Optimum burn scheduling for low-thrust orbital transfers

This paper describes a method for optimizing the point at which thrust should be initiated on each passage of a low-thrust, multiple finite-duration perigee-burn ascent trajectory, with the thrust vector always oriented perpendicular to nadir. The quantity being minimized is the rotation of the line of apsides. The semianalytic method developed here requires only a simple root-finding routine for the numerical portion of the solution. A perturbation solution (two-variable expansion) is used to model the flight path during the burn, yielding a “burn-on” position with a maximum error of approximately 2%.