Approximation of the Attractive Field of a Body Close to Dynamically Symmetrical Using the Attractive Field of Three Balls

Abstract

In this paper, we consider the attraction field of a rigid body close to a dynamically symmetric one. The question of how to approximate this attractive field by the attractive field of three homogeneous balls so that the series expansion of the gravitational potential for these fields coincides up to terms of the fifth order of smallness is studied. As an example, the three-ball approximation as applied to asteroid (433) Eros is considered.