在轨卫星星等建模与计算

Model and calculation of orbital satellite apparent magnitude

星等的大小代表了星体对于人眼的可观测程度。卫星星等的理论计算对于观测跟踪卫星光学系统设计等具有重要的指导意义。结合天文学、轨道动力学、辐射度学、光度学和计算数学理论,建立了计算人造卫星星等的物理数学模型。计算了卫星的可见光反射能量随轨道运行的瞬时特征,结合人眼的视觉特性,推导出了轨道卫星星等的计算方法,并进一步针对卫星表面为灰体的情况给出了一种计算卫星星等的方法及星下点卫星星等的周期性计算曲线,结果表明:星下点观测的卫星星等随卫星在轨道上位置的变化非常显著,对同一卫星,不同星下点观测到的星等差异仅在日照区就可达5个等级之多。

Apparent magnitude represents the observed level of aster to human eyes .The calcu-lation of the satellite apparent magnitude is useful for the design of the optical system to ob-serve and track the satellite .Based on the principle of astronomy ,dynamics of orbits ,radiome-try ,photometry and computational mathematics ,a physical mathematical model for computing satellite magnitude was built .Firstly ,the amount of visible light energy reflected by orbit sat-ellite was calculated .Secondly ,the calculation method was given after deducing the association character of human eyes .Then a kind of brevity method to calculate the apparent magnitude for grey-reflection satellite was given .Finally ,the calculated curve for apparent magnitude ob-served from subastral point was obtained .The result shows that the apparent magnitude ob-served from subastral point varies obviously with the change of the satellite position in orbit . The magnitude difference for one satellite under different subastral points is up to 5 magnitudes only within sunshine region .