Kepler created a new model of the motion of the planets, fitting the data better than any of the circular models. His orbits put the planets in their expected positions in the night sky. His elliptical orbits, by breaking with eternal, uniform circular motion, therefore also needed an explanation of their cause. Kepler’s solution was to see that motion along an elliptical path would be uniform in a new way — not speed but area swept out within the ellipse:

Kepler published this in 1609 in his Astronomia Nova (“New Astronomy”). He included a physics, a cause for the dynamics: the motion occurs because the Sun emanates a motive force that he called anima motrix, moving the planets.

The elliptical orbits also held a new mathematical harmony, which he published in 1619 in his Harmonice Mundi (“Harmony of the World”). The relationship of the planet’s period [T] to its average radius [R]. For each of the planets, T²/R³ is a constant. If we use the dimensions of years [Earth’s period = 1] and Astronomical Units [Earth’s orbit = 1.0], the planetary arrangement is: