Proposed Method for Modeling the Gravitational Interaction Between Finite Bodies

Abstract

A new computational approach to the problem of the mutual gravitational attraction between finite-size bodies is presented. In this case, the gravitational force acting on each body consists of contributions from the mutual interactions between all particles comprising all bodies. The current approach is mostly suitable for high-precision modeling of the gravitational perturbations acting on a satellite in the vicinity of large and irregular objects. This approach is preferable in problems such as a satellite in the vicinity of an asteroid or near a planetary ring. If the shape of the asteroid is irregular, the traditional Legendre polynomials method does not give a good approximation. The series expansion of the potential in the planetary ring problem has a convergence problem because the distance between the satellite and the ring center of mass can be small compared with the size of the ring. These difficulties are overcome by defining new integrals over the attracting body. The operations on these integrals for the purpose of methodical computation are also presented. The potential via radial basis functions is modeled, and the gradients based on these smooth functions are derived.