This thesis aims to improve the accuracy of re-entry epoch prediction for decaying satellites in orbit. It explores the impact of aerodynamic coefficients, rotational dynamics, and initial state uncertainties on re-entry prediction. By using SPARTA software, the study generates aerodynamic coefficients and considers factors such as object shape, attitude, atmospheric density, and relative velocity. The findings emphasize the importance of precise aerodynamic modelling, particularly the inclusion of lift force for specific shapes like Starlink satellites. Rotational dynamics reduce the range of re-entry epoch predictions by narrowing the average drag coefficient. Initial state uncertainties have a limited effect compared to the average drag coefficient. The research also evaluates the re-entry prediction for a Starlink satellite, aligning closely with existing models after applying a correction factor. Recommendations include sensitivity analyses and investigating different satellite shapes to enhance prediction capabilities. These findings ensure more reliable and accurate re-entry epoch predictions for impact analysis.

The accurate prediction of satellite orbits is essential for the proper functioning of space-based services such as navigation, communication, and Earth observation. However, atmospheric drag is a significant source of error in satellite orbit prediction, especially in Low Earth Orbit (LEO), where the majority of space objects operate. The thermosphere, the outermost layer of Earth's atmosphere, plays a crucial role in determining atmospheric drag. However, the thermospheric density is subject to high levels of uncertainty, up to 30%, when computed from atmospheric models. This uncertainty is particularly relevant in LEO, where it can affect the operational lifespan of satellites.

To increase the accuracy of thermospheric density models, this paper presents an assessment of the accuracy of orbit predictions using empirical Thermospheric Mass Density (TMD) observations obtained from the Swarm C satellite. The study uses a Principal Component Analysis (PCA) to decompose a fine grid of density into the main temporal and spatial modes. Then, each of the modes is calibrated with Swarm C observations using a Least Squares Estimation (LSE) algorithm. The calibration is validated with the observation using unbiased metrics. These observations were assimilated into the NRLMSISE-00 atmospheric model, and the resulting calibrated density model was used to predict the orbits of Swarm C, GRACE-FO and Sentinel 1-A satellites. To analyse the consistency of the results, a slicing window analysis was performed, and the median evolution of the windows was computed.

The results of the study indicate that a calibrated density model with a several satellite geometries, such as the cannonball model, a panel model, or a scaled panel model, can significantly improve the accuracy of orbit predictions in LEO. During March 2022, a period of medium solar activity, the median accuracy of orbit predictions for Swarm C was reduced from 20.67 km with NRLMSISE-00 to 13.75 km with the calibrated model and a scaled panel model geometry. During the same period, the median accuracy of orbit predictions for GRACE-FO C was reduced from 17.98 km with NRLMSISE-00 to 2.89 km with the calibrated model and an (unscaled) panel model geometry. These findings have important implications for the sustainable operation of satellites in the increasingly crowded space environment.

On May 22, 2018, the Gravity Recovery and Climate Experiment Follow On (GRACE-FO) mission was launched with the goal to map the spatiotemporal variations in the Earth's gravity field and to extend the 15-year monthly mass change observations of its predecessor, the GRACE mission. Similarly to GRACE, the measurement principle of GRACE-FO is based on three different key elements, namely inter-satellite ranging, precise orbit determination and accelerometry. The accurate estimation of the satellites’ attitude has an influence on all three of them. Therefore, any unmodeled errors in the attitude dataset product can propagate to the gravity field solutions and degrade the results. The objectives of this thesis are twofold. Firstly, to analyse the in-flight performance of the GRACE-FO star cameras, fiber-optic gyroscopes, accelerometers and steering mirrors. Secondly, to propose a method that accounts for the instruments' noise and errors and fuses the data, giving an improved attitude solution.

The noise and error characteristics of each instrument are determined by examining their measurements in the time and frequency domain, as well as investigating their differences in geographic plots. These analyses are performed for May 2020, when all instruments could provide nominal data. Motivated by the improved attitude quaternions and gravity field results that were obtained from the latest GOCE gradiometer data calibration process, the proposed on-ground attitude reconstruction for GRACE-FO is composed of three elements. The first one is the optimal combination of star camera and steering mirror quaternions by minimizing the weighted residual sum of squares of the elements of the noise quaternions. Within this combination, a set of constant parameters are also estimated that describe the relative alignment of these sensors. The second element is the reconstruction of the satellite angular rates in the frequency domain by applying respectively a highpass and a lowpass filter to the IMU and to the combined star camera and steering mirror derived angular rates. Lastly, the third element is the attitude reconstruction, for which attitude quaternions, resulting from the smooth reconstructed angular rates, are fitted to the optimally combined quaternions by means of a generalised least-squares adjustment.

The proposed attitude data fusion method produces an improved attitude solution that incorporates more accurately the noise and error characteristics of the star camera, the steering mirror and the IMU measurements. At the level of quaternions, it performs better than the official method, which is based on Kalman filtering, with noticeable improvements at frequencies above 10 mHz. However, based on a comparison of the corresponding derived antenna offset correction for range rate, very minor improvements are expected at the level of the gravity field. This is due to the K/Ka-band ranging system noise being the dominant source at the higher frequencies. The findings of this thesis work are valuable for the design of future gravity missions such as the Next Generation Gravity Mission proposed by ESA, for which a redundant accelerometer design is considered. Given the estimated noise characteristics of the above instruments and the proposed angular rate reconstruction method, the most favorable placement of the accelerometers is found to be in the along-track direction. If an accelerometer fails in this configuration, the noise in the required centrifugal and Euler acceleration corrections will be less than that of the laser ranging system.

Interplanetary missions have relied on Radio Science (RS) for recovering gravity fields via detecting their signature on the spacecraft’s trajectory. Yet the weak gravitational fields of small bodies, coupled with the prominent influence of confounding accelerations, hinder the efficacy of this method. Meanwhile, quantum sensors based on Cold Atom Interferometry (CAI) have demonstrated absolute measurements with an inherent stability and repeatability, reaching the utmost accuracy in microgravity. This work addresses the potential of CAI-based Gradiometry (CG) as a means to strengthen the RS gravity experiment for small-body missions. Phobos represents an ideal science case as astronomic observations and recent flybys have conferred enough information to define a robust orbiting strategy, whilst promoting studies linking its geodesic observables to its origin. A covariance analysis was adopted to evaluate the contribution of RS and CG in the gravity field solution, for a mission duration of one week.

The favourable observational geometry and the small characteristic period of the gravity signal add to the competitiveness of Doppler observables. Provided that empirical accelerations can be modelled below the nm/s2 level, RS is able to infer the 6x6 spherical harmonic spectrum to an accuracy of 0.1-1% w.r.t. the homogeneous interior values. If this correlates to a density anomaly beneath the Stickney crater, RS would suce to constrain Phobos’ origin. Yet, in event of a rubble pile or icy moon interior (or a combination thereof) CG remains imperative, enabling an accuracy below 0.1% for most of the 10x10 spectrum. Nevertheless, technological advancements will be needed to alleviate the current logistical challenges associated with CG operation. This work also reflects on the sensitivity of the candidate orbits with regards to dynamical model uncertainties, which are common in small-body environments. This brings confidence in the applicability of the identified geodetic estimation strategy for missions targeting other moons, particularly those of the Giant planets, which are targets for robotic exploration in the coming decades.