It took the meticulous astronomical observations of one Tycho Brahe to effect the next major change in the model of the solar system. Although not a proponent of the Copernican model himself, in the right hands, Brahe's careful observations were the necessary ingredient that led to the discovery of the correct laws of planetary motion.
It was the German astronomer, Johanes Kepler who correctly determined that all planetary orbits are in fact ellipses with the sun at one of the focal points, and not the perfect circles people had come to believe were necessary.
This was the first of three major laws of planetary motion devised by Kepler in the 1600s, the other two being that the planets moved at different speeds throughout their orbits, moving faster while closer to the sun; and that the square of their orbital periods vary with the cube of their distance from the sun.
It is important to note that Kepler had no theory to explain these motions, but Brahe's careful measurements left no doubt that they were true.