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''Periodic Orbits About An Oblate Spheroid'' is a scientific book written by William Duncan Macmillan and published in 1909. The book is a comprehensive study of the periodic orbits around an oblate spheroid, which is a three-dimensional shape that is flattened at the poles and bulging at the equator. The author provides a detailed analysis of the mathematical equations that govern the motion of particles around such a spheroid, and he explores the various types of periodic orbits that can be observed.The book is divided into several chapters, each of which focuses on a different aspect of the problem. The first chapter provides an introduction to the topic and explains the basic concepts that are used throughout the book. The second chapter describes the mathematical framework that is used to analyze the orbits, including the equations of motion and the perturbation theory. The third chapter explores the various types of periodic orbits that can be observed, including the prograde and retrograde orbits.In the following chapters, the author discusses the stability of the periodic orbits and the effects of various perturbations, such as the gravitational attraction of other bodies. He also explores the phenomenon of resonance, which occurs when the period of an orbit is related to the period of another orbit in a simple ratio. The final chapter summarizes the main results of the book and discusses their implications for the study of celestial mechanics.Overall, ''Periodic Orbits About An Oblate Spheroid'' is a highly technical book that is intended for advanced students and researchers in the field of celestial mechanics. It provides a thorough and detailed analysis of a complex problem, and it is a valuable resource for anyone interested in the dynamics of celestial bodies.In Candidacy For The Degree Of Doctor Of Philosophy.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world’s literature in affordable, high quality, modern editions, that are true to their original work.
