Planar Orbits about a Triaxial Body: Application to Asteroidal Satellites

Abstract

We have studied the dynamical behavior of a small satellite of a strongly triaxial primary rotating about a principal axis of inertia, restricting ourselves to the planar case (satellite orbits lying in the "equatorial" symmetry plane of the primary). Since we were mainly interested in applying the results to the dynamics of(natural and artificial) asteroidal satellites, we have studied in detail the case of a triaxial ellipsoidal primary, with axial ratios 2:1: 1/2 and rotation periods ranging from 5 to 40 hr. We have employed the classical method of Poincaré's surfaces of section to display the results of numerical integration experiments, showing in particular how the triaxial shape of the primary "perturbs" the dynamics of the Kepler problem seen in the rotating reference frame where the primary is fixed. We have found that a sizeable chaotic zone appears near the 1/1 resonance between the rotation period of the primary and the orbital period of the satellite. Another smaller chaotic zone includes the retrograde orbits passing close to the primary and corresponding to initial velocities close to the escape velocity. The chaotic zones become larger and larger for shorter rotation periods of the primary. However, regular orbits staying close to the primary do also exist, some of them being locked by resonant effects. Finally, we have identified the most suitable orbits for an artificial satellite of an asteroid (or a comet), subject to the requirements of being close (though non-collisional), of avoiding strongly chaotic behavior, and of being weakly affected by the (a priori unknown) asteroidal mass distribution.