Those models predicted the orbits of the planets because they had been fitted precisely to them - and explained only them; but the models did not and could not

Those models predicted the orbits of the planets because they had been fitted precisely to them - and explained only them; but the models did not and could not predict anything else about gravity, or the motions of other bodies. Had Jupiter's moons been visible to them, their motion would have confounded their model entirely. Also, "The change from circular orbits to elliptical planetary paths dramatically improved the accuracy of celestial observations and predictions." Your own link says the predictive power was "dramatically improved."