Note: I had an error in the original calculation for the Sun’s energy output (I blew it converting from ergs to Joules, if you’re curious). I fixed the error in the text below. I usually like to keep my mistakes open, but striking through the text in this case would make it confusing to read, so instead I simply fixed it and admit my error here. Anyway, the change isn’t a big deal; although the numbers changed, it doesn’t change the fact that the impact was teeny tiny compared to anything else the Moon goes through.
On October 9, a Centaur rocket booster, watched and followed by the Lunar Crater Observation and Sensing Satellite, impacted the Moon at several kilometers per second. Slamming into a crater near the lunar south pole, the hope was that the impacts would excavate water frozen permanently under the surface, eject plumes kilometers high, and give us our best evidence yet of ice on the Moon.
NASA played up the event, saying the plume might be visible from Earth. I didn’t think the flash would be visible from Earth (though the rocket booster impact was seen by LCROSS); from here we can’t see the floor of Cabeus crater where the impacts occurred, but I had hopes about the plume. Unfortunately, none of the fleet of terrestrially moribund telescopes detected the plume. A lot of people (bloggers, web commenters, twitterers) expressed disappointment.
Some people were a little more, um, well… crazy.
Now, that’s not too surprising. First off, most people understandably don’t have a great grasp of the scale of the Earth and Moon, and so may have been expecting a lot more out of this event. Others, also lacking that sense of scale, thought that disaster would befall the Moon. Still others in this group think that humans polluting the Moon is a tragedy.
All of them were and are wrong. Why? Let’s see.
First off, let’s talk about the initial flash from the impact. Our view from Earth was blocked, but if it were bright enough it might have illuminated the walls of the crater. Is it realistic to see the flash from a backyard telescope? Before the event I wondered about that, so I calculated about how bright it would be. Since I went to the trouble, I’ll subject you to it too. Plus, the math is fun.
This has to do with energy. When something smacks into something else, the energy in its motion is converted into other types of energy. When you clap your hands, for example, it’s sound. But at very high speeds, a lot of that energy is converted into heat and light. The amount of light you get out depends on lots of things, but mostly on the energy of the moving object, its kinetic energy.
That’s easy to calculate: the kinetic energy of an object is 1/2 x its mass x its velocity squared. The Centaur had a mass of about 2000 kilograms (a little over two standard tons) and was moving at 2.5 km/sec when it hit the Moon. Doing the math, that means it had a kinetic energy of a little over 6 billion Joules, equivalent to the energy release of blowing up about 1.5 tons of TNT.
That sounds like a lot! But that’s the total kinetic energy of the booster, and while it was released upon impact, not all of it turned into light. Some of it went into heating up the ground, some into vaporizing the metal in the rocket, some into displacing the ground — digging a crater and ejecting a plume — and so on.
But let’s be optimistic for a moment, and assume all the energy was converted into visible light. How bright would it have been from Earth?
The easiest way is compare the energy and distance of the impact to the energy and distance of the Sun. We know how bright the Sun is, so by setting up a ratio we can calculate the maximum brightness of the Centaur event.
The distance to the Sun is 150 million km, and it gives off 4 x 1026 Joules every second. The Moon is 400,000 km away, and the Centaur impact had an energy of 6 x 109 Joules. Brightness scales with distance squared, so the ratio of the two brightnesses is
(Energy of Centaur / Energy of Sun) x (Distance of Sun / Distance of Moon)2
So let’s see… divide that there, multiply by this, carry the two… and we get that the ratio of the brightness of the Centaur impact as seen from Earth is about 2 x 10-12. In other words, the Sun is 500 billion times brighter! Wow!
But how bright does that make Centaur? Astronomers measure brightness in magnitudes, and I won’t bore you with the details this time, but knowing the brightness of the Sun and the ratio, that means that the Centaur impact — assuming all the energy went into visible light — would have shone at a magnitude of about 3 or 4, visible to the unaided eye but not glaringly obvious.
So it’s not like you’d have to squint and turn away from the glare. Standing on the Earth looking at the Moon, you’d barely have seen it at all, and the brightness of the Moon itself would have washed it out.
And that’s a best case. In reality we know that the energy doesn’t go into a visible flash; most of it is turned into heat. That means infrared energy, the kind that was easily detected by LCROSS when the Centaur booster hit the Moon. But even then the amount of kinetic energy converted to light is very low; I was quoted a figure of about 1/100th of a percent by an expert some years ago. That means that the flash — even in infrared — would have been at a magnitude of about 13 or 14, which is pushing the limits of small telescopes. And the visible flash would have been smaller yet.
That’s why I wasn’t expecting ground-based telescopes to see the flash. I had hopes, but no such luck.
2) The Big Mo
What about momentum? I read a few places where people were concerned that the impact might change the Moon’s orbit.
When you think about it a little, you’ll see this isn’t a concern. The Centaur was a cylindrical hunk of metal 13 meters high and 3 in diameter. The Moon is a ball of solid rock over 3400 kilometers across! So it’s like a flea hitting a freight train. But let’s make sure.
Momentum is simply the mass of an object times its velocity, and any momentum the Centaur had was given to the Moon. Let’s assume the Moon is standing still (that is, has velocity = 0) and then ask how fast the Moon would move after the booster hit it. That’s easy: we set the two momenta equal, divide the momentum of Centaur by that of the Moon, and solve for the Moon’s velocity:
mass x velocity of Centaur = mass x velocity of the Moon, so the Moon’s velocity after impact = (mass x velocity of Centaur)/ (mass of Moon)
Doing the math, (2000 kg x 2500 m/sec) / 7.4 x 1022 kg = 7 x 10-17 m/s.
Egads. That means the Moon gained a velocity of 0.00000000000000007 meters per second from the impact. In other words, if you waited, say, 460,000,000 years you’d see the Moon will have moved a meter.
In other other words, a flea hitting a freight train. The concerns over the Moon plummeting to Earth or being blasted out of orbit a la Space:1999 were a tad unfounded.
In fact, the Moon is hit by meteorites all the time, and is probably smacked by something with the same momentum as the Centaur several times per year. Since the Moon is still there, we can safely assume the Centaur impact had essentially zero effect.
3) Extra-terrestrial eco-terrorism
OK, so we couldn’t see the flash, and the Moon remained unmoved after the impact. But what about humans being fined for cosmic littering?
I heard from several people personally who felt that we shouldn’t impact our stuff on the Moon because it’s polluting the surface. Some felt that it was just wrong in a vague way, but couldn’t clearly express why. Others felt it was just a dumb macho stunt.
First, it was not a stunt. High-speed impacts are a legitimate way — really the only one we have right now — to see if water lurks beneath the permanently shadowed floors of polar craters. You can accuse NASA of being macho jerks, but I don’t think that sticks. It’s really just a silly accusation.
As for littering, I think that’s a sense of scale. The Moon has a surface area of 37 million square kilometers, and the Centaur dug a crater about 20 meters across. Saying that has any real impact on the Moon is like arresting someone for mowing their back yard*
And remember, the Moon is constantly bombarded from space. Roughly a ton of material hits the Moon every day, so the Centaur is a blip on top of that. And I’ll add that the Moon is essentially a giant rock in space, with no forests, no ecosystems, no delicate climate to knock out of whack. As a scientist I don’t want us defacing the Moon any more than necessary; it’s always best to study objects like it in situ. But I also know the Moon is very, very large, our impact doing this very, very small, and the outcome could be scientifically pretty huge.
One point to be made, of course, is that if we do find water, it makes it far more likely we’ll build colonies on the Moon that could do large scale mining and such, and that really will have an impact. That’s true, but again the Moon is a giant barren rock in space. I challenge anyone who worries that we will hurt the Moon somehow to first tell me exactly how what we’re doing is a bad thing (other than a vague discomfort with it), and also to turn around and defend how they live in a house or apartment or wherever. That has a much larger impact on the Earth, where we know things are in a pretty delicate condition. Plus, we live here and depend on the Earth.
I certainly understand why people might be concerned over what we’re doing on and to the Moon, but it’s a concern borne out of not understanding the scale of the Moon and what we’re doing with it. Think of it this way: when you stand outside and gaze at the Moon with your unaided eye, the smallest crater you can see is about 100 kilometers across. That means you could hit the Moon with an asteroid a mile across, and once the smoke cleared the crater would be too small to see without a telescope!
That’s the scale we’re talking about here. In the meantime, there is real science to be done and real challenges to overcome in going to the Moon. In my opinion, these small efforts to understand it are well worth the effort. And I would bet the bank that in 100 years, if we do boldly go and colonize our nearest cosmic neighbor, they will look back at this era fondly, though with a small bit of chagrin as they wonder, "What took us so long?"
* Yes, I know that lawn mowers pollute the air, and that some places make it illegal to mow in times of really bad air quality. But that’s because hundreds of thousands or millions of people mow their lawns. When NASA launches a million spacecraft to hit the Moon, then we’ll talk.