# Thread: Calculating the mass of an impactor sufficient to fragment the Moon

1. ## Calculating the mass of an impactor sufficient to fragment the Moon

So, Roland Emmerich has a new movie coming out...

Wait come back!

Look, yes it's as stupid as its other ones, but I lack the mathematical ability to determine exactly how stupid.

It's based on a novel called Moonfall which is about an interstellar comet hitting the Moon and causing it to fragment. The fragments then hit the Earth, cue standard Emmerich plotline.

So. Kinda stupid. But exactly how stupid? The gravitational binding energy of the Moon is 1.2 x 10^29 joules, which is arguably not the final number but still pretty close, given that we're only asking for, well, bits to come off.

The fastest any object in our galaxy has ever been recorded travelling is 8 percent the speed of light, which was around SgrA. In our neck of the woods, what's the highest speed we could expect?

Finally, exactly how big would this impactor have to be to get the, ahem, ball rolling, as it were?

2. I put in 100 miles for an impactor's diameter in this impact calculator, which provided that 72 km/sec was the largest speed for an impactor within the solar system. Of course, this is an Earth Impact Effects Calculator, but certain results should be the same, like the energy before atmospheric entry: 1.70 x 1028 Joules. I'm not sure about the moon, but I was a bit surprised that "The Earth is not strongly disturbed by the impact" with such parameters.

3. So the mass you want is just 2E/v2.
Apparently we can expect rare lunar impact velocities of up to 70km/s for stuff coming in from the Oort. So that's about 5x1019kg to give a kinetic energy equal to the binding energy you give. So something a little smaller than a dwarf planet.

The novel on which the movie was based is a good read. McDevitt has never been strong on physics, but he tells a good story.

Grant Hutchison

4. ## Calculating the mass of an impactor sufficient to fragment the Moon

Criminey. I just read the plot summary on IMDB. It says the impactor event a mysterious force knocks the moon from its orbit and puts it on a collision course with Earth. Hilarity ensues.

I like the fragments idea better.

5. In any case, movie physics has always violated simple conservation laws. I don't really see why a lunar impactor that violates conservation of energy is any more stupid as a plot device than the traditional shotgun blast that violates conservation of momentum.

Grant Hutchison

6. So, suppose that some asteroid had long ago been ejected from the Arcturus system. It could have, depending on which side of the Sun's orbit it collided with the Moon a relative velocity of 160 or so km/sec, plus another 30 or so gained by falling into the Sun's gravity well. I think if that asteroid had a diameter of 150 km, it would just about do the job.

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Didn't we calculate the size of an object that created the Tyco(?) crater in another thread recently?

8. Originally Posted by bknight
Didn't we calculate the size of an object that created the Tyco(?) crater in another thread recently?
Copernicus.

Grant Hutchison

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Originally Posted by grant hutchison
Copernicus.

Grant Hutchison
Yes now my short term memory has been rejuvenated. Now if it took a rock 9 km to create Copernicus then the required size would have been larger or the speed of 72 kps (OP estimation) seems to break up the moon as the "crater" diameter would be ~1400 km over 50% of the Lunar diameter ~3475 km. Chunks would very likely be knocked apart. Now the Moon has been around for ~4.5 by so something of this size speed would be relatively rare. Nut that is a back of the envelope calculation on my part.

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Would much actually hit earth? Or would we simply have rings like saturn?

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