On predictability of motion of asteroids passing through the Hill sphere for Earth

This paper describes the problems arising in the study of the orbital motion of asteroids that pass through the Hill sphere for Earth. The studies have shown that 432 asteroids pass through the Hill sphere for Earth during the time interval of about 190 years. For each of them the evolution of the MEGNO parameter was constructed on this interval. It is shown that the motion of most of these objects becomes unpredictable after passing through the Hill sphere for Earth.