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Book Review by Eva Gallant
When I read the title of this book, I thought I was going to be treated to a graceful ballet of planetary motion etched out in chapter verse. In my mind’s eye, our solar system is an elegant stage and we are simply ticket holders to a heavenly performance.
Emeritus Professor of Mathematics at the University of California, Davis, Donald C. Benson presents The Ballet of the Planets: A Mathematician’s Musings on the Elegance of Planetary Motion for your perusal. Author of A Smoother Pebble and The Moment of Proof, Professor Benson is no stranger to the exploration of mathematics’ involvement in science from a historical context and the advances or stumbles and foibles of past experts in their field of authority. The title of the book, derived from the Copernican piece Commentariolus, seeks to portray The Ballet of the Planets, and in part the debut of science as we know it today, evolving in 3 Acts of a show we are privy to witness unfold through the chapters of our journey.
In a comparison between Ancient Astronomy vs. 16th Century Astronomy to modern, Benson categorizes the progression based on 3 revolutionary advances and divides the book as such. Ancient Astronomers and scientists in general were able to theorize, hypothesize and predict based on simple naked eye observations. Scientists today are held to much higher standards, peer review and the scientific method. In that middle era when science blossomed, 1 of the 3 astronomy tenets postulated was that the Sun, not the Earth was the center of planetary movement. Another significant milestone was the theory that planetary motion is elliptical, not circular. Finally, a concept that seems second nature to us now was the theory of gravity and its involvement in planetary motion. For 2012 these seem like three simple acts of a graceful planetary ballet, but in their time, the ideas were ground-breaking.
Although not impossible to traverse, some sections of this book are perhaps more technical than required for a typical interest level in this subject. Additionally, all too often a reference is made to a figure in a future or previous chapter which requires a pause in reading to investigate that to which is being discussed. This book is ideal for someone seriously interested in the mathematical and geometric calculations of the historical and current movements of planetary motion.
Part One of The Ballet of the Planets begins with a discussion centered on the “Bowl of the Night”, an age old misguided view of an Earth centered Universe with the sun, stars and planets affixed to the sky above us. The author then dedicates 3 chapters to epicyclic motion. Chapter 5 also addresses this type of motion studying its uses outside of astronomy. For example, many of us fondly remember the Spirograph educational toy of our youth sold by Milton Bradley. The Spirograph uses “geared wheels rotating on each other to draw epicyclic curves”.
As Part Two of the book unfolds, the author describes “The Reluctant Revolutionary”. Technically, Copernicus was not the first theorist to propose a Sun centered solar system. Due to the circumstances of his era and the heavy influence of the Roman Catholic Church in his lifetime he was hesitant to publish. His theories and eventual published work revolutionized our view of the world. Professor Benson pays brief homage to Galileo, who followed Copernican Theory, before delving into Kepler and the ellipse. Ellipses are fascinating conic sections, their magic geometry gives us whispering galleries such as the one found in St. Paul’s in London. Further examinations of ellipses by the author include constructing tangents to an ellipse, the focal circle, Pascal’s Theorem and Brianchon’s Theorem. This all finally leads to the path of tracking the 3D position of planets.
The last act of the book, Part Three: “Enlightenment” is our reward through centuries of mathematical computations and scientific observations that eventually evolved into Newton’s Dynamics and his three laws of motion. Rotational Dynamics include uniform circular motion and angular momentum. Briefly discussed are the Coriolis effect and the Foucault pendulum. Last, and certainly not least, is the Law of Universal Gravitation. This last act of the book’s narration should be the section we are most able to relate to because it is physics and math as we know it today. However, for some readers there may be too many in depth references which contribute to the choppy feel of the prose throughout the book.
It is important to see the evolution to our 21st century opinions on the planetary ballet around us. There is a beauty to the heavens above and we do stand on the shoulders of those before us. Without their insight we would not be able to deduce how some of the daily wonders in our lives function. A well published Emeritus Professor of Mathematics, David Benson grasps the amazing advances in calculations and theory behind the progress, but the presented textbook like format is difficult to digest in one sitting. The Ballet of the Planets: A Mathematician’s Musings on the Elegance of Planetary Motion is a good read for someone seeking an in depth examination of various motion solutions throughout the years.
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