Analytical formulation of a complex mutual gravitational field

The mutual gravitational potential for proximate bodies with an arbitrary mass topology is investigated. The current research is motivated by an experiment for the verification of the equivalence principle in gravitation. The gravitation model for the experiment is complex and requires high precision. The proposed methodology is to formulate the potential in terms of inertial integrals and the so-called outer integrals. The method is general and can represent any gravitational configuration. Approximating the outer integrals by radial basis functions reduces the complexity for a real-time dynamical simulation