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

Overview


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 ...
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Overview


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 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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Editorial Reviews

From the Publisher

"Although this book complements Norriss S. Hetherington's Planetary Motions: A Historical Perspective, it is unique in its eclectic mix of detailed mathematical proofs, numerous figures, and solved problems...An essential book for any planetary astronomy collection." -- Library Journal

"Benson is an astute writer who conveys these mathematical concepts with a great deal of skill." -- Alastair Gunn, Sky at Night Magazine Book of the Month

"This iteration between theory and observation lies at the heart of the scientific method as practiced to this day. The result of this tutorial is a narrative that is both lucid and comprehensive but well suited to the layperson." --CHOICE

Library Journal
Benson (mathematics, emeritus, Univ. of California, Davis; A Smoother Pebble: Mathematical Explorations) takes readers on a historical journey through the development of mathematics and geometric theories of planetary motion from ancient to modern times. He tells of the historical and revolutionary discoveries that the Sun (not Earth) is the center of planetary movement, that motion is elliptical (not circular), and that gravity is the driving force of planetary motion. Benson illustrates how Archimedes, Plato, Ptolemy, Copernicus, Brahe, Kepler, Newton, and their contemporaries built on previous geometrical theories to better understand why the planets seemingly dance through the night sky. Although this book complements Norriss S. Hetherington's Planetary Motions: A Historical Perspective, it is unique in its eclectic mix of detailed mathematical proofs, numerous figures, and solved problems. VERDICT Benson attempts to write for a general audience, but readers require a technical grounding in calculus, geometry, and algebra to appreciate the elegance of concepts such as epicyclic curves and ellipses. An essential book for any planetary astronomy collection.—Ian D. Gordon, Brock Univ. Lib., St. Catharines, Ont.
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Product Details

  • ISBN-13: 9780199891009
  • Publisher: Oxford University Press
  • Publication date: 5/29/2012
  • Pages: 192
  • Product dimensions: 6.20 (w) x 9.30 (h) x 0.70 (d)

Meet the Author

Donald C. Benson is Emeritus Professor of Mathematics at the University of California, Davis, and the author of A Smoother Pebble and The Moment of Proof.

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Table of Contents

Acknowledgements
Introduction
1 The Survival of the Valid

I. Birth
2 The Bowl of Night
3 Epicycles and Relative Motion
4 The Deferent-Epicycle Model
5 Making Money, Et Cetera

II Rebirth
6 The Reluctant Revolutionary
7 Circles No More
8 The War with Mars

III Enlightenment
9 The Birth of Mechanics
10 The Astronomical Alchemist
A. The Greek Alphabet
B. Vectors

Notes
References
Index

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