[tsimionescu]

> How do we know that the sun isn't orbiting the fixed earth, and accelerating toward the earth? Everything would look _exactly_ the same to everyone.

That wouldn't work out. You can take the earth as a fixed point and describe the Sun's motion relative to it, and it would be perfectly valid, but it wouldn't look as the Sun orbiting the Earth in any kind of almost constant speed elliptical orbit, it would look like a very different kind of motion.