Um, under GR coordinate systems are physically indistinguishable.
That's why Hoyle said:
The relation of the two pictures [geocentricity and heliocentricity] is reduced to a mere coordinate transformation and it is the main tenet of the Einstein theory that any two ways of looking at the world which are related to each other by a coordinate transformation are entirely equivalent from a physical point of view.... Today we cannot say that the Copernican theory is right and the Ptolemaic theory wrong in any meaningful physical sense.
Hoyle, Fred. Nicolaus Copernicus. London: Heinemann Educational Books Ltd., 1973.
"WHAT FORCE COULD MOVE THE SUN AROUND THE EARTH WHILE LEAVING THE EARTH MOTIONLESS? Your inability to answer amuses me to no end."
You insistence on asking a question that is not relevant to the issue amuses me to no end.
Do you understand that a coordinate system explains only motion, and doesn't explain the forces involved in the motion?
Depends a little on what we're trying to predict, eh?
: Retrograde motion, epicycles, and all that.
Some coordinate systems are chosen to simply the calculations *greatly*.
And, if we are talking the orbit of Mercury, classical mechanics won't cut it to more than an approximation.