The statistics of the gravitational field arising from an inhomogenous system of particles

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},dF/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 dF/dt. We calculate the first moment of dF/dt to study the effects of inhomogenity on dynamical friction.