Available ellipsoids#

These are the available ellipsoids and their corresponding defining parameters.

All ellipsoids are instances of the Ellipsoid, Sphere, or TriaxialEllipsoid classes. See the class documentations for a list their derived physical properties (attributes) and computations/transformations that they can perform (methods).

Help!

If an ellipsoid you need isn’t in Boule yet, please reach out to the team and consider adding it yourself. It requires no special knowledge of the code and is a great way to help the project!

Mercury#

Mercury2015: Mercury spheroid using parameters from [Wieczorek2015]:

print(boule.Mercury2015)

Mercury2015 - Mercury spheroid (2015)
Spheroid:
  • Radius: 2439372 m
  • GM: 22031839224000.0 m³/s²
  • Angular velocity: 1.2400172589e-06 rad/s
Source:
  Wieczorek, MA (2015). 10.05 - Gravity and Topography of the
    Terrestrial Planets, Treatise of Geophysics (Second Edition);
    Elsevier. https://doi.org/10.1016/B978-0-444-53802-4.00169-X

Mercury2024: Mercury spheroid using parameters from [Maia2024] and [Mazarico2014]:

print(boule.Mercury2024)

Mercury2024 - Mercury spheroid (2024)
Spheroid:
  • Radius: 2439472.7 m
  • GM: 22031815411154.895 m³/s²
  • Angular velocity: 1.2400141739494342e-06 rad/s
Source:
  Radius: Maia, J. (2024). Spherical harmonic models of the shape of
    Mercury [Data set]. Zenodo. https://doi.org/10.5281/zenodo.10809345
  GM, angular velocity: Mazarico, E., et al. (2014), The gravity field,
    orientation, and ephemeris of Mercury from MESSENGER observations
    after three years in orbit, J. Geophys. Res. Planets, 119,
    2417-2436. https://doi.org/10.1002/2014JE004675

Venus#

Venus2015: Venus spheroid using parameters from [Wieczorek2015]:

print(boule.Venus2015)

Venus2015 - Venus spheroid (2015)
Spheroid:
  • Radius: 6051878 m
  • GM: 324858592000000.0 m³/s²
  • Angular velocity: -2.9924e-07 rad/s
Source:
  Wieczorek, MA (2015). 10.05 - Gravity and Topography of the
    Terrestrial Planets, Treatise of Geophysics (Second Edition);
    Elsevier. https://doi.org/10.1016/B978-0-444-53802-4.00169-X

Earth-Moon system#

GRS80: The Geodetic Reference System (1980) ellipsoid as defined by the values given in [HofmannWellenhofMoritz2006]:

print(boule.GRS80)

GRS80 - Geodetic Reference System (1980)
Oblate ellipsoid:
  • Semimajor axis: 6378137 m
  • Flattening: 0.003352810681182319
  • GM: 398600500000000.0 m³/s²
  • Angular velocity: 7.292115e-05 rad/s
Source:
  Hofmann-Wellenhof, B., & Moritz, H. (2006). Physical Geodesy (2nd,
    corr. ed. 2006 edition ed.). Wien; New York: Springer.

WGS84: The World Geodetic System (1984) ellipsoid as defined by the values given in [HofmannWellenhofMoritz2006]:

print(boule.WGS84)

WGS84 - World Geodetic System (1984)
Oblate ellipsoid:
  • Semimajor axis: 6378137 m
  • Flattening: 0.0033528106647474805
  • GM: 398600441800000.0 m³/s²
  • Angular velocity: 7.292115e-05 rad/s
Source:
  Hofmann-Wellenhof, B., & Moritz, H. (2006). Physical Geodesy (2nd,
    corr. ed. 2006 edition ed.). Wien; New York: Springer.

EGM96: Earth Gravitational Model (1996) ellipsoid as defined by the values given in [Lemoine1998]:

print(boule.EGM96)

EGM96 - Earth Gravitational Model (1996)
Oblate ellipsoid:
  • Semimajor axis: 6378136.3 m
  • Flattening: 0.003352819752990295
  • GM: 398600441500000.0 m³/s²
  • Angular velocity: 7.292115e-05 rad/s
Source:
  Lemoine, F. G., et al. (1998). The Development of the Joint NASA GSFC
    and the National Imagery and Mapping Agency (NIMA) Geopotential
    Model EGM96. NASA Goddard Space Flight Center, NASA/TP 1998-206861.

Moon2015: Spheroid of Earth’s Moon using parameters from [Wieczorek2015]:

print(boule.Moon2015)

Moon2015 - Moon spheroid (2015)
Spheroid:
  • Radius: 1737151 m
  • GM: 4902800070000.0 m³/s²
  • Angular velocity: 2.6617073e-06 rad/s
Source:
  Wieczorek, MA (2015). 10.05 - Gravity and Topography of the
    Terrestrial Planets, Treatise of Geophysics (Second Edition);
    Elsevier. https://doi.org/10.1016/B978-0-444-53802-4.00169-X

Mars#

Mars2009: Mars ellipsoid using parameters from [Ardalan2009]:

print(boule.Mars2009)

Mars2009 - Mars ellipsoid (2009)
Oblate ellipsoid:
  • Semimajor axis: 3395428 m
  • Flattening: 0.005227617843759314
  • GM: 42828372000000.0 m³/s²
  • Angular velocity: 7.0882181e-05 rad/s
Source:
  Ardalan, A. A., Karimi, R., & Grafarend, E. W. (2009). A New Reference
    Equipotential Surface, and Reference Ellipsoid for the Planet Mars.
    Earth, Moon, and Planets, 106, 1-13.
    https://doi.org/10.1007/s11038-009-9342-7

(1) Ceres#

Ceres2018: Ceres ellipsoid using parameters from [Konopliv2018] and [Park2019]:

print(boule.Ceres2018)

Ceres2018 - Ceres ellipsoid (2018)
Oblate ellipsoid:
  • Semimajor axis: 482100 m
  • Flattening: 0.9990750051856462
  • GM: 62629053612.1 m³/s²
  • Angular velocity: 0.00019234038694078873 rad/s
Source:
  Semimajor axis, flattening: Park, R. S., et al. (2019). High-
    resolution shape model of Ceres from stereophotoclinometry using
    Dawn Imaging Data. Icarus, 319, 812–827.
    https://doi.org/10.1016/j.icarus.2018.10.024
  GM, angular velocity: Konopliv, A. S., et al. (2018). The Ceres
    gravity field, spin pole, rotation period and orbit from the Dawn
    radiometric tracking and optical data. Icarus, 299, 411–429.
    https://doi.org/10.1016/j.icarus.2017.08.005
Comments:
  Geocentric ellipsoid with aligned semiminor and rotation axes

(4) Vesta#

Vesta2017: Vesta ellipsoid using parameters from [Karimi2017]:

print(boule.Vesta2017)

Vesta2017 - Vesta reference ellipsoid (2017)
Oblate ellipsoid:
  • Semimajor axis: 278556 m
  • Flattening: 0.17459684946653456
  • GM: 17288000000.0 m³/s²
  • Angular velocity: 0.0003267 rad/s
Source:
  Karimi, R., Azmoudeh Ardalan, A., & Vasheghani Farahani, S. (2017).
    The size, shape and orientation of the asteroid Vesta based on data
    from the Dawn mission. Earth and Planetary Science Letters, 475,
    71–82. https://doi.org/10.1016/j.epsl.2017.07.033
Comments:
  Geocentric biaxial ellipsoid

VestaTriaxial2017: Vesta triaxial ellipsoid using parameters from [Karimi2017]:

print(boule.VestaTriaxial2017)

VestaTriaxial2017 - Vesta triaxial reference ellipsoid (2017)
Triaxial ellipsoid:
  • Semimajor axis: 280413 m
  • Semimedium axis: 274572 m
  • Semiminor axis: 231253 m
  • Semimajor axis longitude: 8.29°
  • GM: 17288000000.0 m³/s²
  • Angular velocity: 0.0003267 rad/s
Source:
  Karimi, R., Azmoudeh Ardalan, A., & Vasheghani Farahani, S. (2017).
    The size, shape and orientation of the asteroid Vesta based on data
    from the Dawn mission. Earth and Planetary Science Letters, 475,
    71–82. https://doi.org/10.1016/j.epsl.2017.07.033
Comments:
  Geocentric triaxial ellipsoid

Jupiter system#

Io2024: Io triaxial ellipsoid using parameters from [Thomas1998], [Anderson2001], and [Jacobson2021]:

print(boule.Io2024)

Io2024 - Io equilibrium triaxial ellipsoid (2024)
Triaxial ellipsoid:
  • Semimajor axis: 1829700 m
  • Semimedium axis: 1819200 m
  • Semiminor axis: 1815800 m
  • Semimajor axis longitude: 0.0°
  • GM: 5959910000000.0 m³/s²
  • Angular velocity: 4.125530833185668e-05 rad/s
Source:
  Semi-axis: Thomas, P. C., et al. (1998). The Shape of Io from Galileo
    Limb Measurements. Icarus, 135(1), 175–180.
    https://doi.org/10.1006/icar.1998.5987
  GM: Anderson, J. D., et al. (2001). Io's gravity field and interior
    structure. J. Geophys. Res., 106, 32963–32969.
    https://doi.org/10.1029/2000JE001367
  Angular velocity: R. A. Jacobson (2021), The Orbits of the Regular
    Jovian Satellites and the Orientation of the Pole of Jupiter,
    personal communication to Horizons/NAIF. Accessed via JPL Solar
    System Dynamics, https://ssd.jpl.nasa.gov, JUP365.
Comments:
  Best-fit equilibrium shape

Europa2024: Europa triaxial ellipsoid using parameters from [Nimmo2007], [Anderson1998], and [Jacobson2021]:

print(boule.Europa2024)

Europa2024 - Europa equilibrium triaxial ellipsoid (2024)
Triaxial ellipsoid:
  • Semimajor axis: 1562600 m
  • Semimedium axis: 1560100 m
  • Semiminor axis: 1559300 m
  • Semimajor axis longitude: 0.0°
  • GM: 3202720000000.0 m³/s²
  • Angular velocity: 2.0627660016976607e-05 rad/s
Source:
  Semi-axis: Nimmo, F., et al. (2007). The global shape of Europa:
    Constraints on lateral shell thickness variations. Icarus, 191(1),
    183–192. https://doi.org/10.1016/j.icarus.2007.04.021
  GM: Anderson, J. D., et al. (1998). Europa's differentiated internal
    structure: Inferences from four Galileo encounters. Science, 281,
    2019–2022. https://doi.org/10.1126/science.281.5385.2019
  Angular velocity: R. A. Jacobson (2021), The Orbits of the Regular
    Jovian Satellites and the Orientation of the Pole of Jupiter,
    personal communication to Horizons/NAIF. Accessed via JPL Solar
    System Dynamics, https://ssd.jpl.nasa.gov, JUP365.
Comments:
  Best-fit hydrostatic ellipsoid (nominal)

Ganymede2024: Ganymede triaxial ellipsoid using parameters from [Zubarev2015], [GomezCasajus2022], and [Jacobson2021]:

print(boule.Ganymede2024)

Ganymede2024 - Ganymede equilibrium triaxial ellipsoid (2024)
Triaxial ellipsoid:
  • Semimajor axis: 2634770 m
  • Semimedium axis: 2632380 m
  • Semiminor axis: 2631590 m
  • Semimajor axis longitude: 0.0°
  • GM: 9887804180701.826 m³/s²
  • Angular velocity: 1.0162973632136227e-05 rad/s
Source:
  Semi-axis: Zubarev, A., et al. (2015). New Ganymede control point
    network and global shape model. Planetary and Space Science, 117,
    246–249. https://doi.org/10.1016/j.pss.2015.06.022
  GM: Gomez Casajus, L., et al. (2022). Gravity Field of Ganymede After
    the Juno Extended Mission. Geophysical Research Letters, 49(24),
    e2022GL099475. https://doi.org/doi:10.1029/2022GL099475
  Angular velocity: R. A. Jacobson (2021), The Orbits of the Regular
    Jovian Satellites and the Orientation of the Pole of Jupiter,
    personal communication to Horizons/NAIF. Accessed via JPL Solar
    System Dynamics, https://ssd.jpl.nasa.gov, JUP365.
Comments:
  Equilibrium ellipsoid III

Callisto2024: Callisto spheroid using parameters from [Anderson2001b] and [Jacobson2021]:

print(boule.Callisto2024)

Callisto2024 - Callisto spheroid (2024)
Spheroid:
  • Radius: 2410300 m
  • GM: 7179292000000.0 m³/s²
  • Angular velocity: 4.357108150919352e-06 rad/s
Source:
  Radius, GM: Anderson, J. D., et al. (2001). Shape, mean radius,
    gravity field, and interior structure of Callisto. Icarus, 153(1),
    157–161. https://doi.org/10.1006/icar.2001.6664
  Angular velocity: Satellites and the Orientation of the Pole of
    Jupiter, personal communication to Horizons/NAIF. Accessed via JPL
    Solar System Dynamics, https://ssd.jpl.nasa.gov, JUP365.

Saturn system#

Enceladus2024: Enceladus triaxial ellipsoid using parameters from [Park2024]:

print(boule.Enceladus2024)

Enceladus2024 - Enceladus triaxial ellipsoid (2024)
Triaxial ellipsoid:
  • Semimajor axis: 256140 m
  • Semimedium axis: 251160 m
  • Semiminor axis: 248680 m
  • Semimajor axis longitude: 0.0°
  • GM: 7210443000.0 m³/s²
  • Angular velocity: 5.3073338876632056e-05 rad/s
Source:
  Park, R. S., et al. (2024). The Global Shape, Gravity Field, and
    Libration of Enceladus. Journal of Geophysical Research: Planets,
    129(1), e2023JE008054. https://doi.org/10.1029/2023JE008054

Titan2024: Titan triaxial ellipsoid using parameters from [Corlies2017], [Durante2019], and [Jacobson2022]:

print(boule.Titan2024)

Titan2024 - Titan triaxial ellipsoid (2024)
Triaxial ellipsoid:
  • Semimajor axis: 2575164 m
  • Semimedium axis: 2574720 m
  • Semiminor axis: 2574314 m
  • Semimajor axis longitude: 0.0°
  • GM: 8978138300000.0 m³/s²
  • Angular velocity: 4.56067789167356e-06 rad/s
Source:
  Semi-axis: Corlies, P., et al. (2017). Titan’s Topography and Shape at
    the End of the Cassini Mission. Geophysical Research Letters,
    44(23), 11,754-11,761. https://doi.org/10.1002/2017GL075518
  GM: Durante, D., et al. (2019). Titan’s gravity field and interior
    structure after Cassini. Icarus, 326, 123–132.
    https://doi.org/10.1016/j.icarus.2019.03.003
  Angular velocity: Jacobson, R. (2022). The Orbits of the Main
    Saturnian Satellites, the Saturnian System Gravity Field, and the
    Orientation of Saturn's Pole. The Astronomical Journal, 164, 199.
    https://doi.org/10.3847/1538-3881/ac90c9
Comments:
  Fit to ellipsoid shape (not derived from spherical harmonic
  coefficients)

Pluto system#

Pluto2024: Pluto spheroid using parameters from [Nimmo2017] and [Brozović2015]:

print(boule.Pluto2024)

Pluto2024 - Pluto spheroid (2024)
Spheroid:
  • Radius: 1188300 m
  • GM: 869600000000.0 m³/s²
  • Angular velocity: 1.1385591834674098e-05 rad/s
Source:
  Radius: Nimmo, et al. (2017). Mean radius and shape of Pluto and
    Charon from New Horizons images. Icarus, 287, 12–29.
    https://doi.org/10.1016/j.icarus.2016.06.027
  GM, angular velocity: Brozović, M., et al. (2015). The orbits and
    masses of satellites of Pluto. Icarus, 246, 317–329.
    https://doi.org/10.1016/j.icarus.2014.03.015

Charon2024: Charon spheroid using parameters from [Nimmo2017] and [Brozović2015]:

print(boule.Charon2024)

Charon2024 - Charon spheroid (2024)
Spheroid:
  • Radius: 606000 m
  • GM: 105880000000.0 m³/s²
  • Angular velocity: 1.1385591834674097e-55 rad/s
Source:
  Radius: Nimmo, et al. (2017). Mean radius and shape of Pluto and
    Charon from New Horizons images. Icarus, 287, 12–29.
    https://doi.org/10.1016/j.icarus.2016.06.027
  GM, angular velocity: Brozović, M., et al. (2015). The orbits and
    masses of satellites of Pluto. Icarus, 246, 317–329.
    https://doi.org/10.1016/j.icarus.2014.03.015

Available ellipsoids

Contents

Available ellipsoids#

Mercury#

Venus#

Earth-Moon system#

Mars#

(1) Ceres#

(4) Vesta#

Jupiter system#

Saturn system#

Pluto system#