 Small-angle gravitational encounter

For a mass $m$ passing at relative speed $u$ and impact parameter $b$, integration of $Gmb/(b^2+u^2{t}^2{)}^{3/2}$ gives the transverse kick $2Gm/(bu)$. Weak deflection requires $b\gg Gm/u^2$, up to the equal-mass order-one factor. This scale supplies a small-impact cutoff for the weak-scattering diffusion approximation, not a physical exclusion of stronger encounters.