On Hill domains for the limited three-body problem

S.P.Sosnitskii

Institute of Mathematics of National Academy of Sciences of Ukraine

Tereshchenkivs'ka str 3, Kyiv, 01601, Ukraine

 

We study the existence problem of Hill regions for the restricted elliptic three-body problem. In the case of elliptic motion of massive bodies with a small eccentricity, it is shown that there exist motions of the small particle, which are bounded with respect to co-ordinates. We obtain conditions of the existence of Hill regions for the bounded elliptic three-body problem by analyzing motions both in the framework of the general three-body problem and in the framework of the restricted three-body problem. In the frame of this approach the boundedness of the problem is meant first of all as small influence of the small particle with mass m₃ on the motion of massive bodies in the complete system and this does not imply that one has to neglect the small mass m₃. Such a combined approach has been already used by the author in the earlier works.