On the consequences of a fragmentation due to a NEO mitigation strategy

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 of 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 achieved for the Apophis test case