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We derive a simple closed-form expression, relating \ (r) -- the mean relative velocity of pairs of galaxies at fixed separation r -- to the two-point correlation function of mass density fluctuations, \ (r). We compare our analytic model for \ (r) with N-body simulations, and find excellent agreement in the entire dynamical range probed by the simulations (0. 1 \ \ \ 1000). Our results can be used to estimate the cosmological density parameter, \, directly from redshift-distance surveys, like Mark III.
Juszkiewicz et al. (Thu,) studied this question.