Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2015 / S30 / 2 / 2

The collision cross section in the incoming impact-parameter plane isWithout gravity it is only ${\sigma }_{\mathrm{geom}}=\pi (r_M+r_m{)}^2$, so gravitational focusing increases the cross-section by $1+f$. Trajectories that would miss geometrically can be bent into contact, especially for slow relative encounters. Gravity does not itself guarantee sticking: the following accretion estimate assumes collisions agglomerate rather than fragment, rebound or erode the target.

A uniform incoming projectile mass density ${\rho }_p$ has mass flux ${\rho }_p{v}_0$, soThe formula counts mass swept per unit time and assumes an adequate continuing projectile supply, the stated speed, and negligible many-body or stellar-tidal modification of the two-body cross-section.