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Yes, but at this point it would be cheaper and quicker to have spacex fly to orbit, capture a 5 ton rock and drop it on a city.
There's a reason Iran has been 'weeks' from making a bomb for decades now.
That would be a really shitty nuke. Like around 10% of a Davy Crockett.
Use a bigger rock. I might change the cost by hundreds of millions, and still be less than the billions in development and production for a nuke.
Where do you get these rocks though? There is actually a similar concept that uses tungsten rods instead of rocks.
But the entire thing isn't really practical. If you want the ability to strike any place on earth in a reasonable time, you'd to have hundreds of tungsten rod equipped satellites (or rocks with rocket engines attached to them) in orbit at the same time.
I'm not sure it would actually be cheaper than just using nukes on ballistic missiles.
The expense of a delivering the nuke is negligible in comparison to the cost and effort of building a nuke. So much so, that large rocks are more economical than building a nuke at this point.
Building nukes isn't that expensive. The most expensive part is probably building the enrichment facilities, but that's a one-time investment. Once you have all the material, a nuke isn't that complicated to build. A bunch of students basically designed one that was deemed to be functional.
On the other hand, launching hundreds, possibly thousands of multi-ton projectiles into orbit is extremely expensive. And of course you have to maintain them in space somehow, possibly for decades. Either that or you have to de-orbit and replace them, which would mean regularly bombarding the ocean or some desert ...
It's just not practical. Even if it was I highly doubt it would be cheaper.