The random component of planetary rotation

Abstract

We compute the root mean square rotational angular momentum accumulated by a planet as a result of stochastic off-center impacts of large planetesimals during the accretionary epoch. Planets which accrete from large planetesimals have, on the average, shorter spin periods and greater obliquities than those which accrete exclusively from small bodies. We use the observed spin periods and obliquities of the planets in order to estimate the masses of the largest bodies to impact each planet during its history. Most, if not all, planets accreted one or more individual bodies having at least 1% of the final planetary mass. Several planets probably suffered at least one collision with a body having ≥5% of the planet's final mass. These results support giant impact theories for the origin of the Moon and Charon, and models which explain the excess iron in Mercury by the partial collisional stripping of that planet's mantle. The high angular momentum of the Pluto/Charon system suggests it formed as the result of a near-grazing collision of two bodies of comparable mass, although one or both of these constraints may be relaxed if the bodies approached each other at a speed significantly larger than their mutual escape velocity. If Saturn's obliquity was produced by stochastic impacts, then that planet must have accreted at least one “planetesimal” several times as massive as the Earth.