Cover; Contents; Acknowledgments; Introduction; 1. The Survival of the Valid; 1.1. Peer Review; 1.2. The Scientific Method; Part One: Birth; 2. The Bowl of Night; 2.1. The Two-Sphere Universe; 2.2. Coordinate Systems; 2.3. The Sun; 3. Epicycles and Relative Motion; 3.1. A Mechanical Linkage; 3.2. Relative Motion; 4. The Deferent-Epicycle Model; 4.1. Retrograde Motion; 4.2. Ptolemy; 4.3. The Deferent-Epicycle Model; 4.4. Intimations of Numerology; 4.5. The Equant; 5. Making Money, Et Cetera; 5.1. Epicyclic Curves as Decorative Patterns; 5.2. Cycloidal Curves; Part Two: Rebirth.;The Ballet of the Planets unravels the beautiful mystery of planetary motion, revealing how our understanding of astronomy evolved from Archimedes and Ptolemy to Copernicus, Kepler, and Newton. Mathematician Donald Benson shows that ancient theories of planetary motion were based on the assumptions that the Earth was the center of the universe and the planets moved in a uniform circular motion. Since ancient astronomers noted that occasionally a planet would exhibit retrograde motion--would seem to reverse its direction and move briefly westward--they concluded that the planets moved in epicyc.