In 1600 Kepler began working as an assistant to the Danish astronomer Tycho Brahe at his observatory near Prague. Tycho's pre-telescopic but extraordinarily careful measurements — especially decades of data on Mars — were accurate to a few arcminutes; when Tycho died unexpectedly in 1601 his notebooks passed to Kepler. Over the following years Kepler set out to understand why the inherited combinations of circles and epicycles could never quite fit Mars.

Under the layers of computation lay a single assumption: orbits are circles. Kepler tried a circular model for Mars repeatedly; the residual mismatch with Tycho's data was only about eight arcminutes. Anyone else might have written that off as observational error. Kepler knew Tycho's data could not carry such an error and abandoned the circle. He tried egg-shaped curves and finally an ellipse — a geometry that placed the Sun at one focus and made the planet move faster near the Sun and slower far from it. In 1609 he published the first two laws in Astronomia Nova: orbits are ellipses; the line joining a planet to the Sun sweeps out equal areas in equal times.

He did not stop there. For another decade he searched for a quantitative relationship between the orbital period of each planet and its distance from the Sun. He found it in Harmonices Mundi (1619): the square of a planet's orbital period is proportional to the cube of the semi-major axis of its orbit. The third law was the first founding equation to extend a single hidden mathematical order across the whole Solar System.

The consequences of Kepler's work were decisive in two ways. First, the dogma that celestial bodies must move in 'perfect' circles — held since Aristotle — collapsed; celestial mechanics was no longer geometry by decree but laws inferred from measured data. Second, Kepler's laws would be derived seventy years later as mathematical consequences of Newton's universal law of gravitation in the Principia — so without knowing it Kepler had laid the ground of modern physics. His work also became a textbook example in the methodology of science: how careful raw observation (Tycho) becomes rigorous theory (Kepler).