Three ways of deflecting an asteroid:

* Nuclear blast: A large nuclear explosion on an asteroid might be enough to deflect an asteroid but has significant political and ethical problems. And what if we just blew it into smaller pieces?

* Using mirrors: A fleet of spacecraft carrying light-reflecting mirrors might be able to vapourise the asteroid's surface using the Sun's rays. The gases from its surface would create a tiny amount of thrust - enough to divert it

* Gravity tractor: Crashing a spacecraft into the asteroid's surface would certainly be the cheapest option. The ship's own tiny gravity would then help move the asteroid's path. But this option would take a long time to make a difference.