Low-Thrust Eccentricity-Constrained Orbit Raising

Abstract

The problem of zero-eccentricity-constrained orbit raising in circular orbit in the presence of shadowing is analyzed using both numerical and analytical methods. Given the shadow arclength, piecewise constant pitch angles are selected analytically, and the location along the orbit where the pitch angle switches is optimized to effect the largest change in semimajor axis per revolution. Two strategies yielding near-optimal performance are presented, differing in whether or not a pitch reorientation maneuver is carried out inside the shadow arc. These analyticresultsarealso compared withtheexacteccentricity-constrainednumericalsolutions,whichuseoptimally varying continuous pitch proe les to maximize the change in semimajor axis after each revolution. The suboptimal analytic strategies arealmost as effectiveastheoptimal strategy especially in higherorbit. Thesestrategiesremove theneedforcontinuouslyreorienting thespacecraftattitudein pitch,providing robustreal-timeon-boardguidance capability for electric orbit transfer vehicle orbit raising applications.