Planet-encounter relative velocity
= Planet-encounter relative velocity
{title2=$u^2=3-T$}
In units where a circular <planet> has orbital radius and speed one, the particle's relative speed $u$ outside a close encounter satisfies $u^2=3-T$, to leading order in the <planet>-to-<star> <mass> ratio. This follows from the <vis-viva equation> and $u^2=v^2+1-2h_z$ at the encounter radius. A short conservative encounter changes the direction of this relative velocity while preserving its magnitude.