How is it possible to prove the earth revolves around the sun? (Please see description) Ive only taken physics 101, but I recently became fascinated with Einstein’s theory of general relativity and have watched many YouTube videos on it. My question may be an indication that I completely misunderstand it, however.
Doesn’t the theory of relativity (I think this part predates Einstein) state that if you have two objects in constant velocity, there is no experiment you can do to prove which object is in motion and which object is still? In other words, both prospectives (that you are in motion or you are still) are perfectly legitimate?
So if I claim that the earth is stationary and the universe, along with the sun, is in motion, how can you prove this is not the case?
 A: If the Solar System contained only Earth and the Sun, the best description of their behaviour would be that both orbit their mutual barycentre, which is in the Sun's interior. As it happens, there are many other bodies in the Solar System, and their barycentre ends up just outside the Sun, primarily due to Jupiter. The "moons orbit planets which, like asteroids, comets etc., orbit the Sun (well, maybe a point just outside it)" description provides an especially convenient choice for a coordinate system's origin if it must track all bodies' movements. You can centre everything on e.g. Earth (or Ganymede, for all I care) instead, but this is especially inconvenient. The other planets in our Solar System end up moving in a very complicated path in the night sky; the ancient Greek etymology of "planet" is "wanderer", because this was recognized a long time ago.
A: There is an important difference between velocity and acceleration: velocity is always relative, but acceleration is not. The Earth's velocity is not constant; the Earth is accelerating around the Sun, so the principle of relativity does not apply.
If you wish, you can assume that the Earth is fixed and everything else in the Universe moves relative to it, but you would find it impossible to construct a  law of gravity that could account for that in a consistent way- in other words, it would be a totally irrational belief.
