Copernicus's new theory for the planets of 1543 had the Sun at the centre, instead of the Earth. In this respect it went against the religious teaching of the time. However the Church allowed it to be taught provided it was always described as a theory.
Galileo took up the theory after 1600 and eventually promoted it aggressively as the truth and not just a theory. This led to his trial and conviction for heresy.
The modern theory of Kepler (1609), that is still in use today, uses the same idea of having the Sun at the centre, but it has the planets in elliptical orbits instead of the circles and epicycles of the old theories of Ptolemy and Copernicus. Kepler's theory was backed up by the new theory of dynamics invented by Newton in the late 1600s long after Kepler's time.
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Copernicus had a theory explaining the way the planets move among the stars. It had the Sun at the centre, instead of the Earth as most people believed.
The main arguments took place 50-100 years after Copernicus's death when Galileo got into trouble with the church authorities for re-interpreting The Bible by saying that Copernicus's idea was not just a theory but the absolute truth.