Dynamics around non-spherical symmetric bodies: II. the case of a prolate body

Abstract

Dynamic exploration around non-spherical bodies has increased in recent decades due to the interest in studying the motion of spacecraft orbits, moons, and particle ring around these bodies. The dynamic structure around these objects is defined by regular and chaotic regions. The Poincare surface of section technique allows mapping these regions, identifying the location of resonances, and the size of regular and chaotic zones, thus helping us to understand the dynamics around these bodies. Using this technique, we map in the a-e space the stable and unstable regions around ellipsoidal bodies, such as the dwarf planet Haumea, the centaur Chariklo, and other five hypothetical bodies, in which we keep part of the physical parameters of Haumea but we varied its period of rotation and ellipticity, to analyse the impact of these alterations in the extensions of the stable and unstable regions due to first kind orbits and spin-orbit type resonances. We identified a large region of stability, in semimajor axis and eccentricity, due to the first kind orbits. Periodic orbits of the first kind are present in a large semimajor axis interval for all considered systems and have almost zero eccentricity, while resonant and quasi-periodic orbits have high eccentricities. Furthermore, we identified the bifurcation of the 2:6 resonance when there is a spin reduction of a body with the same physical parameters as Haumea. This bifurcation generates a chaotic region, reducing the extension of the stability zone.