# Time-dependent time dilation for circular orbits around a Schwarzschild black hole?

Take two clocks, one in a circular orbit around a Schwarzschild black hole and another with a distant observer.

The time dilation factor between the two clocks is said (at https://en.wikipedia.org/wiki/Gravitational_time_dilation ) to be given by $\sqrt{1 - 3GM/rc^2}$ (versions of the proof can be found at Time Dilation in Orbits in the Schwarzschild Metric and Is gravitational time dilation different from other forms of time dilation? ).

What is troubling me is whether this represents some sort of average? Surely a clock in orbit around the black hole is periodically travelling towards/away from the distant observer (unless the orbital plane is at right angles), which will result in a time-dependent time-dilation factor (and indeed a time-dependent doppler shift).

Can someone enlighten me?