QueerMike
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The nukes would be crude, but wouldn't be the wisest. Instead of dealing with one object to track, you'd then have thousands of objects to track. Any object that is more than 35 meters across wouldn't burn up in the atmosphere, so then there could be several impacts.
There are other alternatives, such as sending a spacecraft to collide with the asteroid thereby deflecting it (kinetic impact), or using a "gravitational tractor" (essentially a spacecraft's thrusters) to push it away via gravitation.
You don't think the nukes would change the trajectory enough of an asteroid 30 years away?