Look Out Below!

UARS, a defunct research satellite, will be re-entering Earth's atmosphere and mostly burning up on its way to the ground sometime in late September or early October. The resultant fireball will be quite spectacular even in the daytime assuming it falls where someone can catch a glimpse of it.

Due to the complicated structural geometry of the satellite (that is, it's not a perfect sphere) and since the Earth's atmosphere fluctuates significantly over even short time periods the exact minute of reentry cannot be predicted. This means, when the official decay starts, the center of the 500-mile-long impact zone cannot be determined to within better than +/- 7,000 miles. It could land anywhere.

This article states the odds that someone on the planet will be hit by the surviving portion of this satellite are 3,200 to 1.

“No. No no no no no. That can't be right,” I thought to myself.

A quick aside. I was going to post some comparative odds here that dealt with the usual “being hit by lightning” or “dying in a plane crash” stuff but I found that both of those things are shockingly frequent when you actually do the math, even though “everyone” knows that those things are so rare as to be inconsequential. I'll leave that for a future article.

 In any case I knew from various sources out there that 1) something has survived reentry about once a day (or week, depending on where you look) over the past 40 years and 2) no one (or only one person, depending on where you look) has ever been injured by falling orbital debris. The odds of being hit, according to this source, are “one trillion to one”. Way different than 3,200:1 and way more in line with what I “knew” the right answer was.

So which is correct? After some digging I eventually found a reliable source for the 3,200:1 claim, but there were no justifications given for that number.  Let's do some back-of-the-envelope estimations. Surely we can get to an answer that is within an order of magnitude of the 3,200:1 estimation or the 1,000,000,000,000:1 estimation, assuming one of them is right.

Based on the orbital data, anyone who lives between about 57N and 57S latitude is at risk. The world population is about seven billion, and nearly all (~90%) of those people live between those latitudes. Assuming that each person takes up one square meter and dividing by the surface area of the planet we get 65,580:1 per piece of falling debris. The satellite is calculated to break up into 26 survivable pieces, making the odds that someone will be struck by a piece of this satellite somewhere around 2,500:1.

My rough guesstimate (Really? No red underline, OpenOffice word processing program? What a world...) shows the 3,200:1 number is probably correct after all. Huh. You learn something new every day...

You can catch updated information regarding the orbital decay and reentry of UARS at http://www.space-track.org/.