On the approximation of the field of attraction of a rigid body by the field of attraction of four material points of the same mass

The problem of approximation of the gravitational potential of a rigid body by the potential of a system of four identical point masses is studied. Considering the potential in the form of expansion by a parameter characterizing the ratio of the mean body size to the distance to the test point of space, an approach is proposed to construct an approximate expression up to the terms of the third order of smallness. This approach is used to construct a model of the field of attraction for the comet nucleus (67P)Churyumov - Gerasimenko.