= Apsidal speed sum for an attractive inverse-square orbit
{title2=$v_{\min}+v_{\max}=2Q/h$}
For unit mass with <inverse-square potential> $-Q/r$, $Q>0$, and positive conserved <angular momentum> $h$, a bounded orbit has $-Q^2/(2h^2)\le E<0$. Its <periapsis distance> and <apoapsis distance> are roots of $|E|r^2-Qr+h^2/2=0$, so their sum is $Q/|E|$ and product $h^2/(2|E|)$. Speed is largest at the <periapsis> and smallest at the <apoapsis>, because $v^2=2(E+Q/r)$ decreases with $r$. Radial velocity is zero there, so the two speeds are $h/r_{\min}$ and $h/r_{\max}$. Their sum is $h(r_{\min}+r_{\max})/(r_{\min}r_{\max})=2Q/h$, independent of $E$, including the circular limit.
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