On the stabilization of the collinear libration points of the restricted circular three-body problem

Abstract

The possibility of stabilizing the collinear libration points of the circular restricted three-body problem by using an additional jet acceleration (constant in magnitude) is investigated. Three stabilization laws are considered when the jet acceleration is either directed continuously to one of the primariesm ₁,m ₂ or is parallel to the line joining them. The solution of the problem formulated is based on the method of the driving forces structure analysis created by W. Thomson and P. Tait. It is shown that none of the stabilization laws mentioned ensures the existence of the isolated minimum of changed potential energy, and therefore the secular stability of the collinear libration points is impossible. In the 3rd and 4th paragraphs the possibility of a gyroscopic stabilization of these points is considered. It is shown that the gyroscopic stabilization of the external libration points is possible only when jet acceleration is either directed to the distant mass or is parallel to the line joining the primaries. The necessary and sufficient conditions of the gyroscopic stabilization are given. It is also shown that the internal libration points cannot be stabilized by any of the laws considered. For the Earth-Moon system the numerical data of time-existence of the satellite in the vicinity of the libration point situated near the Moon are given.