| Citation: | WU Xiaojing, ZENG Lingchuan, GONG Yingkuiet al. DRO computation and its perturbative force in the Earth-Moon system[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(5): 883-892. doi: 10.13700/j.bh.1001-5965.2019.0353(in Chinese)
|
For the aerospace engineering application of Distant Retrograde Orbit (DRO), a calculation method and orbit characteristics are studied, and the main perturbation factors of DRO in actual force environment are analyzed to provide a theoretical foundation for DRO's precise modeling and nominal orbit design. Firstly, the effectiveness of the stream function method in calculating the DRO periodic orbit family is verified by simulation examples. Secondly, the DRO periodic orbit family is calculated by adjusting the Jacobi constant, and the DRO orbits with different resonance ratios are obtained. The simulation results show that the trajectory of DRO with an integer resonance ratio in the Earth-Moon inertial coordinate system is a closed curve, while DRO orbits with non-integer resonance ratio are not closed. Finally, the main perturbation factors affecting DRO stability are analyzed by orbit extrapolation. The simulation results show that solar gravitation and lunar orbit eccentricity are the main perturbation factors that affect stability of DRO. In the dynamic model, the standard ephemeris is used to represent the motion state of the planet. When the integration time reaches more than 10 days, the model error is about kilometer-scale. Therefore, in the large spatial scale of the Earth-Moon system, the ephemeris model can be used to analyze the motion state of the DRO approximately in the real force environment, which could provide a basis for mission orbit design.
| [1] |
HENON M.Numerical exploration of the restricted problem.V.Hill's case: Periodic orbits and their stability[J].Astronomy and Astrophysics, 1969, 1: 223-238. doi: 10.1023/A:1022518422926
|
| [2] |
钱霙婧.地月空间拟周期轨道上航天器自主导航与轨道保持研究[D].哈尔滨: 哈尔滨工业大学, 2013.
QIAN Y J.Research on autonomous navigation and stationkeeping for quasi-periodic orbit in the Earth-Moon system[D].Harbin: Harbin Institute of Technology, 2013(in Chinese).
|
| [3] |
SZEBEHELY V. Theory of orbits:The restricted problem of three bodies[M].New York:Academic Press, 1967:381-442.
|
| [4] |
HOU X Y, LIU L.On quasi-periodic motions around the triangular libration points of the real Earth-Moon system[J].Celestial Mechanics and Dynamics Astronomy, 2010, 108:301-313. doi: 10.1007/s10569-010-9305-3
|
| [5] |
HOU X Y, LIU L.On quasi-periodic motions around the collinear libration points of the real Earth-Moon system[J].Celestial Mechanics and Dynamics Astronomy, 2011, 110:71-98. doi: 10.1007/s10569-011-9340-8
|
| [6] |
BEZROUK C J, PARKER J.Long duration stability of distant retrograde orbits: AIAA-2014-4424[R].Reston: AIAA, 2014.
|
| [7] |
TURNER G.Results of long-duration simulation of distant retrograde orbits[J].Aerospace, 2016, 3(4):37. doi: 10.3390/aerospace3040037
|
| [8] |
LAM T, WHIFFEN G J.Exploration of distant retrograde orbits around Europa[C]//Proceedings of the AAS/AIAA Space Flight Mechanics Meeting.San Diego: AAS Publications Office, 2005: AAS05-110.
|
| [9] |
MAZANEK D D, MERRILL R G, BROPHY J R, et al.Asteroid redirect mission concept:A bold approach for utilizing space resources[J].Acta Astronautica, 2015, 117:163-171. doi: 10.1016/j.actaastro.2015.06.018
|
| [10] |
STRANGE N, DAMON L, MCELRATH T, et al.Overview of mission design for NASA asteroid redirect robotic mission concept[C]//33rd International Electric Propulsion Conference, 2013: 6-10.
|
| [11] |
BEZROUK C, PARKER J S.Ballistic capture into distant retrograde orbits from interplanetary space[C]//Proceedings of the AAS/AIAA Space Flight Mechanics Meeting.San Diego: AAS Publications Office, 2015: AAS15-302.
|
| [12] |
BROPHY J R, FRIEDMAN L, CULICK F, et al.Asteroid retrieval feasibility study[C]//Proceedings of 2012 IEEE Aerospace Conference.Piscataway: IEEE Press, 2012: 1-16.
|
| [13] |
OCAMPO C A, ROSBOROUGH G W.Transfer trajectories for distant retrograde orbiters of the Earth[C]//Proceedings of the 3rd Annual Spaceflight Mechanics Meeting.Washington, D.C.: NASA, 1993: 1177-1200.
|
| [14] |
DEMEYER J, GURFIL P.Transfer to distant retrograde orbits using manifold theory[J].Journal of Guidance, Control, and Dynamics, 2007, 30(5):1261-1267. doi: 10.2514/1.24960
|
| [15] |
SCOTT C J, SPENCER D B.Calculating transfer families to periodic distant retrograde orbits using differential correction[J].Journal of Guidance, Control, and Dynamics, 2010, 33(5):1592-1605. doi: 10.2514/1.47791
|
| [16] |
STRAMACCHIA M, COLOMBO C, BERNELLI Z F.Distant retrograde orbits for space-based near Earth objects detection[J].Advances in Space Research, 2016, 58(6):967-988. doi: 10.1016/j.asr.2016.05.053
|
| [17] |
XU M, XU S J.Exploration of distant retrograde orbits around Moon[J].Acta Astronautica, 2009, 65(5-6):853-860. doi: 10.1016/j.actaastro.2009.03.026
|
| [18] |
MURAKAMI N, YAMANAKA K.Trajectory design for rendezvous in lunar distant retrograde orbit[C]//Proceedings of 2015 IEEE Aerospace Conference.Piscataway: IEEE Press, 2015: 1-13.
|
| [19] |
CONTE D, CARLO M D, HO K, et al.Earth-Mars transfers through Moon distant retrograde orbits[J].Acta Astronautica, 2018, 143:372-379. doi: 10.1016/j.actaastro.2017.12.007
|
| [20] |
LARA M.Nonlinear librations of distant retrograde orbits:A perturbative approach-The Hill problem case[J].Nonlinear Dynamics, 2018, 93(4):2019-2038. doi: 10.1007%2Fs11071-018-4304-0
|
| [21] |
LARA M.Design of distant retrograde orbits based on a higher order analytical solutiont[C]//Proceedings of the International Astronautical Congress (IAC).Bremen: International Astronautical Federation(IAF), 2018: 562-578.
|
| [22] |
BEZROUK C, PARKER J S.Long term evolution of distant retrograde orbits in the Earth-Moon system[J].Astrophysics and Space Science, 2017, 362:176. doi: 10.1007/s10509-017-3158-0
|
| [23] |
李明涛.共线平动点任务节能轨道设计与优化[D].北京: 中国科学院空间科学与应用研究中心, 2010.
LI M T.Low energy trajectory design and optimization for collinear libration points missions[D].Beijing: Center for Space Science and Applied Research, Chinese Academy of Sciences, 2010(in Chinese).
|
| [24] |
DICHMANN D J, LEBOIS R, CARRICO J P.Dynamics of orbits near 3: 1 resonance in the Earth-Moon system[J].The Journal of the Astronautical Sciences, 2013, 60(1):51-86. doi: 10.1007/s40295-014-0009-x
|
| [25] |
ANATOLE K, BORIS H.Introduction to the modern theory of dynamical systems[M].Cambridge:Cambridge University, 1996:451-488.
|
| [26] |
CHRISTIAN B, LORENZO J D, MARELO V.Dynamics beyond uniform hyperbolicity:A global geometric and probabilistic perspective[M].Berlin:Springer, 2005:13-24.
|
| [1] | JIN B，LI S Y，LIU N N，et al. Kinematic absolute and relative orbit determination of Swarm satellites with heterogeneous orbits[J]. Journal of Beijing University of Aeronautics and Astronautics，2025，51（2）：409-418 （in Chinese）. doi: 10.13700/j.bh.1001-5965.2023.0039. |
| [2] | LI J Q，SHI P. Optimization of LEO remote sensing constellation with enhanced regional coverage[J]. Journal of Beijing University of Aeronautics and Astronautics，2024，50（12）：3912-3920 （in Chinese）. doi: 10.13700/j.bh.1001-5965.2022.0878. |
| [3] | DAI T X，XU Z. Multi-beam LEO satellite user grouping and resource allocation algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics，2024，50（8）：2575-2584 （in Chinese）. doi: 10.13700/j.bh.1001-5965.2022.0638. |
| [4] | TANG Jingmin, HU Cheng, SONG Yaolian, YU Guicai. NOMA-Based Joint Optimization of Trajectory and Resources for UAV-Enable Integrated Sensing and Communication[J]. Journal of Beijing University of Aeronautics and Astronautics. doi: 10.13700/j.bh.1001-5965.2024.0275 |
| [5] | LI Yue, ZHANG Yaohua, CAI Jing, REN Yinan. Taxiing law of aircraft landing on pavement under condition of regional water accumulation[J]. Journal of Beijing University of Aeronautics and Astronautics. doi: 10.13700/j.bh.1001-5965.2024.0702 |
| [6] | ZHANG Hua-bo, GUO Ying-qing, LI Gui-cai, ZHAO Wan-li, YE Peng. Modeling and parameter design methodology for component-level performance model of ducted ram air generation turbine[J]. Journal of Beijing University of Aeronautics and Astronautics. doi: 10.13700/j.bh.1001-5965.2023.0787 |
| [7] | WU S F，WANG W，WEN J F，et al. Review on development of LEO Internet constellation[J]. Journal of Beijing University of Aeronautics and Astronautics，2024，50（1）：1-11 （in Chinese）. doi: 10.13700/j.bh.1001-5965.2022.0242. |
| [8] | YANG G Y，ZHANG Y，HU L X，et al. Application of inclined slot in airfoil stall control[J]. Journal of Beijing University of Aeronautics and Astronautics，2024，50（8）：2601-2618 （in Chinese）. doi: 10.13700/j.bh.1001-5965.2022.0652. |
| [9] | ZONG H H，LI Y，CAI J，et al. Evaluation index of accumulated water-film on asphalt pavement considering safety of aircraft hydroplaning[J]. Journal of Beijing University of Aeronautics and Astronautics，2024，50（3）：765-773 （in Chinese）. doi: 10.13700/j.bh.1001-5965.2022.0352. |
| [10] | WANG Ming, YANG Chi-hang, ZHANG Hao. Quasi-periodic orbits near 2:1 resonant DRO in the four-body problem[J]. Journal of Beijing University of Aeronautics and Astronautics. doi: 10.13700/j.bh.1001-5965.2024.0061 |
| [11] | ZHANG C. Low-energy transfer from Earth into DRO with hybrid gravity assist and numerical continuation[J]. Journal of Beijing University of Aeronautics and Astronautics，2024，50（4）：1176-1186 （in Chinese）. doi: 10.13700/j.bh.1001-5965.2022.0494. |
| [12] | SUN Y Q，QIANG H R，DONG K H，et al. Derivation and application of iterative scheme for angle-only orbit determination[J]. Journal of Beijing University of Aeronautics and Astronautics，2023，49（12）：3245-3252 （in Chinese）. doi: 10.13700/j.bh.1001-5965.2022.0062. |
| [13] | WANG R P，SONG X，CHEN K，et al. Pedestrian trajectory prediction method based on pedestrian pose[J]. Journal of Beijing University of Aeronautics and Astronautics，2023，49（7）：1743-1754 （in Chinese）. doi: 10.13700/j.bh.1001-5965.2021.0557. |
| [14] | WU Ruo-yu, YANG De-zhen, REN Yi, JIA Lu-lu, LI Xiao-bin, WANG Zi-li. A Modeling Method for Pedestrian Safety Behavior in Shared Spaces of Pedestrian-Traditional Vehicle-Autonomous Vehicle[J]. Journal of Beijing University of Aeronautics and Astronautics. doi: 10.13700/j.bh.1001-5965.2023.0370 |
| [15] | LI Y，ZONG H H，CAI J，et al. Hydroplaning behavior of aircraft wheel group and additional resistance due to accumulated water on pavement[J]. Journal of Beijing University of Aeronautics and Astronautics，2023，49（5）：1099-1107 （in Chinese）. doi: 10.13700/j.bh.1001-5965.2021.0402. |
| [16] | ZHU W S，LYU X J，HOU Z Q，et al. Trajectory optimization of air-to-surface missile in full airspace based on combinational optimization algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics，2023，49（2）：344-352 （in Chinese）. doi: 10.13700/j.bh.1001-5965.2021.0252. |
| [17] | LUO Wudi, REN Junxue, LI Zhihui, TANG Haibin. Study on radiation characteristics of multi-phase plumes containing ice crystals in orbit-control engines[J]. Journal of Beijing University of Aeronautics and Astronautics. doi: 10.13700/j.bh.1001-5965.2023.0439 |
| [18] | FENG Jianguang, ZHENG Zixia, LONG Dongteng, ZHOU Bo, LU Mingquan, ZHENG Heng. Method for predicting on-orbit residual life of satellite atomic clock[J]. Journal of Beijing University of Aeronautics and Astronautics, 2022, 48(11): 2215-2221. doi: 10.13700/j.bh.1001-5965.2021.0087 |
| [19] | ZHANG Shengyu, ZHU Zhencai, HU Haiying. Burst tasks scheduling method for infrared LEO constellation based on multi-strategies[J]. Journal of Beijing University of Aeronautics and Astronautics, 2022, 48(12): 2405-2414. doi: 10.13700/j.bh.1001-5965.2021.0119 |
| [20] | LI Yongping, ZHU Guangwu, ZHENG Xiaoliang, AI Jiangzhao, YAN Yafei, ZHOU Jianhua. In-situ measurement of atmospheric density in very low Earth orbits[J]. Journal of Beijing University of Aeronautics and Astronautics, 2022, 48(10): 1875-1882. doi: 10.13700/j.bh.1001-5965.2021.0618 |
| 1. | 张晨. 基于数值延拓的日月综合借力DRO入轨策略. 北京航空航天大学学报. 2024(04): 1176-1186 .  本站查看 | |
| 2. | 黄逸丹，黄勇，樊敏，李培佳. 基于地基测量数据的月球DRO轨道定轨精度分析. 深空探测学报(中英文). 2024(04): 405-413 .  | |
| 3. | 王波，薛璐瑶，彭玉明，段晓闻，张嵬，谢攀，陆希. 日地DRO近地小行星资源勘探普查任务轨道设计与监测效能分析. 上海航天(中英文). 2024(S1): 253-260 . | |
| 4. | 刘佳，宋叶志，黄乘利，胡小工，谭龙玉. 地月DRO星载光学测量近地小行星轨道确定. 天文学报. 2023(06): 83-100 . | |
| 5. | 陈天冀，周晚萌，和星吉，彭祺擘，徐明，吕纪远. 考虑环月交会约束的地月转移轨道设计. 宇航学报. 2023(12): 1830-1838 . | |
| 6. | 陈冠华，杨驰航，张晨，张皓. 地月空间的远距离逆行轨道族及其分岔研究. 北京航空航天大学学报. 2022(12): 2576-2588 . 本站查看 | |
| 7. | 刘文芳，胡诗杨，刘福窑. 圆型限制性三体问题的动力学特征. 上海工程技术大学学报. 2021(03): 272-280 . |
Figures(10) / Tables(2)
Copyright © Journal of Beijing University of Aeronautics and Astronautics
Address: Editorial Department of Journal of Beijing University of Aeronautics and Astronautics, 37 Xueyuan Road, Haidian District, Beijing Post Code: 100191 Email: jbuaa@buaa.edu.cn
Supported by:
Beijing Renhe Information Technology Co., Ltd.
Li Na, Zhao Huijie. Endmember extraction method based on morphology and orthogonal subspace projection[J]. Journal of Beijing University of Aeronautics and Astronautics, 2010, 36(12): 1457-1460. (in Chinese)
DownLoad:
