Using Low-Thrust Exhaust-Modulated Propulsion Fuel-Optimal Planar Earth-Mars Trajectories

Abstract

The determination of fuel-optimal, planar, Earth–Mars trajectories of spacecraft using low-thrust, variable speciŽ c impulse Isp propulsion is discussed. The characteristics of a plasma thruster currently being developed for crewed/cargomissions toMars are used. This device can generate variable Isp within the range of 1000–35,000s, at constant power. The state equationsarewritten in rotating, polar coordinates, and the trajectory is divided into two phases, patched together at an intermediate pointbetween the Earth andMars. The gravitationaleffects of the sun, Earth, andMars are included in the two phases. The formulationof 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, multipleshootingmethod.Results for a 144-daycrewed mission toMars are presented. The variationof the Isp during spacecraft’s escape from the Earth’s gravitational Ž eld shows an interesting periodic behavior with respect to time. The results obtained are also compared with those obtained by assuming a three-phase trajectory, with the Earth, sun, and Mars, in uencing the spacecraft, one per phase, in sequence.