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Lasers in SF, Part III: How much energy does it take to blow up a planet?

February 9, 2012
Note: this post is the third in a series about lasers in science fiction that I’m writing in preparation for a talk at Madison NerdNite on February 22.  If you have any suggestions on improving these posts before I give the talk, feedback is much appreciated! ~J
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Like any good nerd, I’ve watched the original three Star Wars movies about a bazillion times. This was, again, mostly thanks to my younger brother. When Episode IV was re-released in 1997, my dad took him to see it in the theaters. After that, it didn’t take long for Star Wars mania to strike.

My mom & I soon found ourselves co-opted into marathon movie sessions and games of Star Wars Trivial Pursuit (which, if you’ve never played it, has some devilishly difficult questions). There was even an interactive board game in which you had to play a Rebel operative infiltrating the second Death Star, while Darth Vader threw plot twists at you from a video tape.

So the Death Star is a big part of my mental map of science fiction. And what would the Death Star be without its superlaser?

Now, I will admit right now that post has actually has nothing to do with lasers. I’ll get to the laser stuff next time. But since we’ve been talking about energy and power, I want to start with a question along these lines.

That is, how much energy does it actually take to blow up a planet?

Luckily for us, this is an old question among Star Wars fans, and there are several nice writeups floating around the internet that explain how to calculate the amount of energy needed. Most rely on the idea of gravitational potential. That is, the amount of energy required to smash a planet to smithereens, and to prevent it from collapsing back onto itself, is the same amount of energy required to pull each bit of the planet out of its gravitational field, piece by piece.

These calculations all conclude that if Alderaan were about the same size as earth, then it would take a minimum of 2×10^32 J of energy to blow up the planet (see here, here, and here).

This is a MASSIVE amount of energy. To put that number in perspective, it would take a trillion billion United States’ worth of electrical generating capability to generate this much energy in one second (see here). Alternatively, our sun’s power output is about 4×10^26 J per second, so it would take more than half a million suns to put out this much energy in a second (or it would take our sun almost a week working by itself).(*)

However, this is Star Wars we’re talking about, and I doubt the Death Star relied on electrical generators or solar panels to provide the energy for its superlaser.

In fact, according to the Wookiepedia, the superlaser draws power from the Death Star’s “hypermatter” core. In the Star Wars canon, hypermatter is a type of exotic matter that attaches to ships when they travel through hyperspace, and it consists of tachyons, or particles which travel faster than light.

As far as our current understanding of physics goes, it’s not possible for anything to travel faster than light (recent results from the Large Hadron Collider notwithstanding – but I’m withholding judgement on that for now). So hypermatter is out. But for our discussion, antimatter might be a good stand-in.

Antimatter is a weird counterpart to normal matter, which has to exist in order to maintain “symmetry” in the laws of physics (though I don’t really understand that, so please don’t ask me to explain it). But when antimatter comes in contact with normal matter, the matter and the antimatter blow up and turn into pure energy. This process is called annihilation, and the amount of energy released is given by Einstein’s famous mass-energy relationship, E=mc^2.

According to this relationship, annihilating one kilogram of matter (or antimatter) releases 9×10^16 J of energy. To generate the amount of energy necessary to blow up Alderaan, we would need 1×10^15 kg of antimatter (and an equivalent 1×10^15 kg of normal matter to collide the antimatter with). This is somewhere around the mass of Mount Everest.

Currently, we can’t make nearly that much antimatter, and what antimatter we make is very difficult to store, because it blows up as soon as it comes in contact with normal matter. A group of researchers at CERN recently managed to produce anti-hydrogen atoms (made of an anti-proton and an anti-electron, called a positron). But this procedure isn’t ready to make Everest-sized quantities of antimatter yet: in an entire year’s work the CERN group only made about 300 anti-hydrogen atoms, and only a small fraction of those survived more than a few minutes.

However, I’m willing to believe that in the Star Wars universe, people are much better at making, collecting, and keeping anti-matter than we are today. And for a planet-sized ship, carrying around a mountain-sized chunk of matter or two shouldn’t be too difficult. So, I’ll give the Death Star a pass on this one.

By the way, I’ve been reading an interesting book by physicist Michio Kaku on the science of science fiction. He that talks about other possible sources of energy for a Death Star-like weapon, including fusion reactions, hydrogen-bomb-powered x-ray lasers, and gamma ray bursters. If you’re interested, the book is The Physics of the Impossible; the discussion of the Death Star is in chapter 3.

That’s it for the Death Star for the moment, but I’ll come back to it next week to talk a little more about the lasers side of things. Get ready to learn about some optics!

(*) Actually, in the Star Wars literature, the Death Star is said to be able to put out the same power as “several” main-sequence stars. Some people object to this, because our sun is a main-sequence star (it generates most of its energy from the fusion of hydrogen nuclei to form helium), and clearly “several” suns is not the same as the “half a million” suns we just calculated.

But this isn’t actually such an inconsistency. Our sun is only one example of a main-sequence star, and there are some main-sequence stars that output more than 100000 times as much power as our sun. If you had four or five of these stars, it would only take about a second to produce 10^32 J of energy. So, it’s certainly possible for the Death Star to meet its power needs if it can generate the equivalent of several higher-output main-sequence stars.

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