Electric solar wind sail (E-sail) is an innovative propulsion system, which can generate low and continuous thrust without any propellant by reflecting ions from the solar wind. Because the propulsive acceleration of E-sail is low and continuous, its trajectory is usually characterized by long flight time. In order to explore more flight plans, rapid trajectory design is useful for preliminary mission analysis and design. This paper presents a method for rapid generation of minimum-time, three-dimensional trajectories for an E-sail using the finite Fourier series shapebased method. Unlike the more conventional electric thruster, the thrust vector of an E-sail is constrained. In order to consider the characteristics of the E-sail thrust, inequality constraints of thrust acceleration are investigated based on a recent thrust model. The numerical simulation results show that the proposed method is useful to quickly design the flight trajectory of the E-sail by considering the actual characteristics of the thrust vector

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 J2 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 non-coplanar 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 non-coplanar impulses are provided to verify the effectiveness of the proposed method for solving the envelopes of the reachable domain.

Continuous-thrust relative reachable set is presented for the spacecraft linear relative motion near elliptical orbits. Two cases with different constraints are considered: the energy-constrained case and the fuel-constrained case. Based on the distance-fields-over-grids method, the envelopes of the relative reachable sets for both cases are approximated by a number of grid points on it, and these grid points are obtained from a series of optimization problems. Based on the continuous-thrust analytical state propagation, the original optimization problems for both cases are converted into the nonlinear programming problems. Furthermore, for the energy-constrained case, the analytical solution is obtained by using the Lagrange multiplier method; whereas for the fuel-constrained case, the problem is converted into a mixed-integer linear programming problem to rapidly obtain solutions. Several numerical examples are provided to verify that the developed methods for solving the spacecraft relative reachable sets are feasible and computationally efficient.