[ben_w]

Roughly approximating exponential, but slowing down. And even then with a generational period of… well, of one generation.

Bacteria in the right conditions can do that in 30 minutes.

A hypothetical 1kg clanking replicator that eats moon rock and sunlight and replicates in 1 month would dismantle the moon in just over 6 years. Make it grey goo with a unit size of 1mg while keeping the replication time of a month and it takes 8 years to fully disassemble the moon.

[philipkglass]

Can you avoid running into power limits that would greatly slow the initial exponential progress?

Each square meter of moon receives a time-averaged sunlight input of about 340 watts [1]. The surface area of the moon is 3.79 * 10^13 m^2 [2]. The most efficient silicon solar cell is 27.6% efficient [3]. The gravitational binding energy of the moon is 1.2 * 10^29 joules [4].

Putting all those factors together, gravitational disassembly of the moon will take

(1.2 * 10^29) / (0.276 * 3.79 * 10^13) = 1.15 * 10^16 seconds, or 364 million years.

It will take longer if you model the moon as a shrinking core where all sunlight collection and replication takes place. It can go faster if the replicated units become part of a Dyson swarm beaming power down for disassembling what remains of the moon.

Gravitational disassembly of the moon in 8 years requires an average power of 476 exawatts (10^18 watts). It also seems like you would run into thermal limits trying to turn the moon into more clanking replicators, even if you did have exawatt scale beamed power from your Dyson swarm; you can't beam so much power down that the replicators melt from waste heat before they can finish building.

[1] https://en.wikipedia.org/wiki/Earth%27s_energy_budget#Incomi... -- Earth and its moon are roughly the same distance from the sun, so Earth's top-of-atmosphere solar input is a good approximation to the moon's surface solar input.

[2] https://en.wikipedia.org/wiki/Moon

[3] https://www.nrel.gov/pv/insights/assets/pdfs/cell-pv-eff-cry...

[4] https://www.universetoday.com/121421/how-could-we-destroy-th...

[philipkglass]

I made a critical mistake in my initial "364 million years" estimate -- I forgot to include the wattage per square meter.

Corrected:

(1.2 * 10^29) / (340 * 0.276 * 3.79 * 10^13) = 3.4 * 10^13 seconds, or 1.07 million years.

[ben_w]

> Can you avoid running into power limits that would greatly slow the initial exponential progress?

I doubt it, for all the reasons you give, though I agree the first choice is to do this as part of building a Dyson swarm.

I don’t even know if the interior of the moon is cool enough right now even without the extra heat from manufacturing; but then, I wouldn’t expect to know — I only have a GCSE grade B in chemistry, so I can be sure whoever does invent a von Neumann mechanism, it won’t be me.