Scattering of trajectories of hazardous asteroids

Early detection of possible collisions of asteroids with the Earth is necessary to exept the asteroid-comet hazard. Many collisions associate with resonant returns after preceding approaches. The difficulty of collisions prediction is associated with a resonant returns after encounters with the Earth due to loss of precision in these predictions. On the other hand, we can use the fly-by effect to avoid hazardous asteroid from collision. The main research object is the asteroid Apophis (99942), for which we found about 100 orbits of possible impacts with the Earth and more than 10 - with the Moon. It is shown that the early (before 2029) change of the Apophis orbit allows to avoid all main impacts with the Earth in 21st century, associated with resonant returns, and such a change of the orbit, in principle, is feasible. The scattering of possible trajectories of Apophis after 2029 and after 2051, as well as 2015 RN35 and other dangerous objects, is discussed.