Optimization of very-low-thrust, many-revolution spacecraft trajectories

Optimal minimum flight time solutions are obtained for continuous, very-low-thrust orbit transfers using a direct-transcription approach to convert the continuous optimal control problem into a nonlinear programming problem. The thrust accelerations used are characteristic of solar electric and nuclear electric propulsion, resulting in trajectories that require many revolutions of Earth to achieve the desired final orbits. Among the problems examined are transfers from low Earth orbit to geosynchronous orbit (GEO) and orbit raising from GEO to a specified radius. All initial and terminal orbits are circular, with motion constrained to the equatorial plane. Motion of the spacecraft is described using the equinoctial orbit elements. The variation of spacecraft mass and acceleration due to fuel consumption is modeled. The orbit transfers include the effect of Earth's oblateness through first order as well as third-body perturbations from the moon.