Recently, the White House responded to a petition to “begin construction of a Death Star (the planet buster from the Star Wars movies) by 2016. They declined, partially on the grounds that it would be too expensive, with the numbers having been crunched by the folks over at centives.net, saying that the steel would cost around $852 quadrillion. However, we think that in reality, it would actually be much cheaper, and is a proposition that Mr Obama should reconsider.
Firstly here is a link to the original post analysing the cost on centives.net, an excellent blog on “quirky economics” from how much of a cut Domino’s take on your toppings to the game theory involved in The Hunger Games. I recommend that you take a bit of time to read this before getting started on our article.
The major premise of their calculation is that we can assume the same steel density in the Death Star would be about the same as that on HMS Illustrious. However, this doesn’t take into account the fact that the Death Star is largely empty inside, so really, the vital statistic is in fact surface area, as this is where the majority of the mass of the steel will be. In addition, by scaling up directly with a volume ratio, the post doesn’t consider that that will involve massively thickening the walls of the Death Star to a completely unnecessary level.
Using the geometry of HMS Illustrious, the best estimate I can get for the surface area of the steel hull is about 60000 m2. The weight of the steel is given as 22,000 tonnes, which gives us a “mass per unit surface area” for the ship hull of 377 kg/m2.
The online Star Wars holy grail that is Wookiepedia gives the Death Star a diameter of 140km. The Death Star is (roughly) spherical, so we can find its surface area with the formula A=4πr2, which gives the Death Star a surface area of 6.15 × 1010 m2. Multiplying this by our “mass per unit surface area” constant, we can find the total mass of the Death Star, which is only 2.32 × 1013 kg, or about 23 trillion tonnes. This sounds like a vast mass, but when you compare that to centives’ original estimate of about 1 quadrillion tonnes it is actually pretty trivial in comparison. In fact, the difference is so great that our estimate requires nearly 500,000 times less steel!
This is a complete game changer. With the original calculations, even if the entire world’s resources were put into a giant Death Star piggy bank, it would take 13,000 years just to get the funds to buy enough steel, and then it would take more than 833,000 years to produce the steel! However, with the revised calculations, a death star is beginning to flirt with possibility.
The GWP (Gross World Product) as of 2012 is just over $69 trillion (all values in USD), and using centives’ steel prices, the steel would now only cost about $18.3 trillion. In other words, with the whole world putting money towards it, the funds could be raised in just over three months! However, seeing as the petition was put to the White House, we find it unlikely that the rest of the world is likely to want to fund the USA to build a death star, so they may have to go it alone. Fortunately for them, they are the world’s largest economy, and could raise the funds purely out of their own GDP in just 15 months.
And then we get to steel production. Without international cooperation, this could be problematic. At current rates, the US are producing 86 billion tonnes of steel per year. Whilst better than 833 millenia, it would still take them 270 years to produce enough steel. Should production actually commence, one would hope they’d make steel more of a priority, but if the rest of the world did cooperate and not refuse to sell steel to them on the grounds that they were building a weapon capable of destroying the planet, then it would only take 15 years for enough steel to be produced. This would mean that in order for production to be completed though, the Democrats would either have to win the next three elections (at least), or some cross-party consensus would have to be reached to finish what they started.
So within 15 years, the US could have their very own Death Star! But once this happens, they must choose their first target, and there is no doubt as to where that should be. No, not Swindon, but Mars: that evil red planet which is (maybe) teeming with intelligent life that seeks nothing but to destroy us. It’s the only logical option.
But at this point, all they have is a giant steel sphere. That wouldn’t do much to blow up Mars.
Fundamentally, in order to “blow up” a planet, you need to get the entire mass of the planet to the escape velocity so that it can escape its own gravity. On Mars, this escape velocity is 5000 m/s. We can use the following equation for kinetic energy (assuming a 100% efficiency) to find out how much energy would need to be inputted to blow Mars up.
Where E is energy in Joules, m is mass in kg, and v is velocity in m/s.
We already know that v is 5000, and the mass of Mars is 6.4 × 1023 kg, so plugging those numbers in, we get a required energy of 8 × 1015 Petajoules, or 8 thousand billion billion billion Joules. That’s 40 trillion times more powerful than the most powerful nuclear bomb ever, the Tsar Bomba, but surprisingly, this is still potentially possible – this would require less than a third of the obtainable Uranium-238 reserves in the world in a fusion reaction!
So, Mr Obama, on the day of your inauguration, we do not accept your claim that building a Death Star would be impossible! We urge you to adopt this ambitious and exciting policy at once, and take your opportunity to be remembered as a truly great president!