The cause of the crash of Air France flight 447 has not been determined (and likely won't be for some time). The most likely cause is related to the turbulence in the area at the time of the crash, but other possibilities have been suggested -- including, surprisingly, meteor strike. That certainly seems far-fetched as a cause, but John Conway at the Discover Magazine blog Cosmic Variance does some back-of-the-envelope calculations to check on the likelihood of a meteor striking an aircraft.

The math is pretty simple. There are about 3,000 meteors a day of the requisite mass to strike Earth, or about 125 an hour. (Check the article for the sources of this and other such estimates.) Meteors strike the Earth at supersonic speeds, so from the meteor's point of view an aircraft is essentially stationary. This means the chance a meteor (entering at a random point on the globe) hits a given aircraft is determined by the fraction of the Earth's surface covered by the aircraft: about 5.7x10^{-13} for an average airliner. This is the probability of one aircraft being struck by one meteor. Air France 447 had planned flight time of about 11 hours, over which period 1375 meteors would be expected to fall. So the chance it would have been struck by a meteor during this flight (as calculated by R using the Poisson Distribution) is:

> 1-ppois(0,5.7e-13*1375)

[1] 7.8375e-10

So, about 1 in a billion, give or take. Turbulence is looking like a much more likely cause. Besides, as Phil Plait has noted, this is likely an over-estimate because meteors quickly slow down to terminal velocity, and so a jetliner is more likely to strike a meteor than the other way around. A lower effective surface profile from a head-on collision ... probably need some kind of volumetric calculation ... err ... too hard. But 1 in a billion is a safe upper bound.

But as we've noted before, if you observe an unlikely process enough times and/or for long enough, the chance of it ever happening can become surprisingly likely. Instead of asking about AF447 in particular, let's ask another question: what are the chances that in the next 20 years any aircraft will be struck by a meteor. Assuming, of course, air traffic levels stay constant, meteors are supersonic, entry distribution and flight distributions are uniform -- ok, there are a million assumptions, but it's an interesting back-of-the envelope calculation.

Here goes: at any given time, airliners cover 2 billionths of the Earth's surface. There are 125 meteors an hour, each with probability 2x10^{-9} of striking some airplane. In 20 years, that's about 22 million independent possible impact events. The chance that every one of those meteors misses every airplane is:

> ppois(0,2e-9*22e6)

[1] 0.956954

In other words, there's about a 4.3% chance of a meteor strike on at least one airliner in the next 20 years. (John Conway used a different calculation but came to a similar result.) That's surprisingly large. To repeat: this is almost certainly an over-estimate, and applies not to a single flight but cumulatively to all flights over a 20-year period. Furthermore, there have been no documented cases of a meteor striking an aircraft so far, so even if it did occur we have no idea what kind of damage it would cause, or even if it would lead to a crash. But it's significant enough that it can't be ruled out next time there's an unexplained air crash incident.

Cosmic Variance: Did a meteor bring down Air France 447?

What proportion of its time does the average plane spend on the ground. My guess would be that for large ones, a relatively small amount, for small planes, quite a large proportion. I'd also guess that there are more small planes than large ones (although that might be wrong) and so the surface area of planes on the ground might be *approximately* equal to the surface area of planes in the air.

Also assuming that meteors don't burn up once they've reached airplane height, that would mean that strikes to planes on the ground might be about as likely as strikes on planes in the air. Of course, when they're on the ground, they're much easier to detect too - I wonder if that has ever happened?

Posted by: Jeremy Miles | June 09, 2009 at 12:28

In related news, a teenager in the UK was recently struck by a meteorite. Although I find it hard to believe it was traveling at 30,000mph at impact: even if it only weighed ten grams at impact, a glancing blow with energy of almost a megajoule is gonna leave more than a 3-inch scar.

Posted by: David Smith | June 12, 2009 at 11:56