小天体不规则引力场拓扑动力学与共振轨道研究

In recent years, many countries have already launched or are ready to launch missions to asteroids or comets, which include asteroid-circling, landing, and sampling. China will also implement our own asteroid exploration mission in the future. Observation shows that most of the small bodies are irregular shaped. Therefore, the orbital dynamics in the vicinity of them is not central and very complicated. In order to carry out a successful exploration mission for asteroid, the dynamical environment around them must be studied in depth and well analyzed. Topological dynamics is a tool for studying the evolution of state variables, which reflects the nature of dynamical systems. We introduce this method, as well as orbital resonances, to the study of orbital dynamics in the vicinity of irregular small bodies. The system is rich in topological dynamics phenomena. Interesting and significant results can be expected during the study. The work intended to be carried out is illustrated as follows. First, considering the YORP effect and other perturbations for sun or planets, we improve a more detailed model for dynamical environment in the vicinity of an asteroid. Then, the topological dynamics in the potential fields of small bodies will be analyzed and the bifurcation of equilibrium points will be investigated. The dynamic behavior is associated with physical parameters of certain small body. The relation between them will be studied. Finally, the orbital resonances in the potential fields of small bodies will be investigated. The formation mechanism of asteroid rings will also be studied This research will provide support for the development of asteroid exploration missions in China. And it will also make contributions to our understanding on where the asteroids came from and how they evolve in the future.

近年来，各国相继实施对小行星和彗星等小天体的探测任务，进行环绕、着陆与采样返回等项目，我国作为航天大国中的一员，也将实施自己的小行星探测计划，在深空探测的热潮中大步前进。大部分小天体形状不规则，导致周围的动力学环境十分复杂，为了保证探测任务顺利进行，必须对小天体附近的动力学环境进行深入分析。拓扑动力学反映了动力系统状态演化的本质，将此方法引入小天体附近的动力学研究中，并结合轨道共振理论，可以得到十分丰富的拓扑动力学现象，有期望取得有趣而重大的成果。本项目具体开展以下工作：1）考虑YORP效应以及大天体引力摄动等因素，完善更加精细的小天体附近动力学环境；2）分析小天体附近拓扑动力学与分岔演化规律，研究小天体附近动力学行为对特征参数的依赖性；3）探索小天体附近共振轨道的动力学特性与演化过程，研究小行星环的形成原因。此项目将促进对小天体形成与演化机制的研究，并为我国小天体探测任务的开展提供支撑。

本项目针对小天体附近引力场的不规则特性，在前人的基础上，引入拓扑动力学与轨道共振分析方法，对小天体引力场中的轨道动力学进行研究，解决国际上尚未完善的基础问题，为我国的小天体探测活动提供理论储备。1、不规则小天体附近精细动力学模型与高效模拟算法，小天体在宇宙中所处的动力学环境十分复杂，目前的小行星附近引力场，往往都是采用理想化模型，进行定性的理论研究。本项目则通过对小天体附近的引力场进行深入分析，进一步细化完善，得到更加精细的动力学模型；2、不规则小天体引力场中的拓扑动力学结构与分岔行为，小天体附近引力场呈现非中心引力场特性，具有十分复杂的动力学环境，本项目将拓扑动力学从动力学系统的角度对轨道运动进行分析，使得研究者可以从更本质的角度研究不规则小天体引力场中的轨道演化规律；3、小天体附近轨道的共振机制与演化特性，小天体附近不规则引力场十分复杂，有些小天体的引力场具有限制性三体的特性，可能存在不同类型的共振轨道。对于小天体附近的共振轨道，当其轨道周期与小天体自转形成整数比关系时，就构成了传统意义上的共振轨道。轨道共振具有清扫动力学环境与稳定附近细小尘埃的双重属性，对于此类轨道的动力学特性分析，有助于理解小天体卫星与双小行星系统的形成与演化过程。