The hybrid ground–space target visit problem is solved by applying a single coplanar impulse. Considering the linear $J_{2}$ perturbation, the ground target visit problem is transformed into the ground track adjustment problem, and it is expressed as a time constraint equation. The space target visit problem is viewed as the orbit interception (or flyby) problem, and it is expressed as time and radius constraint equations. Then, based on Gauss’s variational equations, the hybrid ground–space target visit problem is simplified into solving a single-variable equation only of maneuver position. Finally, the exact solution under the high-precision dynamic model is obtained by the differential correction method. Several numerical examples are presented to validate the efficiency of this approach, and the results show that there are a series of discrete solutions to this problem.

中文翻译：

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具有共面脉冲的混合地空目标访问问题

混合地空目标访问问题通过应用单个共面脉冲来解决。考虑到线性$J_{2}$扰动，将地面目标访问问题转化为地面航迹调整问题，并表示为时间约束方程。空间目标访问问题被视为轨道拦截（或飞越）问题，并表示为时间和半径约束方程。然后，基于高斯变分方程，将混合地空目标访问问题简化为求解仅机动位置的单变量方程。最后通过微分校正的方法得到高精度动态模型下的精确解。给出了几个数值例子来验证这种方法的效率，结果表明这个问题有一系列离散的解决方案。