How Big is the Death Star?

I recently became curious about the death star. It’s fictional, I know; but I kept asking questions: What would it take to supply such a large space station? What about to build it? Does it have enough gravity to walk along the surface? Come along down this rabbit hole with me.

Image: JMAS

Note: the Death Star I chose to look at in this article is the larger Death Star II (160 km in diameter vs. 120 for Death Star I). Death Star II is the one Lando Calrissian destroys above the forest moon of Endor in Return of the Jedi, not the one that the Luke destroys in A New Hope. 

The Physics

I started this journey by looking up the specs of the Death Star and calculating its volume, mass, surface gravity etc… I soon found an oft-quoted stat online that mentioned the Death Star’s volume was “17.16 quadrillion cubic meters.” This surprised me because the answer I got was an order of magnitude lower. After looking into it, I found out this calculation had been done using 160 km as the radius, not the diameter, yielding an incorrect answer. Below are the correct stats for the Death Star:

Diameter* ………………..……… 160 km

Volume …………………..………. 2.1 quadrillion m³

Mass** ………………….…………1.6 quadrillion kg

Surface gravity …………………. 0.0002 % of Earth

Total Crew* ……………………… 2,471,647 (This is strangely specific)

*According to Wookiepedia

**Assuming 1/10 of the volume is steel

Earth and the Death Star to Scale

The first thing that struck me that the Death Star is small. I know the movie compared the Death Star to a "small moon," but the Death Star is much smaller than I imagined, on the scale of Jupiter's tiny moon Janus, or, appropriately (it looks just like the death star), Saturn's moon Mimas.

The second thing that caught my attention was the very low surface gravity. If I was out walking along the surface of the Death Star, I would weigh about the same as a large grain of sand. If I had one or two friends with me, we could lift the Titanic off the surface. If you could get enough traction, you could simply walk into orbit (1.15 m/s). The Death Star is massive for a space station, but because there are a lot of empty spaces, it just doesn’t have that much pulling force.

The Crew

What about the crew? How much do they need to eat? How much waste needs to be disposed of?

First off, let's look at butter. Butter is the one of the most calorie rich foods out there, so if we assume everyone just eats butter, we'll get our most conservative estimates.

A stick of butter contains about 800 calories, and an adult human needs a little less than three sticks of butter to survive for a day (do not try). By volume, about 10 people need a liter of butter per day. This means that the Death star requires about a quarter-million liters of butter per day to feed its personnel. That's about 7 Boeing 747 cargo planes' worth of butter, which seems manageable. You would need another 2 and a half planes for the water, but overall, that seems pretty reasonable.

According to Wookiepedia, the Death Star has a 3-year store of food (assuming Earth years, even though Earth is in a faraway galaxy in the distant future), which in butter terms is about 1 Hindenburg.

Overall, no real problems arise when stocking the Death Star with food and water, even if the calorie density is much less than that of butter.

What about waste? One average US citizen in 2008 produced about 2 kilos of food per day. On the Death Star, this equates to 5 million kilos over the whole population, or less than half of the daily trash output of New York City.

A good way to think of the Death Star is about one "Chicago" of people (new unit). The Death Star needs about the same amount of food, and generates the same amount of waste as a large city.

The Death Star has about 1,600 Dropships that, if operated around the clock, could supply food and water to the entire Death Star. Waste could simply be expelled into the atmosphere of the forest moon of Endor. Then it's the Ewok's problem.

Image: David Kingham

The Cost

The answer to the question of how much the Death Star would cost to build started with flawed numbers, so I've redone the calculations.

The current (Sept. 2015) cost of steel is 140 US dollars per tonne. To put our weight in tonnes from kilos, we can just knock off three zeros, getting us 1.6 trillion tonnes of steel, coming in at 224 trillion dollars just for the steel. To lift this amount of steel into orbit would cost 35 quintillion dollars and take 70 billion US Shuttle flights. and to avoid collapsing the global steel market (and to make things cheaper), let's just grab an asteroid with that amount of steel and hollow it out to make our death star.

Image: Josef Ďurech, Vojtěch Sidorin

16 Psyche

16 Psyche should do nicely; it's mainly nickel and iron, 200 km across, and we could find some carbon and smelt steel to make our Death Star. That should keep the total bill under a few trillion to get the raw materials together. As far as turning these elements into the Death Star, that's pretty much out of reach with the planet's current resources.

Overall, it seems that most aspects of the Death Star are out of our reach, and without a bent for galactic domination, I think we should leave the construction of Death Stars to galactic empires in the distant past, and we should focus on, say, getting to Mars. That's a good starting point.


     Cheers,
   
          - Scott

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