Watch the skies! Identified flying objects released into space by NASA might fall on somebody’s head, or at least land nearby a noggin, on Friday, 23 September 2011, at 12:43 pm. Plus or minus a day. Or maybe a day-and-a-half.
Yes, NASA, the agency which claims it can predict global temperature two decades hence to a precision of a tenth of a degree, cannot do better than derive a forty-eight-hour window to predict the dropping to the Earth of a mass of metal and cable, even though they can track that object in space down to the meter.
But I believe them when they say the do not know where and when the UAR satellite will land. And I especially have faith in their statement that the satellite might kill somebody. They say the chance this planned kinetic weapon1 sends somebody to an early grave is 1 in 3200.
How did they arrive at the figure? NASA says it uses the “Object Reentry Survival Analysis Tool”, whose purpose is to assess “human casualty risk associated with uncontrolled reentries.” This tool is undoubtedly sophisticated; but can we duplicate NASA’s calculations using simple probability?
The surface area of the Earth is about 196,935,000 square miles, which is 5.49 x 1015 square feet. The average human, lying prone, takes up roughly 8.25 square feet, and there are 6.8 billion average humans, for a total of 5.61 x 1010 square feet of feet, torsos, skulls, and all the rest.
Assuming we have no knowledge where the satellite will hit, and forcing everybody to lie quietly on Friday, then there is a 5.61 x 1010 / 5.49 x 1015 ~ 0.00001 chance you will be hit. That is significantly smaller than the 1 in 3200, or 0.00031, figure issued by NASA.
One difference is the satellite won’t fall as one piece. NASA says the “Number of potentially hazardous objects expected to survive” is 26. Our number should thus be multiplied by 26. Doing this gives 0.00027, which is nearly the same.
The other difference in our method is we assumed the satellite piece would have to hit you squarely to kill you. But NASA estimates that the “Total mass of objects expected to survive” is 532 kg, or just over 20 kg per piece, which is about 44 pounds. An intact 44 pound weight, burning hot from the friction of reentry, will not need to hit directly to kill you. Merely hitting next to you will provide enough force to send lethal shrapnel careening towards your nose.
Taking into account shrapnel, raging house fires caused by glowing metal, tree limbs separated by impact, being run over by a motorist watching the streaking satellite and not the road, and, if science fiction movies are any guide, the possibility a killer blob-like alien microbe is living in the interstices of satellite and it survives the crash, then the chance of 0.00027 is easily seen as too low.
But there is something wrong with our calculations. NASA says, “Because the satellite’s orbit is inclined 57 degrees to the equator, any surviving components of UARS will land within a zone between 57 degrees north latitude and 57 degrees south latitude.”
Our figure of 5.49 x 1015 square feet is thus much too large, since this is for the whole of the planet. The actual surface area where UARS might strike is about 3.3 x 10 15 square feet. Putting that into our calculations gives us 0.00066, or about 1 in 2300, which is is already higher than NASA’s odds—before considering all those other ways you can be killed.
Of course, the surface area where people actually live is far smaller still, and only a few folks will be lying in the open, fully exposing themselves. Vast areas of the ocean are unpopulated—almost. Luckily, a 44-pound weight won’t kick up much of a wave, so people on boats have less worry about shrapnel. But let’s not forget that airplanes are ill equipped to dodge or survive a direct hit from a space missile.
We cannot reproduce NASA’s calculation, but we can at least say that their 1 in 3200 is not wildly off. But it is still pretty damn high. And NASA knows it. In a briefing about the planned crash, NASA engaged in some preemptive keister covering2 when it said, “No NASA or USG [US government] human casualty reentry risk limits existed when UAR was designed, built, and launched.”
They also said, “Uncontrolled reentries of objects more massive than UARS are not frequent, but neither are they unusual.” However, they were only able to point to one other similarly sized reentry, but even that was of a different class.
They close their briefing with a statement we hope still holds true after Friday: “Since the beginning of the space age, there has been no confirmed report of an injury resulting from reentering space objects.”
1Yes, planned. NASA decommissioned the satellite in space on 15 December 2005 “after maneuvering [it] into a shorter-lived disposal orbit.”
2We cannot blame them for this, for there is nothing that can be done to stop the satellite from hitting. And given enough time and the junk that is floating around up there, the chance that at least one person sometime gets hurts is pretty high.
Thanks to reader Bryan Hoog who suggested this topic.