Genealogy and stability of periodic orbit families around uniformly rotating asteroids

Resonance orbits around a uniformly rotating asteroid are studied from the approach of periodic orbits in this work. Three periodic families (denoted as I, II, and III in the paper) are fundamental in organizing the resonance families. For the planar case: (1) Genealogy and stability of Families I, II and the prograde resonance families are studied. For extremely irregular asteroids, family genealogy close to the asteroid is greatly distorted from that of the two body-problem (2BP), indicating that it is inappropriate to treat the orbital motions as perturbed Keplerian orbits. (2) Genealogy and stability of Family III are also studied. Stability of this family may be destroyed by the secular resonance between the orbital ascending node's precession and the asteroid's rotation. For the spatial case: (1) Genealogy of the near circular three-dimensional periodic families are studied. The genealogy may be broken apart by families of eccentric frozen orbits whose argument of perigee is “frozen” in space. (2) The joint effects between the secular resonance and the orbital resonances may cause instability to three-dimensional orbital motion with orbit inclinations close to the critical values. Applying the general methodology to a case study - the asteroid Eros and also considering higher order non-spherical terms, some extraordinary orbits are found, such as the ones with orbital plane co-rotating with the asteroid, and the stable frozen orbits with argument of perigee librating around values different from 0°, 90°, 180°, 270°.