Long-term evolution of Galileo operational orbits by canonical perturbation theory

• We model the 5:3 tesseral resonance affecting Galileo with an integrable intermediary.
• We derive a Hamiltonian describing the long-term behavior of orbits in MEO region.
• Numeric experiments show the influence of the value moon's RAAN minus Galileo's RAAN.
• Tests carried out with Draper DSST confirm predictions with the long-term Hamiltonian.

Galileo operational orbits are slightly affected by the 3 to 5 tesseral resonance, an effect that can be much more important in the case of disposal orbits. Proceeding by canonical perturbation theory we show that the part of the long-term Hamiltonian corresponding to the non-centralities of the Earth's gravitational potential can be replaced by an intermediary that shows the pendulum dynamics of the 3 to 5 tesseral resonance problem. Inclusion of lunisolar perturbations requires a semi-analytical integration, which is compared with the corresponding results from the well-established Draper Semi-analytical Satellite Theory.