[PatrickHenry]

Of course, a group of sufficiently rich geocentrists might send an observatory far above the ecliptic of the solar system that remains fixed in position wrt to the earth and claim that their claims were thereby "proven".

That's good. Relativistically speaking, I can't find any fault with it. But I donno ...

[VadeRetro]

Of course, a group of sufficiently rich geocentrists might send an observatory far above the ecliptic of the solar system that remains fixed in position wrt to the earth and claim that their claims were thereby "proven".

My instinct--what, you're expecting calculations here?--is that there's no such stable orbit as "far above the ecliptic" and "fixed in position wrt the earth."