Satellite encounters. [In circular orbits]
Satellite encounters. [In circular orbits]
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卫星相遇。
DOI：
10.1016/0019-1035(86)90089-8
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发表时间：
1986
期刊：
影响因子：
--
通讯作者：
M. Hénon
中科院分区：
文献类型：
--
作者：
J. Petit;M. Hénon
我们数值研究两个小卫星的相互作用，最初的圆形轨道略有不同的半径。我们首先表明，通过希尔的极限消失的群众，可以减少问题的一个更简单的形式，其中只有一个无量纲的参数仍然存在：减少影响参数。然后，我们提出了一个详细的研究家庭时，这个参数是不同的。每个轨道由三个阶段组成：两个小天体的接近，相互作用和离开。四阶级数用于表示两个小天体在接近和离开阶段的渐近运动;这些级数与相互作用阶段的数值积分相匹配，以精确表示整个轨道。对于每一个轨道，我们计算的净效应的遭遇，主要特点是增加分离的卫星轨道。我们还计算了两颗卫星的最小接近距离。在大的和小的影响参数的限制情况下，结果进行了比较与微扰理论的预测。最后，我们研究的“过渡”，这是明显的不连续性的家庭突然改变的方向出发。我们表明，他们可以解释的渐近方法的轨道不稳定的周期性解决方案的希尔问题。对于参数的无穷多个值，会发生转变，形成一个类似康托尔的集合。
We study numerically the interaction of two small satellites, initially on circular orbits with slightly different radii. We show first that by going to Hill's limit of vanishing masses, one can reduce the problem to a simpler form in which only one dimensionless parameter remains: the reduced impact parameter. We present then a detailed study of the family obtained when this parameter is varied. Each orbit consists of three phases: approach of the two small bodies, interplay, and departure. Fourth-order series are used to represent the asymptotic motion of the two small bodies in the approach and departure phases; these series are matched with a numerical integration of the interplay phase to give an accurate representation of the entire orbit. For each orbit, we compute the net effect of the encounter, essentially characterized by an increase of the separation of the satellite orbits. We compute also the minimal distance of approach of the two satellites. In the limiting cases of large and small impact parameters, the results are compared with the predictions of perturbation theories. Finally we study the “transitions,” which are apparent discontinuities of the family with a sudden change of the direction of departure. We show that they can be explained by the asymptotic approach of the orbit to an unstable periodic solution of Hill's problem. Transitions take place for infinitely many values of the parameter, forming a Cantor-like set.