Heating of the moon by heterogeneous accretion

Monte Carlo models of lunar accretion are developed by randomly sampling mass and velocity distributions of objects in the solar nebula in circumsolar and circumterrestrial orbits. The thermal effect of an impact is expressed as the volume of melt produced; the melt volumes produced by each Monte Carlo case are sorted into regions to produce percentage melt estimates as a function of radius. One-hundred cases are calculated to obtain a range of plausible thermal histories for lunar accretion. The average melt percentage estimates show substantial deep melting, but the spread of melt percentage values about the mean from the random sampling procedure is wide enough to include 0% melting for radii below 100 km and 100% melting for radii below 500 km.