Third-Order Development of Shape, Gravity, and Moment of Inertia of Ceres

Abstract:

Ceres is the target of the space mission Dawn. It is a protoplanet that is left over from the formation of the solar System about 4.6 billion years ago and its study could improve our knowledge of the early solar system. Quantifying these properties under the assumption of hydrostatic equilibrium forms the basis for interpreting shape and gravity data in terms of interior structure and infer deviations from hydrostaticity that can bring information on the thermal and chemical history of the planet. Here, we investigate the hydrostatic shape and gravitational potential coefficients of Ceres that is large enough to have undergone internal differentiation and chemical stratification. The Dawn spacecraft is expected to obtained a high-resolution shape data, with an accuracy better than 200 m/pixel. In order to reach an accuracy of few tens of meters for this 9 hours self-gravitating body, the shape models developed up to first order are not enough because they attain an accuracy of 1.8 km. Therefore, we numerically integrate Clairaut’s equations of rotational equilibrium expanded up to third order in a small parameter m, the geodetic parameter, to reach an accuracy of 25 meters. The following geodetical quantities under the hydrostatic hypothesis are derived: flattening and other shape parameters, gravitational potential coefficients, and moments of inertia. This type of modeling will be instrumental to the estimation of non-hydrostatic contributions to Ceres’ shape to be measured by Dawn.