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The Yarkovsky Effect - Part 5 of 7

W.K. Hartmann et al. (1999) Reviewing the Yarkovsky effect: New
light on the delivery of stone and iron meteorites from the asteroid
belt (MAPS 34, 1999, A161-A167, excerpts + summary):

A Nonlinear Problem Of Collisional Evolution

As Rubincam (1995a) noted briefly, Yarkovsky drift in semimajor axis may
not be continuous, because collisions may change the rotation rates and
spin axes on timescales less than the removal time for such bodies.
The rate of reorientation by collisions depends directly on the number
density and size distribution of smaller objects. To estimate the number
density of small objects, Farinella et al. (1998) extrapolated
Dohnanyi's (1969) equilibrium size distribution to small sizes and found
that collisions would completely reorient meter-scale bodies on
timescales of several million years, and at the same time would spin
them up to much shorter periods (tens of seconds) than the 5 h assumed
by Peterson (1976). However, as noted by Hartmann and Ryan (1996),
Yarkovsky effects may remove small (sub-meter) bodies efficiently and
change these results; if the belt is significantly depleted in small
bodies, then both the reorientation rates and the erosion rates could
drop drastically among the meter-scale fragments. This would lengthen
the mean free path between collisions, increasing the chance of direct
drift to resonances from a given starting point, rather than a slower
random walk.
In general, the question of random walk to a resonance vs. direct drift
depends on the flux of smaller impactors, which controls the rate of
change of rotation states. In any case, the stone meteorites tend to
move about faster than iron meteorites in the size ranges we have
considered, but the stone meteorites' survival depends again on the flux
of small eroding impactors.
Unlike Peterson and other authors, we do not assume that small bodies
have the mean rotation period of 5 h measured for large asteroids but
rather assume (from our lab work and from common experience) that small
fragments generated by collision rotate much faster. (Following
Farinella et al., 1998, we adopt P = 5 h x (D/1 km), which is 18 s for a
1 m body. This has been nicely confirmed by the recent discovery of the
ca. 10 min spin period of the 40 m near-Earth asteroid 1998 KY26 (see
Ostro et al., 1998). Also, the ca. 50 cm Lost City fireball had a spin
period of 3.3 s according to Ceplecha (1996).
Yarkovsky effects can move meteorite-scale fragments across
characteristic belt distances to a resonance on timescales comparable to
the observed CRE ages. In other words, decameter- to meter-scale
fragments can easily drift in the main belt for tens of million years
for stone meteorites and hundreds of million years for iron meteorites.
Drift rates are faster for stone but iron meteorites have collisional
lifetimes much longer than stone meteorites, so they can move farther
before being disrupted.

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