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Johannes Kepler found out that planets move in ellipses and move at variable speeds as they travel round the sun. The former theory of Copernicus was not wrong, but Kepler's theory was found to be more accurate when accurate observational methods were developed.
Later Kepler's theory was backed up by theory when Newton's law of gravitation came along. However in the 20th century Einstein's theory of relativity produced some small corrections to the Kepler/Newton theory.
Kepler assumed that planetary orbits were eliptical, but only after he found that doing so was the only way to match observation with theory. Nicolae Copernicus, and later Galileo Galilei, could not imagine these orbits being anything but circular.
Kepler used the idea of placing the Sun at the centre instead of the Earth. In that respect he upheld the Copernican idea. However Kepler's model threw out all the other aspects of earlier systems in favour of elliptical orbits for the planets.
By completely replacing all the old circles and epicycles of Ptolemy and Copernicus and deciding to try elliptical orbits instead, which fitted the latest and most accurate observations of Tycho Brahe more closely than the other models.
All Kepler retained from Copernicus's theory was the idea of having the Sun at the centre.
Kepler disagreed with Copernicus on the shape of planetary orbits. Copernicus believed in circular orbits, while Kepler's observations led him to propose elliptical orbits. Kepler's laws of planetary motion refined and corrected some of the assumptions in Copernicus' heliocentric model.
Copernicus and Kepler disagree on the shape of planetary orbits. Copernicus proposed that planets move in perfect circles around the Sun, while Kepler later discovered that planets move in elliptical orbits.
Kepler's theory eventually replaced Copernicus's theory after Tycho Brahe's measurements enabled Kepler to realise that the planets move in elliptical orbits and not in the circles and epicycles of the older Ptolemaic and Copernican models. Copernicus was able to simplify the older model by placing the Sun at the centre instead of the Earth. Kepler in his new theory of 1609 retained Copernicus's idea of placing the Sun at the centre.
Because he was the first astronomer in modern times to devise a new model of the planets' orbits with the Sun at the centre. Copernicus's model of 1543 was rejected after Kepler's theory of 1609 was supported by later theories of dynamics, but Kepler retained the heliocentric principle and Copernicus's work was an important stage in the process of development of ideas.
Johannes Kepler, a German scientist, provided the mathematical framework and evidence to support Copernicus' heliocentric theory. Kepler's laws of planetary motion helped confirm that the Earth and other planets revolve around the sun.