Dynamical evolution and collisions of asteroids with the earth

We study the dynamical evolution of asteroids which are a potential danger for collisions with the Earth. The work is undertaken on basis of a simplified model of the planetary system including the perturbations from Venus to Saturn. For a whole grid of initial conditions (0.7⩽a⩽1.45 and 0.1⩽e⩽0.8) we integrated the equations of motion with the Lie-series integration for 0.5 Myrs for 720 fictitious objects. The analysis of the data provided the following results: (a) the dynamical evolution for such objects which are initially in four different groups namely Subatens, Atens, Apollos and Amors (b) the flow between these groups and (c) the individual collision probabilities.