| Hansen系数及其导数的直接计算方法 |
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| 引用本文： | 吴连大,张明江.Hansen系数及其导数的直接计算方法[J].天文学报,2021,62(5):47. |
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| 作者姓名： | 吴连大 张明江 |
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| 作者单位： | 中国科学院紫金山天文台 南京 210023;中国科学院紫金山天文台 南京 210023;中国科学院空间目标与碎片观测重点实验室 南京 210023 |
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| 基金项目： | 国家自然科学基金项目(11873096)和中国科学院青年创新促进会(2017367)资助 |
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| 摘 要： | 回顾总结了7种Hansen系数及其导数的直接计算方法,比较分析了这些方法的计算效率和计算稳定性.研究表明:Hansen系数的递推关系可以用来判别计算结果的稳定性.最后指出, Wnuk方法(双精度计算)和McClain方法(4精度计算)是稳定的,可以用来计算人造卫星轨道摄动.由于大多数人造卫星采用小偏心率轨道,需要计算无奇点摄动,推荐使用McClain方法1 (4精度计算).
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| 关 键 词： | 天体力学 摄动理论: 摄动函数及其展开方法 方法: 数值 |
| 收稿时间： | 2020/11/24 0:00:00 |
Direct Calculation Methods of Hansen Coefficients and Their Derivatives |
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| WU Lian-d,ZHANG Ming-jiang.Direct Calculation Methods of Hansen Coefficients and Their Derivatives[J].Acta Astronomica Sinica,2021,62(5):47. |
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| Authors: | WU Lian-d ZHANG Ming-jiang |
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| Institution: | Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023; Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023;Key Laboratory of Space Object and Debris Observation, Chinese Academy of Sciences, Nanjing 210023 |
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| Abstract: | Seven direct calculation methods of Hansen coefficients and their derivatives are reviewed. The computational efficiencies of these methods are compared, and their computational stabilities are analyzed. We show that the recursion relations of Hansen coefficients can be used to determine the stabilities of calculation results. Finally, it is pointed out that Wnuk''s method (double precision computation) and McClain''s methods (quadruple precision computation) are stable, which can be used to calculate orbit perturbations. Because of small orbital eccentricities of most satellites, the perturbation calculations without singularities are required, and McClain''s first method (quadruple precision computation) is recommended. |
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| Keywords: | celestial mechanics perturbation theory: perturbation function and its expansion method methods: numerical |
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