In Isaac Asimov’s Foundation series, the planet Trantor is a single, huge city spanning its entire surface (also known as an ecumenopolis), an idea that was famously replicated with Coruscant in Star Wars. As a companion to tomorrow’s podcast on Asimov, I wanted to ask, could a planet-spanning city like Trantor or Coruscant actually work?

Surprisingly, the answer is yes, but not in the way they’re described.

Some basic mathematical analysis shows that a planet-spanning city could have enough resources to support itself, but it wouldn’t be a jungle of concrete and steel from horizon to horizon. It would actually be the greenest city you’ve every seen, full of hanging gardens and solar panels on every surface.

We can compute how many resources a city planet will need by simply scaling up from Earth and looking at the limits of possible technologies. We can assume minerals and other raw materials aren’t a problem since you can just mine whatever you need from asteroids. The main restrictions will be basic necessities for life: food, water, air, housing, and energy.

And we’re not going to do this on Easy Mode, either. We’re going to figure out how many people a “City Earth” can support at an American standard of living.

Important note: this is not a calculation of how many people Earth can support today. We don’t have the technology to get anywhere close to this. It also ignores the environmental damage of paving over the entire planet. This is strictly about how many people an advanced science fiction society could support if they wanted to.

Power

First off, City Earth is going to be almost entirely solar-powered. You might be wondering, “Why? Trantor and Coruscant surely have nuclear power. Wouldn’t that be more efficient?” Well, sort-of, but the problem isn’t generating power; it’s getting rid of waste heat. Nuclear power dumps extra heat into the system on top of what we get from the Sun. For us, it’s not enough to worry about, but it would make City Earth overheat rapidly. This isn’t global warming. This problem is down to raw energy consumption. It’s like studio lights on a TV set. Even though they’re used used for other purposes, they can make the set pretty hot. If a planet is generating enough nuclear power for hundreds of billions of people or more, plus having the same amount of light coming from the Sun, it will overheat in short order.

Thus, we need to go with solar power wherever possible. Even cars and planes will need to use biofuels or hydrogen produced in a solar-electric process, if they aren’t simply all-electric.

So, how much energy will City Earth need? Let’s look at the worst-case scenario. At our peak in 2007 (consumption has actually dropped since then as efficiency increased), the United States consumed 9.797×10¹⁹ joules of energy for 302.1 million people—that’s 2.337 billion barrels of oil equivalent or 27.2 trillion kilowatt-hours. Very roughly, about a third of that energy went to electricity, a third to transportation, and a third to other uses like heating. That comes out to an average consumption of 10,276 watts per person. (As of 2018, it’s about 12% less.) Presumably, City Earth’s entire energy grid is connected, so we can get away with average numbers.

The theoretical limiting efficiency of solar cells is 86.8%, but the best lab results are currently half of this. Let’s suppose that advanced technology allows 50% efficient solar panels to be manufactured in bulk. This means we need 20,000 watts of raw sunlight per person.

Food

The other main consumer of solar energy is food production. In the Foundation trilogy, Trantor is supplied with food from twenty other planets (and presumably has an equally robust supply line to cart away sewage), but this has two obvious problems. The first is the utter catastrophe if the supply lines ever break down. (Heavy reliance on technology is a risk too, but at least it’s distributed.) And the second, once again, is waste heat. You’re importing huge amounts of energy into the system in the form of chemical energy in food, which will eventually be processed into heat. If you want to prevent the planet overheating, you have to produce your food locally.

In fact, Asimov himself recognized these problems and retconned them in Prelude to Foundation, where he states that Trantor grows its own food and is mostly self-sufficient. It even looks green from space; it’s just that you can’t tell from the inside. (Gregory Benford resolved this conflict by saying the farms were shut down after a robot rebellion in the authorized sequel, Foundation’s Fear.)

How much food can you produce per unit area? Photosynthetic efficiency is a measure of how much incoming sunlight gets converted by plants into carbohydrates, and the theoretical limit is about 5%. Most plants only manage a tenth of this, but let’s assume that genetically modified plants can consistently reach this maximum efficiency. The average human needs 2,000 kilocalories per day of food, or about 100 watts. Accounting for this efficiency, that suggests we need about 2,000 watts of sunlight per person.

But wait! This is for a strict vegan diet. Meat costs quite a bit more energy. And this is Hard Mode; I’m not even considering lab-grown meat or meat substitutes because we Americans love our real meat. According to this study (and sources therein), American livestock consume seven times as much grain as American humans, so with an American diet, we can estimate that the power requirements rise from 2,000 watts per person to 16,000 watts.

This means the average American needs 36,000 watts of raw sunlight to maintain their lifestyle. Now, let’s double this for a safety factor, and because we actually want to see the sun sometime. That’s 72,000 watts. The average amount of sunlight reaching Earth’s surface is 245 watts per square meter, so if you multiply by Earth’s surface area (including the oceans) and divide by our power requirements, City Earth could theoretically support…

1.7 trillion people!

Housing

Not what you were expecting, is it? How much space would we need for 1.7 trillion people? And let’s do this one on dry land because most Americans live on dry land. Divide Earth’s land area by the population, and you get 11,500 people per square kilometer (30,000 per square mile). This is only a little more than New York City, and less than many others like Paris, Soeul, or Mumbai. City Earth doesn’t have to be built up miles high to house this many people. Any large, modern urban center could do it. Maybe double the density if you want to move all your food and power generation outside the cities, but the logistics are way easier if things are done locally, so like I said: hanging gardens and buildings tiled with solar panels.

(Incidentally, Trantor’s population is inconsistently described, usually listed as 40 billion, which is way too low, sometimes as 400 billion, which is still too low, considering the oceans are supposed to be paved over, too. Coruscant is listed as 1 trillion.)

Water

There’s another problem we need to worry about: that many people will need a lot of fresh water—for drinking, for washing, and even more for industry and for growing food.

At our peak in 2005, the United States consumed 349 billion gallons of fresh water per day, or 1,181 gallons per person. That’s about 4.5 metric tons. (Again, this is mostly used by industry and agriculture.)

Earth’s average rainfall is about 2 millimeters per day averaged over the globe. That works out to about 1 trillion metric tons of fresh water produced each day, but we need 7.65 trillion. That means the water will mostly have to come from recycling or desalination, and that costs additional energy.

Desalination of seawater takes about 10 kilowatt-hours per thousand gallons. That means an additional 12 kilowatt-hours per person per day, but that’s only about 500 watts per person. Throw in efficiency limitations and safety factors, and it’s still below 5% of the energy we’ve already budgeted.

Oxygen

Oxygen isn’t a problem at all. Growing plants produces oxygen, and consuming plants consumes oxygen at the same rate. As long as the rest of the system stays in balance, oxygen will take care of itself.

Carbon

There might one more problem. For an annual growing cycle, you’re going to need enough biomass on the planet to equal a year’s food supply, and since we’re upping the efficiency of plants, there’s no guarantee that there’s enough carbon in the biosphere to support this.

Earth’s total biomass is estimated at 550 billion tons of organic carbon—that is, the amount of carbon atoms incorporated into organic molecules. That’s equivalent to about 1.375 trillion tons of dry (carbohydrate) biomass. Do we have enough carbon? 1.7 trillion people times 2,000 kilocalories per day divided by 4 kilocalories per gram of carbohydrate, multiplied by 8 for the American diet gives…2.5 trillion tons per year.

Uh oh. We’re a bit short. But luckily, there’s at least another trillion tons of carbon in known fossil fuel reserves, and if you burn some of those off, you’ll be able to make up the difference.

So, there’s your answer. With the right technology, a city-wide planet could theoretically support 1.7 trillion people.