基于日地关系建立地影模型，利用数值法可以高精度计算单个卫星的地影参数，但是难以快速而全面地分析某一类卫星的地影参数变化和分布规律。本文从日、地和卫星三者的几何关系出发，提出了一种基于空间视场的卫星地影直接建模方法。首先，分别利用轨道半长轴和太阳的周年视运动确定卫星地影的大小和位置变化；其次，基于球面几何分析法推导了卫星地影参数的计算公式以及扁率摄动等对长期预报的影响改正公式。对北斗混合星座中3类卫星的地影参数分析试验表明，卫星地影模型和地影参数解析法能够快速获得中高轨近圆轨道类型的星蚀规律信息。
The satellite shadow parameters can be numerically calculated with high accuracy from the positions of the sun, the earth and the specific satellite. Unfortunately, it is difficult for the numerical calculation to give a general profile of the variations and distributions of these parameters for some certain types of orbital spacecraft. A satellite shadow model was presented based on the spatial view at the altitude of the satellite and the correlative geometry amongst the sun, the earth and the satellite. Firstly, the size and location of the satellite shadow were determined by the semi-major axis of the satellite orbit and the annual motion of the apparent sun, respectively. Secondly, the computing formulae of the satellite shadow parameters were derived, together with the correction formulae for the long-term prediction of the parameters due to oblateness perturbation, etc. Examinations on the three types of orbits for the BeiDou navigation constellation show that the proposed satellite shadow model and its shadow parameters computing formulae can provide a prompt profile of the eclipse parameters for the medium-high altitude circular orbit satellites.
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