Pulsed control of a dangerous asteroid in the domain of 1:1 resonance

The paper investigates the possibility of pulsed control of an asteroid approaching the Earth. The control scheme is fixed — this is a two-pulse flight with a gravitational manoeuvre near the Earth. The purpose of the first pulse is to correct the approach to the Earth. With the help of a gravitational manoeuvre, the asteroid is transferred to an osculating heliocentric orbit with a period close to the period of the Earth's revolution around the Sun. The purpose of the second pulse is to transfer the asteroid to an osculating orbit, the period of rotation of which makes long-period fluctuations near the period of the Earth. An approximate method for evaluating the feasibility of a flight is proposed. Two examples are considered: the asteroids Apophis 2004 MN4 and Duende 2012 DA14.