Natural science is inferential. No one piece of info is going to prove something. Proofs are for ideal subjects like mathematics.
Since earthquakes were brought up, after an earthquake, the stars are in a slightly different position. This suggests that earthquake is slightly affecting the earth's rotation. And this cause is local and reasonable according to our personal experiences with angular momentum.
How does a geocentrist view this? Do they say the earthquake causes the locations of the stars to change slightly? An earthquake on earth affects the distant stars in the universe? That just seems like causally backwards.
It seems even more curious to me when we're not talking about the stars, but about man-made spacecraft in the solar system. Consider the Pioneer anomaly. The Pioneer spacecraft was decelerating slightly differently than expected. (The best explanation is a small force from heat radiating from the spacecraft.) But the effect was very small, so careful measurements had to account for earthquakes, tide variations, and other earth-based events in determining the location of Pioneer. And there was a several hour delay in communications with Pioneer. So does a geocentrist say that Pioneer spacecraft changed in ways that predicted, by the delay time, events on earth? Isn't it more natural to say the these events affected earth's rotation, and so the earth-based observation of Pioneer?