Forest Ray Moulton

Forest Ray Moulton (April 29, 1872 – December 7, 1952) was an American professor of astronomy and mathematics at the University of Chicago, author of several books, and ballistics expert serving as a U.S. Army major in World War I. His book An Introduction to Celestial Mechanics was translated into German as Einführung in die Himmelsmechanik (Teubner, 1927). Moulton was elected in 1910 to the U.S. National Academy of Sciences, in 1916 to the American Philosophical Society, and in 1919 to the American Academy of Arts and Sciences.

Quotes

Newton calls the Laws of Motion Axioms, and after giving each, makes a few remarks concerning its import. Later writers, among whom are Thomson and Tait,† regard them as inferences from experience, but accept Newton's formulation of them as practically final, and adopt them in the precise form in which they were given in the Principia. A number of Continental writers, among them is Dr. Ernst Mach, have given profound thought to the fundamental principles of Mechanics, and have concluded that they are not only inductions or simply conventions, but that Newton's statement of them is somewhat redundant, and lacks scientific directness and simplicity. There is no suggestion, however, that Newton's Laws of Motion are not in harmony with ordinary astronomical experience, or that they cannot be made the basis for Celestial Mechanics. But in some branches of Physics, particularly in Electricity and Light, certain phenomena are not fully consistent with the Newtonian principles, and they have led Einstein and others to the development of the so-called Principle of Relativity.
†Natural Philosophy, vol. I, Art. 243.
- An Introduction to Celestial Mechanics. Dover books in astronomy. Courier Corporation. 1970. pp. 3–4. (436 pages; reprint of 1914 2nd, revised edition; 1st edition published in 1902 by Macmillan)

Astronomy is a science. That is, it is one of those subjects, such as physics, chemistry, geology, and biology, which have made the present age in very many respects altogether different from any earlier one. Indeed, it is the oldest science and the parent of a number of the others, and, in many respects, it is the most perfect one. For these reasons it illustrates most simply and clearly the characteristics of science.
- An Introduction to Astronomy (2nd revised ed.). Macmillan. 1916. p. 2. (577 pages; 1st edition 1906)

The problem of three bodies received a great impetus in 1878, when Hill published his celebrated researches upon the lunar theory. His investigations were carried out with practical objects in mind, and comparatively little attention was given to the underlying logic of the processes which he invented. For example, the legitimacy of the use of infinite determinants was assumed, the validity of the solution of infinite systems of non-linear equations was not questioned, and the conditions for the convergence of the infinite series which he used were stated to be quite unknown. These deficiencies in the logic of his work do not detract from the brilliancy and value of his ideas, and his skill in carrying them out excites only the highest admiration.
The work of Hill was followed in the early nineties but the epoch-making researches of Poincaré ...
- Periodic Orbits. Johnson Reprint Corporation. 1963. p. iii. (524 pages; reprint of 1920 book, Volume 161 of Publications of the Carnegie Institution of Washington; 1st part of quote; last part of quote)

Integrals are generally of great importance in physical problems. Consider, for example, the problem of determining the motion of three bodies that attract one another according to the law of gravitation, but are subject to no other forces. Except for very special initial conditions, the solution functions are incapable of being expressed in terms of a finite number of elementary functions. Yet these differential equations have ten independent simple algebraic integrals, seven of which do not depend upon the time. Six of the ten are the mathematical expressions for the fact that the center of gravity of the three bodies moves with respect to the axes of reference in a straight line with uniform speed. Three of the integrals express the fact that the projections of the areal velocity of the system upon the three planes of reference are constant. And one integral expresses the fact that the sum of the kinetic and the potential energies of the system is constant.
The integrals describe invariants of the system, and their importance is easily seen.
- Differential Equations. Macmillan. 1930. p. 17. (395 pages)

Moulton’s Periodic Orbits, published in 1920, is a 500-page volume that collects articles from himself and his doctoral students over the previous 20 years. ...
Poincaré’s work, particularly Les Méthodes Nouvelles de la Méchanique Celeste, had a considerable influence on Moulton, and it was his methods that Moulton worked to extend to more specific practical problems. Poincaré was also a model for Moulton’s emphasis on rigor.
One of Moulton’s major projects was designed to develop a rigorous method to compute the orbit of the moon using a power series proved to converge for a finite interval of time. (Earlier Karl Sundman had shown that there was a uniformly convergent power series solution for the three-body problem, but it was known that this had little practical value because the convergence was so slow.) ...
Moulton’s name is largely remembered today for his textbook on celestial mechanics and for his theorem that the number of equivalence classes of collinear central configurations for the n-body problem is exactly n!/2.
- Bill Satzer, review of Periodic Orbits: F.R. Moulton’s Quest for a New Lunar Theory by Craig A. Stephenson. MAA Reviews, maa.org (July 18, 2021).

Commons

Wikimedia Commons has media related to:

Forest Ray Moulton

Wikisource

Wikisource has original works by or about:

Forest Ray Moulton