Abstract
In the first part of this paper [Marchal, Yoshida, Sun Yi-Sui 1985] we have analyzed three-body systems satisfying the condition r≦kR where k is a suitable constant, r the mutual distance of the two masses of the “binary” and R the distance between the center of mass of the binary and the “third mass”.
That condition r≦kR puts limits on the acceleration of the third mass and these limits allow us to determine the corresponding “escape velocities”.
In this second part we look for initial conditions under which the inequality r≦kR will remain forever satisfied and we develop the corresponding tests of escape and their applications.
This leads to a major improvement of the knowledge of the nature of three-body motions especially in the vicinity of triple close approaches.
The region of bounded motions is much smaller than was generally expected and numerical computations of particular solutions show that we approach very near to the true limit.
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References
Marchal, C.: 1975, 26th Congress of the International Astronautical Federation (Lisbon), ONERA T.P. 1975–77.
Marchal C., Bozis, G.: 1982, Celes. Mech.26, 311.
Marchal C., Yoshida J., Sun Yi-Sui: 1983 36th Congress of the International Astronautical Federation (Budapest), IAF 83-319 (to appear in Acta Astronautica, 1984).
Marchal C., Yoshida J., Sun Yi-Sui: 1984, Celes. Mech.33, 193.
Szebehely V.: 1967,Theory of Orbits, Academic Press, New York.
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Marchal, C., Yoshida, J. & Yi-Sui, S. Three-body problem. Celestial Mechanics 34, 65–93 (1984). https://doi.org/10.1007/BF01235792
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DOI: https://doi.org/10.1007/BF01235792