Dynamics of pairwise motions

We derive a simple closed-form expression, relating $\vs(r)$ -- the mean relative velocity of pairs of galaxies at fixed separation $r$ -- to the two-point correlation function of mass density fluctuations, $\xi(r)$. We compare our analytic model for $\vs(r)$ with N-body simulations, and find excellent agreement in the entire dynamical range probed by the simulations ($0.1 \lsim \xi \lsim 1000$). Our results can be used to estimate the cosmological density parameter, $\Om$, directly from redshift-distance surveys, like Mark III.