Study of satellite shadow function model considering the overlapping parts of Earth shadow and Moon shadow and its application to GPS satellite orbit determination

Abstract

Solar radiation pressure is one of the main perturbations in satellite orbit determination. When a satellite enters the umbra or the penumbra area of an occulting body (e.g., the Earth or the Moon), a satellite shadow function model is used to estimate the occultation degree. Occultation of the Sun by the Earth and by the Moon is considered separately in the existing shadow function model, i.e., any area of overlap of the shadows of the Earth and the Moon is not considered. This directly affects the accuracy of the solar radiation pressure model, which then affects the accuracy of satellite orbit determination. In this study, the existing shadow function model was refined to consider the overlap of the shadows of the Earth and the Moon. Then, using the original and refined shadow function models, Global Positioning System (GPS) satellite orbits from 2008 to 2017 were analyzed and compared. The results show that there are 27 occurrences when GPS satellites enter an area of overlapping shadows of the Earth and the Moon. Among them, the longest duration of passage through the overlapping shadows by one satellite in one day is 474 s, and the maximum difference of the same epoch between the original and refined models is 0.329. In addition, Differences between the GPS observed orbits obtained separately using the original and refined models are small. However, differences between the GPS predicted orbits are substantial; the greatest difference is 46 mm. Furthermore, with the reference of overlapping arcs, when there are differences between the predicted orbits obtained separately using the original and refined models, 86.7% of the orbit determination solutions are improved.