| Citation: | CHEN Guanhua, YANG Chihang, ZHANG Chen, et al. Distant retrograde orbits and its bifurcations in Earth-Moon system[J]. Journal of Beijing University of Aeronautics and Astronautics, 2022, 48(12): 2576-2588. doi: 10.13700/j.bh.1001-5965.2020.0608(in Chinese)
|
There exists a type of stable retrograde orbit around the Moon called distant retrograde orbit (DRO) in the Earth-Moon system. The circular restricted three-body problem (CR3BP) is taken as the dynamical model to study the dynamical structure around DRO. It is possible to determine the bifurcation point and type using Broucke's stability diagram. The numerical continuation method is used to calculate several new orbital branches. Tangent and multi-period bifurcations are the two primary forms of DRO bifurcations (starting from period tripling). New orbit families include planar orbits and 3D orbits. The characteristics of the new orbit family are discussed, including shape, period, energy, stability, hyperbolic manifold structure. The relationship between orbital period and energy is discussed. The bifurcation structure and the hyperbolic manifold structure of multi-periodic orbits are presented geometrically. The dynamic structure will provide theoretical support for the mission based on DRO families.
| [1] |
STRANGE N, LANDAU D, MCELRATH T, et al. Overview of mission design for NASA asteroid redirect robotic mission concept[C] // 3rd International Electric Propulsion Conference, 2013: 1-12.
|
| [2] |
HAMBLETON K. Deep space gateway to open opportunities for distant destinations[EB/OL]. (2018-04-25)[2020-10-27]. https://www.nasa.gov/feature/deep-space-gateway-to-open-opportunities-for-distant-destinations/.
|
| [3] |
GATES M, MUIRHEAD B, NAASZ B, et al. NASA's asteroid redirect mission concept development summary[C] // 2015 IEEE Aerospace Conference. Piscataway: IEEE Press, 2015: 1-13.
|
| [4] |
BEZROUK C J, PARKER J. Long duration stability of distant retrograde orbits[C] // AIAA/AAS Astrodynamics Specialist Conference. Reston: AIAA, 2014: 4424.
|
| [5] |
BEZROUK C J, PARKER J. Long term evolution of distant retrograde orbits in the Earth-Moon system[J]. Astrophysics and Space Science, 2017, 362(9): 176. doi: 10.1007/s10509-017-3158-0
|
| [6] |
彭超, 温昶煊, 高扬. 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[J]. 载人航天, 2018, 24(6): 703-718. doi: 10.3969/j.issn.1674-5825.2018.06.001
PENG C, WEN C X, GAO Y. Solution and stability analysis of resonance orbits of DRO and HEO (3: 1 / 2: 1) in Earth Moon space[J]. Manned Spaceflight, 2018, 24(6): 703-718(in Chinese). doi: 10.3969/j.issn.1674-5825.2018.06.001
|
| [7] |
吴小婧, 曾凌川, 巩应奎. DRO计算及其在地月系中的摄动力研究[J]. 北京航空航天大学学报, 2020, 46(5): 48-57. doi: 10.13700/j.bh.1001-5965.2019.0353
WU X J, ZENG L C, GONG Y K. DRO calculation and its perturbation in the Earth-Moon system[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(5): 48-57(in Chinese). doi: 10.13700/j.bh.1001-5965.2019.0353
|
| [8] |
CHEN H R, CANALIAS E, HESTROFFER D, et al. Effective stability of quasi-satellite orbits in the spatial problem for Phobos exploration[J]. Journal of Guidance, Control, and Dynamics, 2020, 43(12): 1-12. doi: 10.2514/1.G002893.c1
|
| [9] |
CAPDEVILA L R, GUZZETTI D, HOWELL K C. Various transfer options from Earth into distant retrograde orbits in the vicinity of the Moon[J]. Advances in the Astronautical Sciences, 2014, 152: 3659-3678.
|
| [10] |
CAPDEVILA L R, HOWELL K C. A transfer network linking Earth, Moon, and the triangular libration point regions in the Earth-Moon system[J]. Advances in Space Research, 2018, 62(7): 1826-1852. doi: 10.1016/j.asr.2018.06.045
|
| [11] |
ZHANG R K, WANG Y, ZHANG H, et al. Transfers from distant retrograde orbits to low lunar orbits[J]. Celestial Mechanics and Dynamical Astronomy, 2020, 132(8): 1-30.
|
| [12] |
曾豪, 李朝玉, 彭坤, 等. 地月空间NRHO与DRO在月球探测中的应用研究[J]. 宇航学报, 2020, 41(7): 910-919. https://www.cnki.com.cn/Article/CJFDTOTAL-YHXB202007010.htm
ZENG H, LI C Y, PENG K, et al. Application of Earth Moon space NRHO and DRO in lunar exploration[J]. Journal of Astronautics, 2020, 41(7): 910-919(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-YHXB202007010.htm
|
| [13] |
CAVALLARI I, PETITDEMANGE R, LIZY-DESTREZ S. Transfer from a lunar distant retrograde orbit to Mars through Lyapunov orbits[C]//27th International Symposium on Space Flight Dynamics (ISSFD). Melbourne: Engineers Australia Press, Royal Aeronautical Society, 2019: 1393-1398.
|
| [14] |
CONTE D, SPENCER D B. Mission analysis for Earth to Mars-Phobos distant retrograde orbits[J]. Acta Astronautica, 2018, 151: 761-771. doi: 10.1016/j.actaastro.2018.06.049
|
| [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] |
OCAMPO C A, ROSBOROUGH G W. Transfer trajectories for distant retrograde orbits of the Earth[R]. [S. l. ]: NASA STI/Recon Technical Report A, 1993, 95: 1323-1337.
|
| [17] |
徐明, 徐世杰. 绕月飞行的大幅值逆行轨道研究[J]. 宇航学报, 2009, 30(5): 1785-1791. https://www.cnki.com.cn/Article/CJFDTOTAL-YHXB200905006.htm
XU M, XU S J. Exploration of distant retrograde orbits around Moon[J]. Journal of Astronautics, 2009, 30(5): 1785-1791(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-YHXB200905006.htm
|
| [18] |
WANG W B, SHU L Z, LIU J K, et al. Joint navigation performance of distant retrograde orbits and cislunar orbits via LiAISON considering dynamic and clock model errors[J]. Navigation, 2019, 66(4): 781-802.
|
| [19] |
LAM T, WHIFFEN G J. Exploration of distant retrograde orbits around Europa[C] //15th AAS/AIAA Space Flight Mechanics Meeting. Reston: AIAA, 2005.
|
| [20] |
WALLACE M, PARKER J, STRANGE N, et al. Orbital operations for Phobos and Deimos exploration[C] // AIAA/AAS Astrodynamics Specialist Conference. Reston: AIAA, 2012: 5067.
|
| [21] |
GIL P J S, SCHWARTZ J. Simulations of quasi-satellite orbits around Phobos[J]. Journal of Guidance, Control, and Dynamics, 2010, 33(3): 901-914.
|
| [22] |
赵育善, 师鹏, 张晨. 深空飞行动力学[M]. 北京: 中国宇航出版社, 2016: 131-157.
ZHAO Y S, SHI P, ZHANG C. Dynamics of deep space flight[M]. Beijing: China Aerospace Publishing House, 2016: 131-157(in Chinese).
|
| [23] |
KOON W S, LO W Y, MARSDEN J E, et al. Dynamical systems, the three-body problem and space mission design[C] //International Conference on Differential Equations, 2000: 1167-1181.
|
| [24] |
MOON F C. Nonlinear dynamics[M]//MEYERS R A. Encyclopedia of physical science and technology. 3rd ed. Amsterdam: Elsevier, 2003: 523-535.
|
| [25] |
HOWELL K C, CAMPBELL E T. Three-dimensional periodic solutions that bifurcate from halo families in the circular restricted three-body problem[J]. Advances in the Astronatical Sciences, 1999, 102: 891-910.
|
| [26] |
ZIMOVAN-SPREEN E M, HOWELL K C, DAVIS D C. Near rectilinear halo orbits and nearby higher-period dynamical structures: Orbital stability and resonance properties[J]. Celestial Mechanics and Dynamical Astronomy, 2020, 132(5): 1-25.
|
| [27] |
DOUSKOS C, KALANTONIS V, MARKELLOS P. Effects of resonances on the stability of retrograde satellites[J]. Astrophysics and Space Science, 2007, 310(3-4): 245-249.
|
| [28] |
WINTER O C. The stability evolution of a family of simply periodic lunar orbits[J]. Planetary and Space Science, 2000, 48(1): 23-28.
|
| [29] |
CAMPBELL E T. Bifurcations from families of periodic solutions in the circular restricted problem with application to trajectory design[D]. West Lafayette: Purdue University, 1999.
|
| [30] |
BOSANAC N. Leveraging natural dynamical structures to explore multi-body systems[D]. West Lafayette: Purdue University, 2016.
|
Figures(24) / Tables(1)
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.
DownLoad:
