So, BolianAuthor and I started hypothetically thinking about just what it would require, materially, to manufacture a Dyson sphere large enough to encompass the supermassive hypergiant, VY Majoris - largest known star in the sky. Just thought we'd share our interesting little computations with the rest of the nerdy world.
So it's a fairly simple calculation with admittedly a handful of hand-waving generalities but as will become apparent, the dominant factors are the sheer size and scope of what we're talking about.
I'll spare every detail of the computation but naturally, the first step is - surface area of a sphere, quite well known it's just 4pi*r^2.
1. What's your r? We took the diameter of the Dyson sphere to be 1.1 times the diameter of VY Majoris, to put approximately 85 million miles between the surface of the star and the inner surface of the sphere. The surface area, then, is on the order of 10^31 square miles.
2. Next you need an idea of how thick the shell is going to be. Bolian and I disagreed at first and this spec is probably the hardest to defend because - well let's face it, a Dyson sphere, not to mention whatever material it ends up being made out of (we'll get there) is a completely hypothetical technology, so whatever depth you come up with is kind of handwavey anyway. As it turns out, the amount of material is far more dependent on radius than thickness, so it's not all that important. We went with a thickness of 50 miles.
3. With the surface area and thickness you can compute a total volume of material you need - and it comes to around 10^34 cubic feet. I started moving into goofy English units because the densities published for materials like raw steel are in goofy English units.
4. With a density of 4.55 oz / cu in (don't ask), raw steel is pretty heavy - but again, it really doesn't matter as much - because the total mass has a linear dependence on density and a quadratic dependence on radius. The total mass of steel required, is approximately 2 x 10^31 tons (short tons).
5. A quick google search told me that in 2010, the total production of steel reached 1.4 billion tons (that's short tons - 2000 lbs). A few quick calculator steps and a bunch of ridiculous English conversions later, you realize that at OUR rate of production, it would take around 14.1 sextillion years to harvest that much steel. Assuming the universe has a finite lifetime, I'm not familiar with any obscure variant of inflationary big bang theory that claims the Universe is going to live that long - most of the time numbers like 70 billion years or 1 trillion years come out of the mix. So, just for fun, if we assume that an alien species learns how to harvest steel on a planet 100 times faster than we can, then we can chop 2 zero's off that number. 141 quintillion years is still infeasible.
6. Multiple Simultaneous Planetary Harvest - So what if this hypothetical species is harvesting steel on say... a billion planets simultaneously at a rate of 140 billion tons per year? well then you can chop of 9 more zeros and we're down to about 10 billion years. Probably within the lifetime of a finite universe.
In other words, it would take an advanced civilization that can harvest steel 100 times faster than we can 10 billion years, working simultaneously on 1 billion planets across the galaxy (or universe), to produce enough steel to actually manufacture a sphere with a reasonable radius and an extremely conservative thickness.
Now the question is - how much do our assumptions impact this result? Well if you think a species that can operate on 1 billion planets simultaneously could use something lighter than steel, well you can chop 3 zero's off if it's 1000 times lighter - we're only down to 10 million years on 1 billion planets.
If you're thinking 'Well if they're just harvesting entire planets for whatever raw materials needed, maybe they can do it 10,000 times faster than us', that's another 3 zeros - which brings us to 10,000 years... ON A BILLION PLANETS.
Considering this extremely distant possibility, we have to also consider that purification... manufacturing... and presumably, moving the pieces into position... would also be an extremely lengthy process. In other words, a Dyson sphere of this magnitude is not likely a feasible engineering feat for any species whose means of manufacturing is confined to the known laws of physics.
Bow, cue applause.
oh and blame Bolian.
FYI: I forgot to note that the lifetime of supermassive hypergiants is on the order of 100 million years or less, so, in reality that becomes a limiting condition before the age of the universe does.
So it's a fairly simple calculation with admittedly a handful of hand-waving generalities but as will become apparent, the dominant factors are the sheer size and scope of what we're talking about.
I'll spare every detail of the computation but naturally, the first step is - surface area of a sphere, quite well known it's just 4pi*r^2.
1. What's your r? We took the diameter of the Dyson sphere to be 1.1 times the diameter of VY Majoris, to put approximately 85 million miles between the surface of the star and the inner surface of the sphere. The surface area, then, is on the order of 10^31 square miles.
2. Next you need an idea of how thick the shell is going to be. Bolian and I disagreed at first and this spec is probably the hardest to defend because - well let's face it, a Dyson sphere, not to mention whatever material it ends up being made out of (we'll get there) is a completely hypothetical technology, so whatever depth you come up with is kind of handwavey anyway. As it turns out, the amount of material is far more dependent on radius than thickness, so it's not all that important. We went with a thickness of 50 miles.
3. With the surface area and thickness you can compute a total volume of material you need - and it comes to around 10^34 cubic feet. I started moving into goofy English units because the densities published for materials like raw steel are in goofy English units.
4. With a density of 4.55 oz / cu in (don't ask), raw steel is pretty heavy - but again, it really doesn't matter as much - because the total mass has a linear dependence on density and a quadratic dependence on radius. The total mass of steel required, is approximately 2 x 10^31 tons (short tons).
5. A quick google search told me that in 2010, the total production of steel reached 1.4 billion tons (that's short tons - 2000 lbs). A few quick calculator steps and a bunch of ridiculous English conversions later, you realize that at OUR rate of production, it would take around 14.1 sextillion years to harvest that much steel. Assuming the universe has a finite lifetime, I'm not familiar with any obscure variant of inflationary big bang theory that claims the Universe is going to live that long - most of the time numbers like 70 billion years or 1 trillion years come out of the mix. So, just for fun, if we assume that an alien species learns how to harvest steel on a planet 100 times faster than we can, then we can chop 2 zero's off that number. 141 quintillion years is still infeasible.
6. Multiple Simultaneous Planetary Harvest - So what if this hypothetical species is harvesting steel on say... a billion planets simultaneously at a rate of 140 billion tons per year? well then you can chop of 9 more zeros and we're down to about 10 billion years. Probably within the lifetime of a finite universe.
In other words, it would take an advanced civilization that can harvest steel 100 times faster than we can 10 billion years, working simultaneously on 1 billion planets across the galaxy (or universe), to produce enough steel to actually manufacture a sphere with a reasonable radius and an extremely conservative thickness.
Now the question is - how much do our assumptions impact this result? Well if you think a species that can operate on 1 billion planets simultaneously could use something lighter than steel, well you can chop 3 zero's off if it's 1000 times lighter - we're only down to 10 million years on 1 billion planets.
If you're thinking 'Well if they're just harvesting entire planets for whatever raw materials needed, maybe they can do it 10,000 times faster than us', that's another 3 zeros - which brings us to 10,000 years... ON A BILLION PLANETS.
Considering this extremely distant possibility, we have to also consider that purification... manufacturing... and presumably, moving the pieces into position... would also be an extremely lengthy process. In other words, a Dyson sphere of this magnitude is not likely a feasible engineering feat for any species whose means of manufacturing is confined to the known laws of physics.
Bow, cue applause.
oh and blame Bolian.
FYI: I forgot to note that the lifetime of supermassive hypergiants is on the order of 100 million years or less, so, in reality that becomes a limiting condition before the age of the universe does.
