= Inferring an inverse-square force from Kepler laws
{title2=$a_r=-l^2/(Ar^2)$}
Constant <areal velocity> gives constant specific <angular momentum> $l=r^2\dot\theta$, hence zero transverse acceleration and a <central force>. For a focus-based <ellipse> $u=1/r=(1+\varepsilon\cos\theta)/A$, one has $u_{\theta\theta}+u=1/A$. The <Binet equation> then gives the displayed radial acceleration, proving an attractive <inverse-square law>. An orbit's shape alone does not specify its acceleration without a time law.
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