Optimal trajectories for the impulsive deflection of near earth objects

With the current technological level it is possible to deflect an asteroid such as 99942 Apophis in case its orbit refinement reveals an unacceptable collision risk. Thanks to the solution of an ad hoc defined global optimisation problem we show that a pre-keyhole deflection is possible even with a simple spacecraft and with a very late launch in 2026. We also give a mathematical description of the trajectory optimisation problems that have to be faced in the case of a more generic asteroid deflection mission defining analytically the objective function, that is the displacement in the encounter bb-plane of the asteroid uncertainty ellipsoid.