Proper period of a circular Schwarzschild geodesic
= Proper period of a circular Schwarzschild geodesic
{c}
Over one circular orbit at radius $r>3M$, the orbiting clock measures
$$
\Delta\tau=2\pi\sqrt{\frac{r^2(r-3M)}M}.
$$
The factor $r-3M$ combines gravitational and orbital kinematic time dilation.