HYPERION - ROTATIONAL-DYNAMICS

We have numerically integrated the full three dimensional rotation of Hyperion using as initial conditions the moments of inertia, pole posi tion, and spin rate from a solution based on fitting control points, l imb, and terminator positions in high-resolution Voyager 2 images (P. C. Thomas et al. 1995, Icarus). These images were taken over a 38-hr p eriod and cover similar to 114 degrees of rotation. From this solution , it is found that at the time of the Voyager 2 encounter (23 August 1 981) the instantaneous spin axis was tilted similar to degrees from th e 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 degrees(-4)(+3) per day, or about 4.2 times the synchronous r ate. The integrated dynamical model using this solution provides an ex cellent fit to the lightcurve obtained from earlier low resolution Voy ager 2 images, whereas a fit assuming a constant rotation pole and spi n rate clearly does not. The largest amplitude component in the lightc urve is due to the free precession (wobble) rather than to the rotatio n itself. Previous work by J. Wisdom, S. J. Peale, and F. Mignard (198 4, Icarus 58, 137-152) showed that it was likely that Hyperion would b e in a chaotically tumbling state, and groundbased observations by J. J. Klavetter (1989, Astron. J. 97, 570-579; 98, 1855-1874) in 1987 cou ld not be explained by any simply periodic rotation and are consistent with a chaotic state. Although Hyperion's rotation state is indeed fo rmally chaotic, with the shortest Lyapunov time on the order of the or bital 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-regul ar,'' undergoing forced precession with a period of similar to 300 day s and wobbling with a period of similar to 7 days. Our integrations sh ow that the unusual spin state seen by Voyager 2 can persist for sever al thousand years, although the chaotic nature of the motion limits th e 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 produc e the observed state. (C) 1995 Academic Press, Inc.