The next figure in the history of the Copernican revolution is Johannes Kepler. Kepler was a brilliant mathematician, perhaps the best of his time. Well reputed around Europe. He had a star-crossed life. He was weak and covered with boils, sickly, bedridden often. His mother was accused of being a witch and used a lot of his resources to get her off that and stop her from being executed. Even later in his life, when he begged Galileo for a telescope, Galileo wouldn't send him a telescope. So he had some hard luck stories. But his best stroke of fortune was working with Tycho Brahe and inheriting his wonderful set of observations of the planets and their motions. Working with his dataset, he recognized that the orbits of the planets could not be circular. They had to be ellipses with the sun at one focus. That was a profound innovation and discovery. It also went against two millennia of thinking the circles and spheres with the perfection figures of the universe, and so naturally, astronomical objects should follow them. Reading Kepler's work, it's possible to see the attraction of that Greek idea from Pythagoras and the resistance they caused in him to letting go of the idea of circular orbits. But he did, and in his writings he eventually comes up with three laws that codify the laws of planetary motion and still are true today. The first is, that the orbits are elliptical with the sun at one focus and nothing at the other. Now, these ellipses are subtle. The Earth deviates from circular motion around the sun only by four percent, and some of the other planets even less. These are quite subtle effects and the precision of Brahe's data was required to tease that out. The second observation is, the law of equal areas, as it's called, has a mathematical form which is in non-uniform motion around the sun. Every planet traces out an equal area in equal amounts of time. What that means in an elliptical orbit is that the planet is moving faster when it's closer to the sun than when it's further from the sun. He provided a mathematical form for that relationship. His third law is also mathematical, relating the square of the period of the orbit of a planet to the cube of its mean distance from the sun. Kepler noticed that the planets so far known in the solar system perfectly adhere to the scaling in this law. These three laws of planetary motion do not imply the nature of the gravity force that was left for Newton to understand, but they provided convincing evidence that the Copernican model was the correct model of planetary motion. Kepler's mathematical analysis of Tycho Brahe's data confirms to him that the orbits of the planets are described very simply as elliptical and not circular with the sun at one focus. With the speed of motion that varies being faster when the planet is closer to the sun than when it's further away. Also, finding a strict mathematical relationship between the mean distance from the sun and the period of the orbit. These laws of planetary motion described the planets known to Kepler and also the planets found after he died.
