Kepler was a German mathematician, who was lucky enough to be appointed as the Imperial Mathematician in 1601. Tycho Brahe left Kepler all his papers in order to continue his research. Kepler supported Copernicus's heliocentric system and tried to help prove it.
He found that the planets orbit the sun in an elliptical path. The way that he determined this was through his observation of Mars orbital speed. Kepler observed that Mars traveled faster at certain times in its orbit and from this he deduced that the orbital path could not be circular as was believed for over 1,600 years; instead they are elliptical. Since the Sun regulates the speed of the planets orbit, when its closest to the Sun(perihelion) the planet orbits more quickly, and when farthest from the Sun (aphelion) it slows down. During his studies he formulated three laws of planetary motion and urged Galileo to publish his research in order to help prove the Copernican thesis.