The statistics of the gravitational field arising from a random distribution of stars. III. The correlations in the forces acting at two points separated by a finite distance

Abstract

In this paper we consider the theory of the correlations in the forces acting at two points separated by a finite distance in a system containing a random distribution of stars. A problem central in this theory is the evaluation of the average force acting at a point and in the same direction as the force acting at another specified point. It is shown how this and other similar problems in the theory of spatial correlations can be solved. An application of this theory to the problem of the stability of wide binaries is contained in a later paper.