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He created a formula and mathematically proved his theory.
Contrary to most people of the 14th Century, Copernicus believed that the Earth revolved around the sun. Galileo later proved Copernicus' theory to be correct.
The Geocentric or Ptolemaic Model put the earth at the center of the Universe. The Heliocentric Model postulated by Copernicus and, before him, Aristarchus, places the Sun at the center of the Solar System. Galileo's observations proved the validity of the Heliocentric Model.
Johannes Kepler
In physics, theories are not mathematically proved but instead they are compared with physical observations to see if they are correct. Copernicus's theory was not just an idea that the Sun is at the centre, but also a detailed mathematical system of circle and epicycles that provided a model of the planets' orbits. At the time of Copernicus and for a time afterwards, his theory was used to predict the planets' positions, and when the predictions were found to be 'correct', the theory was considered 'proved' . But later Tycho Brahe developed more accurate measurement techniques, and using those he discovered small errors in the predicted positions of the planets. That led to Kepler's work and the discovery of elliptical orbits.