Abstract
Some recent tests have given excellent results in the analysis of three-body systems with three equal masses. These analyses are here extended to systems of unequal masses and lead to the following.
-
A)
For all mass ratios the smallest mass is the most unstable and the most subject to be ejected. The largest mass is generally very stable.
-
B)
The bounded orbits are very rare, their region in phase space is very small, much smaller than was generally expected.
-
C)
The usual Lagrange and Euler three-body solutions are not only some simple solutions of the three-body problem, they have also, under many respects, a role of limit and bifurcation with respect to the other solutions.
-
D)
The latest tests of escape approach very near to the true limit of bounded orbits.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Laskar, J. and Marchai, C: 1984, Celestial Mechanics 32, pp. 15–28.
Marchai, C.: 1980, Acta Astronautica, Vol. 7, pp. 123–126.
Marchai, C., Yoshida, J. and Sun Yi-Sui: 1983, 34th Congress of the International Astronautical Federation (Budapest) IAF 83–319.
Marchai, C., Yoshida, J. and Sun Yi-Sui: 1985a and b, Celestial Mechanics, to appear.
Sun Yi-Sui and Marchai, C.: 1985, Acta Astronomica Sinica, to appear.
Szebehely, V.: 1967, Theory of orbits. The restricted problem of three bodies. Academic-Press. New York.
Szebehely, V.: 1971, Celestial Mechanics, Vol. 4, p. 116.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 D. Reidel Publishing Company
About this chapter
Cite this chapter
Marchal, C. (1985). Three-Body Problem Some Applications of the Tests of Escape. In: Szebehely, V.G. (eds) Stability of the Solar System and Its Minor Natural and Artificial Bodies. NATO ASI Series, vol 154. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5398-7_9
Download citation
DOI: https://doi.org/10.1007/978-94-009-5398-7_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8883-1
Online ISBN: 978-94-009-5398-7
eBook Packages: Springer Book Archive