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V. Carruba, J.A. Burns, W. Bottke (Cornell University), A. Morbidelli (Obs. de la Cote D'Azur)
Until recently the dynamical evolution of small bodies through the asteroid belt was predicted through Monte Carlo codes based on Öpik approach, using the method implemented by Arnold.
Dones et al.(1999), however, showed that, as suspected for a decade, the Öpik code is actually unable to reproduce the results of direct numerical simulations whenever resonances or very close encounters with planets or massive asteroids were present. To gain further insight, they suggested to check Öpik simulations by performing direct integrations of at least a few particles for as long as possible.
In this work we tried to evaluate the semimajor axis mobility of asteroids due to encounters with Ceres, Pallas, and Vesta by comparing a direct numerical simulation obtained by Morbidelli and Nesvorny against analogous results of an Öpik code. We studied whether the two methods give quantitative similar results. Morbidelli et al. used a Mercury simplectic integrator to compute the change in proper orbital elements of 300 asteroids, that we further subdivided in two subgroups, one of which lies in a region populated by strong resonances.
We ran our code for t=10,20,...90 Myr and then calculated the standard deviation of the spread in semimajor axis of the objects in both simulations. The Öpik code predicts smaller values of standard deviation as t increases, as compared with numerical simulations, with a time dependence which is approximately 2 times that predicted by direct integrations.
While no conclusive results yet emerge from this work, there are some indications that in regions far from resonances the Öpik code may provide useful hints about dynamical evolution of asteroid families.
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