= Schwarzschild circular-orbit local speed
{c}
{title2=$v_{\mathrm{loc}}^2/c^2=\mu/(r-2\mu),\quad\mu=GM/c^2$}
A <Schwarzschild static observer> at a circular orbit measures speed $v_{\rm loc}=r(d\phi/dt)/\sqrt{1-2\mu/r}$. Combining the circular <geodesic> <frequency> with this clock rate gives the displayed formula. The observer-relative <Lorentz factor> is $\gamma=\sqrt{(r-2\mu)/(r-3\mu)}$, and $r\,d\phi/d\tau=\gamma v_{\rm loc}$. Thus the local speed is $c/2$ at the Schwarzschild <innermost stable circular orbit>. Coordinate and locally measured speeds are distinct.
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