= Paczyński-Wiita ballistic plunge
{c}
{title2=$j^2=27GMa/4,\quad E=-GM/(8a)$}
The limiting inward departure from the marginal <Paczyński-Wiita circular orbit> at $r=3a$ conserves the displayed <specific angular momentum> and <specific orbital energy>. In the <Paczyński-Wiita potential>, its inward speed satisfies $v_r^2=GM(3a-r)^3/[4ar^2(r-a)]$. The exactly marginal circular orbit does not depart without a perturbation; the formula describes the separatrix limit of inward releases.
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