A secular integrator for asteroid fragments

Abstract

This work is a byproduct of the proper element program by Lemaitre and Morbidelli ( Celest. Mech., submitted, 1993). The Hamiltonian of the problem (massless asteroid perturbed by Jupiter and Saturn) is averaged with respect to the mean longitudes of both the asteroid and the planets, and is coded in a new grid directly in Arnold action-angle variables. These are the most suitable ones in order to take into account the strongly nonlinear dynamics related to the motion of the argument of perihelion, which is dominant at large inclination. Only the three main terms, corresponding to the three main secular resonances v 5, v 6 and v 16, are retained in the perturbation. The averaged equations of motion are integrated directly in action-angle variables. Therefore this secular integrator turns out to be very fast (30 s for 1 million years on a HP710 workstation). However, owing to the simplifications of the model, the results are not quantitatively accurate, albeit preserving the main features of the real dynamics. So, this secular integrator is very suitable for statistical studies on the behaviour of thousands of fictitious objects, such as simulated fragments of real asteroids, in order to study the dynamical mechanisms of meteorite transport.