I've heard the claim that a nuclear weapon used on an asteroid on it's way to earth wouldn't help the situation because it would create thousands of smaller asteroids. But, my question is this: isn't a lot of small asteroids a *lot* better than one big one?
Only if they are really small, like you commented below. We've discussed the hazard of blowing them up here: Re: Blowing up asteroids?
Afterall, most meteors burn up in the atmosphere before they hit the earth. Assuming that any meteor smaller than a volkswagon burns up in the atmosphere without harming anything on the ground, why wouldn't a thousand volkswagon-sized asteroids be better than one big asteroid that's so big that it actually hits the earth?
In keeping with another topic discussed on the show I will be pedantic. The original diameter of an asteroid broken into a thousand Volkswagen sized pieces would be 10 times the diameter of a Volkswagen. A small but horrifying asteroid, say 200 meters in diameter, would need to be broken into about 300,000 pieces to get that Volkswagen atmospheric benefit. But reading the PopSci article Steve discussed it would seem a large asteroid could be nuked and most pieces, big and small, would miss the Earth entirely.
Also, even if there are asteroid fragments large enough to hit the earth, wouldn't most of them still be small enough that they wouldn't, for example, cause a large tsunami like a large asteroid would?
You can plug in the numbers and select an impact target, including water and water depth, into the Earth Impact Effects Program
and it will return tsunami height (at the very bottom). The minimum possible impact velocity for the Earth is 11.2 km/s. The tsunami wave height coming ashore needs to be corrected for shoaling.
Also, wouldn't the kinetic energy of an nuclear weapon dramatically change the velocity of quite a few of those asteroids - causing them to miss the earth entirely?
A potential Earth impacting asteroid that comes from the main asteroid belt would need have its velocity changed while at aphelion by 0.2 meters/sec to miss the Earth on its next swing. The PopSci article didn't mention calculated velocity changes but given the discussion of escape velocity of the pieces I would assume it is more than sufficient.
Hey, welcome to the forum!