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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

吴小婧, 曾凌川, 巩应奎等 . 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): 883-892. doi: 10.13700/j.bh.1001-5965.2019.0353
引用本文: 吴小婧, 曾凌川, 巩应奎等 . 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): 883-892. doi: 10.13700/j.bh.1001-5965.2019.0353
WU Xiaojing, ZENG Lingchuan, GONG Yingkuiet al. DRO computation and its perturbative force in the Earth-Moon system[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(5): 883-892. doi: 10.13700/j.bh.1001-5965.2019.0353(in Chinese)
Citation: WU Xiaojing, ZENG Lingchuan, GONG Yingkuiet al. DRO computation and its perturbative force in the Earth-Moon system[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(5): 883-892. doi: 10.13700/j.bh.1001-5965.2019.0353(in Chinese)

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
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

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

Funds: 

National Natural Science Foundation of China 91438207

More Information
  • 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。

     

  • 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)

    图 2  地球DRO(1:3)共振轨道

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

    图 3  DRO周期轨道族与雅可比常数C

    Figure 3.  DRO periodic family and Jacobi constant C

    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

    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

    图 6  模型1和模型2在xy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

    图 7  模型1和模型3在xy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

    图 8  模型1和模型4在xy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

    图 9  模型1和模型5在xy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

    图 10  星历模型和全力模型xy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

    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
    下载: 导出CSV

    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
    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 90.160 598.6831 597.5
    y坐标0.370 40.191 5170.102 859.2
    到月球距离0.112 20.064 882.7301 705.4
    前2个月x坐标0.625 20.286 1168.151 696.5
    y坐标0.899 30.413 6295.723 161.1
    到月球距离0.239 60.122 6161.871 792.0
    前3个月x坐标0.902 30.374 4334.182 448.4
    y坐标1.183 30.499 9513.365 126.9
    到月球距离0.321 40.154 6254.592 784.8
    下载: 导出CSV
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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

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