= Escape by jumping from a uniform-density asteroid
{title2=$r_{\max}=\sqrt{RH}$}
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 $v_{\rm esc}^2=2gr^2/R$. A take-off <speed> $v_J$ permits escape for $r\leq v_J\sqrt{R/(2g)}$. 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.
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