Fuel-optimal planar interplanetary trajectories using low-thrust exhaust-modulated propulsion

This paper deals with the determination of fuel-optimal trajectories for rockets powered by low-thrust propulsion with variable specific impulse (Isp). The characteristics of a plasma thruster currently being developed for manned/cargo missions to Mars are used in this study. This device can generate variable thrust/Isp at constant power, within the range 1,000-35,000 sec. The state equations are written in rotating, polar coordinates and the trajectory is divided into two phases, patched together at an intermediate point between the Earth and Mars. The gravitational effects of the Sun, Earth, and Mars are included in the two phases. The formulation of the problem treats the spacecraft mass as a state variable, thus coupling the spacecraft design to the trajectory design. The optimal control problem is solved using an indirect method. Since the geocentric and areocentric coordinate systems are rotating, and the transformations between the respective variables in the two phases are nonlinear (excluding the mass), the costates are discontinuous at the patch point. The optimality of the solutions is investigated using neighboring extremals. Results for a 144-day manned mission to Mars are presented.

Fuel-optimal planar interplanetary trajectories using low-thrust exhaust-modulated propulsion Academic Article