Multiple Mars gravity-assist trajectory to inclined Sun–Earth L4

Abstract

The multiple Mars gravity-assist trajectory is compared to the phasing trajectory for placing a spacecraft in a circular Sun–Earth L4 orbit with a 1 AU semi-major axis and inclinations of 10° and $14.5^{\circ }$ relative to the ecliptic plane. The gravity-assist maneuvers are treated as instantaneous velocity changes using a zero-sphere-of-influence model. The trajectory is optimized for two potential launch vehicles (Falcon 9 and Falcon Heavy) to achieve the desired orbit with minimal $C_3$ energy. Through trajectory analysis based on various launch vehicles and their $C_3$-based payload capacities, it was found that the multiple Mars gravity-assist trajectories are outperformed by the phasing trajectory at a 10° inclination but are additions to the Pareto optimal solutions for $14.5^{\circ }$ inclination mission when considering the spacecraft’s arrival mass at the Sun–Earth L4.