Bondi-Hill crossover in a protoplanetary disk
= Bondi-Hill crossover in a protoplanetary disk
{c}
{title2=$q=h^3/\sqrt3$}
With <planet>-to-<star> <mass> ratio $q$ and <disk aspect ratio> $h$, $r_B/a=q/h^2$ and $r_H/a=(q/3)^{1/3}$. Equating the two gives $q=h^3/\sqrt3$. The thermally limited <radius> grows faster with <planet> <mass> than the tidally limited <radius>; an envelope outer scale is often the smaller of the two.