This paper presents an analysis of optimal impact strategies to deflect potentially dangerous asteroids. In order to compute the increase in the minimum orbit intersection distance of the asteroid due to an impact with a spacecraft, simple analytical formulae are derived from proximal motion equations. The proposed analytical formulation allows for an analysis of the optimal direction of the deviating impulse transferred to the asteroid. This ideal optimal direction cannot be achieved for every

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... asteroid at any time, therefore an analysis of the optimal launch opportunities for deviating a number of selected asteroids was performed through the use of a global optimization procedure. The results in this paper demonstrate how the proximal motion formulation has very good accuracy in predicting the actual deviation and can be used with any deviation method since it has general validity. Furthermore the characterization of optimal launch opportunities shows how a significant deviation can be obtained even with a small spacecraft. * Lecturer Ph.D., Department of Aerospace Engineering, James Watt (South Building), m.vasile@eng.gla.ac.uk, AIAA Member. † Ph.D. Candidate, Department of Aerospace Engineering, James Watt (South Building), camilla.colombo@strath.ac.uk, AIAA Student Member. Subscripts   d = value calculated at the instant the deviation maneuver is performed   MOID = value calculated at the Minimum Orbit Interception Distance