Μοντελοποίηση δυναμικών δορυφορικών τροχιών στο πλαίσιο των σύγχρονων αποστολών της διαστημικής γεωδαισίας

Satellite orbit modeling and determination is one of the fundamental fields in space geodesy since the era of the first artificial satellites until the current satellite missions' period. Orbit parameterization along with the space-geodetic observations focuses in the three pillars of geodesy ie the reference system, the gravity field and Earth's rotation. The mathematical connection between satellite motion and gravity field is a major research objective as new gravity missions are in-orbit while future missions, specially dedicated for this purpose, are under studies. The new satellite data lead to the numerical investigation as well as to the evolution of theoretical approaches in gravity field modeling and precise orbit determination. During the last decade, gravity filed mapping has been based on the innovative techniques that come from CHAMP (CHAllenging Mini-satellite Payload), GRACE (Gravity Recovery And Climate Experiment) and GOCE (Gravity field and steady-state Ocean Circulation Explorer) missions. This doctoral thesis treats the mathematical modeling of satellite orbits from a geodetic point of view. Basic topic is the investigation of rigorous approaches to the orbit determination problem. Orbit modeling is implemented in theoretical as well as practical level through software that has been developed in the frame of the present thesis. The scheme of dynamic orbit determination is applied in the frame of current satellite missions for gravity field determination. Orbit analyzes are performed for the cases of GRACE and GOCE missions by taking advantage of their sophisticated observation techniques and orbit design. Computations have been made over a variable set of several parameters and models in order to quantify their effects to orbit and moreover to evaluate the gravitational signal at orbital altitude. Orbit parameterization has been mostly focused in the spectral range of the gravity field. Current state-of-art gravity models are analyzed in a degree-wise (order-wise) cumulative sense ie the computation of the gravitational part for each degree has been performed using all previous spherical harmonics coefficients. The approach implemented here is a pure dynamic orbit analysis and therefore, the results and statistics depend strongly on the forces modeling errors. Such an approach, establish an independent tool for the assessment of Earth gravity models or even it may enable a band-limited analysis. Furthermore, in the case of GRACE, the KBR analysis leads to an external validation tool.