On the statistics of the gravitational field

In this paper we extend Chandrasekhar and von Neumann’s analysis of the statistics of the gravitational field to systems in which particles (e.g. stars, galaxies) are not homogeneously distributed. We derive a distribution function W(F,d F/dt) giving the joint probability that a test particle is subject to a force F and an associated rate of change of F given by d F/dt. We calculate the first moment of d F/dt to study the effects of inhomogenity on dynamical friction.