Abstract
In the case of oscillatory motion in the problem of three bodies it is shown that ast→∞ the mutual distances between particles cannot separate faster thanCt 2/3 whereC is some positive constant. As bounding functions of time exist for the other classifications of motion in the three body problem, it follows in general that the mutual distances between particles is 0(t) ast→∞.
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References
Chazy, J.: 1922,Ann. Sci. École Norm. 39, 1–130.
Pollard, H.: 1966,Mathematical Introduction to Celestial Mechanics, Prentice-Hall, New York.
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Saari, D.G. On oscillatory motion in the problem of three bodies. Celestial Mechanics 1, 343–346 (1970). https://doi.org/10.1007/BF01231138
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DOI: https://doi.org/10.1007/BF01231138