Statistics

# What Are The Chances NASA’s Rogue Satellite Kills You?

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.

Categories: Statistics

### 22 replies »

1. JH says:

Would wearing a helmet improve my chance of survival?

2. DAV says:

The Earth is turning under the spacecraft so I would think the entire surface area between the latitude bounds is exposed to impact. But why use area? If it crosses the volume inhabited by a person won’t they be injured? So, why not consider the volume say 6 feet high over that area?

JH,

I’m going to be wearing my tin-foil one.

3. Doug M says:

Do you have a wager on this running on your Edgehogs site?

4. DAV says:

I’ve been unsuccessful in finding the site about meteor photographed over Pittsburgh that hit a parked car in New York City. Didn’t do much damage but It only weighed about 5 lbs. IIRC. Would have been pretty painful to be hit by it though. Imagine being hit by the equivalent a concrete block moving with the speed of a bullet. Did NASA mention what the the expected terminal velocity (prior to impact, of course) of the surviving pieces?

“Merely hitting next to you will provide enough force to send lethal shrapnel careening towards your nose. ”

But only if you are standing to the front of the impact, yes?

5. It’s making me crazy and I’m not even European!

6. j ferguson says:

Briggs,
Is there a number assigned to death or damage by satellite fragment? What if it deflects the turtle that was going to fall on you? A number for death by laughter?

If the fragment embeds itself in your body, is it yours to keep?

7. Briggs says:

DAV,

You’re forgetting deadly ricochet. Plus, the debris might knock a signpost on top of your volume.

j ferguson,

No, it isn’t. NASA has already warned people not to touch any remnants, including those—we can only assume—that land on you.

8. DAV says:

I’ve been thinking about how dangerous this debris really would be. It started with orbital speed but once it hits the atmosphere it will undergo constant deceleration. Makes me wonder just how much energy would be left over in a 44 lb object arriving in a glancing blow.

CNN has been running a video the last two days of an object striking almost straight into the ground while moving at most 550 mph. That object weighed more than a ton and was under power. It also contained fuel and wasn’t a solid piece.

If our 44lb object survived re-entry, I think it unlikely it would come apart on impact. It would be more like a solid chunk of metal. Don’t forget it’s one of the pieces left over from something that did come apart. Any debris from the impact will probably come from the surroundings. I think it will likely be moving no more than the speed of sound at impact. Picture a 44lb fairly solid block hitting the ground at 500 mph.

If you’re thinking about meteors. Don’t forget that they are mostly pieces that have been clumped together which will come apart on impact. Everything on a spacecraft was bolted to something else. The UARS pieces will have already been subjected to a great deal of rending forces and would somehow still have survived.

On 9/11/2001 we witnessed a large object weighing in the 10’s of tons impacting at roughly 500 mph. Surely, that would be the upper limit to what could happen with our UARS pieces.

9. DAV says:

“NASA has already warned people not to touch any remnants”

Over worry about space cooties no doubt.

10. Patrick says:

1 in 21 trillion chance that it is me.

11. Briggs says:

Patrick,

Check back in with us after it crashes, else we’ll assume it got you.

12. JH says:

Please, please, please, if the satellite camera is going to make it down to Earth, let it land on top of a tree in my heavily wooded backyard. If this happens, I definitely would call it a miracle, not an coincidence.

13. j ferguson says:

NASA: We have no record of complaint from anyone hit by a satellite fragment in the past.

14. PEHarvey says:

I did not try to understand what Mr Briggs means, just what he writes. I read there is 1 chance in 2300 of being hit for everybody in the area.

I think it should be: 1 chance in 2300 that 1 person out of some 3,000 millions will be hit.

Or maybe it is because English is my second language.

15. This is truly valuable public service information professor Briggs has passed on. Based on the numbers, today I took out a 10 day insurance rider [shortest period I could buy] on my old, unlicensed clunker in the hopes I might “get lucky” with the falling UAR satellite debris field. Filing a claim against NASA for destroying my valuable neo-classic automotive collector’s item could pay off handsomely. Particularly since these are better odds than the state lottery’s. So I’m looking forward to an extra payday near the end of the week. And the wearing of my tinfoil hat.

16. Ken says:

RE TOUCHING REMNANTS: Not knowning what materials are used, presumably Beryllium is one–and it is toxic. Also, there may be some radioactive materials, such as a small amount of Plutonium (used as a crude but effective heater in some satellites).

HERE’s where Briggs went profoundly & fundamentally astray, though not with anything important like his analysis: “This tool is undoubtedly sophisticated; but can we duplicate NASAâ€™s calculations using simple probability?”

Therein lies a fundamental problem. When a modeler/consultant/etc. can build a “sophisticated” model, generally after lengthy effort billed by the hour, especially a model that factors in a variety of remotely, even dubiously, applicable influences, the model’s results gain credibility from which the exhorbitant price charged is felt to be suitable (maybe even a bargain). Time, effort, cost, and complexity — and more is “better” — are valuable features in such a model. Especially for government customers. Fortunately, no matter what happens, extraordinarily unlikely or not, the mere fact that it is an unpredicatable probabalistic event allows the modeler’s off any “hook” for culpability as it was just a model conveying a general probablistic outcome.

At least, that’s how things used to be … if one lives in Italy if you guess wrong you may be held accountable in court:

http://www.nature.com/news/2011/110914/full/477264a.html

17. Gary says:

I once read or heard somewhere that when a relatively small falling space object — a meteor, IIRC — reaches terminal velocity in the troposphere, it cools down pretty quickly and is likely to be only warm to the touch. If true, then the unlikelihood of being flash fried by space junk reduces your probability of being killed after merely being bruised.

18. MarkF says:

Let me get this straight. The probability that a person being is killed by this satellite is 0.0003125 (which is 1/3200). This is equally likely for all within the band between 57 degrees N. latitude and 57 degrees S. latitude. Assuming a conservative estimate of 1 billion people in this band, the expected number of deaths should be exactly 312,500 people. Hmmm. Looks like a real catastrophe to me. Maybe the elected leader of all earthlings should do something. Soon.

19. bruce says:

So what would be the odds of being hit & winning the lottery the same night? Not that you’d be around to spend it……

20. Patrick says:

You can all relax. I am safe.