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Nicolaus Copernicus (1473--1543) knew about Aristarchus' ideas and decided to use them to better Ptolemy's Almagest. He finished his tome in the year of his death.
Because Copernicus used circular orbits (not elliptical) he couldn't get the planets in the right places, so he added epicycles.
Copernicus' calculations predicted the positions of the planets with no better accuracy than Ptolemy's. For this reason, epicycles, and the moving Earth, people ignored Copernicus' work for many decades.
However, he did get some things right. For example:
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