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Being that I am a historian and not an astronomer or physicist, I wouldn't know what evidence to produce. Given the history, doubt was removed when Newton developed his laws of planetary motion. Parallaxes work into it, something which was not observed until 1838 (Copernican theory holds that you would observe a shift when viewing a star, though supporters explained the lack of one as being that the stars were too far away to see). It was Newton's work, ultimately, that proved the heliocentric model.

I don't think Newton proved the solar system. He explained the motion of the planets better than before, but he provided no proof that the earth orbits the sun. And I don't know what parallax has to do with this issue. It was ultimately used to determine the distance to the nearest stars, and the method certainly relies on the solar system model to provide the base of the triangle involved (the diameter of earth's orbit, for observations made six months apart), but that's not proof of the solar system either. Frankly, I don't know of a scientific proof even now. The solar system is a theory, and like other currently accepted theories, it's supported by evidence and it makes useful predictions.

Your insistence on Galileo's lack of proof is not a good argument for your position. He had great evidence, and that's really all that any scientific theory has.

Except that Copernican theory requires a parallax, a phenomenon whereby a star seems to shift in position as the Earth moves. Kind of like if I were to hold up a ball directly in front of my face and you were to stand on my left--the ball would obscure my right ear; if you then shifted positions to my right (as the Earth might in orbit) the ball would obscure my left ear. Stars would, in the Copernican model, shift in relation to other stars. Distance also works into the equation--if the Earth is moving, the distance would change, however minutely.

It is OK to call it a fact--the Earth revolves around the Sun. There will not be any other evidence that shows otherwise, unless we get into wormholes or quantum theory or some other such discussion. Satellites revolve. Are you telling me that we can't have any other experiments to set as FACT or LAW that the Earth revolves, and so thus it is a "theory"?
Mind you, I don't dispute the definition of a theory--I don't confuse it with hypothesis. But you are saying that it is supported by evidence and makes useful predictions but is not conclusively proven? Forgive me if I sound incredulous, but I fail to understand your argument--the Earth has been "evidenced" to revolve around the Sun, not "proven"? Please clarify...