Later in his life, Kepler held contact through letters with the perhaps more famous Galileo Galilei. Galileo was among the few people Kepler sent his first book, with the abbreviated title The Secret of the Universe. Still later, when Kepler became an imperial mathematician, he gave Galileo important recognition for his work with the telescope. [1]

One of the most significant discoveries that Kepler made was that the planets orbited the sun in elliptical orbits as opposed to circular. Kepler even invented the word “focus” relating to elipses. The elliptical nature of the planets was the first of Kepler’s laws of astronomy [2]. The second law is described on the Relevance to Infinity page.

Another significant contribution that took Kepler nearly 20 years to discover is a formula relating the distance of a planet from the sun and its period, or how long the orbit is. For planets, Kepler found that the ratio between square of the period squared and the cube of the average distance from the sun is equal to approximately 1.00. This marvelous discovery provides a wonderful relationship describing the solar system. The law can be further expanded, though when different kinds of orbits are being examined, the constant 1.00 may vary. The importance of Kepler’s discovery is how it beautifully describes the relationship between the periods and distances of the planets.[1]

Taken from http://jonathans-examined-life.blogspot.com/2009/11/new-kepler-opera-plan-linz-in-january.html

A statue of Kepler in Linz, Germany.