On the hill stability of motion in the three-body problem

  • S. P. Sosnitskii


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.
How to Cite
Sosnitskii, S. P. “On the Hill Stability of Motion in the Three-Body Problem”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, no. 10, Oct. 2008, pp. 1434–1440, https://umj.imath.kiev.ua/index.php/umj/article/view/3258.
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