Hybrid Ground-Space Target Visit Problem With a Coplanar Impulse

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.