Luni-solar resonances and effect on long-term evolution of inclined geostationary transfer orbits

In this paper, a singly-averaged, semi-analytical orbital dynamic model in terms of Milankovitch elements is given for geostationary transfer orbits (GTOs), which includes the Earth's oblateness, luni-solar perturbations, atmospheric drag and solar radiation pressure (SRP). The orbital dynamic model is verified through a numerical simulation compared with the Semi-analytic Tool for End of Life Analysis software (STELA) by CNES. We find that if the area-to-mass ratio of the object is relatively large, the SRP will have a significant impact on the long-term evolution of GTOs. Then, the long-term dynamical evolution and orbital resonances of rocket upper stages in inclined geostationary transfer orbits (IGTOs) are studied. It has been found that the luni-solar secular resonances, which are inclination-dependent-only, play a leading role in the long-term evolution of IGTOs. By comparing and analyzing long-term dynamical evolution of orbits with different initial inclinations, the effects of luni-solar secular resonances are studied in details. Finally, a mitigation method for IGTO objects by utilizing luni-solar secular resonances is proposed, in which the eccentricity growth caused by the resonances is used for an early atmospheric re-entry.