93-147
Equation For Optimal Power-Limited Spacecraft Trajectories
John E Prussing*
Abstract
For a power-limited spacecraft the necessary conditions for an optimal (minimum-propellant) trajectory and the equations of motion can be combined into a single fourth-order differential equation for the position vector. Every solution to this equation then represents an optimal trajectory through the specified gravitational field. By enforcing the appropriate boundary conditions, the desired optimal trajectory can be determined. Each kg of propellant saved represents an additional kg of payload.
*Professor of Aeronautical and Astronautical Engineering, University of Illinois at Urbana-Champaign, MC-236, Urbana, Illinois 61801-2935. Senior Member AAS, Associate Fellow AIAA.