Phil Plait is an astronomer and major sci-fi geek. He writes the Bad Astronomy Blog for Discover Magazine and is also the host of the Discovery Channel's science show "Phil Plait's Bad Universe." You can follow him on Twitter at @BadAstronomer.
You have a problem. There's this pesky planet, and you need to blow it up. What's a supervillain to do?
Well, if you're Vader, you just fire up the Death Star's main weapon. If you're Serleena, you just fire some doohickey at one planet after another, leaving destruction in your wake on your way to Earth (until the Men in Black defeat you, of course). If you're Commander Kruge, you just wait for the Genesis planet to tear itself apart (though Kirk may kick your face off a cliff first). If you're Marvin the Martian, an Illudium Q-36 Explosive Space Modulator will fit the bill nicely.
Heck, Dr. Rodney McKay once blew up an entire planet by accident.
Point and shoot, right?
Well, hold on there a sec, buckaroo. Blowing up a planet isn't as easy as script writers might think. In fact, it's incredibly difficult.
Why? Energy. Lots and lots of it.
Math is easy, energy ... not so much
Blowing up a planet is essentially the same, physics-wise, as disassembling it piece by piece and flinging those bits away. And you know it takes really big rockets to lift even small amounts of material into space ... so now multiply that by a million million million and you may start to get the idea that this might be a bit of a bigger project than you thought.
Actually, the math isn't that hard. Take a rock. Throw it hard enough (that is, give it enough energy) that it can escape Earth's gravity. The energy needed to do that has been easy enough to figure out since Newton's day! When you get rid of that rock, though, Earth's mass has decreased a teensy bit, so its gravity is a teensy bit weaker. Do it again. And again. And again and again and again. Lather, rinse, repeat.
In fact, you need a bit of calculus (that Newton guy was pretty useful) to do this right, but in the end you can calculate the total energy needed to turn a planet into a glowing debris field. This amount of energy, called the binding energy, depends on the mass of the planet and its size.
I pulled out my trusty back-of-the-envelope and did the math. If you want to vaporize the Earth—and, really, who doesn't?—then you will need about 2 x 1032 Joules. A Joule is a tiny amount of energy, but 200,000,000,000,000,000,000,000,000,000,000 of them add up.
But it's hard to grasp what that really means, so maybe we need to translate this into more understandable units. Hey, got a one-megaton nuclear bomb handy? You'll need 57 quadrillion (5.7 x 1016) more if you want to blow up the planet.
Yikes. The total nuclear arsenal of every nation on Earth combined is probably somewhat less than 100,000 megatons, so we come up a bit short. That Death Star must have had some very large batteries in those reactor rooms.
If you have a real star handy, things are a bit easier. Detonating the Earth takes about as much energy as the sun puts out in a week. Note that if we covered the Earth in solar arrays, it would still take about 40 million years to collect that much energy, but still. There you go.
A matter of antimatter
Hey, wait a sec! In Star Trek they have antimatter. When you mix that with normal matter, it turns into huge amounts of energy. How's that stack up?
Well ... to blow up the whole Earth you'd need about a trillion tons of it. That's a lot: roughly the mass of Mt. Everest. An antimatter asteroid 6 miles wide ought to do it, if you have one handy. Personally, I hope you don't. Given that it currently costs hundreds of billions of dollars to make a single ounce of antimatter, you might have to work an extra job to cover the expense.
Shooting the Moon
An easier way would be to smash another planet into the Earth. At a speed of about 50 miles per second—a reasonable velocity for such things—you'd only need something the size of the moon crashing into us to turn us into a mass of incandescent gas. But then, how do you do that? Moons aren't all that easy to toss around either. Space: 1999 notwithstanding, getting our moon to zip along at 100 times the speed of a rifle bullet poses other problems as well.
Of course, all this assumes you're in a hurry (clearly, Vader had some pressing matters to attend to). And also that you want to totally destroy the planet, which, to be frank, is wasteful. It's dramatic and fun—oh, admit it, you know it would be—but it's a bit silly. After all, simply dropping a couple of dozen mile-wide asteroids on a planet will kill everyone on it, and then you have a new planet to move into just a few decades later, once the dust literally settles. Why vaporize when you can simply sterilize? It's a whole lot easier than building a moon-sized space station!
Of course, TV and movies are all about the drama, and blowing up a planet sure makes a point. Or, to be slightly more precise, a rapidly expanding cloud of billions and trillions of very little points.
Phil Plait writes the Bad Astronomy Blog for Discover Magazine, and has never destroyed a planet, at least not on purpose.