Modeling the Gravitational Potential of a Nonspherical Asteroid

Abstract

In this paper a simple and very general approximation of the gravitational potential for a nonspherical body is presented. The gravitational potential is expanded using spherical harmonics and spherical Bessel functions, and it satisfies Laplace’s equation outside the circumscribing sphere and Poisson’s equation inside the circumscribing sphere. Therefore, trajectories can be integrated near the surface of the asteroid, as well as far away from it. This paper focuses on the construction of a simple expansion of the gravitational potential that preserves the critical nonlinear dynamical behavior of other gravitational models for a nonspherical asteroid that are more complex and computationally more demanding.