DRO计算及其在地月系中的摄动力研究

吴小婧; 曾凌川; 巩应奎

doi:10.13700/j.bh.1001-5965.2019.0353

DRO计算及其在地月系中的摄动力研究

doi: 10.13700/j.bh.1001-5965.2019.0353

中国科学院空天信息创新研究院, 北京 100094

基金项目:

国家自然科学基金 91438207

详细信息

作者简介:
吴小婧  女, 硕士, 工程师。主要研究方向:卫星导航技术

曾凌川  男, 硕士, 工程师。主要研究方向:卫星通信网络技术

巩应奎  男, 博士, 研究员。主要研究方向:计算机仿真技术

通讯作者:
巩应奎, E-mail: ykgong@aoe.ac.cn

中图分类号: P173.1;P173.3;P132⁺.2
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出版历程
- 收稿日期: 2019-07-03
- 录用日期: 2019-10-11
- 网络出版日期: 2020-05-20

DRO computation and its perturbative force in the Earth-Moon system

Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China

Funds:

National Natural Science Foundation of China 91438207

More Information

Corresponding author: GONG Yingkui, E-mail: ykgong@aoe.ac.cn

摘要

摘要:
针对远距逆行轨道（DRO）的航天工程应用问题，研究了DRO的计算方法以及轨道特性，分析了DRO在实际力环境中的主要摄动因素，为DRO的精确建模和标称轨道设计奠定一定的理论基础。首先，利用仿真算例验证流函数法在计算DRO周期轨道族中的有效性。然后，利用该方法，通过改变雅可比常数，延拓计算DRO周期轨道族，获得不同共振比的DRO，仿真结果表明整数共振比的DRO在地月惯性坐标系中的轨迹是封闭的曲线，而共振比非整数的DRO则不封闭。最后，通过轨道外推分析影响DRO稳定性的主要摄动因素，仿真结果表明太阳引力和月球轨道偏心率是影响DRO稳定性的主要摄动因素。在动力学模型中，使用标准星历表示行星的运动状态，当积分时间多于10天时模型误差为km量级，因此在地月系这样大尺度的空间范围内，可以使用星历模型近似的分析DRO在真实力环境中的运动状态，为任务轨道设计提供依据。
- 圆形限制性三体问题 /
- 流函数 /
- 拟周期轨道 /
- 远距逆行轨道(DRO) /
- 共振轨道
Abstract:
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.
- circular restricted three-body problem /
- stream function /
- quasi-periodic orbit /
- Distant Retrograde Orbit (DRO) /
- resonant orbits

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图 1 地月系的φ^*(x)曲线和以点P为初值迭代得到的DRO(C=2.93)

Figure 1. φ^*(x) curve of the Earth-Moon system and DRO obtained by iteration with point P as initial value(C=2.93)

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图 2 地球DRO(1:3)共振轨道

Figure 2. The Earth resonant orbit of DRO(1:3)

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图 3 DRO周期轨道族与雅可比常数C

Figure 3. DRO periodic family and Jacobi constant C

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图 4 DRO在地月惯性坐标系中的运动轨迹

Figure 4. Motion trajectory of DRO in the Earth-Moon inertial coordinate system

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图 5 摄动力模型下地月拟周期DRO

Figure 5. The Earth-Moon quasi-periodic DRO under perturbative force model

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图 6 模型1和模型2在x、y坐标及到月球距离的偏差

Figure 6. Deviation of x, y coordinate and distance to the Moon between Model 1 and Model 2

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图 7 模型1和模型3在x、y坐标及到月球距离的偏差

Figure 7. Deviation of x, y coordinate and distance to the Moon between Model 1 and Model 3

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图 8 模型1和模型4在x、y坐标及到月球距离的偏差

Figure 8. Deviation of x, y coordinate and distance to the Moon between Model 1 and Model 4

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图 9 模型1和模型5在x、y坐标及到月球距离的偏差

Figure 9. Deviation of x, y coordinate and distance to the Moon between Model 1 and Model 5

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图 10 星历模型和全力模型x、y坐标及到月球距离偏差的均方差

Figure 10. Mean square error of deviation between ephemeris model and full force model of x, y coordinate and distance to the Moon

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表 1 摄动平均量级

Table 1. Average magnitude of perturbation

加速度源	加速度平均量级/(m·s^-2)
月球中心引力	1.00×10^-3
地球引力	1.33×10^-3
太阳引力	5.60×10^-6
太阳光压	8.66×10^-8
月球非对称引力	1.88×10^-10
金星引力	6.63×10^-10
木星引力	7.16×10^-11

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表 2 不同摄动模型轨道外推精度的均方差统计结果

Table 2. Statistical results of mean square error of trajectory extrapolation precision for different perturbation models km

积分时间	偏差方向	轨道外推精度的均方差
积分时间	偏差方向	不考虑月球非对称引力	不考虑木星引力和金星引力	不考虑太阳光压	不考虑太阳引力
前1个月	x坐标	0.304 9	0.160 5	98.683	1 597.5
	y坐标	0.370 4	0.191 5	170.10	2 859.2
	到月球距离	0.112 2	0.064 8	82.730	1 705.4
前2个月	x坐标	0.625 2	0.286 1	168.15	1 696.5
	y坐标	0.899 3	0.413 6	295.72	3 161.1
	到月球距离	0.239 6	0.122 6	161.87	1 792.0
前3个月	x坐标	0.902 3	0.374 4	334.18	2 448.4
	y坐标	1.183 3	0.499 9	513.36	5 126.9
	到月球距离	0.321 4	0.154 6	254.59	2 784.8

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