German astronomer Johannes Kepler is credited with demonstrating that abandoning an Earth-centered, or Ptolemaic, view of planetary motion for a Sun-centered, or Copernican, model implied that the motion of the planets had to be clearly elliptical. He reached this conclusion by analyzing the careful observations of his mentor, Tycho Brahe, on the motions of the heavenly bodies as well as his own observations of the orbit of Mars, which showed that planetary motion did not follow the path of a circle. From this insight, Kepler generated his three empirical laws of planetary motion. The first, the law of elliptical orbits, states that the orbits of the planets are ellipses with the Sun at one focus. The second, the law of equal areas, states that a line from the planet to the Sun sweeps over equal areas in equal...