Regular and chaotic motion of high altitude satellites

We have computed the integrated autocorrelation function for different families of geosynchronous, inclined orbits in order to detect the regions of chaotic motion. In order to reduce the problems due to high eccentricity orbits, the logarithmic Hamiltonian regularization was applied and a symplectic integrator of the Wisdom–Holman type was implemented. The orbits were integrated for an interval of 10,000 days. The results indicate that non-predictable orbits can be found in this relatively short time in the separatrix zone of the 1:1 tesseral resonance. Their chaotic nature results from the interchange between libration and circulation type of motion, and from the significant eccentricity growth, caused by the Kozai–Lidov resonance. Some of these orbits intersects the Earth’s surface in time shorter than 20 years for a particular initial geometry of interacting bodies.