为什么大行星可以同时有顺行和逆行卫星

本文用圆型限制三体问题的Jacobi积分来建立一个能确定卫星是否稳定的测检函数.凡是对其主行星所作的瞬时椭圆轨道要素已知的卫星都可检定其稳定性.对于作准圆形轨道运动的卫星,我们可用电子计算机来求出它的稳定域,这域的界面是一个近似的扁椭球面.这闭面所包围的空间比“引力作用球”和其相应的卫星区的“Hill曲面”要小得多.由于卫星对其主行星的相对动能表示式对顺行和逆行轨道两者形式相同,所以两者可以在卫星的稳定域中同时存在.

Why Can the Major Planets Have Their Satellites Moving in Direct and Retrograde Orbits As Well?

Now we use the Jacobian integral of circular restricted three-body problem to establish a testing function of the stability of satellites. This method of criterion may be applied to the stability problem of satellites when the six elements of the instantaneous orbit of the satellite with respect to its parent planet are known. By means of an electronic computer, we can find the stable region of a satellite with a quasi-circular orbit. The boundary surface of this region is a nearly oblate ellipsoid. The volume of this enclosed space is much smaller than that of binding by Hill surface and that of "sphere of action" As the expressions of relative kinetic energy of a satellite with respect to its parent planet have the same form for the direct as well as the retrograde orbits, they can coexist in the same region at the same time.