= Inferring an inverse-cube perturbation from apsidal precession
{title2=$\gamma\simeq p\,\Delta\varpi/\pi$}
For radial acceleration $-GM(1+\gamma/r)/r^2$, conserved <specific angular momentum> $h$ gives an angular radial frequency $\alpha=\sqrt{1-GM\gamma/h^2}$ through the <Binet equation>. Successive pericentres differ by $2\pi/\alpha$, so a small perturbation produces <apsidal precession> $\Delta\varpi\simeq\pi GM\gamma/h^2$. Writing the unperturbed semilatus rectum as $p=h^2/(GM)$ gives the displayed inverse relation. For a nearly circular orbit of period $P$, use $p\simeq[GM(P/(2\pi))^2]^{1/3}$. Positive $\gamma$ means prograde precession; $\gamma$ is a length. A measured rate per century must first be converted to an angle per orbit.
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