One of these later astronomers and mathematicians was Johannes Kepler. Kepler was born in Weil der Stadt on December on December 27, 1571. During his years in school, one of his mathematics teachers, Michael Maestlin taught Kepler of the Copernican Heliocentric theory. Kepler immediately accepted the idea because it was so simple and logical, believing that this simplicity was God's Plan. He published a book called the Cosmographic Mystery. This book explained that the planets orbited the sun because the sun emitted a special force that had pushed the planets around in a circular orbit. Throughout the years of 1594-1600, Kepler was the chair of astronomy and math at the Graz University in Austria. Yet, this was about to change.
In 1600, Kepler had left the position at the University and became an assistant to a great Danish astronomer named Tycho Brahe. After Brahe's death, Kepler had received all of Brahe's notes and observations on the cosmos. This was to be the basis for Kepler's three laws of planetary motion. The first of these revolutionary laws was that all planets orbit the sun in geometric figures called ellipses, though Kepler did not find this out right away. It took him a few times to correctly comprehend the data left to him by Brahe. Kepler first thought that instead of ellipses, the sun was a little off center, but the planets were still traveling in perfect circles. Then he began to think that there was an error in the data. And, on his third try, he figured it out : the elliptical orbits of every planet around the sun.

Kepler's second law of planetary motion is a little more challenging to understand. In regard to the planets, this law basically states that equal areas are swept in equal times. What this means can be explained if one does the following: one must draw 2 positions of a planet on its orbit for a 4-week period on the aphelion and does this again for the same planet for another 4 week period on the perihelion. Then, draw lines from the sun to the points. These lines are called the radius vectors. The area formed in the enclosed triangle will be the same for both the planet on the aphelion and perihelion. This is the explanation for the term "equal areas in equal times." What Kepler also concluded from this law was that the closer a planet is in its orbit to the sun, the faster it will travel, and visa versa.
The third law discovered by Kepler explains, "The ratio of the squares of the revolutionary periods for two planets is equal to the ratio of the cubes of their semi major axis." This law can also be shown mathematically. This technical language is simply explaining that the closer a planet's orbit is to the sun, the faster the planet will travel. The reason for the contrasting speeds of orbits of Neptune (Kepler did not know Neptune existed) and Mercury is because Mercury is much closer to the sun than Neptune is, therefore making its orbit 88 days compared to the 165 years it takes for Neptune.
Kepler, like Copernicus, thought that there were only six planets in the solar system. Though Kepler had come close with his theory in the book, Cosmographic Mystery, he still could not accurately account for what made the planets revolve around the sun, and what held the planets in their orbits. People of his time believed that angels beat their wings behind the planets to make them move. So Johannes Kepler was again stuck in his time and, without today's superior technology, he could not answer the questions he so dwelled upon. Yet, these mysteries of the solar system would be solved in the modern world.