卫星进／出地影位置和时间的计算算法

首先推导出地影图锥面方程和卫星运动方程，然后经过合理的简化得到一个四次代数方程。对该四次方程进行求解，得出卫星进出本影和半影位置的近似解，再以此为初值，利用牛顿迭代法进行迭代，得到卫星进出地影位置和相对精确解。最后给出了该算法的数值算例。

Calculating Method of Satellite Entry and Exit Positions and Times through Umbra/Penumbra

To problem of calculating earth satellite's entry/exit positions and times through the earth's umbra and penumbra, for elliptical satellite orbits, is a problem dating from the earliest days of the space age, but it is still of the utmost importance to many space projects for thermal, power and launch window studies,especially the perturbation force resulting from solar radiation pressure considerations. This is solved by reducing the problem to that of finding the roots of a quartic polynomial. Then we take the roots as initial guess and use Newton's method to solve this nonlinear equation. Finally, typical results from an algorithm constructed from the method are shown.