What?
> I'm not sure where your 8e9 number is coming from. Population doubling every year but the parents leaving the planet after mating?
That's the current human population.
> In your calculation, after 1000 years, there would be 2^40 humans, each weighing 100kg - many orders of magnitude less than Mercury's mass.
You start with one human, I didn't. What are you even imagining that I'm describing, Adam-only parthenogenesis?
> Still, if we give it a few thousand more years of exponential growth, you will eventually reach such masses.
Even with Adam-only parthenogenesis, log2(8e9)*25 years is 822 years, less than one, definitely not plural, millennia.
Material science isn't my field, though it doesn't need to be given how many other places there are for whichever chemicals we want. Water? Oxides in the local rock, and four massive hydrogen gas giants (don't need much proportionally as H2O is 89% oxygen by mass).
> I very much doubt your energy calculation as well, but that's already beside the point.
Gravitational binding energy of Earth: 2.2e32 J; Mercury: 1.8e30 J; Mars: 4.9e30 J; Luna: 1.2e29 J
Luminosity Sol: 3.8e26 W
Time required to explosively disassemble (i.e. each part reaching escape velocity) each object: Earth: 6.6 days; Mercury: 1.3 hours; Mars: 3.6 hours; Luna: 313 seconds.
To preempt the obvious, yes I know that's the number for total luminosity and not the power available at any given moment given how many space habs have been built part way through the process, but that makes very little difference: Given the way the functions behave, you don't need most of the power of the sun until you can harness a significant percentage of it anyway.
I mean, this toy model also assumes that the only thing these humans do with their lives is reproduction, with the average individual adding only a little more than their own body mass to the VN swarm each generation, and not, e.g., building themselves a nice little space hab that's unlikely to mass less than 10,000 kg/person even if I make the grossly simplifying assumption of just adding life support to a tiny house or a camper van. It makes very little difference to exponential growth.