Johannes Kepler (1571-1630) was a German astronomer who dramatically improved on the Copernican model of planetary motion by recognizing that they don’t move in perfect circles, as the ancient astronomers believed; they move in ellipses.
Much of astronomy in the 16th and 17th centuries was funded by kings interested in these strange new scientific ways of thinking. One of these was the Danish nobleman, Tycho Brahe (1546-1601), who convinced Danish king Frederick II to fund the astronomical observatory Uraniborg to study the stars and planets.
Brahe’s observations were masterful, but his models for explaining them were lacking. He did, however, employ Kepler as a promising young German assistant. Although Brahe guarded his observational data with zeal, Kepler was able to gain full access to the records upon Brahe’s death in 1601.
A cone is a round pyramid. Imagine you have two such cones facing each other that meet at the tips. With a knife, you can slice through the cones from different angles. If you slice through a cone horizontally, you will get the shape of a circle. If you cut at a slight angle, you will get an ellipse, like a flattened circle. At 45 degrees, you will get a parabola shape, and at greater angles still, the result is a hyperbola, slicing through both cones.
Kepler studied how you could use lenses and mirrors to construct all these curves. The beauty of the conic sections is that a single mathematical model could explain four different types of curves and how to morph between them gradually.
Influenced by Plato, the ancient astronomers believed that the circle was a perfect form and that the motions of the planets, therefore, had to be circular. Kepler had two important reasons not to believe this. First, he had become influenced by the reinjection of Aristotle into the culture. He was willing to study the world with his senses and draw conclusions from observations rather than from lofty ideas of perfection. Second, the Hindu-Arabic numerals had made mathematics so much easier and had enabled him to understand that circles, ellipses, parabolas, and hyperbolas are just four slices of the same cone.
Kepler’s laws inspired other bright minds in Europe to start similarly investigating the world. It also increased the belief in humanity’s ability to understand creation through scientific inquiry. The pessimism and skepticism of the Dark Ages were slowly melting away.