Someone on another site asked why it took the Empire 18 years to build the Death Star in A New Hope. They seemed to think that was longer than it should take instead of insanely fast (as is my stance.)

Fermi Problem time!

Assumptions I am making and why:

1. The Death Star is a solid sphere. I am doing this to simplify the calculations since I do not know the ratio of empty space to total volume of the Death Star.
2. The Prudential Tower is a solid object with a total volume of approximately 481,000 cubic meters. Same reasons as for the Death Star with the volume being estimated from the height of the building times (the total floorspace divided by 52 floors). Again this just makes computing the values easier.

More Background:

The Death Star in A New Hope had a diameter of 167 km. That means it had a radius of 83,500 meters. 4/3*pi*r^3 means that the total volume of the Death Star in ANH is approximately 2.44x10^15 cubic meters.

The Prudential Tower took four years to construct, we can assume that the Empire would construct it much faster, but the question is how fast.

The Values and Computations:

• At 1 Prudential Tower per year: (2.44x10^15)/481,000 = 5.07x10^9 years. It would take 5.1 billion years to construct the Death Star at this speed. Obviously too slow.
• At 1 Prudential Tower per week: (2.44x10^15)/(52*481,000)=9.75x10^7. It would take 97 million years. Still too slow.
• At 1 tower per day: (2.44x10^15)/(365*481,000)=1.34x10^7. It would take 1.3 million years. We're getting there.
• At 1 tower per hour: (2.44x10^15)/(481,000*365*24)=5.79x10^5. 579 thousand years. So close.

Conclusion:

So how many Prudential Towers would the Empire have to build in one year to complete the Death Star in 18 years?

(2.44x10^15)/(18*481,000)=281,663,423 Prudential Towers per year. That is 8.93 Prudential Towers per second or one Prudential Tower every 0.112 seconds. Insanely. Fast.

Limitations of this estimate:

1. All values are approximate and likely has an uncertainty in the thousands if not greater.
2. Construction is not actually conducted per unit volume.
3. The percentage of volume that is free space in the Death Star is probably on the order of 75% and that of the Prudential Tower is probably about 85%+.
4. The Death Star is not a perfect sphere.
5. I am sure that there is some technology in the Star Wars universe that makes comparing Earth construction to the Death Star pointless. I mean besides the obvious "it's fiction" reason.

Anyway, that was my stupid argument, just thought I'd share.