The statistics of the gravitational field arising from a random distribution of stars. IV. The stochastic variation of the force acting on a star

Abstract

In this paper the theory of the stochastic variation of the force acting on a star is considered, and the solution to the formal problem is obtained in terms of the average force per unit mass F_t acting at time t, given that a force of intensity F₀ acted at time t=0. Various related quantities are also considered, and in particular an explicit formula for the correlation coefficient R(F₀, t) is derived.