Johannes Kepler was educated in Tuebingen, and he learned the Copernican system from Michael Maestlin, one of the leading astronomers of the day. While he was speculating on the mysteries of the universe in mathematical terms, he obtained a chance to work with Tycho Brahe, then Imperial Mathematician to Rudolph II. Kepler then worked on the problem of the orbit of Mars, based on Tycho's data. He struggled with this problem over five years, and the result is Kepler's (first two) laws of planetary motion (the third law appeared ten years later). Norwood Russell Hanson writes on this discovery as follows:
... he slowly came to suspect that perhaps his predecessors of the previous 2000 years were hasty in thinking the planetary orbits circular. Hindsight makes us underestimate the strength of this ancient maxim; ... But no bolder exercise of imagination was ever required: Kepler dared to 'pull the patters' away from all the astronomical thinking there had ever been. Not even the conceptual upsets of our century of natural science required such a break with the past. (Patterns of Discovery, p. 74)
With his laws and Tycho's astronomical data, Kepler then worked on new astronomical tables, which were eventually published as Rudolphine Tables (1627). These turned out to be accurate over decades, and contributed to establishing the heliocentricism or the Copernican view of the world.
For more on Kepler, see 朝永振一郎『物理学とは何だろうか』上、1-1、岩波新書、1979。