太阳帆航天器非对称共振晕轨道设计与分析

doi:10.7527/S1000-6893.2025.32576

Abstract

Abstract:

As a space propulsion system that generates continuous low-thrust using solar radiation pressure and requires no propellant， the solar sail offers unique advantages for long-duration deep space exploration missions. Based on the dynamical models of the Sun-Mercury elliptic restricted three-body problem， this study proposes three progressive solar sail steering laws. These steering strategies enable the normal vector of the solar sail plane to transition from pointing directly toward the Sun， to deviating within the gravitational plane， and finally to deviating out of the gravitational plane. By employing a multiple-shooting method combined with continuation techniques， families of resonant halo orbits with different resonance ratios are obtained for solar sail spacecraft. Under the three proposed steering laws， parameter continuation is performed with respect to the sail’s area-to-mass ratio， cone angle， and pitch angle， respectively. The first two steering laws yield resonant halo orbits that are symmetric about the XZ-plane of the rotating coordinate system. In contrast， the third steering law produces periodic orbits that are asymmetric with respect to any plane or line， exhibiting complex three-dimension structures with periodicity remained. Finally， the stability of the solar sail resonant halo orbits under different steering laws is analyzed within a high-precision ephemeris model. The results indicate that these orbits can maintain their overall shape without significant divergence for approximately 4 to 6 Mercury orbital periods （about 352 to 528 days） without station-keeping maneuvering.

Key words: elliptic restricted three-body problem, solar sail spacecraft, resonant Halo orbit, solar sail steering law, ephemeris model

CLC Number:

V412.4

Dawei WANG, Dong YE, Yan XIAO, Haiyang LI. Design and analysis of asymmetric resonant Halo orbits for solar sail spacecraft[J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(6): 332576.

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References 26

[1]	ZHAO P Y， WU C C， LI Y M. Design and application of solar sailing： A review on key technologies［J］. Chinese Journal of Aeronautics， 2023， 36（5）： 125-144.
[2]	GARWIN RL. Solar sailing—a practical method of propulsion within the solar system［J］. Jet Propulsion， 1958， 28（3）： 188-190.
[3]	TSUDA Y， MORI O， FUNASE R， et al. Achievement of IKAROS： Japanese deep space solar sail demonstration mission［J］. Acta Astronautica， 2013， 82（2）： 183-188.
[4]	JOHNSON L， WHORTON M， HEATON A， et al. NanoSail-D： A solar sail demonstration mission［J］. Acta Astronautica， 2011， 68（5-6）： 571-575.
[5]	LOCKETT T R， CASTILLO-ROGEZ J， JOHNSON L， et al. Near-earth asteroid scout flight mission［J］. IEEE Aerospace and Electronic Systems Magazine， 2020， 35（3）： 20-29.
[6]	RIDENOURE R W， MUNAKATA R， WONG S D， et al. Testing the LightSail program： Advancing solar sailing technology using a CubeSat platform［J］. Journal of Small Satellites， 2016， 5（3）： 531-550.
[7]	SPENCER D A， BETTS B， BELLARDO J M， et al. The LightSail 2 solar sailing technology demonstration［J］. Advances in Space Research， 2021， 67（9）： 2878-2889.
[8]	TAKAO Y， MORI O， MATSUMOTO J， et al. Sample return system of OKEANOS： The solar power sail for Jupiter Trojan exploration［J］. Acta Astronautica， 2023， 213： 121-137.
[9]	SALEEM Y， RAM K. Families of periodic orbits about Lagrangian points L1， L2 and L3 with continuation method［J］. Planetary and Space Science， 2022， 217： 105491.
[10]	张晨，张皓. 基于月球借力的低能DRO入轨策略［J］. 航空学报， 2023， 44（2）： 326507.
	ZHANG C， ZHANG H. Lunar-gravity-assisted low-energy transfer from earth into distant retrograde orbit（DRO）［J］. Acta Aeronautica et Astronautica Sinica， 2023， 44（2）： 326507 （in Chinese）.
[11]	张晨. 基于数值延拓的日月综合借力DRO入轨策略［J］. 北京航空航天大学学报， 2024， 50（4）： 1176-1186.
	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）.
[12]	HOU X Y， LIU L. On motions around the collinear libration points in the elliptic restricted three-body problem［J］. Monthly Notices of the Royal Astronomical Society， 2011， 415（4）： 3552-3560.
[13]	PENG H， XU S J. Stability of two groups of multi-revolution elliptic halo orbits in the elliptic restricted three-body problem［J］. Celestial Mechanics and Dynamical Astronomy， 2015， 123（3）： 279-303.
[14]	PENG H， BAI X L， XU S J. Continuation of periodic orbits in the Sun-Mercury elliptic restricted three-body problem［J］. Communications in Nonlinear Science and Numerical Simulation， 2017， 47： 1-15.
[15]	MCINNES C R. Solar sailing： Orbital mechanics and mission applications［J］. Advances in Space Research， 2003， 31（8）： 1971-1980.
[16]	BOOKLESS J， MCINNES C. Control of Lagrange point orbits using solar sail propulsion［J］. Acta Astronautica， 2008， 62（2/3）： 159-176.
[17]	HEILIGERS J， HIDDINK S， NOOMEN R， et al. Solar sail Lyapunov and Halo orbits in the Earth-Moon three-body problem［J］. Acta Astronautica， 2015， 116（11/12）： 25-35.
[18]	HEILIGERS J， MACDONALD M， PARKER J S. Extension of Earth-Moon libration point orbits with solar sail propulsion［J］. Astrophysics and Space Science， 2016， 361（7）： 241.
[19]	安诗宇，刘明，李化义，等. 地月三体系统新型太阳帆周期轨道设计与分析［J］. 航空学报， 2025， 46（4）： 230828.
	AN S Y， LIU M， LI H Y， et al. Design and applications of novel periodic orbits with solar sail in Earth-Moon system［J］. Acta Aeronautica et Astronautica Sinica， 2025， 46（4）： 230828 （in Chinese）.
[20]	CHUJO T， TAKAO Y. Synodic resonant halo orbits of solar sails in restricted four-body problem［J］. Journal of Spacecraft and Rockets， 2022， 59（6）： 2129-2147.
[21]	GONG S P， LI J F. Solar sail periodic orbits in the elliptic restricted three-body problem［J］. Celestial Mechanics and Dynamical Astronomy， 2015， 121（2）： 121-137.
[22]	HUANG J， BIGGS J D， CUI N G. Families of halo orbits in the elliptic restricted three-body problem for a solar sail with reflectivity control devices［J］. Advances in Space Research， 2020， 65（3）： 1070-1082.
[23]	GÁMEZ LOSADA F， HEILIGERS J. New solar-sail orbits for polar observation of the Earth and Moon［J］. Journal of Guidance， Control， and Dynamics， 2021， 44（12）： 2155-2171.
[24]	RIOS-REYES L， SCHEERES D J. Generalized model for solar sails［J］. Journal of Spacecraft and Rockets， 2005， 42（1）： 182-184.
[25]	SPREEN E M Z. Trajectory design and targeting for applications to the exploration program in cislunar space［D］. West Lafayette， Indiana： Purdue University， 2021.
[26]	ACTON C H. Ancillary data services of NASA’s navigation and ancillary information facility［J］. Planetary and Space Science， 1996， 44（1）： 65-70.

参数	数值
太阳引力常数/（km³∙s^-2）	1.327 1×10¹¹
水星引力常数/（km³∙s^-2）	22 032
水星轨道偏心率	0.205 6
水星轨道半长轴/km	5.971×10⁷

轨道类型	最大面质比/（m²·kg^-1）	延拓终止原因
IC［L1，3∶1，P］	2.160	不收敛
IC［L1，3∶1，A］	2.450	不收敛
IC［L1，4∶1，P］	0.245	不收敛
IC［L1，4∶1，A］	0.240	不收敛
IC［L1，5∶2，P］	2.570	碰撞水星
IC［L1，5∶2，A］	2.000	不收敛
IC［L1，6∶2，A₂］	0.460	不收敛
IC［L1，6∶2，A₃］	0.485	不收敛
IC［L1，7∶2，P］	0.910	不收敛
IC［L1，7∶2，A］	0.900	不收敛
IC［L2，3∶1，P］	4.020	碰撞水星
IC［L2，3∶1，A］	6.650	碰撞水星
IC［L2，4∶1，P］	3.640	碰撞水星
IC［L2，4∶1，A］	4.200	不收敛
IC［L2，5∶2，P］	4.100	碰撞水星
IC［L2，5∶2，A］	5.080	不收敛
IC［L2，6∶2，A₂］	1.260	不收敛
IC［L2，6∶2，A₃］	1.980	不收敛
IC［L2，7∶2，P］	0.435	碰撞水星
IC［L2，7∶2，A］	0.230	碰撞水星

轨道类型	方位角β	面质比/ （m²·kg^-1）	延拓最大锥角α/（°）
IC［L1，3∶1，A］	0	2	14.1
IC［L1，3∶1，A］	π	2	90
IC［L1，5∶2，P］	0	2	90
IC［L1，5∶2，P］	π	2	90
IC［L2，4∶1，A］	0	3	26.5
IC［L2，4∶1，A］	π	3	90
IC［L2，5∶2，A］	0	3.5	90
IC［L2，5∶2，A］	π	3.5	90
IC［L2，6∶2，A₃］	0	1	90
IC［L2，6∶2，A₃］	π	1	90
IC［L2，7∶2，P］	0	0.3	90
IC［L2，7∶2，P］	π	0.3	90

轨道类型	锥角/（°）	方位角范围/（°）
IC［L1，5∶2，P］	1	［-180，180］
	8	［-180，180］
	9	｛［-180，-103］，［-69.8，69.8］，［103，180］｝
	50	｛［-180，-154.4］，［-27.4，27.4］，［154.4，180］｝
	62	｛［-180，-104.8］，［-74.4，74.4］，［104.8，180］｝
	63	［-180，180］
	80	［-180，180］
IC［L2，5∶2，P］	1	［-180，180］
	8	［-180，180］
	9	｛［-180，-103］，［-75.9，75.9］，［103，180］｝
	50	｛［-180，-146］，［-32.4，32.4］，［146，180］｝
	63	｛［-180，-103.6］，［-75.6，75.6］，［103.6，180］｝
	64	［-180，180］
	80	［-180，180］

Design and analysis of asymmetric resonant Halo orbits for solar sail spacecraft

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