Astronomy and Astrophysics – Astronomy
Scientific paper
Mar 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994p%26ss...42..207p&link_type=abstract
Planetary and Space Science (ISSN 0032-0633), vol. 42, no. 3, p. 207-211
Astronomy and Astrophysics
Astronomy
5
Asteroids, Astronomical Models, Collision Parameters, Evolution (Development), Mass Distribution, Protoplanets, Stability, Differential Equations, Mathematical Models, Measure And Integration
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 exponent, 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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