Fundamental Properties of Optimal Orbital Transfers

The Hohmann transfer theory, developed in 19th century, is the kernel of orbital transfer with minimum propellant mass by means of chemical engines. The success of the Deep Space 1 spacecraft has paved the way toward using advanced electrical engines in space. While chemical engines are characterized by high thrust and low specific impulse, electrical engines are characterized by low thrust and high specific impulse. In this paper, we focus on three issues of optimal orbital transfers for a spacecraft controlled via thrust direction and setting: (a) trajectories of compromise between flight time and propellant mass, (b) trajectories of minimum propellant mass, and (c) relations with the Hohmann transfer trajectory. The resulting fundamental properties are as follows: (a) Flight Time/Propellant Mass Compromise. For interplanetary orbital transfer (orbital period of order year), an important objective of trajectory optimization is a compromise between flight time and propellant mass. The resulting trajectories have a three-subarc thrust profile: the first and third subarcs are characterized by maximum thrust; the second subarc is characterized by zero thrust (coasting flight); for the first subarc, the normal component of the thrust is opposite to that of the third subarc. When the compromise factor shifts from flight time toward propellant mass, the average magnitude of the thrust angle for the first and third subarcs decreases, while the flight 1 The development of the multiple-subarc sequential gradient-restoration algorithm employed in this work was supported by NSF Grant CMS-0218878.