There is one thing more painful than learning from mistakes (our own or somebody else's): Not learning from them.  Barbara Johnson 
Johannes Kepler BiographyJohannes Kepler was born in WeilderStadt Germany on January 6th, 1572. His family, whose fortunes were declining, had a relative who was mayor of the town. His adventurous father worked as a mercenary and deserted the family when Johannes was 17. His mother had a reputation for witchcraft. Born prematurely, Johannes was weak and sickly and had a relatively lonely and unhappy childhood. He turned to religion for solace. In 1587, Kepler attended Tubingen University where he proved himself as a capable mathematician. He was an advocate for the controversial Copernican theory of the solar system which he proselytized in public debates. After graduating in 1591, with his religious bent, Kepler attended the Tubingen school of theology with the intent to become a clergyman. However when he was 23 he accepted a teaching position at the Protestant school at Graz Austria where he taught mathematics, astrology and astronomy. He soon after gained fame as a prophet by predicting an exceptionally cold winter and a Turkish incursion into Austria in an annual almanac he produced. On July 19th, 1595, Kepler had a sudden inspiring idea that would guide his work for years to come. He was preparing for a geometry class when he drew a circle inscribed in a triangle inscribed in a circle. He realized that the ratio of the diameters of the two circles corresponded to the ratio of the orbits of Jupiter and Saturn. His idea was that the ratio of all of the planets could be predicted in this same way by using other simple two dimensional figures, the square, pentagon and hexagon, for example. Unfortunately, this didn't work, so he tried other schemes, including using simple three dimensional platonic solids to define the ratio which was much closer given the data available at the time. Kepler published his theory in Mysterium Cosmographicum ("The Cosmic Mystery") in 1596. The new scheme was not perfectly accurate. Kepler believed it was due to inaccurate estimates of the planetary orbits. He then determined to prove his theory by determining the planetary orbits more accurately. Pursuing this quest required transcending formidable obstacles in his personal and professional life. Laws of Planetary MotionOver the years that followed, Kepler formulated three Laws of Planetary Motion which described the planets traveling in elliptical orbits at varying speeds. The first two Laws were published in the Astronomia Nova ("The New Astronomy") in 1609. The third law, which relates the distance from the Sun to the time it takes a planet to complete each orbit, was published nine nears later in Harmonice Mundi ("Harmony of the World") in 1618. This work would, more than 100 years later, provide a foundational background for Isaac Newton's work on universal gravitation. The third law of motion combines the average orbital radius with the period of revolution or the time it takes to make one complete trip around the sun. The formula is normally stated as: T^{2} where T is the period of revolution, D is the average distance from the sun and K is a constant. As an example, for the Earth, T = 1 year, and D = 93 million miles. ConclusionTo Kepler himself, the idea of planets traveling in noncircular orbits was distasteful due to his belief that the orbits had a much deeper spiritual significance of universal harmony. It was through this belief of the planets representing a universal harmony that Kepler researched the ratios of planetary orbits to the ratio of musical notes in the Music of the Spheres. Read more about Kepler. 

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