【摘要】 本文讨论了主体之一为三轴椭球体的限制性三体问题中周期轨道的存在情况。以二体问题的圆轨道为生成轨道,延拓成此力学模型中围绕三轴椭球形状的大主体的一组对称周期轨道。将这组周期轨道和不考虑主体形状的一般限制性三体问题中相应周期轨道的初始条件作比较,看出二者之差为形状摄动量级的量。由此可见,当主体的扁率较大,而且小天体离主体较近时,讨论小天体的周期轨道必须考虑主体形状的影响。更多还原

【Abstract】 The existence of first Sort periodic orbits of the generalized restricted 3-body problem with an ellipsoid is studied in this paper. First, the poincaré’s theorem of analyticcontinuation of periodic orbit for the single parameter is generalized to the case of multiple parameters. For the problem with——（m₂）╱（m₁+m₂） =0.1, ellipticity of meridian α=0.1, eUipticity of equator β=0.05, a number of first sort periodic orbits are constructed by the mumerical approach. The results show the differences between the initial conditions of the preceding case and the case of μ=0.1, α=β=0 are of the order of the ellipticities In conclusion, for the case of the distance between the massless particle and the ellipsoid r≤0.09, the effects of the eUipticities of the ellipsoid are not ignorable. The results of this paper can be used to analyse the rotating emission ring in binary systems.更多还原