= Timelike circular Schwarzschild geodesic
{title2=$h^2=\mu c^2R^2/(R-3\mu),\quad k^2=(R-2\mu)^2/[R(R-3\mu)]$}
For the <Schwarzschild metric> with $\mu=GM/c^2$, let $k=(1-2\mu/r)\dot t$ and $h=r^2\dot\phi$ on an equatorial <timelike geodesic>. The normalization of the <four-velocity> gives $\dot r^2+V(r)=c^2(k^2-1)$, where $V(r)=(1-2\mu/r)h^2/r^2-2\mu c^2/r$. A circular <geodesic> obeys $V'(R)=0$, giving the displayed constants and requiring $R>3\mu$. Its coordinate <angular velocity> is $\Omega^2=GM/R^3$, and its proper clock rate is $d\tau/dt=\sqrt{1-3\mu/R}$. Differentiating $V$ twice at the circular solution gives stability for $R>6\mu$.
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