Perhaps it is possible to get a limit on how many aliens might live on each of their home worlds and colonies. What would limit the number? It might be standing room. It is hard to imagine a world in which aliens were packed so closely together they had a floor space problem. If the alien civilization were on a truly wretched planet, with only one smallish island to live on, this limit might be the right one. If they lived on a planet that orbited just a few inches inside the habitable zone, the only living space might be a small area not covered by glaciers. If they were on the other edge of the habitable zone, it might be the area in a polar crater that was cool enough to survive in. Other situations where the area available for living might be small exist. Let’s assume it is not the case, and see what else could limit population.
It might be resources. On a scarcity planet, there might be a limit based on how much they have been able to put into the recycling loop and how much they are leaving for the coming generations. Perhaps they impose some limit on themselves, so the planet’s resources will not be exhausted until the far future, maybe when some other event is predicted to happen, like the hot star they are orbiting gets a little too hot for comfort. Are there others?
Let’s not forget about temperature. Aliens use energy, which always degrades to heat, which in turn raises the temperature of the planet. How much energy could they use and still not affect the temperature adversely? This is a complicated question, relating to the type of atmosphere they have and how would it radiate additional heat. The atmosphere is already radiating just as much heat on the average as it receives from the star, and upping the total it has to radiate means it would have to be a bit hotter, and in fact, the different levels of the atmosphere would be affected, all the way down to the surface, which would also serve as a radiator and a heat sink. Sounds like a tough problem, which means it is time to wave hands around and say the answer.
Let’s see how many aliens could live on a world and only add 0.1% to the total heat absorbed, and radiated, from their sun. Our sun is an example, and it dumps about 100,000 TW onto the earth. One guess would be to assume that the average alien consumes 2 kW. This is roughly household consumption in the United States, averaged over days and years. Maybe after a millennium of energy efficiency work it would be less. Maybe if you added in all the additional power that recycling needs, it would be more. Maybe we should increase it to take into account industrial uses, and transportation uses. So, if we use 10 kW as the average society-wide alien energy use, this is likely to be in the ball park, by which we mean a factor of ten or so. The number of aliens this comes out to be is 10 billion. This may not be the factor which limits the population on an alien home world or colony. On a very dim red dwarf star's planets, this might have to be rethought.
Let’s return to land area and see how much land a population of 10 billion would need. Remember that aliens, in order to conserve resources for lots of millennia of existence, must recycle quite seriously, 99.9% on an annual basis or something like that. This means they live in nearly closed cities. If we give each alien a very nice accommodation of 200 square meters for living space, and four more times that for industrial space, common space and thoroughfares, the whole population of 10 billion would need 10 million square kilometers. If the closed city had 100 stories, to assume a nice round number, the cities would have a total footprint of 100,000 square kilometers. The land area of the Earth is of the order of 100 million square kilometers (closer to 150 but Earth isn’t the alien planet anyway), so this means about 0.1% of the land area would be used for urban occupation, and that would be all. Everything gets done in the cities where recycling is that high. Little interaction with the rest of the land is necessary.
Thus, land use is in rough agreement with the population limit of 10 billion. If we assume that each alien uses 10,000 kg of materials, covering everything within the boundary of the city, then the total is only 100 trillion kg, compared to the Earth’s mass of about 10,000,000,000,000 trillion kg. Just scratching the surface, so to speak. If they lose out of their recycling system 0.1% of their total infrastructure mass per year, this means that 100 billion kg is lost each year, and over a thousand years 100 trillion kg. Both static use of materials to build the infrastructure and dynamic use from recycling losses are no more of a limit that heat from power plants. Even after a million years, gross material weight is not a problem. Land for cities is the key factor. Specific materials could be a problem, if there is some material which has a high loss rate and is relatively scarce. This bears further evaluation, but for now, land is what seems to be setting the limit.
This extremely crude set of calculations helps us form a picture of what an alien world might look like. If we assume they divide their population up into a thousand cities of 10 million people each, then one city would be 10 km on a side, 100 stories high. Perhaps some would be underwater, assuming they have an ocean or two, some would be in the mountains, some would be on the shorelines, some would be in the heartland of the continents, and perhaps even some would be floating. A floating city would have different dimensions due to the need for buoyancy, and probably much smaller than the other cities, but it is possible to think of a closed city on the surface of a large lake or the oceans.
We are also talking about alien cities built after millennia of existence, and after having reached the limits on engineering knowhow, and having experienced disasters and engineering oversights, and catastrophes of all kinds that their particular world might throw at them. If the planet has earthquakes, it would be certain that the city would have protection measures between it and the bedrock. If the planet has tsunamis, there would be adequate barriers on the shore side of any city built in these areas. And so forth. Insurance would be unnecessary after a few thousand years of figuring out the planet’s potential for catastrophe and how to mitigate it.
Energy stations have not been mentioned, except to check that the total energy is tolerable from a heat point of view. Perhaps these would be built separately, and perhaps redundantly. Designing a fusion power plant, if that is what they would use, is not quite possible for us, although we have high hopes for it in certain technological quarters of the science and engineering community. Neither has the source of energy, such as deuterium, been considered in the calculations here. This might deserve another post.
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