this post was submitted on 02 Dec 2023
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Turns out it'd be a dissapointingly small sphere:
US annual defence budget = $800 billion
2% = $16 billion
Obsidian cost per kg = $5
Total kg in budget = 3.2 billion kg
Density of obsidian = 2.6 g/cm3 = 2600 kg/m3
Total volume of sphere = 3.2b/2600 = 1230769 m3
Volume of sphere = 4/3 π r^3
Radius = (3V/4π)^(1/3) = 66.48 m
The sphere would only stand at 133m tall, I propose we instead utilise the entire defence budget for a much more skyscraper like 490m tall orb
You're assuming one year of budget. I take it as 2% per year and something of that size would likely take 10+ years to build out.