A multiresolution model for small-body gravity estimation

A new model, dubbed the MRQSphere, provides a multiresolution representation of the gravity field designed for its estimation. The multiresolution representation uses an approximation via Gaussians of the solution of the Laplace’s equation in the exterior of a sphere. Also, instead of the spherical harmonics, variations in the angular variables are modeled by a set of functions constructed using quadratures for the sphere invariant under the icosahedral group. When combined, these tools specify the spatial resolution of the gravity field as a function of altitude and required accuracy. We define this model, and apply it to representing and estimating the gravity field of the asteroid 433 Eros. We verified that a MRQSphere model derived directly from the true spherical harmonics gravity model satisfies the user defined precision. We also use the MRQSphere model to estimate the gravity field of Eros for a simulated satellite mission, yielding a solution with accuracy only limited by measurement errors and their spatial distribution.