Accretion process of the moon

Recent geochemical and geophysical data suggest that the initial temperature of the moon was strongly peaked toward the lunar surface. To explain such an initial temperature distribution, a simple model of accretion process of the moon is presented. The model assumes that the moon was formed from the accumulation of the solid particles or gases in the isolated, closed cloud. Two equations are derived to calculate the accretion rate and surface temperature of the accreting moon. Numerical calculations are made for a wide range of the parameters particle concentration and particle velocity in the cloud. A limited set of the parameters gives the initial temperature profiles as required by geochemical and geophysical data. These models of the proto-moon cloud indicate that the lunar outermost shell, about 400 km thick, was partially or completely molten just after the accretion of the moon and that the moon should have been formed in a period shorter than 1000 years. If the moon formed at a position nearer to the earth than its present one, the moon might have been formed in a period of less than one year.