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.

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

PAOLICCHI, PAOLO
1994

Abstract

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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/229343
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