4962494256], [0.005, 0.84308705203, 1047.7473117547], [0.005, 0.05711572303, 84334.66158130829], [0.003, 3.46779895686, 6279.5527316424], [0.003, 2.89822201212, 6127.6554505572]]]

This table contains Earth’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 420.

pymeeus.Earth.VSOP87_B_J2000 = [[[280.0, 3.199, 84334.662], [102.0, 5.422, 5507.553], [80.0, 3.88, 5223.69], [44.0, 3.7, 2352.87], [32.0, 4.0, 1577.34]], [[227778.0, 3.413766, 6283.07585], [3806.0, 3.3706, 12566.1517], [3620.0, 0.0, 0.0], [72.0, 3.33, 18849.23], [8.0, 3.89, 5507.55], [8.0, 1.79, 5223.69], [6.0, 5.2, 2352.87]], [[9721.0, 5.1519, 6283.07585], [233.0, 3.1416, 0.0], [134.0, 0.644, 12566.152], [7.0, 1.07, 18849.23]], [[276.0, 0.595, 6283.076], [17.0, 3.14, 0.0], [4.0, 0.12, 12566.15]], [[6.0, 2.27, 6283.08], [1.0, 0.0, 0.0]]]

This table contains Earth’s most important periodic terms from the planetary theory VSOP87 for the heliocentric latitude, referred to the equinox J2000.0. In Meeus’ book these values can be found in page 420 and page 173.

pymeeus.Earth.VSOP87_L = [[[175347045.673, 0.0, 0.0], [3341656.456, 4.66925680417, 6283.0758499914], [34894.275, 4.62610241759, 12566.1516999828], [3417.571, 2.82886579606, 3.523118349], [3497.056, 2.74411800971, 5753.3848848968], [3135.896, 3.62767041758, 77713.7714681205], [2676.218, 4.41808351397, 7860.4193924392], [2342.687, 6.13516237631, 3930.2096962196], [1273.166, 2.03709655772, 529.6909650946], [1324.292, 0.74246356352, 11506.7697697936], [901.855, 2.04505443513, 26.2983197998], [1199.167, 1.10962944315, 1577.3435424478], [857.223, 3.50849156957, 398.1490034082], [779.786, 1.17882652114, 5223.6939198022], [990.25, 5.23268129594, 5884.9268465832], [753.141, 2.53339053818, 5507.5532386674], [505.264, 4.58292563052, 18849.2275499742], [492.379, 4.20506639861, 775.522611324], [356.655, 2.91954116867, 0.0673103028], [284.125, 1.89869034186, 796.2980068164], [242.81, 0.34481140906, 5486.777843175], [317.087, 5.84901952218, 11790.6290886588], [271.039, 0.31488607649, 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3.83803776214, 12566.1516999828], [0.42, 0.41925861858, 155.4203994342], [0.04, 3.5984758584, 18849.2275499742], [0.041, 3.14398414077, 3.523118349], [0.035, 5.00298940826, 5573.1428014331], [0.013, 0.48794833701, 77713.7714681205], [0.01, 5.6480176635, 6127.6554505572], [0.008, 2.84160570605, 161000.6857376741], [0.002, 0.54912904658, 6438.4962494256]], [[0.878, 3.14159265359, 0.0], [0.172, 2.7657906951, 6283.0758499914], [0.05, 2.01353298182, 155.4203994342], [0.028, 2.21496423926, 12566.1516999828], [0.005, 1.75600058765, 18849.2275499742]]]

This table contains Earth’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 418-420.

pymeeus.Earth.VSOP87_L_J2000 = [[[175347046.0, 0.0, 0.0], [3341656.0, 4.6692568, 6283.07585], [34894.0, 4.6261, 12556.1517], [3497.0, 2.7441, 5753.3849], [3418.0, 2.8289, 3.5231], [3136.0, 3.6277, 77713.7715], [2676.0, 4.4181, 7860.4194], [2343.0, 6.1352, 3930.2097], [1324.0, 0.7425, 11506.7698], [1273.0, 2.0371, 529.691], [1199.0, 1.1096, 1577.3435], [990.0, 5.233, 5884.927], [902.0, 2.045, 26.298], [857.0, 3.508, 398.149], [780.0, 1.179, 5223.694], [753.0, 2.533, 5507.553], [505.0, 4.583, 18849.228], [492.0, 4.205, 775.523], [357.0, 2.92, 0.067], [317.0, 5.849, 11790.629], [284.0, 1.899, 796.298], [271.0, 0.315, 10977.079], [243.0, 0.345, 5486.778], [206.0, 4.806, 2544.314], [205.0, 1.869, 5573.143], [202.0, 2.458, 6069.777], [156.0, 0.833, 213.299], [132.0, 3.411, 2942.463], [126.0, 1.083, 20.775], [115.0, 0.645, 0.98], [103.0, 0.636, 4694.003], [102.0, 0.976, 15720.839], [102.0, 4.267, 7.114], [99.0, 6.21, 2146.17], [98.0, 0.68, 155.42], [86.0, 5.98, 161000.69], [85.0, 1.3, 6275.96], [85.0, 3.67, 71430.7], [80.0, 1.81, 17260.15], [79.0, 3.04, 12036.46], [75.0, 1.76, 5088.63], [74.0, 3.5, 3154.69], [74.0, 4.68, 801.82], [70.0, 0.83, 9437.76], [62.0, 3.98, 8827.39], [61.0, 1.82, 7084.9], [57.0, 2.78, 6286.6], [56.0, 4.39, 14143.5], [56.0, 3.47, 6279.55], [52.0, 0.19, 12139.55], [52.0, 1.33, 1748.02], [51.0, 0.28, 5856.48], [49.0, 0.49, 1194.45], [41.0, 5.37, 8429.24], [41.0, 2.4, 19651.05], [39.0, 6.17, 10447.39], [37.0, 6.04, 10213.29], [37.0, 2.57, 1059.38], [36.0, 1.71, 2352.87], [36.0, 1.78, 6812.77], [33.0, 0.59, 17789.85], [30.0, 0.44, 83996.85], [30.0, 2.74, 1349.87], [25.0, 3.16, 4690.48]], [[628307584999.0, 0.0, 0.0], [206059.0, 2.678235, 6283.07585], [4303.0, 2.6351, 12566.1517], [425.0, 1.59, 3.523], [119.0, 5.796, 26.298], [109.0, 2.966, 1577.344], [93.0, 2.59, 18849.23], [72.0, 1.14, 529.69], [68.0, 1.87, 398.15], [67.0, 4.41, 5507.55], [59.0, 2.89, 5223.69], [56.0, 2.17, 155.42], [45.0, 0.4, 796.3], [36.0, 0.47, 775.52], [29.0, 2.65, 7.11], [21.0, 5.34, 0.98], [19.0, 1.85, 5486.78], [19.0, 4.97, 213.3], [17.0, 2.99, 6275.96], [16.0, 0.03, 2544.31], [16.0, 1.43, 2146.17], [15.0, 1.21, 10977.08], [12.0, 2.83, 1748.02], [12.0, 3.26, 5088.63], [12.0, 5.27, 1194.45], [12.0, 2.08, 4694.0], [11.0, 0.77, 553.57], [10.0, 1.3, 6286.6], [10.0, 4.24, 1349.87], [9.0, 2.7, 242.73], [9.0, 5.64, 951.72], [8.0, 5.3, 2352.87], [6.0, 2.65, 9437.76], [6.0, 4.67, 4690.48]], [[8722.0, 1.0725, 6283.0758], [991.0, 3.1416, 0.0], [295.0, 0.437, 12566.152], [27.0, 0.05, 3.52], [16.0, 5.19, 26.3], [16.0, 3.69, 155.42], [9.0, 0.3, 18849.23], [9.0, 2.06, 77713.77], [7.0, 0.83, 775.52], [5.0, 4.66, 1577.34], [4.0, 1.03, 7.11], [4.0, 3.44, 5573.14], [3.0, 5.14, 796.3], [3.0, 6.05, 5507.55], [3.0, 1.19, 242.73], [3.0, 6.12, 529.69], [3.0, 0.3, 398.15], [3.0, 2.28, 553.57], [2.0, 4.38, 5223.69], [2.0, 3.75, 0.98]], [[289.0, 5.842, 6283.076], [21.0, 6.05, 12556.15], [3.0, 5.2, 155.42], [3.0, 3.14, 0.0], [1.0, 4.72, 3.52], [1.0, 5.97, 242.73], [1.0, 5.54, 18849.23]], [[8.0, 4.14, 6283.08], [1.0, 3.28, 12566.15]]]

This table contains Earth’s most important periodic terms from the planetary theory VSOP87 for the heliocentric longitude, referred to the equinox J2000.0. In Meeus’ book these values can be found in pages 418-420 and page 173.

pymeeus.Earth.VSOP87_R = [[[100013988.799, 0.0, 0.0], [1670699.626, 3.09846350771, 6283.0758499914], [13956.023, 3.0552460962, 12566.1516999828], [3083.72, 5.19846674381, 77713.7714681205], [1628.461, 1.17387749012, 5753.3848848968], [1575.568, 2.84685245825, 7860.4193924392], [924.799, 5.45292234084, 11506.7697697936], [542.444, 4.56409149777, 3930.2096962196], [472.11, 3.66100022149, 5884.9268465832], [328.78, 5.89983646482, 5223.6939198022], [345.983, 0.96368617687, 5507.5532386674], [306.784, 0.29867139512, 5573.1428014331], [174.844, 3.01193636534, 18849.2275499742], [243.189, 4.27349536153, 11790.6290886588], [211.829, 5.84714540314, 1577.3435424478], [185.752, 5.02194447178, 10977.078804699], [109.835, 5.05510636285, 5486.777843175], [98.316, 0.88681311277, 6069.7767545534], [86.499, 5.68959778254, 15720.8387848784], [85.825, 1.27083733351, 161000.6857376741], [62.916, 0.92177108832, 529.6909650946], [57.056, 2.01374292014, 83996.84731811189], [64.903, 0.27250613787, 17260.1546546904], [49.384, 3.24501240359, 2544.3144198834], [55.736, 5.24159798933, 71430.69561812909], [42.515, 6.01110242003, 6275.9623029906], [46.963, 2.57805070386, 775.522611324], [38.968, 5.36071738169, 4694.0029547076], [44.661, 5.53715807302, 9437.762934887], [35.66, 1.67468058995, 12036.4607348882], [31.921, 0.18368229781, 5088.6288397668], [31.846, 1.77775642085, 398.1490034082], [33.193, 0.24370300098, 7084.8967811152], [38.245, 2.39255343974, 8827.3902698748], [28.464, 1.21344868176, 6286.5989683404], [37.49, 0.82952922332, 19651.048481098], [36.957, 4.90107591914, 12139.5535091068], [34.537, 1.84270693282, 2942.4634232916], [26.275, 4.58896850401, 10447.3878396044], [24.596, 3.78660875483, 8429.2412664666], [23.587, 0.26866117066, 796.2980068164], [27.793, 1.89934330904, 6279.5527316424], [23.927, 4.99598548138, 5856.4776591154], [20.349, 4.65267995431, 2146.1654164752], [23.287, 2.80783650928, 14143.4952424306], [22.103, 1.95004702988, 3154.6870848956], [19.506, 5.38227371393, 2352.8661537718], [17.958, 0.19871379385, 6812.766815086], [17.174, 4.43315560735, 10213.285546211], [16.19, 5.23160507859, 17789.845619785], [17.314, 6.15200787916, 16730.4636895958], [13.814, 5.18962074032, 8031.0922630584], [18.833, 0.67306674027, 149854.4001348079], [18.331, 2.25348733734, 23581.2581773176], [13.641, 3.68516118804, 4705.7323075436], [13.139, 0.65289581324, 13367.9726311066], [10.414, 4.33285688538, 11769.8536931664], [9.978, 4.20126336355, 6309.3741697912], [10.169, 1.59390681369, 4690.4798363586], [7.564, 2.6256059739, 6256.7775301916], [9.661, 3.6758679122, 27511.4678735372], [6.743, 0.56270332741, 3340.6124266998], [8.743, 6.06359123461, 1748.016413067], [7.786, 3.67371235637, 12168.0026965746], [6.633, 5.66149277792, 11371.7046897582], [7.712, 0.31242577789, 7632.9432596502], [6.592, 3.13576266188, 801.8209311238], [7.46, 5.64757188143, 11926.2544136688], [6.933, 2.923845864, 6681.2248533996], [6.802, 1.4232980642, 23013.5395395872], [6.115, 5.13393615454, 1194.4470102246], [6.477, 2.64986648492, 19804.8272915828], [5.233, 4.62434053374, 6438.4962494256], [6.147, 3.02863936662, 233141.3144043615], [4.608, 1.72194702724, 7234.794256242], [4.221, 1.55697533729, 7238.6755916], [5.314, 2.40716580847, 11499.6562227928], [5.128, 5.3239896569, 11513.8833167944], [4.77, 0.25554312006, 11856.2186514245], [5.519, 2.09089154502, 17298.1823273262], [5.625, 4.34052903053, 90955.5516944961], [4.578, 4.4656964157, 5746.271337896], [3.788, 4.9072938351, 4164.311989613], [5.337, 5.09957905104, 31441.6775697568], [3.967, 1.20054555174, 1349.8674096588], [4.008, 3.03007204392, 1059.3819301892], [3.476, 0.7608027703, 10973.55568635], [4.232, 1.05485713117, 5760.4984318976], [4.582, 3.76570026763, 6386.16862421], [3.335, 3.13829943354, 6836.6452528338], [3.418, 3.00072390334, 4292.3308329504], [3.598, 5.70718084323, 5643.1785636774], [3.237, 4.16448773994, 9917.6968745098], [4.154, 2.59941292162, 7058.5984613154], [3.362, 4.54577697964, 4732.0306273434], [2.978, 1.3056126882, 6283.14316029419], [2.765, 0.51311975679, 26.2983197998], [2.802, 5.66263240521, 8635.9420037632], [2.927, 5.73787481548, 16200.7727245012], [3.164, 1.69140262657, 11015.1064773348], [2.598, 2.96244118586, 25132.3033999656], [3.519, 3.62639325753, 244287.60000722768], [2.676, 4.2072570085, 18073.7049386502], [2.978, 1.74971565805, 6283.0085396886], [2.287, 1.06975704977, 14314.1681130498], [2.863, 5.92838131397, 14712.317116458], [3.071, 0.23793217002, 35371.8872659764], [2.656, 0.8995930178, 12352.8526045448], [2.415, 2.79975176257, 709.9330485583], [2.814, 3.51488206882, 21228.3920235458], [1.977, 2.6135829755, 951.7184062506], [2.548, 2.47684686575, 6208.2942514241], [1.999, 0.5609038816, 7079.3738568078], [2.305, 1.05376461628, 22483.84857449259], [1.855, 2.86090681163, 5216.5803728014], [2.157, 1.31396741861, 154717.6098876827], [1.97, 4.36929875289, 167283.7615876655], [1.635, 5.85571606764, 10984.1923516998], [1.754, 2.14452408833, 6290.1893969922], [2.154, 6.03828341543, 10873.9860304804], [1.714, 3.70157691113, 1592.5960136328], [1.541, 6.21598380732, 23543.23050468179], [1.611, 1.99824499377, 10969.9652576982], [1.712, 1.34295663542, 3128.3887650958], [1.642, 5.55026665339, 6496.3749454294], [1.502, 5.43948825854, 155.4203994342], [1.827, 5.91227480261, 3738.761430108], [1.726, 2.16764983583, 10575.4066829418], [1.532, 5.3568310707, 13521.7514415914], [1.829, 1.66006148731, 39302.096962196], [1.605, 1.90928637633, 6133.5126528568], [1.282, 2.46014880418, 13916.0191096416], [1.211, 4.4136063155, 3894.1818295422], [1.394, 1.77801929354, 9225.539273283], [1.571, 4.95512957592, 25158.6017197654], [1.205, 1.19212540615, 3.523118349], [1.132, 2.69830084955, 6040.3472460174], [1.504, 5.77002730341, 18209.33026366019], [1.393, 1.62621805428, 5120.6011455836], [1.077, 2.93931554233, 17256.6315363414], [1.232, 0.71655165307, 143571.32428481648], [1.087, 0.99769687939, 955.5997416086], [1.068, 5.28472576231, 65147.6197681377], [0.98, 5.10949204607, 6172.869528772], [1.169, 3.11664290862, 14945.3161735544], [1.202, 4.02992510402, 553.5694028424], [0.979, 2.00000879212, 15110.4661198662], [0.962, 4.023807714, 6282.0955289232], [0.999, 3.6264300279, 6262.300454499], [1.03, 5.84989900289, 213.299095438], [1.014, 2.84221578218, 8662.240323563], [1.185, 1.51330541132, 17654.7805397496], [0.967, 2.67081017562, 5650.2921106782], [1.222, 2.65423784904, 88860.05707098669], [0.981, 2.36370360283, 6206.8097787158], [1.033, 0.13874927606, 11712.9553182308], [1.103, 3.08477302937, 43232.3066584156], [0.781, 2.53372735932, 16496.3613962024], [1.019, 3.04569392376, 6037.244203762], [0.795, 5.80662989111, 5230.807466803], [0.813, 3.57710279439, 10177.2576795336], [0.962, 5.31470594766, 6284.0561710596], [0.721, 5.96264301567, 12559.038152982], [0.966, 2.74714939953, 6244.9428143536], [0.921, 0.10155275926, 29088.811415985], [0.692, 3.89764447548, 1589.0728952838], [0.719, 5.91791450402, 4136.9104335162], 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10973.55568635], [0.038, 6.17935925345, 9917.6968745098], [0.049, 0.83021145241, 11506.7697697936], [0.053, 1.45828359397, 233141.3144043615], [0.047, 6.21568666789, 6681.2248533996], [0.037, 0.3635930998, 10177.2576795336], [0.035, 3.33024911524, 5643.1785636774], [0.034, 5.63446915337, 6525.8044539654], [0.035, 5.36033855038, 25158.6017197654], [0.034, 5.36319798321, 4933.2084403326], [0.033, 4.24722336872, 12569.6748183318], [0.043, 5.26370903404, 10575.4066829418], [0.042, 5.08837645072, 11015.1064773348], [0.04, 1.98334703186, 6284.0561710596], [0.042, 4.22496037505, 88860.05707098669], [0.029, 3.1908862817, 11926.2544136688], [0.029, 0.15217616684, 12168.0026965746], [0.03, 1.61904744136, 9779.1086761254], [0.027, 0.76388991416, 1589.0728952838], [0.036, 2.74712003443, 3738.761430108], [0.033, 3.08807829566, 3930.2096962196], [0.031, 5.34906619513, 143571.32428481648], [0.025, 0.10240267494, 22483.84857449259], [0.03, 3.47110495524, 14945.3161735544], [0.024, 1.10425016019, 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6283.14316029419], [0.02, 6.10644140189, 167283.7615876655], [0.015, 4.09775914607, 11712.9553182308], [0.016, 5.717699407, 17298.1823273262], [0.016, 3.28894009404, 5884.9268465832], [0.015, 5.64785377164, 12559.038152982], [0.016, 4.4345208093, 6283.0085396886], [0.014, 2.31721603062, 5481.2549188676], [0.014, 4.43479032305, 13517.8701062334], [0.014, 4.73209312936, 7342.4577801806], [0.012, 0.64705975463, 18073.7049386502], [0.011, 1.514433322, 16200.7727245012], [0.011, 0.88708889185, 21228.3920235458], [0.014, 4.50116508534, 640.8776073822], [0.011, 4.64339996198, 11790.6290886588], [0.011, 1.31064298246, 4164.311989613], [0.009, 3.02238989305, 23543.23050468179], [0.009, 2.04999402381, 22003.9146348698], [0.009, 4.91488110218, 213.299095438]], [[144.595, 4.27319435148, 6283.0758499914], [6.729, 3.91697608662, 12566.1516999828], [0.774, 0.0, 0.0], [0.247, 3.73019298781, 18849.2275499742], [0.036, 2.8008140905, 6286.5989683404], [0.033, 5.62216602775, 6127.6554505572], [0.019, 3.71292621802, 6438.4962494256], [0.016, 4.26011484232, 6525.8044539654], [0.016, 3.50416887054, 6256.7775301916], [0.014, 3.62127621114, 25132.3033999656], [0.011, 4.39200958819, 4705.7323075436], [0.011, 5.22327127059, 6040.3472460174], [0.01, 4.28045254647, 83996.84731811189], [0.009, 1.56864096494, 5507.5532386674], [0.011, 1.37795688024, 6309.3741697912], [0.01, 5.19937959068, 71430.69561812909], [0.009, 0.4727519993, 6279.5527316424], [0.009, 0.74642756529, 5729.506447149], [0.007, 2.9737489156, 775.522611324], [0.007, 3.28615691021, 7058.5984613154], [0.007, 2.19184402142, 6812.766815086], [0.005, 3.15419034438, 529.6909650946], [0.006, 4.54725567047, 1059.3819301892], [0.005, 1.51104406936, 7079.3738568078], [0.007, 2.98052059053, 6681.2248533996], [0.005, 2.30961231391, 12036.4607348882], [0.005, 3.71102966917, 6290.1893969922]], [[3.858, 2.56384387339, 6283.0758499914], [0.306, 2.2676950123, 12566.1516999828], [0.053, 3.44031471924, 5573.1428014331], [0.015, 2.04794573436, 18849.2275499742], [0.013, 2.05688873673, 77713.7714681205], [0.007, 4.4121885448, 161000.6857376741], [0.005, 5.26154653107, 6438.4962494256], [0.005, 4.07695126049, 6127.6554505572], [0.006, 3.81514213664, 149854.4001348079], [0.003, 1.28175749811, 6286.5989683404]], [[0.086, 1.21579741687, 6283.0758499914], [0.012, 0.65617264033, 12566.1516999828], [0.001, 0.38068797142, 18849.2275499742]]]

This table contains Earth’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 420-421.

pymeeus.Earth.WGS84 = Ellipsoid(6378137.0, 0.00335281066475, 7.292115e-05)

Reference ellipsoid World Geodetic System 1984, a modern ellipsoid used by the GPS system, and the standard in many applications