Earth–Moon Weak Stability Boundaries in the restricted three and four body problem
Earth–Moon Weak Stability Boundaries in the restricted three and four body problem
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DOI：
10.1007/s10569-008-9169-y
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发表时间：
2009
影响因子：
1.6
通讯作者：
D. Romagnoli;C. Circi
中科院分区：
文献类型：
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作者：
D. Romagnoli;C. Circi
本文在受限三体和四体问题的框架下研究月球弱稳定边界(WSB)的结构。通过改变航天器绕月轨道参数，研究了逃逸轨迹的几何和性质。用WSB的算法定义得到的结果与基于雅可比常数值的解析近似进行了比较。在三体模型和四体模型中研究了平面和三维情况，并研究了太阳引力和月球轨道偏心对WSB结构的影响。对月球捕获后航天器动力学演化的研究使我们能够找到与稳定和安全的轨道相对应的WSB区域，即捕获后不会影响月球表面的轨道。然后，通过使用双圆四体模型，可以研究低能量转移轨迹，并给出了关于偏心率、中心附近高度和俘获轨道倾角的结果。对赤道俘获轨道和极地俘获轨道进行了比较，指出了这两种轨道在能量方面的差异。最后，WSB几何结构的知识使我们能够修改低能量捕获轨迹的设计，以实现稳定的捕获，这使得使用低推力推进系统的轨道环行。
This work deals with the structure of the lunar Weak Stability Boundaries (WSB) in the framework of the restricted three and four body problem. Geometry and properties of the escape trajectories have been studied by changing the spacecraft orbital parameters around the Moon. Results obtained using the algorithm definition of the WSB have been compared with an analytical approximation based on the value of the Jacobi constant. Planar and three-dimensional cases have been studied in both three and four body models and the effects on the WSB structure, due to the presence of the gravitational force of the Sun and the Moon orbital eccentricity, have been investigated. The study of the dynamical evolution of the spacecraft after lunar capture allowed us to find regions of the WSB corresponding to stable and safe orbits, that is orbits that will not impact onto lunar surface after capture. By using a bicircular four body model, then, it has been possible to study low-energy transfer trajectories and results are given in terms of eccentricity, pericenter altitude and inclination of the capture orbit. Equatorial and polar capture orbits have been compared and differences in terms of energy between these two kinds of orbits are shown. Finally, the knowledge of the WSB geometry permitted us to modify the design of the low-energy capture trajectories in order to reach stable capture, which allows orbit circularization using low-thrust propulsion systems.