What if the Death Star was real?

I was just reading about this petition earlier this year to the US President to build a Death Star and so that got me to thinking about what if we did actually build a Death Star. So the Death Star is the implement of destruction in Star Wars movies that floats around and blows up planets. We've got the International Space Station up there at the moment but let's stop messing around and replace it with the Death Star, let's scale up a bit. So the first obvious question is how big would it look from down here on Earth and the answer is enormous actually. It would be about 45 times the width of the full moon across if you just looked up at it so it would be by far the biggest thing in the sky. So it's about, according to the specification you have to go and read on the Star Wars websites and find out exactly what the technical specifications are if you do decide to build your own Death Star and if you do it works out that it's about 160 kilometres across and so if you do that and then put it in the lower orbit that the International Space Station is which is about 400 kilometres up, that's actually absolutely huge and actually you run into a few problems because 400 kilometres up if you build something 160 kilometres across that's a decent fraction of the distance back down to the Earth again so you're going to start worrying about whether it's getting back into the atmosphere so you might want to push it a bit further away rather than putting it quite as low down as the International Space Station. If you're going to build a Death Star you want to kill things right, you want to blow things up and so the big thing about the Death Star is this laser cannon that it's got that it uses to explode planets with. A super laser. A super laser, pardon me, yes, so again if you go back to the technical specifications for a Death Star it's not very clear about how powerful this super laser actually is but you can figure it out just by watching the film because it actually destroys a planet kind of about the size of the Earth and it fires for just a couple of seconds and in that couple of seconds that provides enough energy to basically vaporise the planet to send it all flying apart. That was Alderaan that planet. Pardon me, yes, the planet of Alderaan and so actually you can just from that one piece of information you can figure out how powerful the laser has to be. So the way this works is I mean it basically destroys the planet by making it all fly apart and the amount of energy you need to make a planet fly apart doesn't matter how you do it. The amount of energy is the same if you do it explosively in that way or if you did it sort of the slow way of just taking the planet apart bit by bit and so you can figure out how much energy you need to completely destroy a planet just by doing the sort of experiment of what would happen if I took it apart bit by bit. You can calculate the total energy you need to destroy a planet on that basis but if you want to know what the power of the laser is that's how much energy it gives per unit time. So if you want it in watts that's joules per second energy per unit time and so actually if you want to figure out the power of the laser you need both the amount of energy it delivers but how long it takes to deliver it as well. So I sat there and timed it and this whole thing is going to be very back of the envelope order of magnitude type calculation because it's really not worth trying to do this calculation terribly carefully but basically it fires for a couple of seconds which is accurate enough for these purposes. We need to do the maths now if you want to actually figure out what the energy is. So if I have a planet and I want to start taking little bits of it out so supposing the planet will give it a mass big M and I want to take out the first little mass so we'll call this little m1. I want to take that little bit of the earth and kind of pull it away all the way off to infinity or just a long way away. The amount of energy I need to put in to do that is given by one of Newton's laws and it's basically g m1 m over little r like that. Okay so that was one little bit and then I can you know take the next little bit away and then I have to do the same thing again so you end up with g so I need to add a bit more energy to pull it that bit apart m2 over r and so on. Just keep doing that and I can rewrite this equation if I want to as g times big M divided by little r times all these little sums here and then all the other bits as well. But of course when I've taken the entire planet away that's going to be the mass of the planet this whole lot. So the formula I'm going to end up with is g times m2 divided by r. Now this is a little bit of a fraud because this is the r that you start from and that's the r that goes in there. Of course as I'm digging away more and more of the planet r's getting smaller and smaller because I'm getting closer and closer to the centre and actually m's getting smaller and smaller as well because there's less and less mass left behind to kind of pull back on the bits that I'm pulling away because that's what I'm doing is pulling away against the force of gravity. And so this formula isn't exactly right, it's just approximately equal to that and there's some numerical factor out in front of it but it's probably right within a factor of two which again for the purpose of these kind of calculations is entirely adequate. So if I want to, to figure out to destroy an Earth-like planet if I put the symbol for the Earth here, cross with a circle around it and the symbol for the Earth down here, that's basically the energy I would need to expend to destroy an Earth-like planet. Gravitational constant times the mass of the planet squared, mass of the Earth squared divided by the radius of the planet, radius of the Earth. If you plug all the numbers in for the Earth, that works out at a few times 10 to the 32 joules so that's like 2 or 3 with 32 zeros after it. And of course remember it actually took a few seconds so basically the power of the laser then has to be about 10 to the 32 watts so that's 1 with 32 zeros after it. So to put it in perspective, the most powerful laser in the world, which is actually Lawrence Berkeley Lab which they're using to accelerate electrons, that's 17 orders of magnitude less powerful. So the most powerful laser in the world is 17 orders of magnitude, that's 1 with 17 zeros after it times less powerful. Or in other words I would need 1 with 17 zeros of it, of these lasers if I wanted to generate the laser power of one Death Star. So that seems hefty. And actually that's not the worst of the problems because then even if I could build such a laser then I need the energy to power it. So I was thinking now how could I power my Death Star? And electricity seems like a sensible way of doing it. So I went and looked up what the total power generation capacity of the Earth is. So where are all the power stations on Earth? And if you were to take all the power stations on Earth and put them to work to generate enough energy to fire this laser once, then you'd actually have to set them to work for a few trillion years. So which is what, 100 times the lifetime of the universe to actually just get the thing to fire once. Well that's not going to happen. That's not going to happen. But again I messed up, right, because I should have looked again in the technical guide as how to build a Death Star. And it says actually a Death Star isn't powered by electricity, it's powered by a thing called hypermatter. What's hypermatter? I have no clue. But I can... You must know what it is, you're a physicist. It is a creation of science fiction I believe. Even though I don't know what it is, I can at least put an upper bound on how good it is because I know that the maximum amount of energy I can get out of anything is given by Einstein's famous equation E equals mc squared. So I could figure out what the most efficient way I could possibly generate the energy needed to fire the Death Star once by using that formula. I know what the energy I need is, I just plug it in, that then tells me how much mass I need to completely annihilate in order to generate that much energy. And it works out that's about 10 to the 15 kilograms, one with 15 zeros after it, kilograms, which turns out to be almost exactly the mass of Mount Everest. So every time you fire your Death Star you've got to completely vaporise Mount Everest's worth of mass. There seems something quite poetic about the fact that you would need the largest mountain on Earth to destroy the Earth. Oh yeah, it has a certain ring to it, doesn't it?