Even in the Round Earth model, it's impossible to prove whether the earth is rotating round the sun or the sun is rotating round the earth, or where comets go after they leave our sight. True knowledge in matters of astronomy is something of an uncertain mode, constantly changing, more in line with opinion than fact. The cosmos can only be observed an interpreted. Not studied. Not put through controlled experimentation. Astronomers look into the skies and see what they were taught to see.
There is something beautiful and even profound in this, which I hope is grasped by those citizens of the earth that come across this site.
The gift round earth theory provided man was to subdue his arrogance (I am man, center of the universe- no more)
Man became just one planet like any other.
Then with Darwin, man became just another species.
Then with Freud, even the mind, the "I", became just another scientific theory.
Now, man has a new religion of science and certain knowledge that must be questioned to subdue his arrogance. Facts which are always trusted and, in our imaginations, can describe even the inner workings of the entire universe with precision.
Quantum mechanics and relativity are the first chinks in that solidity. Our knowledge can never be certain, even theoretically (heisenburg uncertainty, wave particle duality), and our frame of reference can never be absolute.
Flat earth theory is the final nail. It proves that Yes, the science and society are capable of grand error. Science cannot replace religion, for even this new god is flawed.