地月空间DRO与HEO(3∶1/2∶1)共振轨道延拓求解及其稳定性分析  

DRO and HEO (3∶1/2∶1) Resonant Orbits in Cislunar Space Calculated by Continuation and Their Stability Analysis

作　　者：彭超[1,2,3] 温昶煊 高扬 PENG Chao;WEN Changxuan;GAO Yang(Technology and Engineering Center for Space Utilization,Chinese Academy of Sciences,Beijing 100094,China;Key Laboratory of Space utilization,Chinese Academy of Sciences,Beijing 100094,China;University of Chinese Academy of Sciences,Beijing 100094,China)

机构地区：[1]中国科学院空间应用工程与技术中心,北京100094 [2]中科院太空应用重点实验室,北京100094 [3]中国科学院大学,北京100094

出　　处：《载人航天》2018年第6期703-718,共16页Manned Spaceflight

摘　　要：针对地月空间共振轨道延拓求解及稳定性分析问题,首先从远离与接近月球的地心开普勒共振轨道(月球公转周期与轨道周期符合1∶1、2∶1与3∶1的比例关系)得到圆形限制性三体模型中的两组轨道初值,然后通过增大与减小"近地点距"的延拓方法得到圆形限制性三体周期轨道族。研究发现:逆行绕月的远距逆向轨道(DRO)可由1∶1开普勒共振轨道延拓得到,延拓过程中轨道共振比从1∶1逐渐演变为2∶1与3∶1,并展现出明显的非开普勒轨道特性;另外,一类大偏心轨道(HEO)通过2∶1与3∶1地心开普勒共振轨道的延拓得到,但仍可看作受摄的开普勒轨道。采用周期轨道Monodromy矩阵的特征值分析了DRO和HEO的稳定性,同时描述了各自轨道运动特点,可为相关的空间应用任务设计提供理论依据。与此同时,澄清了不同参考模型中"共振比"的概念以及同一共振比可能对应不同类型共振轨道的现象。To study the resonant orbits in Earth-Moon system and analyze their stabilities,two sets of initial orbital states,one close to the Moon and the other close to the Earth,in the planar Earth-Moon circular restricted three-body systems(CR3BS)were generated from the resonant orbits in the two-body model(the resonant ratio p∶q=1∶1/2∶1/3∶1,where p means the revolutions of the moon around the Earth,and q is the revolutions of the spacecraft in the same time period).Then the families of periodic orbits in CR3BS were obtained by employing a continuation scheme where the perigee or the perilune increased continuously.The results showed that the lunar Distant Retrograde Orbit(DRO)could be found by continuing the family of 1·1 resonant orbits to 2·1 or 3·1 or smaller and significant non-Keplerian orbit characteristics appeared.However,two families of Highly Eccentric Orbits(HEO)in CR3BS obtained by continuing the 2·1/3·1 resonant orbits in the two-body model,remained to be perturbed Keplerian orbits.The stabilities of DRO and HEO were derived by exami ning the eigenvalues of the monodromy matrix corresponding to each orbit in the family.Based on their stabilities and orbital characteristics,the potential applications of these periodic orbits were presented.Moreover,the resonant ratio notion in different models was clarified,and the phenomenon that the same resonant ratio may correspond to different resonant ratios was found.

关 键 词：共振轨道 DRO HEO 稳定性 周期轨道 延拓 开普勒 

分 类 号：V412.4[航空宇航科学与技术—航空宇航推进理论与工程]