Global Gravity Field Modeling of Small Bodies with Heterogeneous Mass Distributions

This paper develops a global and general characterization of the gravity field around small celestial bodies, which commonly have heterogeneous mass distributions. The availability of such a characterization is important in providing guidance for close-proximity exploration missions, rover deployments, and dynamic studies. The determination of the gravitational potential is formulated as a boundary value problem for Laplace's equation, which can be solved using the boundary element method. To address the near-singularity arising from the fundamental solution, a semi-analytic form of the boundary integral with an adaptive collocation strategy is derived, and the virtual boundary method (VBM) is incorporated. The existence and uniqueness of the analytic continuation of gravitational potential inside the small body are proved by investigating the convergence of arbitrary derivatives on the boundary, which serves as the necessary condition of the application of VBM. Furthermore, the well-posed nature of the boundary integral equation expressed as a single-layer representation on the virtual boundary is proved using the Lax-Milgram theorem, which guarantees the robustness of VBM. Simulations conducted on comet 67P/Churyumov-Gerasimenko and asteroids (216) Kleopatra and (433) Eros demonstrate the ability of the proposed characterization to provide a global high-fidelity gravity field.