Constraints on the pre-impact orbits of Solar System giant impactors

We provide a fast method for computing constraints on impactor pre-impact orbits, applying this to the late giant impacts in the Solar System. These constraints can be used to make quick, broad comparisons of different collision scenarios, identifying some immediately as low-probability events, and narrowing the parameter space in which to target follow-up studies with expensive N-body simulations. We benchmark our parameter space predictions, finding good agreement with existing N-body studies for the Moon. We suggest that high-velocity impact scenarios in the inner Solar System, including all currently proposed single impact scenarios for the formation of Mercury, should be disfavoured. This leaves a multiple hit-and-run scenario as the most probable currently proposed for the formation of Mercury.