Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 316 / 1 / vii

An encounter can occur only near an orbital node of the comet's inclined orbit. Its tangential velocity projected into the planet's plane is reduced by $\cos I_c$, so the relative-speed calculation becomesThe missing projected component is a vertical relative velocity, so the moon encounter is three-dimensional: $b$ becomes a vector in the impact plane, and a collision also requires the trajectory to pass close to the moon's orbital plane. Once the total asymptotic speed is used, the two-body gravitational focusing formulae in parts (v) and (vi) retain their form, but the geometrical collision probability is lower.