地球静止轨道CW方程建模误差分析  

Modeling error analysis of the GEO CW equation

作　　者：任家栋[1] 张大力[1] 曾庆双[1] REN Jiadong;ZHANG Dali;ZENG Qingshuang(School of Aeronautics, Harbin Institute of Technology, Harbin 15001, China)

机构地区：[1]哈尔滨工业大学航天学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2021年第6期785-792,共8页Journal of Harbin Engineering University

摘　　要：针对地球静止轨道的小倾角、小偏心率的特点,本文在瞬时密切轨道坐标系推导分析了CW方程的各类误差要素,包括地球非球形摄动、三体引力等环境误差,以及线性化误差、非圆轨道相关误差等。采用误差线性化方法结合CW方程解析解得到了J_(2)、偏心率相关误差项的解析表达式。数值计算表明:地球静止轨道下CW方程的误差项要素较多,与相对运动构型的尺寸、漂移特性等均相关。二次项误差、偏心率相关误差、J_(2)项相关误差量级相当,是地球静止轨道CW方程的主要误差源,同时呈现出常数和低频波动相结合的误差形式,分析结果可作为地球静止轨道高精度相对导航和制导设计的理论依据。Aiming at the characteristics of the small inclination and small eccentricity of geostationary orbits(GEOs),various error elements,such as environmental errors(e.g.,non-spherical perturbation and three-body gravity),linearization errors,and non-circular orbit correlation errors,of the Colebrook-White(CW)equation have been deduced and analyzed in the instantaneous close orbital coordinate system.The analytical expressions of J_(2) and eccentricity-related error terms are obtained using the error linearization method combined with the analytical solution of the CW equation.Numerical calculations show that there are more error term elements in the GEO CW equation,and they are related to the size and drift characteristics of the relative motion configuration.The magnitudes of the quadratic term error,eccentricity-related error,and J_(2)-related error are equivalent.They are the main error sources of the GEO CW equation and present the error form of the combination of constant and low-frequency fluctuations.The results can be used as the theoretical basis for high-precision relative navigation and guidance design in GEO.

关 键 词：地球静止轨道 卫星 相对运动 CW方程 J_(2)项摄动 太阳光压摄动 三体引力摄动 误差分析 

分 类 号：V412.4[航空宇航科学与技术—航空宇航推进理论与工程]