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

The three-body problem has fascinated mathematicians and astronomers for centuries due to its complexity and application to lunar theory. Euler and Lagrange discovered the first periodic solutions, but it was Hill's discovery of variational orbits in the late 1870s that truly emphasized their importance. This book explores the early history and contributions of Hill, Poincare, Darwin, and Moulton to the subject, highlighting Moulton's ambitious lunar theory and his innovative methods.

Format: Paperback / softback
Length: 255 pages
Publication date: 01 June 2021
Publisher: American Mathematical Society

Due to its straightforward formulation and intractable nature, coupled 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 Poincare, 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, Poincare, 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.

Weight: 480g
Dimension: 183 x 256 x 18 (mm)
ISBN-13: 9781470456719