While much has been written on the ramifications of Newton's dynamics, until now the details of Newton's solution were available only to the physics expert. The Key to Newton's Dynamics clearly explains the surprisingly simple analytical structure that underlies the determination of the force necessary to maintain ideal planetary motion. J. Bruce Brackenridge sets the problem in historical and conceptual perspective, showing the physicist's debt to the works of both Descartes and Galileo. He tracks Newton's work on the Kepler problem from its early stages at Cambridge before 1669, through the revival of his interest ten years later, to its fruition in the first three sections of the first edition of the Principia . " The Key to Newton's Dynamics is lucid, important, and fills a large gap in the existing literature. Brackenridge is undoubtedly that gifted, patient teacher that one expects from a quality liberal arts college." Alan E. Shapiro, University of Minnesota " The Key to Newton's Dynamics is lucid, important, and fills a large gap in the existing literature. Brackenridge is undoubtedly that gifted, patient teacher that one expects from a quality liberal arts college."―Alan E. Shapiro, University of Minnesota J. Bruce Brackenridge is Alice G. Chapman Professor of Physics at Lawrence University. The Key to Newton's Dynamics By J. Bruce Brackenridge University of California Press Copyright © 1996 J. Bruce Brackenridge All right reserved. ISBN: 9780520202177 One A Simplified Solution: The Area Law, the Linear Dynamics Ratio, and the Law of Gravitation Isaac Newton's Philosophiae Naturalis Principia Mathematica (The mathematical principles of natural philosophy), hereafter referred to as the Principia , justifiably occupies a position as one of the most influential works in Western culture, but it is a work more revered than read. Three truths concerning the Principia are held to be self-evident: it is the most instrumental, the most difficult, and the least read work in Western science. A young student who passed Newton on the streets of Cambridge is reported to have said, "There goes the man who writ the book that nobody can read." It fits Mark Twain's definition of a classic as a work that everyone wants to have read but that nobody wants to read. The essential core of the Principia , however, does not lie beyond the reach of any interested and open-minded individual who is willing to make a reasonable effort. In 1693, Richard Bentley, a young cleric who was later to become Master of Newton's college, wrote to ask Newton for advice on how to master the work. Newton suggested a short list of background materials, and then, concerning the Principia itself, advised Bentley to read only the first three sections in Book One (i.e., the first sixty pages of the four hundred pages that make up the first edition). These sections provide the theoretical background for the astronomical applications that Newton presented in Book Three and regarded as of popular scientific interest. In the introduction to Book Three, Newton repeated the advice that he had given to Bentley: I had composed the third book in a popular method so that it might be read by many. But since those who had not sufficiently entered into the principles could not easily discern the strength of the consequences nor put aside long-held prejudices, I chose to rework the substance of that book into the form of propositions in the mathematical way, so that they might be read only by those who had first mastered the principles. Nevertheless, I do not want to suggest that anyone should read all of these propositionswhich appear there in great numbersince they could present too great an obstacle even for readers skilled in mathematics. It would be sufficient for someone to read carefully the definitions, laws of motion, and the first three sections of the first book; then let [the reader] skip to this [third] book.1 Newton's sage advice to the general reader to concentrate on the first three sections of Book One of the Principia appeared in the first edition of 1687 and remained unchanged in the two revised editions published in 1713 and 1726, all during Newton's lifetime. It is the third and final edition that has been reproduced in many subsequent editions and translated into many other languages. Because this third edition is readily available and because it is seen to represent Newton's most fully developed views, it is almost exclusively taken as a basis for the study of Newton's dynamics. The general reader, however, should not begin with this final edition and its many additions and revisions, but rather with the first edition and its relatively straightforward presentation. In 1684, Newton sent to London a tract entitled On the Motion of Bodies in Orbit (On Motion) that was to serve as the foundation for the first edition of the Principia of 1687. This comparatively short tract presents in a clean and uncluttere