10% of lunar mass impacting earth.

[LordShaithis]

Saw that movie The Time Machine (the new one) and in it, mankind accidentaly shatters the moon with a twenty megaton nuke, causing chunks of it to rain down and destroy civilization.

I really don't buy a nuke that small shattering the moon, but so be it. Anyway, my question for you geniuses in the field of mass destruction is this:

If a chunk of rock with mass one-tenth that of the moon were to strike the earth, moving with only the momentum supplied by earth's gravity, how much kinetic energy would be imparted and what would the effect be on civilization?

The movie didn't show the actual impact of any large moon chunks, so I'm using ten percent as a rough guess at the mass of the largest single one, and discounting all the smaller pieces. I'm also assuming that the puny nuke mentioned in the movie wouldn't supply any appreciable momentum.

[Wicked Pilot]

If a chunk of rock with mass one-tenth that of the moon were to strike the earth, moving with only the momentum supplied by earth's gravity, how much kinetic energy would be imparted and what would the effect be on civilization?

Civilization? What civilization?

[Master of Ossus]

It would devastate the Earth, perhaps destroying unstable civilizations, or ones that had grown dependent on certain aspects of the environment. It would also depend on whether the section of the moon hit land or an ocean. It would NOT be enough to wipe out life on Earth.

[Durandal]

That depends. We don't know how the chunks scattered. And, as cool as the special effect of the shattered moon in the sky was, there's no way that a 20 megaton nukes would do what we saw.

However, just for fun...

The moon's mass is approximately 7.35E22kg. 10% of this is 7.35E20kg. The moon orbits the Earth at a distance of approximately 3.8E7m. The Earth is approximately 6.4E6m in radius with a mass of 5.97E24kg. The moon is roughly 1.5E6m in radius. This puts the distance between their centers of gravity at roughly 4.6E7m. This gives the 1/10 of the moon about -2E30J of potential energy relative to the Earth. When it reaches the surface of the Earth (r~6.4E6m), it will have -1E32J of potential energy. That means that it has converted about 5E30J of potential energy into kinetic energy. This would give it a velocity of about 82km/sec upon impact.

This assumes that the chunk was in one piece, and it neglects the velocity imparted to it by the nuke. I get the feeling I've made a mistake somewhere, but who knows? I may just be right. :)

[Durandal]

Yup I did make a mistake. The mass figure for the moon fragment should be an order of magnitude higher, but you should still get the idea. Adjust all derived figures by plus one order of magnitude.

[Asst. Asst. Lt. Cmdr. Smi]

5E31 joules? I think that could reshape the earth into a totally different shape. Can it?

[His Divine Shadow]

5E31 joules? I think that could reshape the earth into a totally different shape. Can it?

Heck thats nearly enough to overcome the Earths gravitational binding energy.

[Durandal]

Yes, but as I said before, the distribution is what counts. If the fragments were small enough, they'd simply burn up in the atmosphere. However, I'm inclined to think that that much mass burning in our atmosphere would release tremendous amounts of heat (granted, some of it would go into space).

Also, there would be a noticeable effect on the movement of tides, as well. High tide and low tide would be different heights and occur at different times.

If all the mass hit the ocean, you'd have a gigantic tsunami, probably a few large scale earthquakes, as well.

[Captain Hornblower]

Thats about 7E14 megatons!

[Captain Hornblower]

Or about 9000 kg of matter/anti-matter annhilation.

[LordShaithis]

Wait, wait, wait... SEVEN HUNDRED TRILLION MEGATONS!??!?! So if we're going to rationalize the movie at all, we'll have to assume that the biggest single hit measured a fuck of a lot less than ten percent of the total lunar mass. Otherwise there wouldn't be any more human beings 800,000 years later.

Hats off to Durandal for doing the calcs, and a general question: Even if we assume the moon had some sort of ENORMOUS fault line for the nuke to break, would it fall to earth? Unless I'm way off the mark, wouldn't simple gravity hold it together anyway, since 20 megatons is NOTHING compared to the gravitational binding energy?

[Darth Wong]

Actually, I couldn't come up with the same numbers Durandal did. I ended up with a figure two orders of magnitude smaller. Consider the facts: 5E31 J for a 1/10 moon fragment of 7E21 kg mass would be nearly 7E9 J/kg. However, you only need 6E7 J/kg to achieve escape velocity. In other words, the GPE figure is two orders of magnitude above the energy requirement to escape Earth's gravity entirely, which doesn't make any sense.

The mass of the moon is 7.35E22 kg. The mass of Earth is 5.97E24 kg. The orbital radius of the Moon's orbit is roughly 382,000 km (3.82E8 m). The mass of one tenth of the moon is 7.35E21 kg, and the orbital radius at time of impact (assuming one tenth radius) would be roughly 6550 km (6.55E6 m)

Newton's law is that GPE is -G*(M1)*(M2)/r, where G = 6.67E-11 for SI units. Therefore, the GPE of one tenth of the moon at time of impact is -4.47E29 J. The GPE of one tenth of the moon in normal orbit would be -7.67E27 J. Therefore, the change in GPE would be 4.39E29 J: roughly two orders of magnitude down, as expected.

I don't mean to be a nitpicker or anything, but two orders of magnitude is, well, two orders of magnitude.

[LordShaithis]

I think that when I become King of Earth, I'm going to keep Darth Wong on hand so I can ask him silly questions like this.

"What would happen if you turned off the world's gravity? Would it fly apart? What would happen if we put the world's biggest nuke into the San Andreas fault and set it off? What would happen if I put a cubic centimeter of anti-neutronium in Uranus?"

[AdmiralKanos]

I think that when I become King of Earth, I'm going to keep Darth Wong on hand so I can ask him silly questions like this.

"What would happen if you turned off the world's gravity? Would it fly apart? What would happen if we put the world's biggest nuke into the San Andreas fault and set it off? What would happen if I put a cubic centimeter of anti-neutronium in Uranus?"

I'm not letting you near anyone's anus.

[LordShaithis]

To go off on a tangent, nice pic. Transformers the Movie was the fucking bomb. I made sure to run out and get the DVD. :)

[LordShaithis]

I bet anti-neutronium would clear out one's bowels.

[Durandal]

I cannot fucking believe that I forgot to multiply by G (6.67E-11). I knew that figure was too high. Fuck fuck fuck. That's what I get for posting after burning my brain out on studying for a final.

So, yes Mike, you're right.

[Captain Hornblower]

ok, so its only 6.27E13 million megatons

[DasBastard]

Quasi-off topic:

How the fuck did a 20-megaton bomb blow the moon apart? A ~1e17J detonation just may just be insufficient to overcome the moon's ~2e29J gravitational binding energy.

In terms of force, the remaining moon will exert roughly 1.7e22N of gravititational force on the 10% fragment, while Earth will exert roughly 2.0e19N on the 10% fragment (note than I am assuming that the fragment is directly between the earth and the remainder of the moon).

This means that, for small distances, every meter the fragment moves towards Earth and away from the rest of the moon, its total GPE will increase by ~1.7e22J. Conservation of energy tells us this energy must come from somewhere, and the only source here is the detonation.

We can therefore calculate that the 1e17J provided by the bomb could move the fragment about 6 microns towards Earth before it is dragged back by the moon's gravity (assuming, of course, that none of the bomb's energy is lost to heating or deforming pieces of the moon).

In other words, whoever was technical advisor for the Time Machine deserves a Tabasco enema.