Multi-target ground-track adjustment with a single coplanar impulse

The ground-track adjustment problems for overflying one, two, and three ground targets with a single coplanar impulse are studied by considering the J₂-perturbed model. For the single-target case, the minimum-fuel solutions are obtained by the Newton-Raphson iterations. For the two-target case, when the impulse position is fixed, the analytical approximate solutions for the impulse vector are derived; then the minimum-fuel solution is obtained by considering free impulse position. For the three-target case, the original three-dimensional problem is transformed into solving a single-variable equation only of impulse position. In addition, for free impulse position, the short-period term of semimajor axis is considered, and it is numerically proven to effectively reduce the overflight error. Several numerical examples are provided to verify the effectiveness of the proposed method for solving the ground-track adjustment problem for multiple targets.