Post-shock capture criterion in ballistic accretion
= Post-shock capture criterion in ballistic accretion
{title2=$d_{\rm cap}=2GM/v^2$}
If transverse <kinetic energy> is dissipated at the downstream axis, the remaining <specific orbital energy> is $v^2/2-GM/b$. Binding requires $b<2GM/v^2$, corresponding to incident impact parameter $d<2GM/v^2$. Integrating the captured <mass flux> gives the <Bondi--Hoyle--Lyttleton accretion rate>.