Long-term orbit dynamics of decommissioned geostationary satellites

In nominal mission scenarios, geostationary satellites perform end-of-life orbit maneuvers to reach suitable disposal orbits, where they do not interfere with operational satellites. This research investigates the long-term orbit evolution of decommissioned geostationary satellite under the assumption that the disposal maneuver does not occur and the orbit evolves with no control. The dynamical model accounts for all the relevant harmonics of the terrestrial gravity field at the typical altitude of geostationary orbits, as well as solar radiation pressure and third-body perturbations caused by the Moon and the Sun. Orbit propagations are performed using two algorithms based on different equations of motion and numerical integration methods: (i) Gauss planetary equations for modified equinoctial elements with a Runge-Kutta numerical integration scheme based on 8-7th-order Dorman and Prince formulas; (ii) Cartesian state equations of motion in an Earth-fixed frame with a Runge-Kutta Fehlberg 7/8 integration scheme. The numerical results exhibit excellent agreement over integration times of decades. Some well-known phenomena emerge, such as the longitudinal drift due to the resonance between the orbital motion and Earth's rotation, attributable to the J(22) term of the geopotential. In addition, the third-body perturbation due to Sun and Moon causes two major effects: (a) a precession of the orbital plane, and (b) complex longitudinal dynamics. This study proposes an analytical approach for the prediction of the precessional motion and show its agreement with the (more accurate) orbit evolution obtained numerically. Moreover, long-term orbit propagations show that the above mentioned complex longitudinal dynamics persists over time scales of several decades. Frequent and unpredictable migrations toward different longitude regions occur, in contrast with the known effects due only to the perturbative action of J(22).