• rank deficiencies
• relativity experiment
• BepiColombo
• MORE
• symmetries

The Mercury Orbiter Radio science Experiment (MORE) is one of the experiments on-board the ESA/JAXA BepiColombo mission to Mercury, launched in October 2018, whose arrival is scheduled for December 2025.
The scientific goals of the mission concern both the geodesy and geophysics of Mercury and fundamental physics. Taking advantage from the fact that Mercury is the best-placed planet to investigate the gravitational effects of the Sun, MORE will allow an accurate test of relativistic theories of gravitation.

In this Thesis we aim to investigate a critical issue of the MORE relativity experiment: the presence of symmetries affecting the outcome of the experiment.
Generally speaking, symmetries in an orbit determination problem lead to rank deficiencies in the normal matrix of the least square fit, which can result in a significant degradation of the solution. Thus, it is especially important to understand whether we are in the presence of symmetries and develop suitable methods to handle them.
The investigation is undertaken by means of both theoretical considerations and numerical simulations, using the ORBIT14 software: a dedicated software developed by The Celestial Mechanics Group of the University of Pisa.