Covariance Analysis of Periodic and Quasi-Periodic Orbits Around Phobos with Applications to the Martian Moons Exploration Mission

Understanding the internal composition of a celestial body is fundamental for formulating theories regarding its origin. Deep knowledge of the distribution of mass under the body's crust can be achieved by analyzing its moments of inertia and gravity field. In this regard, the two moons of the Martian system have not yet been closely studied and continue to pose questions regarding their origin to the space community; thus, they deserve further characterization. The Martian Moons eXploration mission will be the first of its kind to sample and study Phobos over a prolonged period. This study aims to demonstrate that the adoption of periodic and quasi-periodic retrograde trajectories would be beneficial for the scientific value of the mission. Here, a covariance analysis was implemented to compare the estimation of high-order gravitational field coefficients from different orbital geometries and for different sets of processed observables. It was shown that the adoption of low-altitude non-planar quasi-satellite orbits would help to refine the knowledge of the moon's libration angle and gravitational field.