## The Ballet of the Planets: A Mathematician's Musings on the Elegance of Planetary MotionThe 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 epicyclic curves, circles with smaller interior loops, similar to the patterns of a child's Spirograph. With the coming of the Copernican revolution, the retrograde motion was seen to be apparent rather than real, leading to the idea that the planets moved in ellipses. This laid the ground for Newton's great achievement—integrating the concepts of astronomy and mechanics—which revealed not only how the planets moved, but also why. Throughout, Benson focuses on naked-eye astronomy, which makes it easy for the novice to grasp the work of these pioneers of astronomy. |

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#### The Ballet of the Planets: A Mathematician's Musings on the Elegance of Planetary Motion

User Review - Ian D. Gordon - Book VerdictBenson (mathematics, emeritus, Univ. of California, Davis; A Smoother Pebble: Mathematical Explorations) takes readers on a historical journey through the development of mathematics and geometric ... Read full review

### Contents

1 The Survival of the Valid | 3 |

Birth | 9 |

Rebirth | 77 |

Enlightenment | 119 |

A The Greek Alphabet | 163 |

B Vectors | 165 |

Notes | 167 |

173 | |

175 | |

### Other editions - View all

The Ballet of the Planets: A Mathematician's Musings on the Elegance of ... Donald Benson Limited preview - 2012 |

The Ballet of the Planets: A Mathematician's Musings on the Elegance of ... Donald Benson Limited preview - 2012 |

The Ballet of the Planets: A Mathematician's Musings on the Elegance of ... Donald Benson No preview available - 2012 |

### Common terms and phrases

acceleration analemma ancient astronomers ancient Greek angle angular momentum angular velocity Archimedes axis calculation celestial sphere center of mass chapter clockwise concept constant Copernican Copernicus Copernicus’s Coriolis effect deferent and epicycle deferent circle deferent-epicycle model direction discussed distance Earth’s orbit Earthship ecliptic longitude ellipse elliptical orbit epicyclic curves epicyclic motion equal equant equant point example fixed stars force Galileo geocentric geometry heliocentric theory inferior planets intersection interval inverse-square law Jupiter Kepler Kepler’s third law latitude length line segment linkage Martian mathematical mathematician measured mechanics merry-go-round motion of Mars motionless movement moving Newton observations opposite parallax particle path planetary motion point Q problem Proposition Ptolemy Ptolemy’s radius respectively retrograde loops retrograde motion right ascension rods rotation rate scientific second law Section shown in Figure shows solar system speed spherical superior planets tangent terrestrial triangle two-circle epicyclic curve Tycho uniform circular motion vector Venus vernal equinox Δθ