Re: How would Earth be affected if a large asteroid or comet hit our moon?

The body that killed the dinosaurs was probably around 10 km across (based on the crater). That may sound like a big chunk of ice or rock, but in astronomical terms, it isn't. Still, it can do quite a bit of damage. Can it do enough to affect the Moon? Probably not.

Most impacts (for bodies large enough to not really notice any atomosphere, anyway) occur at just a little above the escape speed from the planet's surface. For the Moon, that's about 2.4 km/sec. Now, a body 10 km in diameter (5 km in radius) will have a mass of around 1.6x10¹⁸ grams. (Assuming it has a density around that of rock, about 3 grams per cubic centimeter. If the the body is ice or has a lot of empty spaces, the density will be lower. But I'm trying to over-estimate the effect, here.) The total kinetic energy released at impact, then is around 4.9x10²⁸ ergs. That's also 4.9x10²¹ Joules or a bit over million megatons of TNT. A pretty big boom.

But wait! How does that energy compare with, say, the energy needed to knock the Moon out of orbit? Well, that energy is one half of the gravitational potential energy (there's a theory that shows that this is generally true, although for a circular orbit it's much easier to work out). So plugging in the mass of the Earth (5.98x10²⁷ grams), the mass of the Moon (7.35x10²⁵ grams), G, and the distance between the Earth and Moon (384400 km, or 3.844x10¹⁰ cm) we get around 10²⁹ ergs, or one hundred million times more energy than the asteroid impact released! So the Moon is safe. It's just as well because the Moon has taken blows that large before: the impacts that formed the basins (now filled with lava) we call maria were probably at least that big.

Well, could the impact instead knock the Moon into the Earth? As it turns out, no. You actually have to expend more energy to move in close to a body than to break free of it entirely. (Speaking glibly, without bogging down with numbers...) In astronomy it is an often-repeated tidbit that it's easier to get to Pluto than to Mercury. (Check out the route that MESSENGER has to make to get to Mercury and you can get a sense of how difficult it is.)

So will anything hit the Earth? It doesn't seem likely that much material will be blasted off of the Moon's surface, first of all. A lot of the energy is turned into heat during the impact, so not a lot is left to use to blow the debris off the Moon's surface. Remember that in order to escape the Moon's surface, a given peice of rock will need 2.4 km/sec of speed. On top of that, I estimate that the rock would, after escaping the Moon and getting far away, need to be moving at 3 km/sec slower than the Moon moves in its orbit around the Earth. Now, adding these speeds up is a little bit weird: you don't just add the numbers, you take the square root of the sum of their squares (it has to do with tracking the kinetic energy, if you're wondering why; if you aren't wondering why, don't worry about it). But this means that a peice of debris has to leave the Moon's surface travelling in the backwards direction (relative to the Moon's orbit) at about 4 km/sec. That's pretty fast, but far from impossible. But we don't expect a lot of material to acheive this speed. So perhaps some material will strike the Earth. The material will take different times to arrive at Earth depending on what route each bit takes, so things won't all rain down on us at once or in one place. And most it will be small debris. So what would I predict? Really good meteor showers for a while, but probably nothing that would really cause any other noticable effects.

Does it matter what side of the Moon the impactor hits? A little. If the impactor hits the leading (forward, in the direction of the Moon's orbit) side of the Moon, it will probably hit a bit harder since the two velocities add together. If it hits the trailing side, the opposite will probably occur, decreasing the energy. However, since the impactor is coming from outside the Earth-Moon system, the roughly 1 km/sec orbital speed of the Moon probably won't be a big player. (The Earth's orbital speed around the Sun is about 30 km/sec, for comparison.) On the other hand, if we're trying to get material to rain down on Earth, I speculate that hitting the trailing side of the Moon might work better since we want to send stuff off heading off behind the Moon.