On the Theory of the Motion of the Small Planets with a Periodic Orbit for the Hilda Type
On the Theory of the Motion of the Small Planets with a Periodic Orbit for the Hilda Type

Author: Louis Allen Hopkins

Publisher: Palala Press

Published: 2015-09-19

Total Pages: 24

ISBN-13: 9781343205192

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

Author: Craig A. Stephenson

Publisher: American Mathematical Soc.

Published: 2021-05-19

Total Pages: 255

ISBN-13: 1470456710

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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.

Science
Science

Author: John Michels (Journalist)

Publisher:

Published: 1909

Total Pages: 1038

ISBN-13:

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Since Jan. 1901 the official proceedings and most of the papers of the American Association for the Advancement of Science have been included in Science.

Periodic Orbits, Stability and Resonances
Periodic Orbits, Stability and Resonances

Author: G.E.O. Giacaglia

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 540

ISBN-13: 9401033234

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The subjects of resonance and stability are closely related to the problem of evolution of the solar system. It is a physically involving problem and the methods available to mathematics today seem unsatisfactory to produce pure non linear ways of attack. The linearization process in both subjects is clearly of doubtful significance, so that, even if very restrictive, numerical solutions are still the best and more valuable sources of informations. It is quite possible that we know now very little more of the entire problem that was known to Poincare, with the advantage that we can now compute much faster and with much more precision. We feel that the papers collected in this Symposium have contributed a step forward to the comprehension of Resonance, Periodic Orbits and Stability. In a field like this, it would be a surprise if one had gone a long way toward that comprehension, during the short time of two weeks. But we are sure that the joint efforts of all the scientists involved has produced and will produce a measurable acceleration in the process. If this is true it will be a great satisfaction to us that this has happened in Brasil. The Southern Hemisphere in America has now begun to participate actively in the Astro nomical Society and for this, we are grateful to everyone who has helped.