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The next figure in the history of the Copernican revolution is Johannes Kepler.

Â Kepler was a brilliant mathematician,

Â perhaps the best of his time, well reputed around Europe.

Â He had a star-crossed life.

Â He was weak and covered with boils, sickly, bedridden often.

Â His mother was accused of being a witch and he used a lot of his resources

Â to get her off that and stop her from being executed, and even later in his life

Â when he begged Galileo for a telescope, Galileo wouldn't send him a telescope.

Â So he had some hard luck stories, but his best stroke of fortune was working with

Â Tycho Brahe and inheriting his wonderful set of observations of the planets and

Â their motions.

Â Working with this dataset,

Â he recognized that the orbits of the planets could not be circular.

Â They had to be ellipses with the sun at one focus.

Â And that was a profound innovation and discovery.

Â It also went against two millennia of thinking the circles and

Â spheres with the perfection figures of the universe.

Â And so naturally astronomical objects should follow them.

Â Reading Kepler's work,

Â it's possible to see the attraction of that Greek idea from Pythagoras.

Â And the resistance it caused in him to letting go of the idea of circular orbits,

Â but he did.

Â And in his writings, he eventually comes up with three laws that codify the laws of

Â planetary motion, and still are true today.

Â The first is that the orbits are elliptical, with the sun at one focus, and

Â nothing at the other.

Â Now these ellipses are subtle.

Â The Earth deviates from circular motion around the sun only by 4%, and

Â some of the other planets even less.

Â So these are quite subtle effects, and

Â the precision of Brahe's data was required to tease that out.

Â The second observation is law of equal areas, as it's called,

Â it has a mathematical form, which in its non-uniform motion around the sun.

Â 2:23

Kepler noticed that the planets so

Â far known in the solar system, perfectly adhere to the scaling in this law.

Â These three laws of planetary motion do not imply the nature of the gravity force.

Â That was left for Newton to understand.

Â But they provided convincing evidence that the Copernican model was the correct model

Â of planetary motion.

Â [MUSIC]

Â 5:15

Kepler's mathematical analysis of Tycho Brahe's data confirms to him that

Â the orbits of the planets are described very simply as elliptical, and

Â not circular with the sun at one focus.

Â And with the speed of motion that varies,

Â being faster when the planet is closer to the sun than when it is further away.

Â And also finding a straight mathematical relationship between the mean distance

Â from the sun and the period of the orbit.

Â These laws of planetary motion describe the planets known to Kepler and

Â also the planets found after he died.

Â