Influence of Earth's shadowing effects on space debris stability

► We show that Earth's shadows make chaotic the geostationary orbit of space debris with high area-to-mass ratios. ► We compare adapted conical and cylindrical Earth's shadowing models. ► We symplectically integrate both Hamiltonian equations of motion and variational equations. ► We propose a new method to compute efficiently the Mean Exponential Growth factor of Nearby Orbits criterion. ► We discuss the choice of symplectic integration scheme.