To the disappointment of thousands who signed the petition, the Obama administration recently informed us that it has, and will have, no plans to build a Star-Wars-style death star. Now, there may indeed be good reasons to forgo this addition to the nation's defense, but the first one listed — that it would cost 850 quadrillion dollars — was based on an extremely flawed estimate. Which isn't surprising, because among the people doing the estimating, only one has any experience in aerospace engineering (and probably none in costing of such projects).
They go off the rails in their estimate right from the beginning, when they assume that a death star would be simply a scaled-up battleship, and built primarily from steel. But a battleship is not actually a good analogue for a death star. First, a death star is not a "floating" weapons platform — it is an orbiting one. Battleships are built of steel because, given sufficient thickness, it has reasonable (though not impervious) resistance to explosive weapons, such as torpedoes or shells from other battleships, and it is possible to build a ship out of that material that will float in the ocean.
But rockets and satellites (a death star would be the latter) have never been built from steel, because its strength-to-weight ratio is far too low — a steel rocket, if it could get into orbit at all, would have very poor payload performance, and a steel satellite would be far too heavy to be able to lift affordably. Traditionally, aluminum was the structural material of choice, though over the past decades, carbon composites have become more popular, because they outperform aluminum. Thus, while it might be that a death star would have steel plating on its hull (that assumes weapons similar to naval ones, when it's more likely that it will have to defend against high-energy power beams), the vast amount of its structural mass would be a different, much lighter material. Thus, calculating a scale up of the steel would only involve the surface area, not the volume of the death star.
Typical armor thickness for heavy artillery can be up to a hundred millimeters (or about four inches), so for a smallish death star of only 160 km in diameter, the surface area would be about 80,000 square kilometers, or 30,000 square miles, or about 90 billion square feet. Multiply that by four inches (a third of a foot) and you get 30 billion cubic feet of steel. At a density of about 500 pounds per cubic foot, that means we need a little less than two quadrillion pounds, or close to a trillion tons (the estimate scaling up from the battleship was about a quadrillion). Prices currently range from $500-$800 per ton, but I'd go for the lower estimate, given that for a project of this size, we'd likely get a bulk discount. So the cost of the steel for the death star would be about half a quadrillion dollars, far below the original estimate of over eight hundred quadrillion for the steel. That number is only a few times the world gross domestic product.
Of course, it doesn't include the cost of the aluminum or composite in the interior. If we were to scale up a satellite (much more appropriate than scaling up a battleship), we would take the biggest satellite ever (the International Space Station), and scale it. But that would be making a lot of assumptions about the interior volume, nature and density of the death star that we frankly just don't have enough information on. And even if we did, it still wouldn't be a reflection of the accurate cost of constructing one, due to an even more egregious and fundamental error in the original estimate:
Scaling up to the Death Star, this is about 1.08×1015 tonnes of steel. 1 with fifteen zeros.
Which seems like a colossal mass but we've calculated that from the iron in the earth, you could make just over 2 million* Death Stars. You see the Earth's crust may have a limited amount of iron, but the core is mostly our favourite metal and is both very big and very dense, and it's from here that most of our death-star iron would come.
I fearlessly predict that, should we ever build a death star, it will not only not be made of steel (and if it is, it certainly won't come from the planetary core), but it will not be constructed from terrestrial materials at all. One commenter over there notes that current launch costs are about ten thousand dollars a pound (not really true, any more, and if Falcon Heavy performs as promised, they will be closer to a thousand). But there are already vast amounts of construction materials in space. If you really wanted to use steel, you could do it by mining an iron or stony iron asteroid. Mix it with a little carbon from a carbonaceous one, and voila — steel. But the stony asteroids (not to mention the moon) also have aluminum and titanium, and with all the carbon available, composite structures would be possible as well. In fact, a new company, Deep Space Industries, announced last week that it has plans to do just that.
While the original costing exercise was obviously (I assume) tongue-in-cheek, it does make a useful if inadvertent point — the absurdity of attempting to predict future costs on the basis of existing technology. The ability to construct an artifact like a death star implies a vast off-planet industrial civilization, one that is utilizing all of the material and energy resources of the solar system (and perhaps doing most of the major manufacturing off planet, lowering the environmental burden on the home planet). The technologies would doubtless include large amounts of automation, and the price per pound of construction materials in space would likely plummet, particularly compared to the cost of mining them on earth and lifting them out of the gravity well, even with low-cost launch systems or even space elevators. Such a civilization would also be vastly more wealthy than the current planet, rendering meaningless death-star cost comparisons with existing GDP. As noted at the outset, there are many reasons that such a thing might be useless, or worse than that, but to think that it will be unaffordable to our descendants is to take a bleak view of the human future.