Remember me

Next Dates: - Introduction to QuantLib Development with Luigi Ballabio, September 2 - 4, 2013 - £1700

Get under the table?

Fri, 23 Sep 2011 03:30:19 GMT

The remnants of the Upper Atmosphere Research Satellite (UARS) are due to hit the earth later today and NASA have put up some details of their risk assessment. But this doesn't say where their '1 in 3200 chance of anyone being hit' comes from, and so can we get this figure from a back-of-an-envelope calculation?

The satellite has been up 20 years, stopped working in 2005, and weighs 5700 kg, about the size and weight of a double-decker bus. NASA say it will break into 26 objects that will survive re-entry, weighing 532 kg in total, about the weight of 8 washing machines. These will be spread over about 500 miles, but cover a damage area of around 22 sq m (around 3 parking places).

The earth has surface area 500,000,000 sq km which is 500,000,000,000,000 sq m, and so assuming the bits can land anywhere, there is around a 1 in 20,000,000,000,000 chance of any particular square metre being hit. If You (that means You) make a target of say around 1 sq m, then assuming a random landing place there is around a 1 in 20,000,000,000,000 chance of You being hit - that's the same chance as flipping a coin 44 times in a row and it coming up heads every time. Or slightly better than the chance of winning the lottery twice in a row.

But there are 6,700,000,000 people on earth, if they each take 1 sq metre that’s 6,700 sq km, only 1/80,000 of the earth’s surface. So if everyone in the world went to Glastonbury Festival, they would only take up Somerset and Wiltshire combined, although the toilets can't be imagined.

So the chance of anybody at all being hit is 6,700,000,000 / 20,000,000,000 which is 1 in 3000, very close to NASA’s quoted figure of 1 in 3200.

In fact they have some idea where the debris will land (not in North America is all they seem to care about), but even with 2 hours to impact, they still can’t tell within 8000 miles where the bits will come down.

The largest object will weigh 158 kg [25 stone], about the weight of an adult gorilla, but that sounds a bit soft so perhaps better to think of a couple of washing machines tied together travelling at 100 mph. So no point in wearing a crash helmet.

If it's any consolation, bigger stuff came down last year, and nobody has ever been hit by space debris – yet.