Analysis of the effects of earth shadowing on GNSS satellite orbits

Abstract

Precise positioning by GNSS might incur some error when one or more of the satellites that are being observed happen to be in Earth shadow – in eclipse. This effect might be worsened if the Earth is passing through a period of stormy solar weather. It is therefore of considerable interest to be able to examine satellite orbital degeneration while in eclipse compared to when not in eclipse. This paper develops the connections between the methods of describing the motions of the Sun and GNSS satellites in, respectively, the astronomical and the Earthcentred systems. On this basis, tools are prepared for determining and predicting when individual satellites are, or are not, in eclipse, leading further to more advanced tools for predicting eclipse seasons in advance. Additionally, some experiments are described comparing predicted orbits with observed satellite orbits under both eclipse and non-eclipse conditions. In conclusion this paper describes how the normal modern high precision land surveyor should take account of the eclipse phenomenon in planning measurement missions.