Fuel-optimal planar Earth-Mars trajectories using low-thrust exhaust-modulated propulsion

The determination of fuel-optimal, planar, Earth-Mars trajectories of space craft using low-thrust, variable specific impulse I-sp propulsion is discus sed. The characteristics of a plasma thruster currently being developed for crewed/cargo missions to Mars are used. This device can generate variable I-sp within the range of 1000-,35,000s, at constant power. The state equati ons are written in rotating, polar coordinates, and the trajectory is divid ed into two phases, patched together at an intermediate point between the E arth and Mars, The gravitational effects of the sun, Earth, and Mars are in cluded in the two phases. The formulation of the problem treats the spacecr aft mass as a state variable, thus, coupling the spacecraft design to the t rajectory design. The optimal control problem is solved using an indirect, multiple shooting method. Results for a 144-day crewed mission to Mars are presented. The variation of the I-sp during spacecraft's escape from the Ea rth's gravitational field shows an interesting periodic behavior with respe ct to time. The results obtained are also compared with those obtained by a ssuming a three-phase trajectory, with the Earth, sun, and Mars, influencin g the spacecraft, one per phase, in sequence.