Escape by jumping from a uniform-density asteroid ($r_{\max }=\sqrt{RH}$)

For a spherical nonrotating asteroid of the same mean mass density as a reference planet of radius R and surface gravity g, the mass scales as r cubed. Its surface escape speed therefore obeys $v_{\mathrm{esc}}^2=2g{r}^2/R$. A take-off speed $v_J$ permits escape for $r\le v_J\sqrt{R/(2g)}$. If that same take-off speed gives ballistic height H above the reference planet, $v_J^2=2gH$, and the limiting asteroid radius is $\sqrt{RH}$. A chosen H is an explicit performance estimate, not a universal human constant.