Kepler-harmonic epicyclic precession
= Kepler-harmonic epicyclic precession
{c}
{title2=$\Omega^2/\kappa^2=\frac{GM/r^3+\alpha\omega^2}{GM/r^3+4\alpha\omega^2}$}
For $\Phi=-GM/r+\alpha\omega^2r^2/2$, nearly circular motion has $\Omega^2=GM/r^3+\alpha\omega^2$ and $\kappa^2=GM/r^3+4\alpha\omega^2$. Their generally nonrational ratio makes small-eccentricity orbits precess even if $\alpha$ was added slowly. This illustrates <adiabatic actions do not preserve orbital closure>.