Dynamics of pairwise motions

We propose a simple closed-form expression relating v(12)(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). Our Ansatz is an interpolation between the perturbative and stable clustering expressions for v(12). We compare our analytic model for v(12)(r) with N-body simulations and find excellent agreement in the entire dynamical range probed by the simulations (0.1 less than or similar to xi less than or similar to 1000). Our results can be used to estimate the cosmological density parameter, Omega, directly from redshift-distance surveys.