[Previous] | [Session 21] | [Next]
C.F. Chyba (SETI Institute and Stanford University), P. J. Thomas (U. Wisconsin, Eau Claire)
Planets and satellites in the Solar System despin to a spin-evolved end-state due to tidal dissipation. The usual derivation for the despinning timescale sets the change in spin angular momentum equal to to the gravitational torque acting on the object’s tidal bulge (MacDonald 1964, Goldreich and Soter 1966, Peale 1974, 1977). The despinning timescale is found to be proportional to the difference between the initial and final spin angular velocities, and is finite. However, this approximate derivation ignores the orbital mean motion n of the despinning object, and is less and less satisfactory as the object’s spin angular velocity w approaches n. We have instead calculated tidal despinning times by applying the formalism of Peale and Cassen (1978) to calculate tidal energy dissipation due to tides raised on a non-spin-locked object. Tidal heating in the latter case is larger than tidal heating in the spin locked case by a factor (1/7)[(w-n)/n](1/e2), where e is the orbital eccentricity. This factor is initially greater than 104 for many objects in the Solar System. Calculating despinning times from energy loss, we find that the despinning timescale includes a previously neglected term that goes to infinity logarithmically as w approaches n. In this sense all despinning timescales are in fact infinite. We therefore define an effective despinning timescale as the time required for despin tidal heating to fall below tidal heating due to orbital eccentricity. For many satellites in the Solar System, including such major moons as Io and Europa, the neglected term in the despinning timescale is in fact the dominant term. For some especially short-period satellites, such as Phobos or Amalthea, the resulting despinning timescales are one to two orders of magnitude longer than those previously accepted.
The author(s) of this abstract have provided an email address for comments about the abstract: chyba@seti.org