It is possible to derive a limit to the total planetary active nanorobot mass by considering the global energy balance. Total solar insolation received at the Earth's surface is ~1.75 x 10^17 watts (IEarth ~ 1370 W/m2 + 0.4% at normal incidence). Global energy consumption by mankind reached an estimated 1.2 x 10^13 watts (~0.02 W/m2) in 1998. This latter figure may also be regarded as the total heat dissipation of all human technological civilization worldwide, as distinct from the ~10^12 watt metabolic output of the global human biomass.
Converting the limit to the amount of nanobots
The hypsithermal ecological limit in turn imposes a maximum power limit on the entire future global mass of active nanomachinery or "active nanomass." Assuming the typical power density of active nanorobots is ~10^7 W/m3, the hypsithermal limit implies a natural worldwide population limit of ~10^8 m3 of active functioning nanorobots, or ~10^11 kg at normal densities. Assuming the worldwide human population stabilizes near ~10^10 people in the 21st century and assuming a uniform distribution of nanotechnology, the above population limit would correspond to a per capita allocation of ~10 kg of active continuously-functioning nanorobotry, or ~10^16 active nanorobots per person (assuming 1 micron3 nanorobots developing ~10 pW each, and ignoring nonactive devices held in inventory). Whether a ~10-liter per capita allocation (~100 KW/person) is sufficient for all medical, manufacturing, transportation and other speculative purposes is a matter of debate.
Of course with advanced technology it will be trivial to travel around and colonize the solar system and use the resources of the solar system.
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