Optimal Planetary Orbital Transfers via Chemical Engines and Electrical Engines

Because the orbital periods for planetary orbital transfers are of order hour, the primary objective of an optimal trajectory is to minimize the propellant consumption. In this paper, we present a systematic investigation of optimal trajectories for planetary orbital transfer. Major results on thrust control, propellant consumption, and flight time are presented with particular reference to LEO-to-GEO transfer. The following results were obtained with the sequential gradient-restoration algorithm in either single-subarc form or multiple-subarc form:

(i)	For minimum propellant consumption, the thrust direction is tangent to the flight path. The thrust magnitude has a three-subarc form: powered flight with maximum thrust is followed by coasting flight, which is followed by powered flight with maximum thrust.
(ii)	The flight time is determined mainly by the thrust-to-weight ratio. A transfer via chemical engines is relatively short: usually, it requires less than one cycle to achieve the mission, which involves a large portion of coasting flight. A transfer via electrical engines is relatively long: usually, it requires a multicycle spiral trajectory to achieve the mission, which involves a large portion of powered flight, mostly in the first subarc.
(iii)	The propellant consumption is determined mainly by the specific impulse: the electrical engine is more efficient than the chemical engine, resulting in lower propellant consumption and higher payload.

portions of this paper were presented by the senior author at the 14th annual aas/ aiaa space flight mechanics meeting, maui, hawaii, 8–12 february 2004 (paper aas-04-232). This research was supported by NSF Grant CMS-02-18878.