LOL Whose arc? Are you still claiming that we see the sun where it actually is? Are my questions that hard to answer?
Regardless, you can deduce obvious differences with respect to the motion of the Sun against the constellations. But I bet the rest of the universe is not allowed in this pointless atheist exercise.
The point of a two body model is to simplify everything as much as possible, and reduce the number of variables.
Can you explain to me, how the sun, planets and the moon are exactly where you see them, when you know that everything is in motion and it takes time for light to reach our eyes? Does everything stop and wait in your universe until the light hits your eyes?
Well then, let's take the simplest solution. Merely observe how the Sun moves against the stars and that's the end of it.