On the Statistical Distribution of Massive Impactors

Abstract

If there is no preferred mass scale in the distribution of small bodies or planetesimals in the Solar System, the mass distribution of impactors striking a target will be a power law, N(>m) ∝ m-γ . For γ ≤ 1 most of the mass is accreted in a few giant impacts. We apply this simple model to cratering and derive probability distributions for quantities such as the largest impactor mass relative to the total mass of impactors and the nth largest impactor relative to the largest. We also use our model to study the distribution of giant impacts that is likely to occur in planet formation.