So earlier today, Neil Tyson posted an estimate of the mass of Mjölnir, (http://en.wikipedia.org/wiki/Mj%C3%B6lnir)  assuming that it's made out of neutron star matter. And  followed up with a calculation of how big a crater it would leave if Thor dropped it. (http://goo.gl/ZYlqS) But I'm afraid this calculation left something out, because while the hammer (if dropped from a height of 10 meters) would only be travelling at 14 meters per second or so when it hit the ground, it turns out that a mass of 300 billion elephants (about 2.1*10^14 kilograms, or roughly the mass of enough dirt to cover Texas a foot deep) hitting the ground at that speed will make a bit of a bang.

Specifically, it will have a kinetic energy of about 2.1*10^16 Joules, or just over 5 megatons.

(For comparison, that's about the bang you would get from a 42,500 ton meteorite hitting the Earth – one about six times the size of the one that detonated over Chelyabinsk a few days ago – or from a single W-71 thermonuclear bomb)

But OK, just how much is five megatons? What would that do?

We can't compare this to the burst of a nuclear bomb, because bombs (by their nature) create large shells of supersonically expanding gas which fly into the air – that's how they blow things up – whereas this dumps all its energy into the ground. (If you do want to know how large explosions work, then you should look at the Nuclear Weapons FAQ, nuclearweaponarchive.org, perhaps the greatest nonclassified source in the world for understanding things that go "boom") Instead, it's probably best to compare this to an earthquake. Fortunately, the Richter scale is effectively a log scale of energy deposition, so we can make at least a rough guess of the intensity by using that.

The moment magnitude scale for earthquakes (one of the more modern improvements to the Richter scale – http://en.wikipedia.org/wiki/Moment_magnitude_scale) is actually even better, because it directly measures energy dumped into the ground. Using the definition of that, we find that the resulting earthquake would have a moment magnitude of 4.8. Since the Moment and Richter scales were calibrated to match at 5.0, that's about a 4.8 on the Richter scale, too.

But before you go saying "oh, that's not too bad," remember that most earthquakes are a bit more spread out than the size of the average hammer. Rupture areas are normally hundreds of square miles, not less than a square meter. And earthquakes generally go off at least somewhat underground, not right at the surface. So to get a more realistic estimate, we should instead compare this to meteor impacts.

There are a couple of ways to estimate crater sizes, and here's a handy website which runs through them: http://pirlwww.lpl.arizona.edu/~jmelosh/crater_c.cgi . You can just feed in the info; assuming that Mjolnir has a radius of about half a meter, and that it's striking a target of rock (as opposed to loose dirt), you find out that over the next 200 milliseconds, it's going to form a crater with a rim-to-rim diameter of about 21.7 miles.

Boy. It's a good thing he didn't drop it from any higher than that.﻿
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