  While almost all potentially hazardous asteroids (PHAs) with a size larger
than one kilometre have been discovered, it is well-known that the vast
majority of the smaller ones are in fact yet to be found. There is therefore an
excellent motivation to consider at once all possible Earth-crossing orbits,
and to undertake a systematic study of mitigation missions for the entire
parameter space of orbital elements. It is shown that the whole parameter space
can be reduced, without loss of generality, to only three relevant
dimensionless parameters: the eccentricity and inclination of the asteroid
orbit, and the asteroid true anomaly at impact. Ballistic kinetic-impactor
mitigation missions are studied for the entire parameter space, considering
critical feasibility constraints such as the launcher performance and the
illumination conditions at deflection. Different classes of optimal solutions
are found to exist and can be directly linked to asteroid orbital properties.
The aim of this work is to help identify an appropriate response to the
potential threat of a collision of a near-Earth object with our planet, to
provide a preliminary mission design, and to determine in which parts of
parameter space difficulties may arise. (abridged)
