Stability of equatorial satellite orbits

We study satellite orbits lying in the equatorial plane of a planet via the geometric methods of the theory of dynamical systems. To model the planetary gravitational potential, we expand it to the sixth zonal harmonic. The motion equations are regularized by means of McGehee-type transformations of the second kind. Naturally considering the motion to be collisionless and escapeless, we take into account the whole interplay among field parameters, total-energy level and angular momentum. This gives rise to various phase-portraits. In the most general case as regards the changes of sign of parameters, we meet: saddles generating simple or double homoclinic loops, double loops inside one loop of a larger double loop, centers surrounded by periodic and quasiperiodic trajectories, heteroclinic orbits, etc. Of course, less general cases lead to simpler phase portraits. Every type of phase orbit is translated in terms of physical motion. Such qualitative results are useful to the analysis of circumplanetary motion of major or infinitesimal satellites, rings, etc