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# How Much Power Would the Death Star Need to Blow up the Earth?

We ran the numbers. They're substantial.

by Sean Hutchinson
StarWars.com

It’s no moon, it’s a space station! One of the most lethal weapons in the galaxy — at least in science fiction — was the Death Star, first seen as a fully functioning force for evil in Star Wars. The spherical space station was the evil Galactic Empire’s mobile avatar of kaboom. Its deadliest weapon was a massive superlaser formed by eight smaller beams that merged into an ultra-powerful stream strong enough to obliterate Princess Leia’s home planet of Alderaan. It makes us wonder: What would it actually take to blow up a planet? Earth, let’s say. Y’know, for kicks.

Star Wars isn’t long on stats, but its legions expanded-universe geeks have calculated that Alderaan isn’t terribly far off from our own planet. Our hypothetical demise might, thus, look like this:

Artist’s conception, natch. According to Wookieepedia, the comprehensive encyclopedia for everything Star Wars, Alderaan was about 7,700 miles in diameter, a bit more compact than Earth’s 7,900-mile width. As referenced by Luke, the original Death Star is the size of a “small moon.” The Star Wars wiki says the Death Star was just over 99 miles in diameter, significantly smaller than our own moon whose diameter is 2,159 miles around. Size doesn’t matter, but of course you already knew that. It’s a good bet that the Death Star could blow up the Earth; the only question is how much juice it would take.

Astrophysicist Neil deGrasse Tyson, on his podcast Star Talk, explained how to figure out what such a job would require. “Ask yourself, how much energy is keeping [the planet] together?” Tyson says in an episode. “Then you put more than that amount of energy into the object. It will explode.”

Sounds easy, right? Tyson explains that we need to calculate the binding energy of Earth — how much energy the force of gravity exerts to hold the planet together. Then get an energy source (e.g., the Death Star) to pump energy in excess of that amount into the planet. Voila, the planet in question turns into a pretty puff in some other world’s night sky.

I asked professor Michael Tuts, the chair of the Columbia University physics department, how to get that number. “The energy to ‘blow up’ is the same as the energy it would take to ‘assemble’ a planet from dust — that energy would be the gravitational potential energy,” he said, echoing Tyson.

Tuts ran the numbers we’d need to blow up the world. If m = the mass of planet Earth (equal to 6 x 10^24 kilograms), and r = the radius of planet Earth (equal to 6 x 10^6 meters), the gravitational potential energy for a uniform density spherical planet Earth would equal 2 x 10^32 joules, or 200,000,000,000,000,000,000,000,000,000,000 joules. For comparison, 1 joule is how much energy you exert by lifting a small object 1 meter into the air.

Michael Shara, a curator in the Department of Astrophysics in the Division of Physical Sciences at the American Museum of Natural History in New York City, explained the situation in more astronomical terms. He compressed the amount of energy into a figure that would represent the energy needed to blow up Earth.

“The gravitational self-binding energy of the Earth is roughly 10^39 ergs,” Shara said. An “erg” is a unit of measure astronomers use, equal to 10^-7 joules. Conversely, 1 Joule equals 10^7 ergs. (The conversion can seem tricky; Shara compared it to a monetary exchange where \$1 is worth ‎¥10,000.) “If this much energy were instantaneously released at the core of the Earth, our planet would be blown apart,” he explained. “The way to do this is to instantaneously mix 10^18 grams of matter (1,000 billion metric tons) with an equal amount of antimatter at the Earth’s core. The resulting burst of gamma rays would vaporize the core of the Earth, which would blast the Earth apart in minutes.”

The numbers don’t lie: Release 10^39 ergs or 10^32 joules in the middle of the planet and Earth will turn into a cosmic sneeze. Turns out that is a fantastic amount of energy to release, even on the scale of space. Shara said one of the only forces in the universe with that capability is an exploding nova or supernova. “Fortunately,” he said, “none are nearby.” Unfortunately for our purposes, however. What do we have on terra firma that could get the job done?

Maybe we could ignite the radioactive elements in the core? Not so, says Jung-Fu Lin, a Ph.D. geophysicist working at the University of Texas. “The Earth’s core is mainly made of molten iron in the outer core and solid iron in the inner core, together with some percentage of light elements such as sulfur, silicon, and/or oxygen,” he told me. “There may be some diluted amounts of radiative elements in the core, but their amounts are so small that scientists do not believe nuclear reaction would occur in the core.”

So blowing the planet up using its juicy center was out, but what if we got back to the Death Star idea and enlisted the most powerful laser in the world? The current titleholder is at Osaka University in Japan: a laser capable of a 2-petawatt (or 2 quadrillion-watt) pulse. We didn’t hear back from Osaka U’s researchers, but we did get ahold of Michael Donovan, associate director for the Texas Petawatt, the most powerful laser in the U.S., located at the University of Texas, capable of a 1-petawatt pulse. He quickly dashed our hopes.

The Texas Petawatt’s energy output equals about 150 to 200 Joules, the amount found in your morning coffee — far from the world-shattering firepower we need. “If you deliver energy over a very, very short period of time at an immense rate, you still don’t deliver much energy,” Donovan said. “Damage is about how much work you do, or equivalently how much energy you deliver that makes an irreversible, unwanted change.” He then added, much to my dismay, “Since the laser energy is modest, you can’t do large-scale damage, and that is the case of a petawatt laser.”

Donovan was skeptical, because he’s a person who deals in the realm of real facts in the real world, but we could conceivably blast the Earth with a lethal amount of energy from petawatt lasers. That would, of course, consume resources only a tyrannical Galactic Empire could pull off. What damage could do with what we’ve got on hand? The best answer then, perhaps unsurprisingly, points to nukes.

The world hasn’t used nuclear weapons since the United States dropped Fat Man and Little Boy on Hiroshima and Nagasaki in 1945. But that doesn’t mean the weapons haven’t advanced. The U.S.S.R. detonated the Tsar Bomba, the most powerful destructive force the world has yet seen, on October 30, 1961. Its 50-megaton blast was more than 3,000 times more powerful than the Hiroshima and Nagasaki bombs, strong enough to shatter windows more than 500 miles away. That amount of force would put the total number of Tsar Bomba-level nukes to destroy Earth somewhere around 15,600 bombs.

This figure is down considerable since the end of the Cold War, but the world has about 15,700 nuclear warheads at its disposal today. Few-to-none are as potent as that Soviet monster that sent a mushroom cloud 40 miles into the atmosphere. But let’s just call that sucker proof of concept. All we’d need is 15,600 copies of a vintage model nuke deposited at the center of the planet to literally blow up the world. We’re closer to the evil Empire than we realize.

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