Before his death he grants Johannes Kepler access to the observatory and its records setting the stage for the triumph of the heliocentric model. He was moved to mystical rapture by the harmonies he saw in the spacing of planetary orbits and saw in this a reflection of a subtler harmony in the construction of the world. Mathematics best expresses those ideal forms. While teaching a high school class he realizes that the ratio of Saturn and Jupiter's orbits in the Copernican model can be described as spheres nested in a triangle. When confronted with Tycho's data Kepler is forced to abandon this idea.
Success comes with a geometrical figure called the ellipse.
By using ellipses Kepler found he could match the observations to their own level of accuracy. This was itself a new idea. Kepler found three Universal Rules for all planetary motion. A line drawn from the sun to the planet sweeps out equal area's in equal times. This is a statement of how the velocity of the planet in its orbit changes with time.