[Previous] | [Session 12] | [Next]
T.A. Hurford, R. Greenberg (LPL)
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 [Weidenschilling 1989], contrary to estimates based on the likely age of the asteroid itself (~ 1 byr) [durda 1996]. We investigate whether the problem may be due to the conventional formula 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. While this model is far from perfectly realistic, it is at least as meaningful as applying the conventional formulae for a spherical planet to something so very different from that geometry. 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. The difference between the evolution rate from the two models (a factor < 2), is less then the uncertainty regarding basic physical parameters.
Petit \emph{et al.} (1997) have identified stable orbits that are resonant with Ida's rotation. Dactyl may be trapped into one of these orbital resonances. We confirm that Dactyl's tidal evolution is rapid enough to shift Dactyl's period significantly over its lifetime, thus allowing it an opportunity to be trapped in one of these resonances.
[Durda 1996] Durda, D.D., The Formation of Asteroid Satellites in Catastrophic Collision, \emph{Icarus} \textbf{120}, 212-219, 1996
[Weidenschilling 1989] Weidenschilling, S.J., P. Paolicchi, V. Zappala, Do Asteroids have Satellites?, in Asteroids II, Edited by Binzel, Gehrels, Matthews, pp. 643-658, 1989
[Petit 1997] Petit, J-M, D.D. Durda, R. Greenberg, T.A. Hurford, P.E. Geissler, The Long-Term Dynamics of Dactyl's Orbit, \emph{Icarus} \textbf{130}, 177-197, 1997