= Comparison of circular-orbit and static Schwarzschild clocks
{title2=$\tau_s/\tau_E=\sqrt{(1-3\mu/R_s)/(1-2\mu/R_E)}$}
A clock following a <timelike circular Schwarzschild geodesic> of <radius> $R_s$ advances at $\sqrt{1-3\mu/R_s}$ per unit Schwarzschild coordinate time. A static clock at <radius> $R_E>2\mu$ advances at $\sqrt{1-2\mu/R_E}$. Their ratio over the same coordinate-time interval gives the displayed result. For periodic signal comparisons, successive corresponding signals must also have the same propagation delay, as happens for repeated overhead passages in a fixed circular orbit observed from a static pole. To first order in $\mu/R$, the ratio is $1+\mu/R_E-3\mu/(2R_s)$.
Back to article page
