Spin-orbit resonances of prolate asteroids and minor planets at high eccentricity (e > 0.9)

Minor celestial bodies of prolate shape in the Solar system and extra-solar systems may orbit their hosts with very high eccentricity (e > 0.9). The close pericenter passages result in impulse-like bursts of triaxial torque, which change the spin rate about the principal axis of inertia in a chaotic manner. In the course of millions such interactions, the body inevitably acquires high prograde spin rates. We discovered the existence of tiny islands of stable dynamical equilibrium for our prototype asteroid 2006 HY51 with e = 0.9684 at spin rates higher than 960 times the mean motion, i.e., rotation periods shorter than 1.6 days. We performed 512 random-seeded trials of chaotic rotation simulations of 2006 HY51 for 1 Gyr each and found that all of them ended in one of the high spin-orbit resonances. We detected two types of resonances: a regular one with a permanently fixed mean rate of rotation, and a new type of jumping resonance with the spin rate switching between two fixed quantum states. Long-term stability of these high-eccentricity resonances in the presence of external perturbations is a matter of future theoretical and observational investigation.