  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 gravity field at
the 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 J22 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 shows
its agreement with the 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 J22 perturbation.
