Fuel-optimal planar Earth-Mars trajectories using low-thrust exhaust-modulated propulsion
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The determination of fuel-optimal, planar, Earth-Mars trajectories of spacecraft using low-thrust, variable specific impulse Isp propulsion is discussed. The characteristics of a plasma thruster currently being developed for crewed/cargo missions to Mars are used. This device can generate variable Isp within the range of 1000-35,000 s, at constant power. 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, multiple shooting method. Results for a 144-day crewed mission to Mars are presented. The variation of the Isp during spacecraft's escape from the Earth's gravitational field 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, influencing the spacecraft, one per phase, in sequence.
