**History of Mathematics**

Volume: 45;
2021;
255 pp;
Softcover

MSC: Primary 70;
Secondary 01; 85

**Print ISBN: 978-1-4704-5671-9
Product Code: HMATH/45**

List Price: $120.00

AMS Member Price: $96.00

MAA Member Price: $108.00

**Electronic ISBN: 978-1-4704-6508-7
Product Code: HMATH/45.E**

List Price: $120.00

AMS Member Price: $96.00

MAA Member Price: $108.00

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#### Supplemental Materials

# Periodic Orbits: F. R. Moulton’s Quest for a New Lunar Theory

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*Craig A. Stephenson*

Owing to its simple formulation and intractable nature, along with its
application to the lunar theory, the three-body problem has since it
was first studied by Newton in the Principia attracted the
attention of many of the world's most gifted mathematicians and
astronomers. Two of these, Euler and Lagrange, discovered the
problem's first periodic solutions. However, it was not until Hill's
discovery in the late 1870s of the variational orbit that the
importance of the periodic solutions was fully recognized, most
notably by Poincaré, but also by others such as Sir George
Darwin.

The book begins with a detailed description of the early history of
the three-body problem and its periodic solutions, with chapters
dedicated to the pioneering work of Hill, Poincaré, and
Darwin. This is followed by the first in-depth account of the
contribution to the subject by the mathematical astronomer Forest Ray
Moulton and his research students at the University of Chicago. The
author reveals how Moulton's Periodic Orbits, published in
1920 and running to some 500 pages, arose from Moulton's ambitious
goal of creating an entirely new lunar theory. The methods Moulton
developed in the pursuit of this goal are described and an examination
is made of both the reception of his work and his legacy for future
generations of researchers.

#### Readership

Graduate students and researchers interested in the three-body problem and Forest Ray Moulton's work.

#### Table of Contents

# Table of Contents

## Periodic Orbits: F. R. Moulton's Quest for a New Lunar Theory

- Cover Cover11
- Title page iii4
- Acknowledgements ix10
- Photograph and Figure Credits xi12
- Chapter 1. Introduction 114
- Chapter 2. The Three-Body Problem and Its First Periodic Solutions 720
- Chapter 3. Hill’s Variational Orbit 1528
- Chapter 4. Poincaré’s Research on Periodic Orbits 3346
- 4.1. King Oscar II’s prize competition 3346
- 4.2. Les Méthodes Nouvelles de la Mécanique Céleste 3548
- 4.3. The general problem of dynamics 3750
- 4.4. The reduction of the three-body problem 3851
- 4.5. The importance of the periodic solutions 4154
- 4.6. Poincaré’s first paper on periodic orbits 4457
- 4.7. Poincaré’s method 4558
- 4.8. Symmetric conjunctions and mirror configurations 4760
- 4.9. Poincaré’s classification of the periodic orbits 4861
- 4.10. Stability 4962
- 4.11. Bifurcations 5164

- Chapter 5. Darwin’s Numerical Search for Periodic Orbits 5568
- Chapter 6. Forest Ray Moulton 8598
- Chapter 7. Moulton’s Mathematical Methods 105118
- Chapter 8. Oscillating Satellites 123136
- Chapter 9. A New Lunar Theory 137150
- Chapter 10. Moulton’s Periodic Orbits 151164
- Chapter 11. Epilogue 185198
- Appendix A. Moulton’s Doctoral Students 203216
- Appendix B. Letters 207220
- Appendix C. The Moulton Plane 219232
- Appendix D. Glossary 223236
- Bibliography 227240
- Name Index 249262
- Subject Index 253266
- Back Cover Back Cover1269