Investigation of the satellite dynamics versus the metrological characteristics of the three-axial accelerometer on board the METRIC mission

This thesis endeavors to investigate various fundamental aspects of METRIC, a proposed scientific mission aimed at enhancing the accuracy of mathematical models describing Earth's atmosphere, general relativity effects and geodesy. The analysis initiates by simulating the space environment METRIC would encounter. This simulation accurately models gravitational accelerations, which encompass not only those resulting from Earth's gravity but also those arising from tidal forces and third-body effects, as well as non-gravitational forces such as atmospheric drag, solar radiation pressure, albedo and planetary infrared radiation. Additionally, it examines factors associated with relativistic effects. These simulations enable a comprehensive understanding and quantification of the impact of all the undesired perturbations affecting the spacecraft's ideal orbit. These perturbations are primarily determined through precise tracking from both Earth and space, i.e. through Satellite Laser Ranging and GNSS respectively. METRIC is equipped with an on board accelerometer capable of detecting non-gravitational accelerations acting on the spacecraft. The measurements obtained from this instrument are used to estimate these perturbations with a high degree of precision - commensurate with the instrument's accuracy level - with the aim of isolating the only relativistic effects once that also the gravitational contribution is modeled. To assess the error in estimating the relativistic effects resulting from non-gravitational accelerations below the instrument accuracy, the thesis conducts a parametric analysis by varying the accuracy of the accelerometer. This is done by evaluating the time-evolution of two Keplerian parameters: the Right Ascension of the Ascending Node (RAAN) and the Argument of Perigee (AOP). A comparison is then made between this altered estimation and the one that would result if the instrument were to perfectly measure the non-gravitational contributions (ideal condition). After that, a series of non-idealities are introduced to account for the accelerometer's real behavior, as for instance axes misalignment with respect to their ideal direction or noise affecting the measurements. These non-idealities have effects contributing to an overall error budget, affecting the quality of the acceleration measurements.