一种计算卫星弓形激波/磁层顶拦截位置和时间的解析方法
An Analytical Method for Calculating the Satellite Bow Shock/Magnetopause Interception Positions and Times
摘要：
本文介绍了计算卫星轨道与地球磁层元素（弓形激波和磁层顶）相交的位置和力矩问题的解析解。卫星的运动用开普勒近似表示。磁层顶和弓形激波用二阶椭圆抛物面描述。这些表面被用作确定它们与卫星轨迹的交点（如果有的话）的情况条件。在这里，情境条件被变换到开普勒轨道的平面上，此后它被简化为二阶平面曲线-二次曲面（椭圆或抛物线）。这个系统的解决方案，包含该曲线的方程和开普勒的椭圆方程，允许确定的地方，轨道与磁层顶或弓形激波相交。建议将该系统化为一个四阶方程来求解。
英文摘要：
This paper contains a presentation of analytical solution of the problem of calculating the places and moments of intersection of satellite trajectories with elements of the Earth's magnetosphere (bow shock and magnetopause). The satellite motion is presented in a Kepler's approximation. Magnetopause and bow shock are described by second-order surfaces- elliptic paraboloides. These surfaces are employed as situational conditions for determining the points of intersection they have (if any) with the satellite trajectory. The situational condition is herein transformed into the plane of Kepler's orbit, thereafter it is reduced to a second-order plane curve- quadric (ellipse or parabola). The solution of this system, containing the equation of this curve and Kepler's ellipse equation, allows determining the places where orbits intersect with the magnetopause or the bow shock. The solution of this system is suggested to be given by reducing the system to a fourth-order equation.
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