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
Nobody said it had to be a solid sphere, how else would you get it to emit the ominous hum without attuning its natural frequency by carefully designing the thickness of the obsidian layer?
ignores engineering and construction cost. but we can assume that all people involved would work for free, because its a massive honour
Wouldn’t it be better to use all that obsidian to build nether portals so we can build a public transit system on the bedrock roof?
Now that you mentioned public transportation the US will never agree to the project
