On the Approximation of the Attraction Field of a Rigid Body by the Attraction Field of Four Material Points of the Same Mass

In this paper, we study the problem of approximating the gravitational potential of a rigid body by the potential of a system of four identical point masses. Considering the potential as an expansion in terms of a parameter characterizing the ratio of the average size of a body to the distance to a test point in space, we propose an approach to constructing an approximate expression up to terms of the third order of smallness. This approach is used to build a model of the gravitational field of the nucleus of comet 67P/Churyumov–Gerasimenko.