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47. Collisional model of asteroids and their debris

Published online by Cambridge University Press:  14 August 2015

J. S. Dohnanyi
J. S. Dohnanyi*
Affiliation:
Bellcomm, Inc., Washington, D.C., U.S.A.

Abstract

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A collisional model for interplanetary debris, formulated earlier by the writer, is applied presently to the problem of asteroids and their debris. Following observational evidence, a population-index type-number density function is assumed. The integro-differential equation describing the evolution of a system of colliding brittle particles derived earlier is satisfied for this special case. The result is a stable steady state solution subject to certain boundary conditions. It is found that catastrophic collisions dominate over the erosion process in the present steady state model.

Using a root mean-squared average collision velocity of 5 km/sec, the population index, α, for asteroids is calculated to be α = 1·837. This value of α is rather insensitive to the physical parameters and is within the margin of error of an empirical least squares fit by the writer α = 1·80 ± ·04 to the distribution of asteroids reported by Kuiper et al. If the largest three asteroids are statistically interpreted, the distribution of asteroids in the asteroidal belt is consistent with the present collisional model. This would imply that most asteroids are fragments from some parent object(s).

The theoretical distribution is normalized to the observed number of asteroids in the survey by Kuiper et al., and using the present theory various statistical properties of the population of asteroids and their debris are calculated. The total mass of objects in the asteroidal belt is almost entirely concentrated in the masses of the three largest objects. The total asteroidal mass, crushed yearly, is of the order of 1012 kg and the rate of mass loss to radiation forces is about 7 × 1010 kg/yr.

The mean lifetime of large asteroids is found to be of the order of 108–109 years. The lifetime of objects is limited by the probability of catastrophic collisions; erosion and radiation damping only have a minor influence on the particle lifetimes.

The erosion rate of the largest objects is of the order of 1m /106 yr, and this rate decreases for smaller objects. Comparison with erosion rates estimated by Whipple indicates that the lifetimes, with respect to erosion, of objects smaller than about 1 kg may be dominated by collisions with cometary particles.

Type
Session 8
Information
Symposium - International Astronomical Union , Volume 33: Physics and Dynamics of Meteors , 1968 , pp. 486 - 503
Copyright
Copyright © Reidel 1968 

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