How Much Does it Cost to Blow Up a Planet?

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.)

Now, that’s clearly a lot. But just how much? Our reader wanted an answer in kilowatt-hours, since that’s how electricity is usually billed, but a kilowatt-hour is just another unit of energy, like the joule. A watt is one joule per second (so a sixty-watt lightbulb uses sixty joules of energy/second), but a watt-hour is the amount of energy that a one-watt device would use if it ran for an hour. This is the same as the number of seconds in an hour: 3600 seconds at 1W is 3600 joules. A kilowatt-hour, then, is 1,000 times that much, or 3,600,000 joules: 3.6 megajoules (MJ). Since we can easily interconvert from joules to kWh using this factor, we can do our math in joules and then worry about converting to kWh and cost later.

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?

A kilowatt-hour of energy, 3.6 MJ, costs 12 cents here in the US. That number’s as high as 40¢ in places like Denmark, but we’ll go ahead and assume the Empire is using the ancient galactic equivalent of cheap-and-dirty fossil fuels to generate power.  (It’s obviously impossible to account for things like economies of scale on a galactic level, along with inflation since “a long long time ago”, so we’re going to have to just sweep those under the rug. Although I’m SURE someone’s gone and figured out how much a “credit” is worth in modern USD, I don’t even have the patience for real economic analysis, let alone the fictional kind.)

So 10³² joules of energy at 12¢/kWh (and remember, a kWh is 3.6 MJ) gives us: