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)

Sphere(name='Mercury2015', radius=2439372, geocentric_grav_const=22031839224000.0, angular_velocity=1.2400172589e-06, long_name='Mercury spheroid (2015)', reference='Wieczorek, MA (2015). 10.05 - Gravity and Topography of the Terrestrial Planets, Treatise of Geophysics (Second Edition); Elsevier. doi:10.1016/B978-0-444-53802-4.00169-X', comments=None)

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

print(boule.Mercury2024)

Sphere(name='Mercury2024', radius=2439472.7, geocentric_grav_const=22031815411154.895, angular_velocity=1.2400141739494342e-06, long_name='Mercury spheroid (2024)', reference='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, doi:10.1002/2014JE004675.', comments=None)

Venus

Venus2015: Venus spheroid using parameters from [Wieczorek2015]:

print(boule.Venus2015)

Sphere(name='Venus2015', radius=6051878, geocentric_grav_const=324858592000000.0, angular_velocity=-2.9924e-07, long_name='Venus spheroid (2015)', reference='Wieczorek, MA (2015). 10.05 - Gravity and Topography of the Terrestrial Planets, Treatise of Geophysics (Second Edition); Elsevier. doi:10.1016/B978-0-444-53802-4.00169-X', comments=None)

Earth-Moon system

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

print(boule.GRS80)

Ellipsoid(name='GRS80', semimajor_axis=6378137, flattening=0.003352810681182319, geocentric_grav_const=398600500000000.0, angular_velocity=7.292115e-05, long_name='Geodetic Reference System (1980)', reference='Hofmann-Wellenhof, B., & Moritz, H. (2006). Physical Geodesy (2nd, corr. ed. 2006 edition ed.). Wien\u202f; New York: Springer.', comments=None)

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

print(boule.WGS84)

Ellipsoid(name='WGS84', semimajor_axis=6378137, flattening=0.0033528106647474805, geocentric_grav_const=398600441800000.0, angular_velocity=7.292115e-05, long_name='World Geodetic System (1984)', reference='Hofmann-Wellenhof, B., & Moritz, H. (2006). Physical Geodesy (2nd, corr. ed. 2006 edition ed.). Wien\u202f; New York: Springer.', comments=None)

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

print(boule.EGM96)

Ellipsoid(name='EGM96', semimajor_axis=6378136.3, flattening=0.003352819752990295, geocentric_grav_const=398600441500000.0, angular_velocity=7.292115e-05, long_name='Earth Gravitational Model (1996)', reference='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.', comments=None)

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

print(boule.Moon2015)

Sphere(name='Moon2015', radius=1737151, geocentric_grav_const=4902800070000.0, angular_velocity=2.6617073e-06, long_name='Moon spheroid (2015)', reference='Wieczorek, MA (2015). 10.05 - Gravity and Topography of the Terrestrial Planets, Treatise of Geophysics (Second Edition); Elsevier. doi:10.1016/B978-0-444-53802-4.00169-X', comments=None)

Mars

Mars2009: Mars ellipsoid using parameters from [Ardalan2009]:

print(boule.Mars2009)

Ellipsoid(name='Mars2009', semimajor_axis=3395428, flattening=0.005227617843759314, geocentric_grav_const=42828372000000.0, angular_velocity=7.0882181e-05, long_name='Mars ellipsoid (2009)', reference='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), 1. doi:10.1007/s11038-009-9342-7', comments=None)

(1) Ceres

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

print(boule.Ceres2018)

Ellipsoid(name='Ceres2018', semimajor_axis=482100, flattening=0.9990750051856462, geocentric_grav_const=62629053612.1, angular_velocity=0.00019234038694078873, long_name='Ceres ellipsoid (2018)', reference='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)

Ellipsoid(name='Vesta2017', semimajor_axis=278556, flattening=0.17459684946653456, geocentric_grav_const=17288000000.0, angular_velocity=0.0003267, long_name='Vesta reference ellipsoid (2017)', reference='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)

TriaxialEllipsoid(name='VestaTriaxial2017', semimajor_axis=280413, semimedium_axis=274572, semiminor_axis=231253, geocentric_grav_const=17288000000.0, angular_velocity=0.0003267, semimajor_axis_longitude=8.29, long_name='Vesta triaxial reference ellipsoid (2017)', reference='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)

TriaxialEllipsoid(name='Io2024', semimajor_axis=1829700, semimedium_axis=1819200, semiminor_axis=1815800, geocentric_grav_const=5959910000000.0, angular_velocity=4.125530833185668e-05, semimajor_axis_longitude=0.0, long_name='Io equilibrium triaxial ellipsoid (2024)', reference="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)

TriaxialEllipsoid(name='Europa2024', semimajor_axis=1562600, semimedium_axis=1560100, semiminor_axis=1559300, geocentric_grav_const=3202720000000.0, angular_velocity=2.0627660016976607e-05, semimajor_axis_longitude=0.0, long_name='Europa equilibrium triaxial ellipsoid (2024)', reference="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.2007.04.021https://doi.org/10.1006/icar.1998.5987; 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)

TriaxialEllipsoid(name='Ganymede2024', semimajor_axis=2634770, semimedium_axis=2632380, semiminor_axis=2631590, geocentric_grav_const=9887804180701.826, angular_velocity=1.0162973632136227e-05, semimajor_axis_longitude=0.0, long_name='Ganymede equilibrium triaxial ellipsoid (2024)', reference='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, 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)

Sphere(name='Callisto2024', radius=2410300, geocentric_grav_const=7179292000000.0, angular_velocity=4.357108150919352e-06, long_name='Callisto spheroid (2024)', reference='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.', comments=None)

Saturn system

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

print(boule.Enceladus2024)

TriaxialEllipsoid(name='Enceladus2024', semimajor_axis=256140, semimedium_axis=251160, semiminor_axis=248680, geocentric_grav_const=7210443000.0, angular_velocity=5.3073338876632056e-05, semimajor_axis_longitude=0.0, long_name='Enceladus triaxial ellipsoid (2024)', reference='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', comments=None)

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

print(boule.Titan2024)

TriaxialEllipsoid(name='Titan2024', semimajor_axis=2575164, semimedium_axis=2574720, semiminor_axis=2574314, geocentric_grav_const=8978138300000.0, angular_velocity=4.56067789167356e-06, semimajor_axis_longitude=0.0, long_name='Titan triaxial ellipsoid (2024)', reference="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)

Sphere(name='Pluto2024', radius=1188300, geocentric_grav_const=869600000000.0, angular_velocity=1.1385591834674098e-05, long_name='Pluto spheroid (2024)', reference='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; ', comments=None)

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

print(boule.Charon2024)

Sphere(name='Charon2024', radius=606000, geocentric_grav_const=105880000000.0, angular_velocity=1.1385591834674097e-55, long_name='Charon spheroid (2024)', reference='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; ', comments=None)