Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2016 / S29 / 2

Impact cratering begins with contact and compression, in which a shock rapidly heats and compresses target and impactor. During excavation, material moves outward and upward, producing a transient cavity and ejecta. Modification then involves gravitational collapse, wall slumping, fallback and, for large structures, rebound and central features. The stages overlap in time; crater size and morphology depend on gravity, impact conditions and target strength, not just the projectile's geometric hole size.

For a locally flat airless surface, constant gravity and equal launch/landing heights, $x=v\cos \theta t$ and $z=v\sin \theta t-g{t}^2/2$. The positive flight time is $2v\sin \theta /g$. ThusNeglected effects include curvature, varying gravity, rotation and terrain. At ranges comparable to the body's radius a spherical ballistic calculation is necessary.

In a gravity-dominated excavation model, displaced mass scales as $\rho D^3$ and lifting it through a distance of order $D$ costs order $\rho g{D}^4$. If a comparable fraction of impact energy supplies this work across similar impacts, $\boxed{D\propto E_{\mathrm{impact}}^{1/4}}$. This is a scaling justification, not a universal crater law: strength-dominated small craters or varying coupling efficiencies can have different exponents.

At fixed projectile mass and the assumed common quarter-power law, changing diameter from 30 to 75 m increases energy by $(75/30{)}^4$ and speed by $(75/30{)}^2=6.25$. The corresponding primary impact speed is about 15.6 km s${}^{-1}$. Five percent transferred to secondary-forming ejecta gives $v_{ej}\simeq 781$ m s${}^{-1}$. ThereforeThis assumes a 45-degree launch and similar target properties/coupling, as well as the source's fixed mass and velocity-transfer rules. Such a range is a noticeable fraction of the lunar radius, so curvature would produce a correction; the supplied flat-surface formula is an estimate rather than exact lunar orbit dynamics.

Permanently shadowed polar craters can remain cold enough to trap water ice and other volatiles for long periods. LCROSS used an impact plume to expose and spectroscopically sample material from such a cold trap, testing the interpretation of polar hydrogen signatures and the availability/history of lunar volatiles. Shadow was therefore a physical target-selection criterion, not merely an observational inconvenience.^[ref]