Abstract
In this paper it is explained how most of asteroids can avoid very close approach to Jupiter, to the earth for earth orbit crossing asteroids, and to Neptune for Kuiper-belt asteroids by mechanisms which work also for Neptune-Pluto system. In fact the mutual distance of the planets cannot become very small as the critical argument librates around $180^{\circ}$ because of 2:3 mean motion resonance and the argument of perihelion of Pluto librates around $90^{\circ}$. And it is found that among nearly 40 Kuiper-belt asteroids discovered in recent years $40\%$ have orbits similar to Pluto. For main-belt asteroids the distribution with respect to the semi-major axes has peculiar characteristics and the author tries to explain how their peaks and gaps are created. It is also found that $30\%$ of 80 earth orbit crossing asteroids which have minimum perihelion distances less than 1.04AU have no chance to collide with the earth. Still $30\%$ of them have a few probability to collide with the earth as they have dynamical characteristics of short-periodic comets.