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Keplers Third Law Interactive (200.0K)
Since Kepler's time, we have found many new bodies orbitting the Sun, most with more eccentric orbits than any studied by Kepler, but still the third law is invaluable. In January 2004, astronomers were surprised by the discovery of the first large body beyond the Kuiper Belt, perhaps an inner member of the Oort Cloud. It was named Sedna, after the Inuit goddess of the frozen arctic seas.
Newton would expand this far beyond the solar system; lets look at problems with practical applications of this Third Law, where the mass of the star is not equal to our Sun's. In fact, the ratio of distance cubed/period squared is equal to the mass of the star; as long as it has one solar mass, and the distance is in AU, and the period is in years.
Johannes Kepler loved math, and was delighted to find that there was a "harmony of the spheres" between the period of revolution of a planet around the Sun in years, and its average distance from the Sun in astronomical units. Let's apply it to the planet closest to our Sun.
Johannes Kepler loved math, and was delighted to find that there was a "harmony of the spheres" between the period of revolution of a planet around the Sun in years, and its average distance from the Sun in astronomical units. In his time, Saturn was the most distant "test case" he had to work with.