Analysis of Possible Changes of the Orbit of an Asteroid Approaching the Earth by Impact of a Spacecraft

As a part of analysis of guarding against the Earthʹs collision with an approaching asteroid we investigate the influence of kinetic impact of a spacecraft on the orbit of this asteroid. For an orbit of the Toutatis asteroid, the global analysis of asteroid deflections (caused by the spacecraft impact) is carried out in the Earthʹs picture plane, depending on the spacecraft flight time and the moment of a spacecraft arrival to the asteroid. Locally optimal (with respect to the asteroid deflection) spacecraft trajectories are determined. The influence of the spacecraft initial mass on the limiting size of an asteroid, which is deflected from the Earth to a safe distance, is examined. The principal possibility of employing modern rocket-space systems for the spacecraft impact to prevent the Earth from colliding with an asteroid of a medium size is demonstrated.