The five libration points of a sun–planet system are stable or unstable fixed positions at which satellites or asteroids can remain fixed relative to the two orbiting bodies. A moon orbiting around the planet causes a time-dependent perturbation on the system. Here, we address the sense in which invariant structure remains. We employ a transition state theory developed previously for periodically driven systems with a rank-1 saddle in the context of chemical reactions. We find that a satellite can be parked on a so-called time-periodic transition state trajectory – which is an orbit restricted to the vicinity of the libration point L2 for infinitely long time – and investigate the stability properties of that orbit.

太阳-行星系统的五个平衡点是稳定或不稳定的固定位置，在这些位置卫星或小行星可以相对于两个轨道天体保持固定。围绕行星运行的月球会对系统造成与时间相关的扰动。在这里，我们解决了保持不变结构的意义。我们在化学反应的背景下采用了先前为具有 1 级鞍座的周期性驱动系统开发的过渡态理论。我们发现卫星可以停在所谓的时间周期过渡态轨迹上——这是一个无限长时间限制在平衡点 L2 附近的轨道——并研究该轨道的稳定性特性。