The impact of Earth's shadow on the long-term evolution of space debris

Direct solar radiation pressure and Earth's shadow crossings are known to be responsible for short-term variations of space debris orbital elements, the higher the area-to-mass ratio the larger the perturbation. Nevertheless, existing studies have always been performed on periods of time shorter than 150 years. Considering longer time scales of the order of a 1000 years, this paper focuses on the long-term periodic evolution of space debris trajectories caused by successive Earth's shadow crossings. Other perturbations as the geopotential and third-body gravitational attractions obviously play a role and compete with the one which is described in this paper. Symplectic numerical propagations and new (semi-)analytical models are developed to identify a frequency associated to shadow entry and exit eccentric anomalies. It is shown that Earth's shadow is responsible for large deviations from the initial orbital elements, even on shorter period of times, and that this effect increases along with the area-to-mass ratio.