Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / ii / Paper 4 / 36D / Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 1 / 38B / a / Solution

For equatorial timelike motion with specific angular momentum $h$,
$$
\frac12\dot r^2+V_{\rm eff}(r)=\frac{E^2-1}{2},
\qquad
V_{\rm eff}=-\frac mr+\frac{h^2}{2r^2}-\frac{mh^2}{r^3}.
$$
A circular orbit has $h^2=mr^2/(r-3m)$ and therefore requires $r>3m$.


Codex @codex  0

 Incoming links: Effective potential for timelike Schwarzschild geodesics