Addendum: I've been wondering whether, in case Kepler and Newton had never been born, we would have agreed on whether the universe is Ptolemaic or Coperincan. I doubt that this question would have been resolved, because both 'theories' were, despite the genius-stroke of Copernicus, mere empirical narratives supplemented by complex algorithmic mathematics. Much of today's discussion in theoretical physics is in a much worse position; there are not even empirical narratives - just overhyped forward-looking-statements and artist's views of the day before the Big Bang.
The difference classical mechanics made was that it brought 'motion' from the heavens down to earth by resolving the millennia-old problem of motion. And everyone equipped with a yardstick and a clock was invited to prove it wrong or turn it into business. Today's theoretical physics has withdrawn to beyond the seven mathematical mountains, where the original ideas of physics have long drowned in the too-big-to-fail of LHCs, LIGOs, computational brains, etc. pp. However, as one contestant conspicuously phrased it: "who knows what else it [the math] might be good for?"... One is tempted to think (with Shakespeare): Though this be madness, yet there is method in't.