class boule.TriaxialEllipsoid(name, semimajor_axis, semimedium_axis, semiminor_axis, geocentric_grav_const, angular_velocity, long_name=None, reference=None)[source]#

A rotating triaxial ellipsoid.

The ellipsoid is defined by five parameters: semimajor axis, semimedium axis, semiminor axis, geocentric gravitational constant, and angular velocity The thee semi-axis are different and the ellipsoid spins around it’s largest moment of inertia.

This class is read-only: Input parameters and attributes cannot be changed after instantiation.

Units: All input parameters and derived attributes are in SI units.


Gravity calculations have not been implemented yet for triaxial ellipsoids. If you’re interested in this feature or would like to help implement it, please get in touch.

  • name (str) – A short name for the ellipsoid, for example "WGS84".

  • semimajor_axis (float) – The semimajor (largest) axis of the ellipsoid. Definition: \(a\). Units: \(m\).

  • semimedium_axis (float) – The semimedium (middle) axis of the ellipsoid. Definition: \(b\). Units: \(m\).

  • semiminor_axis (float) – The semiminor (smallest) axis of the ellipsoid. Definition: \(c\). Units: \(m\).

  • geocentric_grav_const (float) – The geocentric gravitational constant. The product of the mass of the ellipsoid \(M\) and the gravitational constant \(G\). Definition: \(GM\). Units: \(m^3.s^{-2}\).

  • angular_velocity (float) – The angular velocity of the rotating ellipsoid. Definition: \(\omega\). Units: \(\\rad.s^{-1}\).

  • long_name (str or None) – A long name for the ellipsoid, for example "World Geodetic System 1984" (optional).

  • reference (str or None) – Citation for the ellipsoid parameter values (optional).


We can define an ellipsoid by setting the 5 key numerical parameters:

>>> ellipsoid = TriaxialEllipsoid(
...     name="VESTA",
...     long_name="Vesta Triaxial Ellipsoid",
...     semimajor_axis=286_300,
...     semimedium_axis=278_600,
...     semiminor_axis=223_200,
...     geocentric_grav_const=1.729094e10,
...     angular_velocity=326.71050958367e-6,
...     reference=(
...         "Russell, C. T., Raymond, C. A., Coradini, A., McSween, "
...         "H. Y., Zuber, M. T., Nathues, A., et al. (2012). Dawn at "
...         "Vesta: Testing the Protoplanetary Paradigm. Science. "
...         "doi:10.1126/science.1219381"
...     ),
... )
>>> print(ellipsoid) 
TriaxialEllipsoid(name='VESTA', ...)
>>> print(ellipsoid.long_name)
Vesta Triaxial Ellipsoid

The class then defines several derived attributes based on the input parameters:

>>> print(f"{ellipsoid.mean_radius:.0f} m")
262700 m
>>> print(f"{ellipsoid.volume * 1e-9:.0f} km³")
74573626 km³



The arithmetic mean radius of the ellipsoid. Definition: \(R = \dfrac{a + b + c}{3}\). Units: \(m\).


The volume bounded by the ellipsoid. Definition: \(V = \dfrac{4}{3} \pi a b c\). Units: \(m^3\).


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