Don't need to understand gravity to make a model of the observable solar system. Yet just because you make a model that is consistent with your observations, doesn't mean your model is correct.

The Antikythera Mechanism didn't model wasn't accurate because their understanding of the planetary model was incorrect. It also did not compute comets at all.

Aristotle thought that comets were atmospheric in nature, not bodies orbiting around the solar system, and on gravity he thought that everything was attracted to the Earth because it was the center of the universe, as well as that heavier objects would fall faster. These are not the basis for calculating the positions of undiscovered planets or gravitational disturbances of orbits of comets.

Your statements here are so wildly contradictory to history that I can only assume you are mistaken. If you really do feel you are correct, then please find some sources they actually back up your claims.