Thermal evolution of Earth and Moon growing by planetesimal impacts

Abstract

Improved estimates of impact energy partitioning are combined with models of planetesimal size distribution and planetary growth to infer the early thermal evolutions of the earth and the moon. The early stage partitioning of impact energy to kinetic energy is used to limit the contribution of impacts to heat transfer by turbulent mixing. The greatest uncertainty in the models is the portion of the impact energy partitioned to internal energy which is retained after material falls back in great impacts. Models of the earth with dynamically plausible growth times of the order of 50 m.y. are found to get hot enough for vaporization to occur if more than about 12% of the heat energy is retained upon impact. There is a slight positive correlation of heating with growth time, since a longer time implies larger planetesimals. Binary accretion models of the moon allowing for enhancement of velocities by the proximity of the earth do not get hot enough for appreciable melting unless a planetesimal mass distribution starting at a rather high value, M E/20 or more, is assumed. This melting occurs deeper than is inferred from petrological and thermotectonic data. Hence these results favor formation of the moon as a consequence of a great impact (or impacts) into the earth (Kaula, 1977).