THE DISTRIBUTION OF FORCES IN A PERTURBED SYSTEM OF SELF-GRAVITATING POINT MASSES

This paper analyses the effect of introducing random perturbations deltar in the positions r of each member of a self-gravitating system of point masses. Exact and approximate expressions are derived for the bivariant probability density W(F,f) that a given test particle at some point r0 feel a total unperturbed force F and a perturbation f. Analysis of this W(F,f) supports the prediction that close encounters and the bulk mean field should be of comparable importance in determining the response of the system to an initial perturbation.