  The growth of the population of space debris in the geostationary ring and
the resulting threat to active satellites require insight into the dynamics of
uncontrolled objects in the region. A Monte Carlo simulation analyzed the
sensitivity to initial conditions of the long-term evolution of geostationary
spacecraft near an unstable point of the geopotential, where irregular behavior
(e.g., transitions between long libration and continuous circulation) occurs. A
statistical analysis unveiled sudden transitions from order to disorder,
interspersed with intervals of smooth evolution. There is a periodicity of
approximately half a century in the episodes of disorder, suggesting a
connection with the precession of the orbital plane, due to Earth's oblateness
and lunisolar perturbations. The third-degree harmonics of the geopotential
also play a vital role. They introduce an asymmetry between the unstable
equilibrium points, enabling the long libration mode. The unpredictability
occurs just in a small fraction of the precession cycle, when the inclination
is close to zero. A simplified model, including only gravity harmonics up to
degree 3 and the Earth and Moon in circular coplanar orbits is capable of
reproducing most features of the high-fidelity simulation.
