Go away asteroid nobody likes you!

IN class we learned how impossible diverting a asteroid with a nuke truly is. My idea also involves missiles but in a completely different way. NASA needs to create a rocket that is tough enough to strike a asteroid and not blow up. this is so that the missile can embed itself into the asteroid.  This rocket would then use its thrusters to push against the asteroid to change its collision coarse. Also in the movie there may have been a lot of problems with the physics but possible the biggest problem was that one nuke isn't strong enough to get the job done. they couldn't of brought more nukes because of storage space, this is the beauty of my idea. If on rocket isn't enough then we can just send more. It may cost a pretty pennie but so what its better then dying.