Collision Chains among the Terrestrial Planets. III. Formation of the Moon

In the canonical model of Moon formation, a Mars-sized protoplanet "Theia" collides with proto-Earth at close to their mutual escape velocity $v_{\rm esc}$ and a common impact angle 45{\deg}. The "graze-and-merge" collision strands a fraction of Theia's mantle into orbit, while Earth accretes most of Theia and its momentum. Simulations show that this produces a hot, high angular momentum, silicate-dominated protolunar system, in substantial agreement with lunar geology, geochemistry, and dynamics. However, a Moon that derives mostly from Theia's mantle, as angular momentum dictates, is challenged by the fact that O, Ti, Cr, radiogenic W, and other elements are indistinguishable in Earth and lunar rocks. Moreover, the model requires an improbably low initial velocity. Here we develop a scenario for Moon formation that begins with a somewhat faster collision, when proto-Theia impacts proto-Earth at ~1.2 $v_{\rm esc}$, also around 45{\deg}. Instead of merging, the bodies come into violent contact for a half-hour and their major components escape, a "hit-and-run collision." N-body evolutions show that the "runner" often returns ~0.1-1 Myr later for a second giant impact, closer to $v_{\rm esc}$; this produces a postimpact disk of ~2-3 lunar masses in smoothed particle hydrodynamics simulations, with angular momentum comparable to canonical scenarios. The disk ends up substantially inclined, in most cases, because the terminal collision is randomly oriented to the first. Proto-Earth contributions to the silicate disk are enhanced by the compounded mixing and greater energy of a collision chain.