The fragmentation of an Earth threatening asteroid as a result of a hazard mitigation mission is examined in
this paper. The minimum required energy for a successful impulsive deflection of a threatening object is
computed and compared with the energy required to break-up a small size asteroid. The fragmentation of an asteroid that underwent an impulsive deflection such as a kinetic impact or a nuclear explosion is a very plausible outcome in the light of this work. Thus a model describing the stochastic evolution of the cloud of fragments is described. The stochasticity of the fragmentation is given by a Gaussian probability distribution that
describes the initial relative velocities of each fragment of the asteroid, while the size distribution is expressed
through a power law function. The fragmentation model is applied to Apophis as illustrative example. If a barely
catastrophic disruption (i.e. the largest fragment is half the size the original asteroid) occurs 10 to 20 years prior
to the Earth encounter only a reduction from 50% to 80% of the potential damage is achieve for the Apophis test
case
