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J. Kadish, J.R. Barber, D.J. Scheeres, P.D. Washabaugh (Univ. of Mich.)
The terrestrial planets, asteroids, and comets all formed by the accretion of solid planetesimals. The maximum spin of these objects is determined from their stress fields and failure criterion. The typical elasticity analysis cannot be used to determine the stress fields of accreted bodies because it does not account for the manner in which the body was constructed (e.g. Holsapple, Icarus 154).
We have analytically determined the explicit stress field of an accreted, triaxial ellipsoid whose spin rate varies during the accretion process using linear, small deformation theory. In the resulting stress field a state of residual stress is present for all time; if the object were stopped spinning and gravity ``turned off", then a non-zero state of stress would still exist in the body.
We find that the effective strength of the object (parameterized by its maximum spin) is significantly affected by its growth history. Assuming that an accreted body's spin is constant during its growth and using a no-tension failure criterion, its effective strength can be as much as 21.2% higher than that of a non-accreted body and can be as much as 13.0% higher if the Mohr-Coulomb failure criterion is used with friction properties of sand or gravel.
Dones and Tremaine (Icarus 103) showed that an object's spin is not necessarily constant during accretion. Using physical data on asteroids and comets, their model allows us to characterize differences in the growth histories of comets and asteroids. From this we find that asteroids can have an effective strength up to 45% higher than that of comets, after accounting for density differences. This could explain why the spin rates of comets are relatively slow as compared to asteroids.
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Bulletin of the American Astronomical Society, 36 #4
© 2004. The American Astronomical Soceity.