Small-angle gravitational encounter
= Small-angle gravitational encounter
{title2=$\Delta v_\perp\simeq2Gm/(bu)$}
For a <mass> $m$ passing at relative <speed> $u$ and <impact parameter> $b$, <integration> of $Gmb/(b^2+u^2t^2)^{3/2}$ 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.