地月三体系统新型太阳帆周期轨道设计与分析

doi:10.7527/S1000-6893.2024.30828

Abstract

Abstract:

Periodic orbits in the Earth-Moon three-body system hold significant theoretical and engineering values for deep space exploration. Solar sail spacecraft， which do not require propellant， show great potential for long-term space missions. Introducing the solar sail propulsion technology in the Earth-Moon three-body system can create more valuable orbits. In previous studies， the state transition matrices of dynamical systems are not found to include the solar sail acceleration term. In this paper， a new solar sail pointing law is proposed based on a simplified non-autonomous dynamical model for the solar sail Earth-Moon circular restricted three-body problem， making acceleration of the solar sail dependent on the sail state vector. On this basis， the Jacobian matrix of the system is derived. This pointing law is applied to the near rectilinear Halo orbit. Using an improved differential correction method in combination with a continuation on solar sail acceleration， new orbit families are generated. Numerical simulations verify the effectiveness of the pointing law and numerical computation method. Analysis shows that the newly established solar sail periodic orbit families can be used for lunar illumination and observation of high-latitude lunar regions. Finally， periodic orbits are migrated to a non-coplanar bi-elliptical perturbation model， and the quasi-periodic orbits under perturbation are obtained using the second-order differential correction method. It is shown through analysis that the orbits’ illumination and coverage performance can be maintained under perturbation. Further calculations of the quasi-periodic orbits corresponding to different initial moments indicate that the closer the Earth-Moon Barycenter （EMB） and the Moon are to the perigee of their orbits， the greater the impact of perturbative factors on the orbit is.

Key words: Earth-Moon system, restricted three-body problem, solar sail, periodic orbit, perturbation model

CLC Number:

V412.4

Shiyu AN, Ming LIU, Huayi LI, Fan WU. Design and applications of novel periodic orbits with solar sail in Earth-Moon system[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(4): 230828.

Figures/Tables 26

Fig.1

Fig.2

Table 1

Parameters in dynamics system （based on JPL HORIZONS at 2 January 2030， 05：30 GMT， JDN=2 462 503.729 166 667）

参数	数值
地月系统质量参数 $μ$	0.012 150 585 6
地月系统长度单位L_EM/km	$3.844 01 × 105$
月球轨道平均角速度 $ω$ /（ $r a d ⋅ s - 1$ ）	$2.665 293 292 445 35 × 10 - 6$
太阳无量纲质量 $μ 4$	$3.289 3 × 105$
月球轨道偏心率e	0.054 9
黄白交角i/（°）	5.145
EMB轨道半长轴 $a E$ /km	$1.495 978 707 × 108$
EMB轨道偏心率 $e E$	0.016 7
EMB轨道平均角速度 $n E$ /（ $r a d ⋅ s - 1$ ）	$1.993 639 382 749 122 × 10 - 7$

Table 1

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

Fig.12

Fig.13

Fig.14

Fig.15

Table 2

Fig.16

Fig.17

Fig.18

Fig.19

Fig.20

Fig.21

Table 3

Service time of NRHO in SCR3BP and perturbation models

反射器直径/m	照明时间/s
反射器直径/m	SCR3BP	扰动模型
50		2 279.57
100		4 536.88
200		13 187.30
500	76 228.93	73 617.49
1 000	$3.337 5 × 105$	$3.251 5 × 105$

Table 3

Table 4

Fig.22

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目标点	覆盖率/%
目标点	SCR3BP	扰动模型
南极点	94.23	93.55
艾特肯盆地	92.08	91.03

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Design and applications of novel periodic orbits with solar sail in Earth-Moon system

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Figures/Tables 26

References 35

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反射器直径/m	1个周期内有效服务时间/s
50	1 786.06
100	4 369.85
200	7 750.88
500	17 411.61
1 000	80 230.22