The Rotation of Irregularly Shaped Natural Satellites in the Solar System

Löeger, Thomas and Firneis, Maria G. (2006) The Rotation of Irregularly Shaped Natural Satellites in the Solar System. In: 4th Austrian-Hungarian Workshop on Celestial Mechanics Edited by Á. Süli, F. Freistetter, A. Pál. Publications of the Astronomy Department of the Eötvös University (18). ELTE Sokszorosítóüzeme, Budapest, pp. 47-60.

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Abstract

The temporal evolution of the rotational motion along with the attitude of a set of irregularly shaped small planetary satellites is studied. For this problem a computer application was developed featuring an FFT implementation scalable in terms of the available computer hardware optimized for fast execution, performed by reducing the amount of mass-storage operations with the aid of an adaptive multi-buffer cache strategy. Every satellite is modelled as a homogenous triaxial ellipsoid precessing under the torque of the main body. For a set of eight satellites the evolution of their spin-angular velocity vectors is numerically tracked using non-singular matrix differential equations. Calculations were carried out with a 4th order Runge-Kutta algorithm using a grid of 1620 different initial conditions for the attitudes of the satellites. An FFT was applied to the results to observe, whether the spin axis tumbles chaotically in conjunction with chaotic rotation, or if the obliquity and the spin angular velocity remains constant or changes periodically for certain initial conditions. It is shown that for each satellite investigated a regular rotation is possible for spin axes with an obliquity near zero degrees. Other stable regions exist for each satellite as well. For Proteus, a satellite of Neptune, the stable region is maximally extended of all objects investigated.

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