Solution
= 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 $n=2+\epsilon$, the near-circular ellipse orientation precesses at $-\epsilon\Omega/8$ to first order.
Full derivation: <past-exam-of-the-physics-b-course-of-the-university-of-cambridge/2010/paper-2a/section-c/c13/solution>.