The U.S. Air Force actually considered detonating a nuclear device on the moon in the 1950s. Known as Project A119, the single explosion would have had little impact on the Moon.

In a CNN interview, Leonard Reiffel, one of the physicists on the project, was asked what it would take to actually “do some damage” or even push the Moon out of orbit. He said that we don’t actually have enough nuclear weapons to get anywhere close to doing that. It would likely take something on the order of 10 trillion megatons of TNT to move the Moon, maybe 10 billion to do some serious damage.
The 70s television show Space: 1999 was built around the concept of a nuclear accident sending the Moon off into space. Of course, it was all very silly, and it just couldn’t happen like that.
We don’t really know enough about the Moon’s radioactivity. It’s exposed to cosmic rays and the Sun’s radiation, and there is no protection as with Earth. NASA sent the Lunar Reconnaissance Orbiter in 2009, and one of its tasks is to characterize the radiation environment of the Moon. Detonating nuclear weapons would be unlikely to increase radiation levels to any great degree.

To be honest, it would be like throwing peanuts at a whale.
The W88 warheads deployed on Trident II submarine-launched missiles have an estimated yield of 475 kilotons. That’s a somewhat upper average nuclear explosive used in a casual nuclear style monday apocalipse. We could say that’s the norm.
Of course there are also stronger ones, but if we’re in need of more than just a few, this will do.
Okay. Let’s start with something with a warm-up.
One such W88 on the way.
3…
2…
1…
And boom.
Did you see it?
Oh. You expected something like this?

Too bad. No you got more like a teeny-tiny bright on the moon. Meh…
Let’s go bigger.
10 such things on the bright side.
3… 2… 1… Boom. Caught it this time? Still no? Maybe with a better telescope.
Go big or go home.
100 of those beauties would definitely inflict serious damage on any city, and probably country you hit it with… 47.5 Megatons TNT of rough, untempered power. Almost as much as the Tsar explosive

You got to have seen it this time.
It was ginormous. Maybe with some good binocular?
Good. At least it hasn’t gone to waste.
That’s still not enough though.
1000 of those beauties should do the trick, shouldn’t they?
Don’t forget it costs the average taxpayer a awful lot of money to pay for this, but at least it’s worth it.
And Kaboooooom.
Wait until all the dust has settled.
Nice. We can see it pretty easily this time with the bear eyes.
475 MT of TNT. Could certainly destroy a large part of the US and most of Europe.
Unfortunately, besides a large, very large crater, it hasn’t done too much damage to the lunar orbit.
OMG, Fuck it. Launch them all. 14000 Nuclear Explosives to the moon. Apocalypse level destruction…
Forget the sound. There is none in space. Noone can hear you.
Yayy… Finally… We modified the lunar trajectory…
By almost 1 meter :O
Besides that, serious damage to the lunar surface.
Aren’t the russians our new friends too?
Let them join the party, and get China, and the other Nuclear friends too…
Currently, world wide, there’re about about 35k nuclear bombs active…. Holy mother of god…
About 16625 MT of TNT.
According to Ian Atkin, this ain’t enough to do serious damage to the moon. Huh… We can on the other hand definitely cancel that pesky Santa Clause forever. Go for North Pole. Go team Apocalypse.
