On the Approximation of the Gravitational Field of a Small Celestial Body by the Attractive Field of an Equimomental Quadruple of Material Points

The problem of constructing a system of four point masses the totality of which is equimomental to a predetermined rigid body is solved. A family of such systems, depending on six parameters, is constructed. The freedom of selection of the parameters allows one to formulate the problem of finding a set of masses best approximating the third-order moments of the mass distribution of a body. The problem in this formulation is solved with reference to the nucleus of comet 67P/Churyumov–Gerasimenko. The criterion for the quality of coincidence of the third-order moments of the mass distribution is the root mean square deviation of the moments of the point mass system from the corresponding moments of the comet nucleus. A system of four material points that minimizes the root mean square error is constructed. This value turned out to be smaller than previously obtained ones. It is noteworthy that the masses of the points found were different from each other and are all located inside the nucleus, so that the three smallest of them are located in a larger part of the nucleus, and the fourth, concentrating in itself $$ \approx {\kern 1pt} 28.5\% $$ of the total mass of the nucleus, is located inside a smaller part. Such a mass distribution agrees well with the known estimate of the volume of the smaller fraction of the comet nucleus from the total volume.