Of course there is! Is called parallax. The stars "shift" position against the background as the Earth moves around the Sun. Of course, this only can be measured on the closest stars. The farther off a star is, the more difficult it gets to measure its parallax.
Also, orbital mechanics demand it. There are several probes in solar orbit, some of them in polar solar orbit. Their orbits are well known and would been quite impossible to figure out if the Solar System were geocentric.
It seems to me that your confusing a great deal of things regarding knowledge domains, and the interrelationship between natural philosophy ("science") and theology. This an old argument which I think was solved in one of the Lateran Councils of the Middle Ages. Back then, there were some that said that what is true in philosophy may not be true in theology and vice-versa, there was no Unity of Truth.
That's what you're doing, but you don't do it through dialectics, but by blurring the line, confusing categories, and special pleading.
I think that your protest against modernity has made you take an off-the-wall stance, a kind of sede vacantism of reason and faith, where both seem to be temporarily absent from your wits.
By adopting this stance, you undermine your own credibility, but thankfully, not that of the Church.
-Theo