基于月球借力的低能DRO入轨策略

doi:10.7527/S1000-6893.2022.26507

Abstract

Abstract:

Deploying the space station on a stable periodic orbit （e.g.， distant retrograde orbits， DROs） in the vicinity of the Moon can significantly reduce the lunar exploration cost， and the space station can also be used as a steppingstone for manned asteroid or mars missions. Reducing fuel consumption is an important issue during construction and cargo resupply of the cislunar station. For transter trajectory from Earth into DRO， DRO insertion cost can be effectively saved with the aid of weak stability Boundary （WSB） transfer， but reading WSB directly requires higher launch velocity. This paper aims at improving the numerical sensitivity of transfer trajectory which leverage Lunar Gravity Assist （LGA） and WSB transfer simnltaneously. The initial guess of trajectories are obtained by “perilune Poincare map” and “v infinity matching” strategies， then multiple shooting with analytic gradient is applied under high fidelity model， better computerational efficiency are obtained by applying improved methods. In numerical simulation， for the DRO with a resonant ratio of 2∶1， for the minimum cost solution， the Earth launching injection is 3.127 km/s （60-70 m/s is reduced compared with directly launching into WSB）. The time of flight is 102.88 d， and DRO insertion maneuver only needs 66.1 m/s.

Key words: N-body problem, Distant Retrograde Orbit （DRO）, trajectory optimization, weak stability boundary, Poincare map, lunar gravity assist

CLC Number:

V412.41

Chen ZHANG, Hao ZHANG. Lunar-gravity-assisted low-energy transfer from Earth into Distant Retrograde Orbit (DRO)[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(2): 326507.

Figures/Tables 18

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Table 1

Fig 9

Fig 10

Table 2

Simulation parameters

参数	数值
地月质量参数 μ	0.012 151
太阳质量常数 μ_S/（（km）³·s^-2）	132 712 440 017.987 0
地球质量常数 μ_E/（（km）³·s^-2）	398 600.432 896 939 2
月球质量常数 μ_M/（（km）³·s^-2）	4 902.800 582 147 764
重力加速度 g₀/（m·s^-2）	9.806 65
地球平均半径 R_E/km	6 378
月球平均半径 R_M/km	1 738
归一化距离单位 LU/km	384 400
归一化时间单位 TU/d	4.348 113 05
归一化速度单位 VU/d	1.023 232 81
粒子群种群数	200
粒子群迭代数	200
多步打靶离散点 n	20
LEO地心距 R^*/km	6 578
LEO轨道倾角 i^*/（°）	28.5
DRO历元 τ^*/（jd，tdb）	2 460 096.482 613 85
DRO初值 r^_dro（τ^）/km	［-276 870.471 840 84， -141 758.243 742 15， -59 274.294 275 02］
DRO初值 $v$ ^_dro（τ^）/（km·s^-1）	［0.740 021 87， -0.999 801 19， -0.567 720 67］

Table 2

Fig 11

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Table 3

Table 4

References 28

1	National Aeronautics and Space Administration. NASA’s lunar exploration program overview ［EB/OL］.（2020-09-01）［2022-02-28］..
2	国家航天局. 中俄两国签署合作建设国际月球科研站谅解备忘录［EB/OL］.（2021-03-09）［2022-02-28］..
3	WHITLEY R， MARTINEZ R. Options for staging orbits in cislunar space［C］∥2016 IEEE Aerospace Conference. Piscataway： IEEE Press， 2016.
4	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.
5	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.
	ZENG H， LI Z Y， PENG K， et al. Research on application of Earth-Moon NRHO and DRO for lunar exploration［J］. Journal of Astronautics， 2020， 41（7）： 910-919 （in Chinese）.
6	CONDON G L， WILLIAMS J. Asteroid redirect crewed mission nominal design and performance［C］∥ SpaceOps 2014 Conference. Reston： AIAA， 2014.
7	DAWN T F， GUTKOWSKI J， BATCHA A，et al. Trajectory design considerations for exploration mission 1： AIAA-2018-0968［R］. Reston： AIAA， 2018.
8	BELBRUNO E. Lunar capture orbits， a method of constructing Earth Moon trajectories and the lunar GAS mission： AIAA-1987-1054［R］. Reston： AIAA， 1987.
9	PARKER J S， ANDERSON R L. Low-energy lunar trajectory design： Parker/low-energy［M］. Hoboken： John Wiley & Sons， Inc.， 2014.
10	BELBRUNO E A， MILLER J K. Sun-perturbed Earth-to-Moon transfers with ballistic capture［J］. Journal of Guidance， Control， and Dynamics， 1993， 16（4）： 770-775.
11	ZUBER M T， SMITH D E， WATKINS M M， et al. Gravity field of the moon from the gravity recovery and interior laboratory （GRAIL） mission［J］. Science， 2013， 339（6120）： 668-671.
12	WALKER R， CROSS M. The European student Moon orbiter （ESMO）： A lunar mission for education， outreach and science［J］. Acta Astronautica， 2010， 66（7-8）： 1177-1188.
13	PARRISH N L， KAYSER E， UDUPA S，et al. Ballistic lunar transfers to near rectilinear halo orbit： Operational considerations： AIAA-2020-1466［R］. Reston： AIAA， 2020.
14	SONG Y J， KIM Y R， BAE J， et al. Overview of the flight dynamics subsystem for Korea pathfinder lunar orbiter mission［J］. Aerospace， 2021， 8（8）： 222.
15	KOON W S， LO M W， MARSDEN J E， et al. Dynamical systems， the three-body problem and space mission design［M］. Singapore： World Scientific Publishing Company， 2000： 1167-1181.
16	YAGASAKI K. Sun-perturbed Earth-to-Moon transfers with low energy and moderate flight time［J］. Celestial Mechanics and Dynamical Astronomy， 2004， 90（3-4）： 197-212.
17	XU M， XU S J. Exploration of distant retrograde orbits around Moon［J］. Acta Astronautica， 2009， 65（5-6）： 853-860.
18	TAN M H， ZHANG K， LV M B， et al. Transfer to long term distant retrograde orbits around the Moon［J］. Acta Astronautica， 2014， 98： 50-63.
19	SCHEUERLE S T， MCCARTHY B P， HOWELL K C. Construction of ballistic lunar transfers leveraging dynamical systems techniques［C］∥AAS/AIAA Astrodynamics Specialist Conference. Reston： AIAA， 2020.
20	ZHANG Z T， HOU X Y. Transfer orbits to the Earth-Moon triangular libration points［J］. Advances in Space Research， 2015， 55（12）： 2899-2913.
21	TOPPUTO F. On optimal two-impulse Earth-Moon transfers in a four-body model［J］. Celestial Mechanics and Dynamical Astronomy， 2013， 117（3）： 279-313.
22	TSELOUSOVA A， TROFIMOV S， SHIROBOKOV M. Geometric approach to the design of lunar-gravity-assisted low-energy Earth-Moon transfers［C］∥AAS/AIAA Astrodynamics Specialist Conference.Reston：AIAA， 2021.
23	Space Exploration Technologies Corporation. Falcon 9 launch vehicle payload user’s guide［R］. Hawthrone：SpaceX， 2008.
24	ZIMOVAN E M. Characteristics and design strategies for near rectilinear halo orbits within the Earth-Moon system［D］. West Lafayette： Purdue University， 2017： 1-152.
25	HÉNON M. Numerical exploration of the restricted problem. V. Hill's case： Periodic orbits and their stability［J］. Astronomy and Astrophysics， 1969，（1）：223-238.
26	BEZROUK C， PARKER J S. Long term evolution of distant retrograde orbits in the Earth-Moon system［J］. Astrophysics and Space Science， 2017， 362（9）： 1-11.
27	WELCH C M， PARKER J S， BUXTON C. Mission considerations for transfers to a distant retrograde orbit［J］. The Journal of the Astronautical Sciences， 2015， 62（2）： 101-124.
28	CONTE D， CARLO M D， HO K， et al. Earth-Mars transfers through Moon distant retrograde orbits［J］. Acta Astronautica， 2018， 143： 372-379.

变量	取值范围
Ω/rad	［0， 2π）
ω/rad	［0， 2π）
η/d	［3， 6］
γ/rad	［0， 2π）
ρ/km	［1 838， 20 000］

参数	数值
LEO出发脉冲/（km·s^-1）	3.127 286 50
DRO到达脉冲/（km·s^-1）	0.066 090 92
总脉冲/（km·s^-1）	3.193 377 42
总时间/d	102.880 327 67
出发时间/（jd，tdb）	2 459 966.777 246 46
出发时卫星位置/km	［-6 467.153 118 231 2， -1 184.790 001 988 07， -209.953 275 562 116］
出发时卫星速度/（km·s^-1）	［1.892 057 726 846 54， -9.407 190 176 785 86， -5.194 880 417 429 38］
近月点时间/（jd，tdb）	2 459 970.766 318 36
近月点卫星位置/km	［367 442.092 848 141， 42 046.615 513 482 8， -980.575 109 454 213］
近月点卫星速度/（km·s^-1）	［1.270 167 875 014 64， 0.009 235 056 270 175 26， -0.023 871 760 089 912 7］
入轨时间/（jd，tdb）	2 460 069.657 574 13
入轨时卫星位置/km	［-239 144.207 929 066， -187 302.212 790 807， -85 040.874 971 346 8］
入轨时卫星速度/（km·s^-1）	［0.881 503 757 995 025， -0.982 638 475 555 1， -0.534 365 964 086 031］
入轨时DRO位置/km	［-239 144.207 929 066， -187 302.212 790 807， -85 040.874 971 346 8］
入轨时DRO速度/（km·s^-1）	［0.845 193 643 816 302， -0.927 576 393 506 761， -0.538 579 266 758 445］

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Lunar-gravity-assisted low-energy transfer from Earth into Distant Retrograde Orbit (DRO)

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