Phase space structure around planetary satellites

Resumen

Hill's equations can be used for approximating the dynamic behavior around many celestial bodies. When considering also the perturbation due to the non-sphericity of the central body, the model closely reproduces the real dynamics of an orbiter around planetary satellites. Classically, the long-term behavior of this problem is studied by averaging techniques. The double averaged problem is integrable, but it presents a symmetry of direct and retrograde inclination orbits that does not exist in the original problem. We use Lie transforms to reduce the problem to an integrable one, performing the transformations up to third order where the inclination symmetry is broken. Then, the proper use of the double reduced space, which is a sphere, allows us to make a full description of families of frozen orbits and their bifurcations. We identify saddle-center and pitchfork bifurcations related to stable, frozen orbits. Finally, for the specific case of a Europa orbiter, we relate the equilibria of the reduced problem with periodic solutions of the non-averaged problem in a synodic frame. Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.