About 65 million years ago, the world of dinosaurs was destroyed by an asteroid about 10 km wide. Such size of an asteroid can have global effects because of the debris it ejects on the powerful impact. It can spread dust clouds over the entire planet and block out sunlight from reaching the surface causing a catastrophe.
There are over 24,000 near-earth objects detected until now which pose a serious threat to us. One great example of this is the ‘Chelyabinsk meteor’(20m wide), which entered the Earth’s atmosphere over Russia on 15th February 2013. It exploded in the air about 30km high and was brighter than the Sun for a brief moment. The shockwave generated by this blast injured over 1400 people and damaged around 7200 buildings in 6 cities in the region.
Bomb an Asteroid
Send an explosive rocket system onto a trajectory that meets the asteroid in its path and then detonate the explosives causing the asteroid to blow up. This will turn the asteroid into a rubble pile but if the explosion is not massive enough, the gravitational attraction between these new fragments can still pull everything together. And now we will have an asteroid rain instead of an asteroid hitting the surface in one place.
Attach a rocket to an asteroid
This involves placing the rocket propulsion on the surface of the asteroid and changing its trajectory just enough such that it misses the earth and flies past it. This is considering that the asteroid is completely a solid body and not collective fragments in which case, the rocket systems can only push one fragment that it is attached to. Even if the asteroid is a complete body, It rotates around its center of mass and so the rocket attached to its surface will be rotating with it making it more complicated to propel it in the desired direction in the required time.
Using Gravity Tractor
One clever way is to use the gravitational attraction between the spacecraft and asteroid to move it away from the path to the collision. Park the spacecraft near an asteroid instead of landing on its surface, the gravity pulls both these objects together but the spacecraft with thrusters onboard can counter this force and ultimately only the asteroid moves towards the spacecraft pulling it out of the collision trajectory.
Put a Reflective layer on the asteroid
Cover the surface of the Asteroid with a highly reflective foil such that the side facing towards the sun will have a large number of photons of light impacting the asteroid and reflecting back into space. This will create an equal and opposite force on the asteroid forcing it to move away from the Sun and essentially changing its trajectory of collision with earth.
Using Powerful Lasers
Lasers can be used as a powerful weapon against incoming asteroids. The idea is to point the laser on the surface of the asteroid and obliterate it at a point opposite to which it needs to be propelled. This point ejects debris into space and as an equal and opposite reaction to this, the asteroid moves away from its trajectory. The only requirement is to have powerful enough laser systems which we currently do not have.
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