Rushing to equilibrium: A simple model for the collisional evolution of asteroids

Details Rushing to equilibrium: A simple model for the collisional evolution of asteroids Rushing to equilibrium: A simple model for the collisional evolution of asteroids

Dec 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994p%26ss...42.1093p&link_type=abstract

Planetary and Space Science (ISSN 0032-0633), vol. 42, no. 12, p. 1093-1097

Mathematics

11

Asteroids, Collisions, Equilibrium Equations, Evolution (Development), Mass Distribution, Mathematical Models, Differential Equations, Stability

Scientific paper

A simple mathematical model for the evolution of a system of collisionally interacting bodies -- such as the asteroid population -- consists of two coupled, nonlinear, first-order differential equations for the abundances of 'small' and 'big' bodies. The model easily allows us to recover Dohnanyi's value (11/6) for the exponent of the equilibrium mass distribution. Moreover, the model shows that any initial value for the ratio of 'big' to 'small' bodies rapidly relaxes to the equilibrium ratio, corresponding to the 11/6 experiment, and that integrating the evolution equations backward in time -- an attractive possibility to investigate the mass distribution of primordial planetesimals -- leads to strong numerical instability.

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