 Solution

Stable circular power-law orbits require $nB>0$ and $n>-2$, excluding $n=0$. Bertrand's theorem selects $n=-1,2$ when every bound orbit must close. For $n=2+ϵ$, the near-circular ellipse orientation precesses at $-ϵ\Omega /8$ to first order.

Full derivation: solution.