Earlier I asked readers to think about (and comment on) why, if motion is relative, it still makes more sense to say that the Earth orbits the Sun than vice versa. I had my own take, but the answer is not super-obvious. So I asked Official Website Physicist™ Sean Carroll for the answer, and here’s his response.
The short answer would be that it is possible to choose whatever coordinate system you like, including ones centered on the Earth, and then say “in that coordinate system the Sun goes around the Earth.” Hell, it’s possible to choose coordinate systems in which neither the Earth nor the Sun move at all! But some coordinate systems are better than others, and for understanding Solar System dynamics, an Earth-centered one is particularly dumb. If some Orthodox Jews want to argue that they have the right to be dumb, who am I to stop them?Somewhat more careful (dare I say “rabbinical”?) discussion by me here:Note, however, that while you can say “I am using a coordinate system where the Earth is at the center,” you can not say “Coordinate systems where the Sun [or the Solar System’s barycenter] is at the center are wrong.” So “geocentrism” is flatly incorrect.Also, not to belabor the obvious: early geocentrists were not relying on coordinate invariance, and attempts by modern ones to save the old ideas are kind of pitiful.