**DPS Meeting, Madison, October 1998**

*Session 21. Planetary Formation and Dynamics*

Contributed Oal Parallel Session, Tuesday, October 13, 1998, 2:00-3:40pm, Madison Ballroom D.
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## [21.06] Tidal Despinning Timescales in the Solar System

*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/e^{2}), where e is the orbital
eccentricity. This factor is initially greater than 10^{4}
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

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