Research on Modeling Method of Gravitational Field for Binary Asteroid System

Abstract

In this paper, the sphere-sphere model, the ellipsoid-sphere model and the improved restrictive ellipsoid-ellipsoid model are adopted for the gravitational field modeling of the weak gravitational binary asteroid system, and the corresponding complexity and accuracy of the three models increase gradually. The elliptic integral model and the second degree second order spherical harmonic function (which has high calculation efficiency and no integrals) model are adopted to calculate the gravitational potential energy, respectively. The dynamical model of the restricted full three-body problem consisting of binary asteroid system and spacecraft is accurately described. The different gravitational field models of the binary asteroid system 1999KW4 are simulated. And the surfaces of potential energy function and zero velocity curves under different models are given respectively. The coordinate deviations of libration point under different models are compared. The results show that the ellipsoid-ellipsoid model calculated by the second degree second order spherical harmonic function has the advantages of high precision, low complexity, less calculation, higher computing speed, and can accurately model the gravitational field of the binary asteroid system.

Keywords

binary asteroid system / gravitational field / sphere-sphere model / ellipsoid-sphere model / restrictive ellipsoid-ellipsoid model