  Gravitational features are a fundamental source of information to learn more
about the interior structure and composition of planets, moons, asteroids and
comets. Gravitational field modeling typically approximates the target body
with a sphere, leading to a representation in spherical harmonics. However,
small celestial bodies are often irregular in shape, and hence poorly
approximated by a sphere. A much better suited geometrical fit is achieved by a
tri-axial ellipsoid. This is also mirrored in the fact that the associated
harmonic expansion (ellipsoidal harmonics) shows a significantly better
convergence behavior as opposed to spherical harmonics. Unfortunately, complex
mathematics and numerical problems (arithmetic overflow) so far severely
limited the applicability of ellipsoidal harmonics. In this paper, we present a
method that allows expanding ellipsoidal harmonics to a considerably higher
degree compared to existing techniques. We apply this novel approach to model
the gravitational field of comet 67P, the final target of the Rosetta mission.
The comparison of results based on the ellipsoidal parameterization with those
based on the spheroidal and spherical approximations reveals that the latter is
clearly inferior; the spheroidal solution, on the other hand, is virtually just
as accurate as the ellipsoidal one. Finally, in order to generalize our
findings, we assess the gravitational field modeling performance for some 400
small bodies in the solar system. From this investigation we generally conclude
that the spheroidal representation is an attractive alternative to the complex
ellipsoidal parameterization on the one hand, and the inadequate spherical
representation on the other hand.
