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Spec Tech: Blowing Up Planets

November 25, 2010

Doomsday scenarios are a dime a dozen. When a villain claims to be on the verge of ‘destroying the Earth’ he/she usually means killing everyone/everything on it. But sometimes simply killing all humans isn’t good enough. Unfortunately even the vast amounts of energy necessary to wipe out all civilization is woefully inantiquate to physically destroy the planet. To do that would take some serious power.

Planets Die Hard

The Earth has been here for about 4.5 billion years. Nothing yet has been able to destroy it, including being slammed into by another planet. Why is it so hard to destroy? The short and somewhat obvious answer is Earth is big—really big. And if you simply break it into a bunch of pieces it will just fall back together again because of gravity. In order to really destroy it you have to break it up and then fling to pieces away at a high enough speed such that they will never come back together (escape velocity). This requires going above and beyond with one’s diabolical destruction schemes.

Energy

To get a rough gauge on how much energy you need to blow up the whole Earth we can treat the Earth as loose bunch of particles held together by gravity. The energy required to pull them apart and fling them away fast enough that they never come back is called the gravitational binding energy. For the Earth this is about 2.24 × 1032 joules. But the Earth is not just held together by gravity. It has a solid crust and liquid interior with surface tension. These are electromagnetic forces called van der Waals forces. I have yet to find a good estimate for the energy required to break the Earth apart in to a collection of gravitationally bound particles, but we can guess. Lets make things simple by just melting it, rounding up and hoping that’s good enough for the gravitational binding energy to do the rest.

It takes about 900 kilojoules to melt one kilogram of crust. There is about 1.365 × 1023 kg of mass in the crust. The rest is mostly molten already. So it would take something like 2.0 × 1029 joules to melt the Earth. It turns out that This is significantly less than the gravitation bounding energy. So we still are left with about 2.24 × 1032 joules as the minimum necessary energy to destroy the Earth. Any scheme we can think of will likely be less than 100% efficient (high energy explosions require all the heat and particles to be completely absorbed, this rarely happens). Lets just say 10% efficiency and round up and say we would need to somehow get 3.0 × 1033 joules.

What Can Do This?

Well, nukes are out. The amount of energy we’re talking about is about 70,000,000,000,000 10-megaton nuclear bombs. That’s about 2 billion times more nuclear bombs than we currently have on this planet. So what can we use instead?

Antimatter is a good candidate. Even with E=mc2 on your side it will still take 300 billion kgs of antimatter to get a big enough blast. We currently seem to be able to make antimatter a few particles at a time. So this is only doable if you have some fancy antimatter making machine.

Lasers also don’t seem up to the task. How exactly a laser would distribute it’s energy across the whole planet isn’t clear to me. Besides that you need to turn store up a huge amount of energy and release it all at once. It’s hard to do this without burning up the laser itself. The National Ignition Facility uses a bank of capacitors filling a stadium sized building. And yet it only has 1/1024 the power necessary.

Slamming it really hard with another planet. Well, this has happened before with no success. All we got was a moon. But if a Mars sized object was moving at 220,000 mph and transfered all it’s energy to Earth that should do the trick. Good luck accelerating a small planet to 220,000 mph though. Perhaps a crafty orbit getting flyby boosts from nearby stars? This has the other disadvantage of having to have good aim. Just like avoiding asteroid collisions a small orbital correction done early enough can cause an object to miss Earth by thousands of miles.

Supernova if right next to the Earth should do the trick, but moving stars is harder then just blowing up the Earth in the first place. Now if you can create a supernova in the middle of the Earth you get bonus points! This would require putting about 3 solar masses in a tight ball in Earth’s core.

Just Hurl It Into the Sun

Instead of blowing up the Earth directly you could also just toss it into the Sun. In fact the Sun has more than enough energy to totally vaporize the Earth, though just not all at once. It would take a few months. Still, destruction is pretty much guaranteed. For the supervillan on a budget it actually turns out to take less energy to throw the Earth into Jupiter! This is because you have to slow down the Earth from it’s current solar orbital velocity (67,000 mph) to almost 0 for it to fall into the Sun, but you only have to accelerate it another 19,800 mph to get it out to Jupiter. Jupiter won’t vaporize Earth but it will swallow it up and incorporate it into it’s core. Accelerating a mass the size of the Earth 19,800 mph to get to Jupiter would take approximately 1019 Saturn 5 rockets all firing at once.

No wonder the Death Star was the size of a moon.

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