Hyperion: Rotational Dynamics

• Published in: Icarus (New York, N.Y. 1962) Vol. 117; no. 1; pp. 149 - 161
• Main Authors: Black, G.J., Nicholson, P.D., Thomas, P.C.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.09.1995
• ISSN: 0019-1035; 1090-2643
• DOI: 10.1006/icar.1995.1148

We have numerically integrated the full three dimensional rotation of Hyperion using as initial conditions the moments of inertia, pole position, and spin rate from a solution based on fitting control points, limb, and terminator positions in high-resolution Voyager 2 images (P. C. Thomas et al. 1995, Icarus ). These images were taken over a 38-hr period and cover ∼114° of rotation. From this solution, it is found that at the time of the Voyager 2 encounter (23 August 1981) the instantaneous spin axis was tilted ∼60° from the orbit normal and was roughly aligned with the axis of minimum moment of inertia. In addition, the instantaneous spin rate is found to have been 72° +3 -4 per day, or about 4.2 times the synchronous rate. The integrated dynamical model using this solution provides an excellent fit to the lightcurve obtained from earlier low resolution Voyager 2 images, whereas a fit assuming a constant rotation pole and spin rate clearly does not. The largest amplitude component in the lightcurve is due to the free precession (wobble) rather than to the rotation itself. Previous work by J. Wisdom, S. J. Peale, and F. Mignard (1984, Icarus 58, 137-152) showed that it was likely that Hyperion would be in a chaotically tumbling state, and groundbased observations by J. J. Klavetter (1989, Astron. J. 97, 570-579; 98, 1855-1874) in 1987 could not be explained by any simply periodic rotation and are consistent with a chaotic state. Although Hyperion's rotation state is indeed formally chaotic, with the shortest Lyapunov time on the order of the orbital period or less (J. Wisdom et al. 1984, Astron. J. 94, 1350-1360), the short-term motion of the spin axis in 1981 appears "quasi-regular," undergoing forced precession with a period of ∼300 days and wobbling with a period of ∼7 days. Our integrations show that the unusual spin state seen by Voyager 2 can persist for several thousand years, although the chaotic nature of the motion limits the predictability of our model to less than 1 year. Longer integrations indicate that rapid spin states such as that observed by Voyager are a natural consequence of the chaotic motion and are easily reached by states initially in or near the synchronous spin-orbit state. There is thus no need to invoke a recent event, i.e. a large impact, to produce the observed state.