  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.
