环在平面圆型限制性三体问题中对秤动点稳定性的影响

THE EFFECT OF A THIN RING ON THE LOCATION AND THE STABILITY OF THE LIBRATION POINTS IN THE PLANAR CIRCULAR RESTRICTED THREE-BODY PROBLEM

一、引言将两个主星体和小天体都看成质点的圆型限制性三体问题的秤动点的稳定性,Szebehely 作过详细讨论.自然界的多数天体都有一定扁率,也有些天体,如太阳系的木星、土星和天王星还带有光环.[3,4]就扁率摄动对限制性三体问题的秤动的影响有过讨论.本文讨论了一主星体带环时对秤动点的稳定性的影响。

In this paper the effect of a thin ring on the location and the stability in the linear of the libration points in the planar circular restricted three- body problem is studied.It is shown that when one of the primaries has a thin ring the location and the stability in the linear depend on the mass parameter μ,the inside radius α,the outside radius b and the mass ratio q of the ring and the primary.The method and the conclusion presented here are useful in the Case which the bigger primary is an oblate spheroid.