Dynamics of Pairwise Motions

We propose a simple closed-form expression relating v₁₂(r)--the mean relative velocity of pairs of galaxies at fixed separation r--to the two-point correlation function of mass density fluctuations, ξ(r). Our Ansatz is an interpolation between the perturbative and stable clustering expressions for v₁₂. We compare our analytic model for v₁₂(r) with N-body simulations and find excellent agreement in the entire dynamical range probed by the simulations (0.1<~ξ<~1000). Our results can be used to estimate the cosmological density parameter, Ω, directly from redshift-distance surveys.