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 triaxial 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.

The aim of this study is first to determine the gravity field of the comet 67P/Churyumov-Gerasimenko and second to derive the solar component of the precession rate and nutation coefficients of the spin axis of the comet nucleus, i.e. without the direct, usually larger, effect of outgassing. The gravity field, and related moments of inertia, are obtained from two polyhedra, that are provided by the OSIRIS and NAV-CAM experiments on Rosetta, and are based on the assumption of uniform density for the comet nucleus. We also calculate the forced precession rate as well as the nutation coefficients on the basis of Kinoshita's theory of rotation of the rigid Earth and adapted it to be able to indirectly include the effect of outgassing on the rotational parameters. The 2nd degree denormalized Stokes coefficients of comet 67P/C-G turn out to be (bracketed numbers refer to second shape model) C 20 ≃ −6.74 [−7.93] × 10 −2 , C 22 ≃ 2.60 [2.71] × 10 −2 consistent with normalized principal moments of inertia A/M R 2 ≃ 0.13 [0.11], B/M R 2 ≃ 0.23 [0.22], with polar moment c = C/M R 2 ≃ 0.25, depending on the choice of the polyhedron model. The obliquity between the rotation axis and the mean orbit normal is ε ≃ 52 o , and the precession rate only due to solar torques becomesψ ∈ [20, 30] ′′ /y. Oscillations in longitude caused by the gravitational pull of the Sun turn out to be of the order of ∆ψ ≃ 1 ′ , oscillations in obliquity can be estimated to be of the order of ∆ε ≃ 0.5 ′ .