Motivated by the practical interest in the third-body perturbation as a natural cleaning mechanism for high-altitude Earth orbits, we investigate the dynamics stemming from the secular Hamiltonian associated with the lunar perturbation, assuming that the Moon lies on the ecliptic plane. The secular Hamiltonian defined in that way is characterized by two timescales. We compare the location and stability of the fixed points associated with the secular Hamiltonian averaged with respect to the fast variable with the corresponding periodic orbits of the full system. Focusing on the orbit of the Galileo satellites, it turns out that the two dynamics cannot be confused, as the relative difference depends on the ratio between the semi-major axis of Galileo and the one of the Moon, that is not negligible. The result is relevant to construct rigorously the Arnold diffusion mechanism that can drive a natural growth in eccentricity that allows a satellite initially on a circular orbit in Medium Earth Orbit to reenter into the Earth’s atmosphere.

中文翻译：

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关于快速振荡在伽利略卫星上月球共面扰动的长期动力学中的作用


在对第三体扰动作为高空地球轨道的自然清洁机制的实际兴趣的推动下，我们研究了与月球扰动相关的长期哈密顿量产生的动力学，假设月球位于黄道平面上。以这种方式定义的世俗哈密顿量以两个时间尺度为特征。我们将与长期哈密顿量相关的固定点的位置和稳定性与整个系统的相应周期轨道进行了比较。专注于伽利略卫星的轨道，事实证明这两种动力学是不能混淆的，因为相对差异取决于伽利略的半长轴和月球的半长轴之间的比率，这是不可忽略的。结果与严格构建 Arnold 扩散机制相关，该机制可以驱动偏心率的自然增长，从而允许最初在中地球轨道上的圆形轨道上的卫星重新进入地球大气层。