Background
Johannes Kepler was a German astronomer who is most well known for the three laws of planetary motion he formulated and verified. These Laws are known as Kepler's Laws. Kepler strongly believed in the the simplicity of the Copernican view of the solar system and looked for a way to prove it.
To explain planetary orbits Kepler first formulated a complex geometric hypothesis to account for the distances between the planetary orbits. Next Kepler proposed that the Sun emits a force that pushes the planets around in their orbits, which he deduced must diminish inversely with distance. Since the Sun regulates the speed of the planets orbit, when it is closest to the Sun (perihelion) the planet orbits more quickly and when farthest from the Sun (aphelion) it slows down. This force would be later explained by Newton's Law of Universal Gravitation. Kepler published these finding in a book entitled "Cosmographic Mystery" in 1596. This work was very important because it was the first explanation of the geometric advantages of the Copernican theory.
Kepler worked with Tycho Brahe for a year in an observatory near Prague until Brahe's death in 1601. Upon his death Brahe left Kepler all his data on the planets and stars which he put to good use. He used data that Brahe had collected on Mars in order to calculate its orbit. Out of this painstaking effort came two of Kepler's Laws. The first stated that the planets travel in elliptical orbits with the Sun at one focus and the second also known as the "area rule" showed that a hypothetical line from the Sun to the planet sweeps out equal areas of the ellipse during equal time intervals. This second law can be more easily understood when if you think of it as saying that the closer the planet comes to the sun the more rapidly it moves.
After more years of observations Kepler published "Harmony of the World" in 1619 that contained his third and final law. This third amazing discovery of planetary motion was that the ratio of the square of the planet's orbital period and the cube of the planet's distance from the Sun was the same for all the planets, or in other words, a constant.
Epitome of Copernican Astronomy
Following these discoveries Kepler went to work on creating a single volume that brought all of his discoveries together. Finally in 1621 this volume called "Epitome of Copernican Astronomy" was complete and for the next three decades it was a major influence in converting many skeptical astronomers to the Copernican view of the solar system. Epitome was historically important because it was the first textbook of astronomy based on the Copernican principles.
Tables of Planetary Motion
Kepler completed one more major work before his death in 1630. It was called the "Rudolfine Tables" and was published in 1625. It was based on Tycho Brahe's data and were revised tables of planetary motion. These calculations reduced the mean errors from 5 degrees to about 10 minutes of the actual position of a planet. Sir Isaac Newton relied heavily on Kepler's work and observations when developing his law of universal gravitation.
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