An asteroid impact by 10km asteroid on the Earth is widely viewed as an extinction-level event, likely to cause catastrophic damage to its existing biosphere. There is also a threat of impacts by comets falling into the inner Solar System after having been disturbed from their orbits in the "Oort Cloud", a huge, tenuous sphere of comets surrounding the Solar System. Such "long period" comets are only infrequent visitors into the inner Solar System and they do not generally fall in orbits in the same plane as that of Earth, but there is nothing to rule out the possibility that one might collide with the Earth. The impact velocity of a long-period comet would likely be several times greater than that of a near-Earth asteroid, making it much more destructive.
One might propose firing nuclear missiles at incoming asteroids would solve the problem, but it can be easily demonstrated that the energy required to destroy a 1km wide asteroid would be much larger than the energies available from nuclear explosives.
A more promising idea is to explode smaller nuclear devices alongside the asteroid. Providing this was done well in advance, a small deflection from a nuclear blast would be enough to alter the orbit and avoid an Earth impact. In 1968, students at the Massachusetts Institute of Technology designed a system using nuclear explosions to prevent a hypothetical impact on the earth by the asteroid Icarus. This design study was later published as the Icarus Project.
However, NASA scientist Dan Durdan has argued that if an asteroid was of low density and high porosity, it would be more likely to absorb the energy from a stand-off explosion, rather than be deflected. Although 1950DA is dense, many other asteroids in the Solar System were found to be of low density and high porosity, and therefore could not be deflected in this way.
In addition, deflecting an asteroid impact requires that the asteroid be identified years before impact.
Cynics suggest that nuclear scientists are simply trying to find new excuses to keep nuclear missiles around, and to keep 'improving' them, as their careers have been endangered since the end of the Cold War.
Researcher Jay Meloch has proposed that it may be possible to deflect the orbit of an asteroid by focusing solar energy on its surface. This would create a small thrust from the resulting vaporisation of material, which over time would be enough to deflect any incoming asteroids, regardless of their density and porosity. Such a 'solar collector' is not as far fetched as it sounds, as the US military have already launched satellites designed to collect and focus radio waves.