February 1, 2010 | 5:25 pm

The high price of unobtainium

Posted by Adam Wills

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SETI Institute’s senior scientist Seth Shostak recently took on some implausible elements in “Avatar” on Space.com, most notably the feasibility of mining that precious mineral worth $20 million a kilogram—unobtainium. It’s not worth the expense, he says:

I do want to note something about the premise, because Tinseltown has used the idea of interstellar mining over and over. Simply put: Is there some naturally occurring element or compound that would really be worth hauling back to Earth from another star system?

This question was addressed two centuries ago, when England began to send people (mostly low-grade criminals) to Australia. This population needed something to export to London to earn foreign currency, and they settled on wool. This was not because the Aussies are particularly fond of sheep (although New Zealanders have plenty of jokes about that), but only because wool is very expensive per pound. Sending it back to Europe was expensive, and Australian wool would only be competitive in the London markets if the shipping costs were a small fraction of the product value. Even in the day of wooden ships, this criterion was met.

Now let’s consider the tariff for sending a kilo of unobtainium back to Earth. Our descendents in this film have some pretty nifty looking rockets, and we hear shortly after the opening titles that the trip to Pandora takes only about five years (as measured on-board). Well, even the nearest other star system, Proxima Centauri, is 4.3 light-years from where you’re sitting. That means that transport between Earth and Pandora occurs at 85% the speed of light or more!

Getting a kilogram of unobtainium (or anything else) up to that speed, and then decelerating it at the end of the ride, takes at least 1017 joules of energy. That’s freshman physics. What’s the cost of that energy? Our cheapest joules are supplied by your local utility company at about ten cents a kilowatt hour, or 36 million joules per dollar. At that rate, the price of shipping a kilo of unobtainium works out to $3 billion, or — assuming 2% annual inflation between now and 150 years from now — $50 billion in 2154 c.e. dollars (that’s the year in which the film takes place).

In other words, the transport costs for unobtainium exceed the value of the merchandise by a factor of more than 2,500!

So that settles that. You are not about to pay $60,000 to Amazon as the shipping charge for this month’s best seller. Interstellar mining — and the affront to natives it might imply — should be tactfully removed from Hollywood’s box of tropes.

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