Study of Integration Schemes Suited for the Long-Term Extrapolation

Abstract : This paper is focused on the integration methods for the orbit extrapolation on the long term time. This issue is of importance when it comes to choosing the graveyard orbit during the orbit design process for a space mission. In this paper, classical and geometric integration schemes will be discussed and compared on LEO (Low Earth Orbit) cases. We will give a particular interest to the variational scheme, in the last chapter, since this geometric integrator has the property of preserving the geometry of the problem like symplectic schemes but, contrary to symplectic integrators, it can be also used in case of non conservative dynamics.