Our first paper on this subject was published in the July 2000 issue of Icarus. Electronic reprints are available here (your site needs to have a subscription to IDEAL). The revised preprint is still available below.
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There is increasing evidence that many km-sized bodies in the Solar System are self-gravitating piles of rubble instead of monolithic slabs of rock. For example, the NEAR rendezvous with Mathilde revealed an asteroid with a surprisingly low bulk density (1.3 g/cc) and a remarkable number of giant craters. Hydrocode simulations suggest that solid bodies would have been completely destroyed by impacts that made such craters. Mathilde's low bulk density implies it may be porous, perhaps a pile of rubble, and can therefore absorb impacts more effectively by confining the collision energy to a small zone near the impact site. The asteroids 243 Ida and 951 Gaspra, as well as the martian moon Phobos, also have large craters.
We have performed a series of simulations to investigate what happens
when two rubble piles collide. We use a hard-sphere model for our
rubble piles so we are restricted to the low-speed regime where
impacts are gentle enough not to actually crush the rock. This may be
appropriate for the early stages of planet formation, for example. Follow the links
below to see stills and animations
from our experiments. The simulations were carried out on a 16-node
cluster of Intel Pentium IIs using a modified version of
pkdgrav, created at the N-Body Shop. We find
that our rubble piles are relatively easy to disperse, even at low
impact speed, suggesting that greater dissipation is required if
rubble piles are the true progenitors of protoplanets. This work has
been submitted as a paper to Icarus;
the (revised) preprint is available
below.
| Model A | Equal size, no spins |
| Model B1 | Equal size, opposite spins |
| Model B1x | Bonus B1 results |
| Model B2 | Equal size, same spins (retrograde) |
| Model B3 | Equal size, same spins (prograde) |
| Model C | Unequal size, no spins |
These experiments involved impactors of 1 km radius and 2 g/cc bulk density (except Model C where one impactor was 0.5 km in radius). The dissipation parameter (coefficient of restitution) was fixed at 0.8, i.e. 20% dissipation. The impact parameter b is measured in units of the sum of the impactor radii, so b = 0 means a head-on collision and b = 1 means a grazing collision. The encounter speed v is in units that depend on the binding energy. For Models A and B the unit is 2.1 m/s; for Model C it's 2.9 m/s. Remember to click on the thumbnails for animations!
Rubble piles can also be disrupted and distorted by planetary tides. Check it out!
We are in the process of studying crater formation in rubble piles. Stay tuned!
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This material has been published in Icarus 146, 133-151 (2000), the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Academic Press. This material may not be copied or reposted without explicit permission.
Direct N-Body Simulations of Rubble Pile Collisions
Copyright © 2000 by Academic Press. Available through IDEAL.
Zoë
M. Leinhardt, Derek C. Richardson, and Thomas
Quinn
University of Washington
Revised Jan 7, 2000
31 manuscript pages including 3 tables
9 figures including 1 in color
ABSTRACT (plain text)
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| Last modified: Oct 9, 2000 |
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