> epicylical theories (...) happened to be completely incorrect.
They weren't completely incorrect. There are two aspects you want to look at when evaluating those models. The first is their predictive power, which was the best for the times, and better than the stuff Galileo proposed[0]. Which made Galileo's model incorrect in this regard. The second aspect is explaining the model in terms of more basic laws - this they did not do at all, and nor did Galileo's model. The required theories that allowed to derive heliocentric model from first(er) principles were only formulated later by Newton, which only then invalidated the geocentric models.
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[0] - from mathematical point of view, all models that give the same results are equally correct; the only thing one cares about is which one is simpler / more useful for you.
Had 16th century Astronomers had the power to re-arrange the orbits of the planets according to their theories, the results would certainly not have been the same, so even from that particularly mathematical point of view, they were still incorrect.
This isn't mere pedantry, a good example of epicylic type theories being used to modify the system under study, can be found today in modern economics.
They weren't completely incorrect. There are two aspects you want to look at when evaluating those models. The first is their predictive power, which was the best for the times, and better than the stuff Galileo proposed[0]. Which made Galileo's model incorrect in this regard. The second aspect is explaining the model in terms of more basic laws - this they did not do at all, and nor did Galileo's model. The required theories that allowed to derive heliocentric model from first(er) principles were only formulated later by Newton, which only then invalidated the geocentric models.
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[0] - from mathematical point of view, all models that give the same results are equally correct; the only thing one cares about is which one is simpler / more useful for you.