Reachable Domain of Ground Track with a Single Impulse

The reachable domain of ground track under a single upper-bounded impulse for a given initial orbit is solved based on the Gauss's variational equations. Considering the linear J-2 perturbation, the reachable domain problem is transformed into solving the ranges of longitude difference between the maneuvering and reference orbits at all feasible latitudes. For the coplanar impulse, the longitude difference is a monotonically decreasing function only of the transfer-time difference, and then the extreme values of the transfer-time difference are obtained by the Newton-Raphson iterations. For the noncoplanar impulse, the reachable domain is related to both the orbital plane change and the transfer-time difference, and then the extreme values of the longitude difference are solved by the sequence quadratic programming algorithm. Finally, the envelopes of the reachable domain are obtained by comparing the extreme values and the boundary values of the longitude difference. Several numerical examples with coplanar and noncoplanar impulses are provided to verify the effectiveness of the proposed method for solving the envelopes of the reachable domain.