Periodic Orbits Around a Satellite Modelled as a Triaxial Ellipsoid

摘要

There are planetary satellites, particularly Phobos, which can be modeled s triaxial ellipsoids. To study orbital dynamics of a mass near such a satellite, Hamilton's canonical equations are developed and used to numerically evaluate the existence of periodic orbits around the satellite. Calculations were also done to check the stability of these orbits by evaluating the Poincare exponents. For Phobos, periodic orbits were found in Phobos's orbital plane from near the surface to beyond Phobos's sphere of influence. None of these orbits were found to be stable. Discussion of these orbits includes a bifurcation region caused by nearby inclined orbits. These inclined orbits appear as Lissajous figures with frequency ratios of two. Though the inclined orbits are numeric solutions they all pass below Phobos's surface at the anti-Mars point and are of only academic interest.