  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 Myr. The resonances are confirmed by direct
integration of the equation of motion in the vicinity of end-points. 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 $\pi$) and sidewise ($\pi/2$)
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.

Earth and Planetary Astrophysics