Tidal evolution by elongated primaries: Implications for the ida/dactyl system

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, contrary to estimates based on the likely age of the asteroid itself (~ 1 byr). 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.