(Disclaimer: this has nothing to do with special relativity, despite dealing with the speed of light! Delays in observing an event, due to light travel time, are not what relativity is. This is simpler stuff).

(Also, don't confuse this with doppler spectroscopy [2] -- measuring shifts in the frequency (color) of light, rather than the frequency of orbits. This is the "Doppler" that's used to discover exoplanets!)

[2] https://en.wikipedia.org/wiki/Doppler_spectroscopy