Planetary accretion rates: Analytical derivation

Analytic formulae for estimating planetary accretion rates have long been available for conditions where random motion of planetesimals controls velocities relative to a growing planet. Recent Monte Carlo studies have explored a wider range of conditions, but gave impact rates only for the specific conditions under which those numerical experiments were performed. Now analytical formulae, which are valid even when keplerian shear controls the approach velocity, and which accurately reproduce the Monte Carlo results, give accretion rates over a wide range of conditions relevant to the problem of planet formation.