Replacement of the part of gravity model and of remaining dynamic models by empirical accelerations in the fit processes of a low-Earth satellite orbit and factors limiting their accuracy

Abstract

This work contains the results of calculations performed to prove the ability of estimated orbital parameters for the replacement of dynamic models in the orbit determination of a sample low-Earth-orbiting satellite. The obtained solutions include two cases of the absorption of dynamic models. In the first case, the contribution of dynamic models, apart from the gravity field, was absorbed, i.e., the satellite motion was described by the gravity field and estimated parameters. In the second case, the contributions of all dynamic models, including the gravity field, were absorbed. For the gravity field model, the absorption concerned its selected parts. In this case, the satellite motion was modeled only by the gravity model truncated to different degrees and orders and an appropriate set of orbital parameters. In both aforementioned cases, the initial conditions were also improved. Cartesian coordinates of the Gravity Field and Steady-State Ocean Circulation Explorer Mission satellite along selected reference arcs of the official reduced-dynamic orbit served as pseudo-observations in this study. The orbital parameters, also known as empirical accelerations, were determined using the least-squares method by a dedicated orbital package. The results were presented and compared in the form of the root-mean-square (RMS) values of the differences between the estimated orbits and the reference orbits, as well as the corresponding values of the obtained empirical accelerations for selected variants of solutions. The obtained accuracy of the process of the fit of the satellite orbit expressed by the corresponding RMS values, reached a millimeter level. For selected typical solutions, the distribution of residuals and power spectra are presented with an indication of characteristic errors: random and systematic periodic components. Key factors influencing the obtained fit accuracies of estimated orbits are given. Contributions of these factors in the error budget of fits of estimated orbits are also presented. Additionally, in the fit process, the performance of selected gravity models coming from different years is compared to assess the impact of gravity field errors on the results of aforementioned process.