Dynamical lifetimes and final fates of small bodies: Orbit integrations vs Opik calculations

The dynamical lifetimes of small bodies against ejection from the Solar System or collision with the Sun or a planet are often estimated by Monte Carlo codes based on the equations of Opik and using a method implemented by Arnold. Such algorithms assume that orbital changes are dominated by close encounters, and that successive encounters are uncorrelated, We have compared the results of an Opik code (H. J. Melosh and W. B, Tonks, Meteoritics 28, 398 (1993)) and a fast integrator (H, F. Levison and M, J, Duncan, Icarus 108, 18 (1994)) to investigate the regimes of validity of the Opik-Arnold approach, We investigate the transfer of ecliptic comets from Neptune-crossing orbits to observable Jupiter-family comets, the dynamics of Halley-type comets, and the transport of meteorites among the terrestrial planets, In all cases, the Opik code overestimates the median lifetime of the small bodies, although both codes show a rapid initial loss of objects followed by a slow decay, For martian impact ejecta, some of which find their way to Earth as the SNC meteorites, the Opik code substantially overestimates lifetimes because of its neglect of secular resonances, which rapidly pump eccentricities (B, J, Gladman ed at, Science 271, 1387 (1996)). (C) 1999 Academic Press.