Dynamical Lifetimes and Final Fates of Small Bodies: Orbit Integrations vs Öpik Calculations

San Jose State University Foundation, NASA/Ames 245-3, Moffett Field, California, 94035, .eduf1; Observatoire de Nice, Departement Cassini, BP 229, Nice Cedex 4, 06304, France; Lunar and Planetary Laboratory, University of Arizona, Tucson, Arizona, 85721; Department of Physics, Ricks College, Rexburg, Idaho, 83460; Southwest Research Institute, 1050 Walnut St, Suite 426, Boulder, Colorado, 80302; Department of Physics, Queen's University, Kingston, Ontario, K7L 3N6, Canada
Icarus 01/1999; DOI: 10.1006/icar.1999.6220

ABSTRACT 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 Öpik 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 Öpik code (H. J. Melosh and W. B. Tonks, Mete-oritics28, 398 (1993)) and a fast integrator (H. F. Levison and M. J. Duncan, Icarus108, 18 (1994)) to investigate the regimes of validity of the Öpik–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 Öpik 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 Öpik code substantially overestimates lifetimes because of its neglect of secular resonances, which rapidly pump eccentricities (B. J. Gladman et al., Science 271, 1387 (1996)).

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