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The cumulative effects of weak resonant and secular perturbations by themajor planets produce chaotic behavior of asteroids on long timescales.Dynamical chaos is the dominant loss mechanism for asteroids with diameters D >10 km in the current asteroid belt. In a numerical analysis of the long termevolution of test particles in the main asteroid belt region, we find that thedynamical loss history of test particles from this region is well describedwith a logarithmic decay law. In our simulations the loss rate function that isestablished at t = 1 My persists with little deviation to at least t = 4 Gy.Our study indicates that the asteroid belt region has experienced a significantamount of depletion due to this dynamical erosion - having lost as much as ~50%of the large asteroids - since 1 My after the establishment of the currentdynamical structure of the asteroid belt. Because the dynamical depletion ofasteroids from the main belt is approximately logarithmic, an equal amount ofdepletion occurred in the time interval 10-200 My as in 0.2-4 Gy, roughly ~30%of the current number of large asteroids in the main belt over each interval.We find that asteroids escaping from the main belt due to dynamical chaos havean Earth impact probability of ~0.3%. Our model suggests that the rate ofimpacts from large asteroids has declined by a factor of 3 over the last 3 Gy,and that the present-day impact flux of D > 10 km objects on the terrestrialplanets is roughly an order of magnitude less than estimates currently in usein crater chronologies and impact hazard risk assessments.

Dynamical erosion of the asteroid belt and implications for large impacts in the inner solar system