Using Edelbaum's Method to Compute Low-Thrust Transfers with Earth-Shadow Eclipses

A new low-thrust trajectory program based on Edelbaum's analytic solution is presented that can accurately compute the transfer time for low-thrust maneuvers in the presence of Earth-shadow arcs without relying on numerical integration of the equations of motion. The new method uses Kechichian's reformulation of Edelbaum's analytic trajectory solution. Transfer time in the presence of Earth shadow is computed from the Edelbaum and weighted thrust acceleration. The resulting algorithm is extremely fast and does not require numerical integration of equations of motion or numerical iteration for convergence. Many solutions are obtained for two orbit transfer cases between inclined circular orbits, and the transfer times predicted by the Edelbaum-based method show an good match with the numerically optimized trajectories. These results indicate that the new algorithm would serve as a valuable preliminary design tool for solar electric propulsion spacecraft missions.