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 5.7×10
-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
…
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 5.7×10
-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 2×10-9 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.
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