We consider the special case of the three-body problem where the mass of one of the bodies is considerably smaller than the masses of the other two bodies and investigate the relationship between the Lagrange stability of a pair of massive bodies and the Hill stability of the system of three bodies. We prove a theorem on the existence of Hill stable motions in the case considered. We draw an analogy with the restricted three-body problem. The theorem obtained allows one to conclude that there exist Hill stable motions for the elliptic restricted three-body problem.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 10, pp. 1434–1440, October, 2008.
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Sosnyts’kyi, S.P. On the hill stability of motion in the three-body problem. Ukr Math J 60, 1675–1682 (2008). https://doi.org/10.1007/s11253-009-0160-x
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DOI: https://doi.org/10.1007/s11253-009-0160-x