Oh, the mechanism has been provided, if you knew how to understand the model. I even explained your error, but it does no good. Every experiment designed to detect the motion of the earth around the sun has failed.
A coordinate system can work fine either way with a truck going towards a motionless building at 60 mph, or the building moving towards a motionless truck at 60 mph. As a coordinate system either works fine. But the coordinate system doesn't explain what mechanism is moving the truck, or alternatively moving the building. You insist that no mechanism need be explained beyond your magic talisman of “general relativity” and “coordinate system”. But neither explains what is moving the truck towards the building, or alternatively, the building towards the truck.
But the proposed mechanism of an internal combustion engine explains how a truck could be moving at 60 mph; but nothing within the system as known could move the building towards the motionless truck at 60 mph.
Similarly the proposed mechanism of gravity explains how the tiny Earth could be moved around the massive Sun, you have not even proposed a mechanism whereby the massive Sun could be dragged around the tiny Earth while leaving the Earth motionless.
So what mechanism could do so?
What Biblical passages do you feel support Geocentricism?
Why are you so unwilling to answer these two fundamental questions?