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| 双小行星系统引力场建模方法研究 |
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步士超1, 王宇凯1,2, 李文丹1, 李爽1, 牛升达3
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1.南京航空航天大学 航天新技术实验室, 南京 210016;2.上海微小卫星工程中心, 上海 201210;3.上海卫星工程研究所, 上海 201109
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| 摘要: |
| 针对弱引力双小行星系统的引力场建模问题，本文采用复杂度和精度依次递增的球体-球体模型、椭球体-球体模型和改进的限制性椭球体-椭球体模型来进行引力场建模，并分别采用椭圆积分以及无积分环节、计算效率高的二阶二次球谐函数来表征引力势，从而比较精确地刻画双小行星系统和探测器构成的限制性全三体问题的动力学模型；针对双小行星系统1999KW4，对其不同的引力场模型进行了仿真研究，分别给出了不同模型下的等效势能函数曲面及零速度曲线，比较了不同模型下的平动点位置坐标偏差。结果表明，二阶二次球谐函数计算引力势的椭球体-椭球体模型计算精度高，复杂程度低，计算量更少，计算速度更快，能够较精确的对双小行星系统进行引力场建模。 |
| 关键词: 双小行星 引力场 球体-球体模型 椭球体-球体模型 椭球体-椭球体模型 |
| DOI：10.15982/j.issn.2095-7777.2017.05.010 |
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| 基金项目:上海航天科技创新基金资助项目（SAST2015036） |
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| Research on Modeling Method of Gravitational Field for Binary Asteroid System |
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BU Shichao1, WANG Yukai1,2, LI Wendan1, LI Shuang1, NIU Shengda3
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1.Laboratory of Space New Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;2.Shanghai Engineering Center for Microsatellites, Shanghai 201210, China;3.Shanghai Institute of Satellite Engineering, Shanghai 201109, China
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| Abstract: |
| In this paper, the sphere-sphere model, the ellipsoid-sphere model and the improved restrictive ellipsoid-ellipsoid model are adopted for the gravitational field modeling of the weak gravitational binary asteroid system, and the corresponding complexity and accuracy of the three models increase gradually. The elliptic integral model and the second degree second order spherical harmonic function (which has high calculation efficiency and no integrals) model are adopted to calculate the gravitational potential energy, respectively. The dynamical model of the restricted full three-body problem consisting of binary asteroid system and spacecraft is accurately described. The different gravitational field models of the binary asteroid system 1999KW4 are simulated. And the surfaces of potential energy function and zero velocity curves under different models are given respectively. The coordinate deviations of libration point under different models are compared. The results show that the ellipsoid-ellipsoid model calculated by the second degree second order spherical harmonic function has the advantages of high precision, low complexity, less calculation, higher computing speed, and can accurately model the gravitational field of the binary asteroid system. |
| Key words: binary asteroid system gravitational field sphere-sphere model ellipsoid-sphere model restrictive ellipsoid-ellipsoid model |