Two-body relaxation time

Summary

A stellar system has many weak gravitational encounters between pairs of stars. Its two-body relaxation time is the time after which these encounters have changed the velocity of a typical star by about its own size. For a system of $N$ equal stars it is about $N/(8 \ln N)$ crossing times. On shorter times a star moves in the smooth mean field of the system, as in collisionless stellar dynamics. On longer times encounters redistribute energy between stars and drive the system toward mass segregation and core collapse.