Kepler became Tycho's mathematical assistant in Prague where he moved in 1599 at the invitation of the Holy Roman Emperor, Rudolf II. This was after Frederick II of Denmark had died and his heir was not so amenable to Tycho's requests. When Tycho died, rather suddenly at the age of 54, the use of the telescope for celestial observations was still a few years in the future, but his superb observations made the link from the old Ptolemaic scheme to the new heliocentric view of the solar system. They enabled Kepler to explain planetary orbits, as ellipses with the sun at one focus, plus two additional rules on the orbital speeds and periods.

Like Tycho's observations, Kepler's laws were spot on, and can now be derived by any competent mathematics student using Newton's law of gravity and differential calculus. Kepler of course paved the way for Newton, but it was Tycho Brahe's superb observational work that fully propelled things forward from the complicated and detailed geocentric universe of Ptolemy to the modern solar system that we now know and accept. Tycho did what all modern scientists should do: first nail down the evidence, then develop the theories. That is what leads to progress. If the theory comes first and observations are massaged to fit in or small theoretical tweaks are made, the result is stagnation, as it was when Ptolemy's Almagest held sway.