Optimization of MMX relative quasi-satellite transfer trajectories using primer vector theory

Quasi-satellite orbits (QSO) are stable retrograde parking orbits around Phobos that are currently being considered for JAXA’s upcoming robotic sample return mission Maritan Moons Exploration (MMX). During the proximity operations of MMX, the spacecraft inserted in a high altitude QSO will gradually descend to lower altitude QSOs with suitable transfer and station-keeping techniques between different relative QSOs. Preliminary analysis of two-impulsive planar transfers between relative retrograde orbits utilizing the bifurcated QSOs families is studied to estimate the $\Delta V$ costs and time of flights of the transfers. In this paper, differently from previous works, we utilize the initial guesses found through the preliminary results that provide two-impulsive transfer $\Delta V$ execution points and optimize the transfers between relative QSOs around Phobos. Primer vector theory is applied to investigate the primer vector of the MMX transfer trajectories to evaluate whether intermediate maneuver or initial/final coasting times along the trajectories can minimize the total $\Delta V$ cost between the transfers. Based on the primer vector analysis of the impulse transfer trajectories, it is found that departing and arriving at the same periphobian sides with an additional mid-course impulse results in the optimal impulse solution.