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Ptolemy's model is less accurate than Copernicus', but it is said to have been in use for a long time.

What was the Ptolemaic model be used for?

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    $\begingroup$ Aside from satisfying curiosity about the heavens, it was mostly used for horoscopes and later navigation and map making, see Mahoney, Ptolemaic Astronomy in the Middle Ages. Copernican system was not more accurate than geocentric models of his time, they were mathematically equivalent. Improvement in accuracy only came with Kepler's innovations. $\endgroup$
    – Conifold
    Oct 7 at 11:57
  • $\begingroup$ I once read a paper (which I haven't been able to find again) claiming that Ptolemy was well aware that both the heliocentric and geocentric models were possible. But that the observational data in his times were better explained by the geocentric model. $\endgroup$
    – brainjam
    Oct 11 at 23:47
  • $\begingroup$ Ptolemy’s system is as accurate as Copernicus’ - indeed, observationally indistinguishable from it. $\endgroup$ Oct 18 at 6:57

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One specific application was the eclipse prediction. For example, Columbus used a predicted Lunar eclipse at least once, trying to determine his longitude. He was not very successful.

Ref. S. E. Morison, Admiral of the ocean sea: a life of Christopher Columbus.

One of the main applications in the Middle age was computus, computation of the date of Easter, which is changing every year. Ptolemy's theory of Sun and the Moon was used.

Remark. Applications to astrology were very limited. Astrologers used (and still use) a more ancient system, of Babylonian origin. Astrologers were not very interested in advancement of science, even at the time of Ptolemy. Of course, there were exceptions.

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