闪电卫星星座的动力学特性：轨道偏心率的长期演变
Dynamical properties of the Molniya satellite constellation: long-term evolution of orbital eccentricity
摘要：
这项工作的目的是分析的平均偏心率的轨道演变的双线元素（TLE）的闪电卫星星座。该方法是自下而上的，旨在观察到的动态和数学建模之间的协同作用。作为焦点的偏心率的长期演变，所采用的动力学模型是由于太阳和月球的第三体摄动的双平均公式，加上扁率对卫星的取向的影响。偏心率的数值演变，通过两个自由度的模型，假设不同的顺序在第三体效应的系列扩展，对TLE给出的平均演变进行了比较。结果表明，尽管是高度椭圆轨道，二阶展开捕捉非常好的行为。另外，日月效应对升交点经度和近心辐角的影响也是不可忽略的。混沌的作用，在考虑的时间跨度也得到解决。最后，提出了一个频率序列分析，以显示可以检测到的观测数据的主要贡献。
英文摘要：
The aim of this work is to analyze the orbital evolution of the mean eccentricity given by the Two-Line Elements (TLE) set of the Molniya satellites constellation. The approach is bottom-up, aiming at a synergy between the observed dynamics and the mathematical modeling. Being the focus the long-term evolution of the eccentricity, the dynamical model adopted is a doubly-averaged formulation of the third-body perturbation due to Sun and Moon, coupled with the oblateness effect on the orientation of the satellite. The numerical evolution of the eccentricity, obtained by a two-degree-of-freedom model assuming different orders in the series expansion of the third-body effect, is compared against the mean evolution given by the TLE. The results show that, despite being highly elliptical orbits, the second order expansion catches extremely well the behavior. Also, the lunisolar effect turns out to be non-negligible for the behavior of the longitude of the ascending node and the argument of pericenter. The role of chaos in the timespan considered is also addressed. Finally, a frequency series analysis is proposed to show the main contributions that can be detected from the observational data.
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