The Navy is apparently going to try to shoot down that wayward spy satellite sometime in the next 48 hours. The attempt to shoot it down is justified in terms of protecting human life from the risk of harm caused by the satellite’s uncontrolled reentry. This post discusses whether or not the shoot down attempt can be justified in cost-benefit terms. I don’t think it can, at least in terms of the formal justifications provided by the U.S. government. There must be other factors involved. The costs per expected life saved are about $2-$3 billion dollars! Read on for details.

CNN reports how the U.S. government has justified the shoot down attempt:

Pentagon officials argue the effort is worth the expense because of the slim — but real — chance that the satellite’s unused fuel, 1,000 pounds of toxic hydrazine, could land in a populated area.

Because the super-secret spy satellite malfunctioned immediately after launch in December 2006, its fuel tank is full, and it would probably survive re-entry and disperse harmful, even potentially deadly fumes over an area the size of two football fields.

Here are the details of a cost-benefit calculation.

In early 2001 I was asked by NASA to organize a workshop to examine the risks and benefits associated with the reentry of the TRMM (Tropical Rainfall Measuring Mission) satellite. NASA faced a choice between using the satellite’s remaining fuel to conduct a controlled reentry into the Pacific, or allow the orbiter to continue gathering data on tropical cyclones and other weather and eventually plunge to earth in an uncontrolled manner. What option had the most benefits as compared to the risks?

Our workshop report can be found here. What is relevant for this current discussion is that NASA prepared an analysis of the probability of casualty due to an uncontrolled reentry of TRMM, which is roughly of the same size as the spy satellite. The NASA presentation can be seen here in PDF.

The area affected by the re-enetering TRMM satellite was estimated by NASA to be about 110 square feet. Because the fuel tank was to be empty there was no concern about a toxic cloud of hydrazine, as is apparently the case with the spy satellite which is carrying a full tank of fuel. As the CNN article cited above notes, the concern is that the ruptured fuel tank might affect an area as large as two football fields, or about 115,000 square feet, or about 1050 times larger than the area that was expected to be affected by TRMM.

In the NASA presentation at our TRMM workshop a risk of human casualty associated with an uncontrolled re-entry was calculated to be 1 in 5,000 (please see the PDF for details of the calculation), based on the size of the debris field and the population density of the area under the orbital path. A risk of 1 in 5000 is pretty small, hence in the end NASA decided to let TRMM fall in uncontrolled fashion (which will happen in a few years).

But the much larger potential debris field associated with the spy satellite suggests a risk of casualty — using the NASA risk estimate for TRMM scaled to the larger debris field — of about a 1 in 4.8 risk of casualty, or a bit worse than the odds of surviving Russian Roulette.

Now at an estimated cost of $40-$60 million to shoot down the satellite results in an expected cost per casualty avoided of about $190-$290 million (i.e., $40M*4.8 – $60M*4.8). Given that the vast majority of the casualties might be temporary discomfort from inhalation of hydrazine gas this is a very high cost, this is a very high figure (I’d probably inhale a bit of hydrazine gas for $250 million;-). If we consider the cost per life saved, say, by avoiding a direct hit on a person by the satellite, the cost per life saved rises to $2-$3 billion! (That is, 5000*$40M – 5000*$60M.)

In any reasonable calculation of the costs and benefits to human life of the spy satellite reentry, it does not seem justifiable in terms of human safety according to standard measures of the economic value of lives saved (which tend to be measured on the order of $10 million). So there must be other perceived benefits as well — such as testing the U.S. military’s ability to hit a satellite, showing adversaries U.S. military prowess, and simply eliminating uncertainty associated with the satellite’s reentry. The odds may be tiny, but if it happens to land on the Russian Embassy in Ecuador, or some other highly inconvenient place, there would certainly be a huge diplomatic crisis.

Being rich sometimes means that you can afford to eliminate uncertainty via decision making, regardless of the cost. But don’t be fooled by the justification, it doesn’t stand up to scrutiny, which seems fairly typical of the current administration.