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 the Apophis from the Earth in 2036 is analyzed. Some correction strategies are investigated: by one-two impulsive short-term effects (impact-kinetic and nuclear ones) 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 case of the long-term correction, there is studied a slow gravity influence by a special controlled spacecraft SC, which is placed near the asteroid and corrects the asteroid orbit by the SC attraction. The effect time and fuel mass consumption for the SC motion control are presented depending on the initial time of the correction, the asteroid deflection from the Earth, the SC mass and its distance from the Apophis, the exhaust velocity for the SC jet engines.

Theoretical and applied problems of mechanics