Debating Dyson spheres

a wonderfully geeky debate is unfolding about the practicality of Dyson Spheres. Or rather, a subset type called a Dyson Swarm. George Dvorsky begins by breaking the problem down into 5 steps:

  1. Get energy
  2. Mine Mercury
  3. Get materials into orbit
  4. Make solar collectors
  5. Extract energy

The idea is to build the entire swarm in iterative steps and not all at once. We would only need to build a small section of the Dyson sphere to provide the energy requirements for the rest of the project. Thus, construction efficiency will increase over time as the project progresses. “We could do it now,” says Armstrong. It’s just a question of materials and automation.

Alex Knapp takes issue with the idea that step 1 could provide enough energy to execute step 2, with an assist from an astronomer:

“Dismantling Mercury, just to start, will take 2 x 10^30 Joules, or an amount of energy 100 billion times the US annual energy consumption,” he said. “[Dvorsky] kinda glosses over that point. And how long until his solar collectors gather that much energy back, and we’re in the black?”

I did the math to figure that out. Dvorsky’s assumption is that the first stage of the Dyson Sphere will consist of one square kilometer, with the solar collectors operating at about 1/3 efficiency – meaning that 1/3 of the energy it collects from the Sun can be turned into useful work.

At one AU – which is the distance of the orbit of the Earth, the Sun emits 1.4 x 10^3 J/sec per square meter. That’s 1.4 x 10^9 J/sec per square kilometer. At one-third efficiency, that’s 4.67 x 10^8 J/sec for the entire Dyson sphere. That sounds like a lot, right? But here’s the thing – if you work it out, it will take 4.28 x 10^28 seconds for the solar collectors to obtain the energy needed to dismantle Mercury.

That’s about 120 trillion years.

I’m not sure that this is correct. From the way I understood Dvorsky’s argument, the five steps are iterative, not linear. In other words, the first solar panel wouldn’t need to collect *all* the energy to dismantle Mercury, but rather as more panels are built their increased surface area would help fund the energy of future mining and construction.

However, the numbers don’t quite add up. Here’s my code in SpeQ:

sun = 1.4e9 W/km2
sun = 1.4 GW/km²

AU = 149597870.700 km
AU = 149.5978707 Gm

' surface of dyson sphere
areaDyson = 4*Pi*(AU^2)
areaDyson = 281229.379159805 Gm²

areaDyson2 = 6.9e13 km2
areaDyson2 = 69 Gm²

' solar power efficiency
eff = 0.3
eff = 0.3

' energy absorbed W
energy = sun*areaDyson2*eff
energy = 28.98 ZW

'total energy to dismantle mercury (J)
totE = 2e30 J
totE = 2e6 YJ

' time to dismantle mercury (sec)
tt = totE / energy
tt = 69.013112491 Ms

AddUnit(Years, 3600*24*365 seconds)
Unit Years created

' years
Convert(tt, Years)
Ans = 2.188391441 Years

So, I am getting 2.9 x 10^22 W, not 4.67 x 10^8 as Knapp does. So instead of 120 trillion years, it only takes 2.2 years to get the power we need to dismantle Mercury.

Of course with the incremental approach of iteration you don’t have access to all of that energy at once. But it certainly seems feasible in principle – the engineering issues however are really the show stopper. I don’t see any of this happening until we are actually able to travel around teh solar system using something other than chemical reactions for thrust. Let’s focus on building a real VASIMIR drive first, rather than counting our dyson spheres before they hatch.

Incidentally, Dvorsky points to this lecture titled “von Neumann probes, Dyson spheres, exploratory engineering and the Fermi paradox” by Oxford physicist Stuart Armstrong for the initial idea. It’s worth watching:

UPDATE: Stuart Armstrong himself replies to Knapp’s comment thread:

My suggestion was never a practical idea for solving current energy problems – it was connected with the Fermi Paradox, showing how little effort would be required on a cosmic scale to start colonizing the entire universe.
Even though it’s not short term practical, the plan isn’t fanciful. Solar power is about 3.8×10^26 Watts. The gravitational binding energy of Mercury is about 1.80 ×10^30 Joules, so if we go at about 1/3 efficiency, it would take about 5 hours to take Mercury apart from scratch. And there is enough material in Mercury to dyson nearly the whole sun (using a Dyson swarm, rather than a rigid sphere), in Mercury orbit (moving it up to Earth orbit would be pointless).

So the questions are:

1) Can we get the whole process started in the first place? (not yet)

2) Can we automate the whole process? (not yet)

3) And can we automate the whole process well enough to get a proper feedback loop (where the solar captors we build send their energy to Mercury to continue the mining that builds more solar captors, etc…)? (maybe not possible)

If we get that feedback loop, then exponential growth will allow us to disassemble Mercury in pretty trivial amounts of time. If not, it will take considerably longer.