Analytical Optimal Solution for the Reachable Domain of Low-Thrust Spacecraft

Low-thrust electric propulsion system has drawn increasing attention from researchers because of its high propellant efficiency. The reachable domain of low-thrust spacecraft can provide a geometric insight for space mission planning. In this paper, analytical solutions of the envelope of reachable domain are obtained by employing the Pontryagin’s maximum principle in the well-known linearized model of relative motion, the Tschauner–Hempel equations. Specifically, this study focuses on two contributions. First, an analytical solution of the envelope of reachable domain is obtained, and the associated optimal control profile is derived. Second, an ellipsoid approximation of the reachable domain is proposed to represent the envelope directly based on the analytical solution. Numerical simulations are conducted to demonstrate the accuracy of the proposed solutions. The results show that the reachable domain obtained analytically coincides well with that solved by the numerical indirect method based on the two-body model with low thrust.