Abstract: In this paper, we consider the trajectories of real and model asteroids that lead to collisions with Earth. They highlight the close approaches to Earth that precede impact. The presence of such approaches allows us to detect a dangerous object in advance, clarify its orbit, and use the effect of a gravitational maneuver to economically prevent an asteroid from hitting Earth. In the paper we consider various families of collision trajectories: possible trajectories of real dangerous asteroids, as well as model trajectories that are not linked to a specific object. It is shown that in the first case, the approaches preceding the collision are noticeably greater.