Some results in a study of the hazard mitigation problem for the possible Apophis-Earth collision are presented in the paper. There are given the characteristics of the Apophis nominal orbit and of a “tube” of its trajectories that is defined by the errors of the observations and by the errors of the orbit determination, as well as the characteristics of a set of the asteroid’s trajectories from this “tube” that collide with the Earth in 2036 with the kinetic energy of ~ 800 MT TNT. The necessary correction of the asteroid orbit to deflect Apophis from the Earth in 2036 is analyzed in the paper. Some correction strategies are investigated: by one-two impulsive short-term effects and by slow long-term ones. It is shown that the correction is desirable to be performed before the asteroid-Earth approaching in 2029. In this case, the energy consumption for the correction will be less considerably than after this approaching. For the impulsive case, parameters of the impact-kinetic effect and of the nuclear one are estimated. For the case of the long-term correction, there is studied a slow gravity influence by a special controlled spacecraft, which is placed near the asteroid and corrects the asteroid orbit by the spacecraft attraction.

Theoretical and applied problems of mechanics