A curious reader wrote in today with an odd and ominous inquiry—how much would it cost to power the laser of the Death Star? We're by no means the first ones to turn an analytical eye to everyone's favorite space opera, but outlandish questions like this are always a good opportunity to bring a bit of fun to mathematics.
Fortunately, thanks to our legions of fellow nerds on the internet, most of the work's already been done for us: the good people at "StarDestroyer.net" went and calculated the approximate amount of energy the Death Star's laser must have imparted on to Alderaan, making the assumption that it's a planet with a roughly Earthlike mass. To do this, they found the gravitational binding energy of the planet—the amount of energy it would take to drag all the particles that comprise Earth away from one another to an infinite distance.
It might be surprising that you can pull attractive objects infinitely far apart on a finite energy budget, but it's possible thanks to the fact that the attraction between them falls off rather quickly—growing weaker as the square of the distance between them. Using this knowledge and a good bit of calculus, the StarDestroyer crew found that it would take roughly 1032 joules of energy to completely disintegrate an Earthlike planet.
|We're not just talking "made uninhabitable" here, 1032 J is enough to make it look like the place never existed.|
Image Credit: Still from A New Hope, poached for educational purposes.
(Please don't sue us, Disney.)
Exponential numbers like 1032 are inconceivably large, though, so to get a sense for the amount of energy we're talking about here, let's look at the sun (don't literally look at the sun, please.) The sun has a luminosity of about 3.8*1026 watts, meaning it gives off that many joules per second. Already, things aren't looking good for this month's Imperial Power & Light bill—that six order-of-magnitude difference between the sun's per-second output and the Death Star's firepower means we're going to need to harness ALL the energy of a sunlike star for a while in order to get the energy necessary to blow up the planet. How long?
So 1032 joules of energy at 12¢/kWh (and remember, a kWh is 3.6 MJ) gives us:
I know that nobody wants to say it to the temperamental Sith lord with a penchant for remote asphyxiation, but with the kind of resources it took to pull off this one show of strength, the Empire could have bribed the whole galaxy into compliance a few times over.
So if you're trying to start an evil empire, maybe take a hint from a more successful one and go the Bread and Circuses route.