I stumbled upon an infographic the other day about the death star and the numbers seemed off to me. I couldn’t quite put my finger on what seemed wrong, but there just seemed to be something that didn’t quite match up. So, being a physicist and fairly good with numbers, I decided to do some calculations on my own.
The first thing that caught my eye was the number of personnel that worked at the death star. Adding up the numbers given by the infographic (which seemed oddly specific) brings the total number of crew to 1,161,293. This seemed very high to me as I was reading through this because I thought that many of the menial jobs would be taken care of by automatic systems and/or droids since this is the future we are talking about. My concern about the number of people stationed at the death star came from realizing how much food, water, waste, working and living space that many people would require. But I put these concerns aside and read on, seeing what other tidbits about the death star I would soon learn. After reading about the number of ships and weapons the death star has, I was blown away by the size of the battle station. The infographic claims that the death star was 160 km in diameter! This seems way too big to be true, so I decided to do some calculations and find out.
First, I needed to find out the volume of the death star, which comes to 2.1*10^15 cubic meters. After that, I estimated the size of the living quarters for personnel stationed at the death star to be roughly the size of a mobile home, or 20x5x3 (300) cubic meters. To make things simple, I just went ahead and assumed that each person would also have that much space for their work area as well as that much space for their recreational activities. The total living/working/recreation space needed by all the personnel then amounts to 1.0*10^9 cubic meters.
Next, I assumed that each person ate approximately 5 lbs of food and used 1 cubic meter of water a day. I used the density of water to approximate the volume that these would occupy if the death star was to have enough stores for one year. This volume amounted to 4.3*10^8 cubic meters.
Finally, I estimated the size of the vehicles listed in the infographic using information from wookieepedia and from visual estimates based on the movies. I will spare the gruesome details of all the numbers and just tell you that the total volume of all the vehicles stationed in the death star is approximately 4.8*10^7 cubic meters.
Putting these numbers together, these considerations only account for 0.00007% of the total volume of the death star! The infographic does note that some sources put the diameter at 120 km rather than 160, but even with the smaller size, the amount of occupied volume of the death star is 0.0002% of the total volume. Going back to the 160 km size, if you were to spread out the volume uniformly over the surface of the sphere, the layer would only be two centimeters thick.
To put things another way, if the entire population of the death star only lived on the surface of the sphere, kind of like if it was a planet, then the population density would be about 14.4 people/square kilometer. This is less than half of the population density of the United States which has a population density of 33.7 people/square kilometer.
So, either the death star is actually much smaller than the infographic claims, or it was just a big empty ball. I know that by questioning the star wars universe I may incur some geek wrath, but the numbers in this case are staggering. If you want to question my estimates or figures, leave a comment and I will be happy to provide my calculations in more detail.