Spin–orbit resonances of high-eccentricity asteroids : regular, switching, and jumping

Few solar system asteroids and comets are found in high-eccentricity orbits (e > 0.9), but in the primordial planetesimal disks and in exoplanet systems around dying stars such objects are believed to be common. For 2006 HY51, the main belt asteroid with the highest known eccentricity 0.9684, we investigate the probable rotational states today using our computer-efficient chaotic process simulation method. Starting with random initial conditions, we find that this asteroid is inevitably captured into stable spin–orbit resonances typically within tens to a hundred megayears. The resonances are confirmed by direct integration of the equation of motion in the vicinity of endpoints. Most resonances are located at high spin values above 960 times the mean motion (such as 964:1 or 4169:4), corresponding to rotation periods of a few days. We discover three types of resonance in the high-eccentricity regime: (1) regular circulation with weakly librating aphelion velocities and integer-number spin–orbit commensurabilities, (2) switching resonances of higher order with orientation alternating between aligned (0 or π) and sidewise (π/2) angles at aphelia and perihelia, (3) jumping resonances with aphelion spin alternating between two quantum states in the absence of spin–orbit commensurability. The islands of equilibrium are numerous at high spin rates but small in parameter space area, so that it takes millions of orbits of chaotic wandering to accidentally entrap in one of them. We discuss the implications of this discovery for the origins and destiny of high-eccentricity objects and the prospects of extending this analysis to the full 3D treatment