Newton's Gravity
An Introductory Guide to the Mechanics of the Universe

Concentrates strongly on the historical development of the mathematics and science of orbital motion
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Uses concrete, interesting problems and case studies to teach and illustrate
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Explores the surprisingly basic mathematics behind gravity, the most fundamental force that governs the movements of satellites, planets, and the stars
Comet Lovejoy C/2011 W3, December 24, 2011, photograph courtesy of James Tse of Christchurch, new Zealand
My simulation with mathematical software of select passes of Halley's Comet through the solar system, from 374 AD
About the Book
My purpose in writing Newton's Gravity was to convey the power of simple mathematics to tell fundamental things about nature. Many people know the tides are caused by the pull of the Moon and to a lesser extent the Sun. But few can explain how and why that happens. Fewer still can calculate the actual pulls of the Moon and Sun on the oceans. The book attempts to show this and much more with simple tools. Newton's Gravity endeavors to cross disciplines and provide context — history, astronomy, physics and mathematics — and to explain things passed over or taken for granted in other books. The book doesn't purport to be a textbook or tome on classical celestial mechanics. Rather, it samples key areas of interest and invites further inquiry. It emphasizes intuitive appreciation rather than rigor. I hope the book will lead its readers to investigate the fundamentals of mass and motion on their own, and to puzzle through the problems that Newton and others faced in trying to make sense of why things move as they do. Most of all, I hope the book will encourage a sense of wonder at the beauty of the physical world and an appreciation of the brilliant minds who struggled to comprehend and express it in almost equally beautiful mathematics.
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As you may suspect from the title, the focus of the book is Newton’s, rather than Einstein’s, gravity. In other words, it deals with the classical mechanics which originated in the seventeenth century and which remains the basis for the core problems of celestial mechanics today. It therefore does not treat the curved spacetime of Einstein’s General Theory of Relativity. There is nothing in the book about the behavior of masses at relativistic speeds, black hole physics, or other aspects of Einstein’s geometrical view of gravity. I hope you enjoy it!
More About the Book
The book has three main characteristics that define it:
First, it concentrates strongly on the historical development of the mathematics and science of orbital motion, beginning with Galileo, Huygens, Kepler, and Newton, each of whom is prominently represented. Quotes and problems from Galileo’s Dialogs Concerning Two New Sciences, Huygens’s The Pendulum Clock, and particularly Newton’s Principia should help the reader get a little bit inside the mind of those thinkers and see the problems as they saw them, and experience their concise and typically eloquent writing.
Third, its mathematics is the simplest possible. The math is generally at the high school or early college level (algebra and the most basic geometry and a little trigonometry), with detailed explanations of the methods needed to solve the problems and understand the concepts. Calculus is the standard method for presenting this subject in most textbooks, and it produces quick, concise results. But it does not necessarily follow that calculus is needed for those results, or that a calculusbased presentation is the most intuitive vehicle for a beginner learning the fundamentals. I use methods and derivations that have appeared to be the most intuitively comprehensible, with stress on practical application. The surprise is how deeply one can dive with only the most basic mathematics and an intuitive grasp of the physics. This having been said, certain fundamental precalculus concepts involving limits introduced by Newton in his Principia are dealt with in this book, and should help one who has not had calculus get a foothold on the subject.
Second, it is problembased: it uses concrete, hopefully interesting problems and case studies to teach and illustrate. This method is critical for a handson understanding of this topic. Many of the problems use actual historical data, and results are compared with those obtained using modern data and methods. To underscore the relevancy of the original thinking on these issues, modern problems dealing with near Earth asteroids, NASA missions, and newly discovered dwarf planets are set next to historical problems that deal with the same mathematical or physical principles. Emphasis is on problems with dramatic interest and power of illustration.