ORBIT DESIGN AND MAINTENANCE IN THE ELLIPTICAL HILL PROBLEM WITH APPLICATIONS TO THE PHOBOS SAMPLE RETURN MISSION MMX

摘要

Martian Moon eXploration mission, currently under development by JAXA, will be launched in 2024 with the goal of retrieving pristine samples from the surface of Phobos. Soon after arrival, the spacecraft will inject into retrograde relative trajectories known as quasi-satellite orbits and study the geophysical environment of the Martian satellite for more than three years. This paper presents the orbit design and maintenance strategy of MMX in the framework of the elliptical Hill problem with ellipsoidal secondary. Specifically, we introduce a numerical continuation procedure on the eccentricity of Phobos to generate families of two-dimensional quasi-periodic invariant tori that replace purely periodic solutions that exist in the circular case. Two-dimensional torus maps can be then constructed and used to represent physical quantities of interest (e.g., spacecraft longitude and altitude), as well as to generate reference trajectories for tracking purposes. Sensitivity and stability analyses are carried out to investigate the dynamical properties of retrograde relative trajectories in the time-periodic case. Finally, a Linear Quadratic Regulator is implemented in order to assess the robustness of the computed trajectories under injection, navigation, and execution errors. Monte Carlo simulations demonstrate that all of the computed quasi-satellite orbits can be maintained with as low as 18.065 m/s per month.