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T.A. Hurford, R. Greenberg (LPL, Univ. of Arizona)
Classical tidal theory addresses the effect a tidal potential has on a spherical body, and thus has been applicable to most planetary bodies for which tidal amplitudes and torques are of interest. However, tides in highly elongated, irregular bodies are also of interest, especially as some evidently have satellites. The Ida/Dactyl system is one example. It is not obvious that general results from classical tidal theory apply to these elongated bodies. For example, the age of asteroid 243 Ida's satellite Dactyl is < 100~myr according to the conventional formula for the rate of tidal evolution outward from Ida [1], contrary to estimates based on the collisional lifetime of the asteroid itself (~ 1 byr) and the likelihood that Dactyl formed at the same time [2]. We investigate whether this discrepancy may be due to the conventional formula for tidal evolution being based on a spherical primary, whereas Ida is actually highly elongated. A model for Ida consisting of three spheres connected by damped springs is used to estimate what effects the elongation may have on the tidal dissipation. In fact, our model gives torques and energy dissipation similar to that in an equivalent sphere, indicating that the spherical model gives reasonable results even when applied to an elongated or irregular body. Some subtleties of tidal theory for spherical bodies will be discussed as well.
[1] Weidenschilling, S.J., P. Paolicchi, V. Zappala, Do Asteroids have Satellites?, in Asteroids II, Edited by Binzel, Gehrels, Matthews, pp. 643-658, 1989
[2] Durda, D.D., The Formation of Asteroid Satellites in Catastrophic Collisions, \emph{Icarus} \textbf{120}, 212-219, 1996