Optimization Procedure for Preliminary Design of Opposition-Class Mars Missions

TLDR

High‑thrust impulsive missions to Mars, including Venus flybys, are considered with burns inside or outside planetary spheres of influence and often subject to time constraints. The study develops a numerical optimal‑control procedure to identify flight opportunities for a manned Mars mission. The method extends Lawden’s primer vector theory, applying optimal‑control necessary conditions to analyze opposition‑class transfers during syzygy periods while accounting for orbital eccentricity, inclination, and time‑constraint adjustments. Optimal transfers in syzygy periods are characterized, and the impact of time‑constraint adjustments on these transfers is discussed.

Abstract

A numerical procedure, based on the theory of optimal control, is developed and used to Ž nd the  ight opportunities for a mannedmission toMars. High-thrust (impulsive)missionsare considered; burns can occur either inside or outside the planets’ spheres of in uence. Venus  yby opportunities also are exploited, and time constraints are often present. The necessary conditions for optimality, derived to deal with such complex missions, constitute an extension of Lawden’s primer vector theory. In particular, the optimal transfers that occur in a syzygistic period and that belong to the opposition class are analyzed, taking the eccentricity and inclination of the planetary orbits into account; adjustments produced by the addition of time constraints are discussed.