基于矢量分析的中高轨道偏心率激发机制研究

According to theoretical studies and observational results, near circular medium and high Earth orbits are possible evolve into highly elliptical orbits naturally, which brings greater complexity and more challenges to the current space environment considering that orbits with large eccentricity increases the collision possibility. Meanwhile, it also limits the lifetime of some orbits and provides new space debris mitigation strategies. Hence, it is worth to investigate the dynamical mechanism of the eccentricity growth. Superior to the traditional methods that based on Kepler elements or Delaunay variables, vector analysis uses eccentricity vector and angular momentum as independent variables, the perturbation function does not rely on the specific coordinate system and the equation of motion is symmetrical and simple. As a result, we propose to address the following problems: (1) under what condition, a near circular orbit would evolve into highly elliptical, (2) what is the maximum eccentricity and how long it needs, and (3) is there any new characteristics of an orbit that the eccentricity has been activated? The objective of our proposed research is to calculate the quantitative results such as circular stability indicator, maximum eccentricity and eccentricity growth rate for initially near circular medium and high Earth orbits and obtain the distribution of these quantities in the parameter space.

已有的理论研究和实际观测表明，初始近圆的中高地球轨道，在自然力作用下长期演化，有可能逐步演变成大椭圆轨道，使得空间环境更为复杂：大椭圆轨道增加了在轨物体的碰撞风险。然而，偏心率的显著增长又可能减少中高轨道空间碎片的在轨寿命，为空间碎片的减缓提供了机会。因此，有必要对中高轨道偏心率激发机制开展深入研究。矢量分析方法，有别于传统的基于Kepler根数或Delaunay变量的理论，具有变量物理意义明确、摄动函数表达式不依赖于坐标系、运动方程形式简单等优势。本项目提出，基于矢量分析方法，从动力学角度探究以下问题：（1）近圆轨道在什么条件下以及为什么会逐步演化为大椭圆轨道？（2）偏心率最大会达到多少，需要多长时间？（3）偏心率被激发后会产生什么新的演化现象？最终，对初始近圆的中高地球轨道，给出近圆稳定性指数、最大偏心率、偏心率增长速率等指标的定量结果以及它们在参数空间中的分布特征。

导航卫星轨道是一类特殊的近圆中高轨道，这类轨道在长期动力学演化过程中呈现出一些不稳定性，其中典型的就是偏心率出现长期增长现象。这些现象会导致导航卫星结束工作后，其轨道在自然里长期作用下演化成大椭圆轨道，从而与低轨道、同步轨道等重要的工作卫星轨道产生交汇风险。本项目研究围绕这一现象，试图从动力学角度揭示近圆中高轨道的偏心率激发机制。由于受到多种摄动力影响，近圆中高轨道的动力学模型比较复杂，人们更多的采用数值方法进行研究。本项目采用矢量形式的轨道参数，建立了适用于中高轨道空间碎片长期演化规律研究的平均化动力学模型。给出了考虑月球轨道进动的轨道长期演化一阶分析解，讨论了月球1:1和2:1节点共振的产生条件和相空间结构。最终，在此基础上，将偏心率激发问题转化为微分方程的零解稳定性问题，利用Floquet指数和Lyapunov指数在相空间中描绘了偏心率不稳定区域，计算和偏心率激发速率指标。