Population Limit

The population limit is the maximum population that an ecosystem can support on a terraformed or paraterraformed planet or inside a space station.

The following calculations are made simple and are not designed for a mathematician, but for simple people trying to answer simple questions like: How many people can live on Mars?

Unfortunately, I don't know how to edit wikia using math formulas, so all will be displayed with simple text.

Terraformed planets

First, we will consider an Earth - like planet inside the Solar System. It has the same Geographic patterns, same ratios of ground and oceans and same chemistry. We will only change its radius and distance to the Sun. In this scenario, the only factors that will influence population limit are surface and luminosity. Why luminosity? Because plants, receiving less light, will be able to produce less food.

Outer planets

Also, less light means less heat. We will need more greenhouse gasses for terraforming processes. More greenhouse effect means that the planet will radiate less heat. Human industrial activities generate heat. So, to avoid runaway greenhouse effects, we will need to limit population.

Basically, for planets outside the orbit of the Earth, the formula is

P = (S/St)*(L/Lt)

Population constant = (Planet surface/Earth's surface)*(Planet's luminosity/Earth's luminosity)

If we consider Earth's surface and luminosity to have the values of 1, the formula becomes:

P = S*L

It is good to use in calculations Earth's luminosity and Earth's surface with the value of 1. This will result that on Earth, the population constant is 1. Earth ecosystems can support a population of 5 billion people, so, to get the exact amount of people that can live on Earth, we get:

Pt = P*5 000 000 000, where Pt is total population.

To get the surface of a planet, the formula is:

Surface = 4*π*square radius.

Since we use 1 for Earth's surface, the formula can be transformed into:

(R*R)/(Rt*Rt)

where R is planet's radius and Rt is Earth's radius.

We also assumed that solar luminosity is 1 for Earth. The formula for luminosity is as follows:

L = Ks/(d*d)

where L is luminosity, Ks is the stellar luminosity constant and d is the distance to the Sun.

Again, we consider for Earth, the solar luminosity constant as 1 and the distance (d) as 1 (one AU).

Inner planets

This formula will give false results if the planet is closer to the Sun. We might expect that Mercury can host more people then Earth. Unfortunately, the truth is quite the opposite. Inner planets will need devices to shield them from extra light. We can maintain the same amount of light for plants, but human activity will need to be controlled. Human activity can affect the atmospheric shielding layers the mirrors or lens floating in stratosphere or in cosmos and easily create a runaway greenhouse effect. So, the formula becomes:

P = (S/St)/(L/Lt)

Or, considering Earth's surface and luminosity to have the value of 1, we get:

P = S/L

Around other stars

The stellar luminosity constant is different for each star. Not only that the energy output is different, but also the spectra of light. See Luminosity for more details. For an average value of luminosity, you can get easy values from ISDB. The site also describes the visual comfort zone around each star.

However, M - type stars, the most common in the Universe, have more energy output in the infrared spectra. If you search the Wikipedia or SolStation databases, you will find habitable zones described according to thermal comfort zones. You will have to do two different calculations: one for visual light and one for infrared. The infrared calculation will allow you to see how much greenhouse gas you will need. In visual light, if the value drops below 0.1% of Earth's constant, plants will not be able to survive.

It is also good to make two different calculations, for red and blue light, since plants will need both types of light. Then, conduct a calculation with the total (bolometric) light of the star (including infrared). The best value to be used is the lowest. Suppose you get for a planet around Barnard's Star, for red light P = 0.07, for blue light P = 0.03 and for infrared P = 0.45, use the lowest value (0.03). The target planet will support 3% of Earth's population (150 million people).

Habitable surface

Earth's surface does not offer the same habitability in each spot. Oceans are not habitable for humans, deserts and tundra have limited resources. So, each different areal has a different habitability. A good terraformer must calculate the percent of habitability for each region of the new planet, then compare them to similar Earth regions. We know that on Earth, what is the population density in each climate area. Now, we have to see on the targeted planet what types of climate we have.

Seasonal changes

A good terraformer has to keep in mind that Earth life forms will look for similar climate patterns (similar day length and similar year length). On Mars, the year will be almost twice as long as on Earth. Many animals will find hard to hibernate in winter or to survive the long lasting summers. Shorter seasons will always mean less needs to adapt.

Paraterraformed asteroids

Paraterraformed celestial bodies will offer far better values then a planet, because the climate can be artificially set to the best. However, the available surface for plants will limit the population. The formula will be:

P = 50*(S/St)*(L/Lt) - for bodies outside the orbit of the Earth

P = 50*(S/St) - for bodies closer then the Earth

The added 50 means that a paraterraformed celestial body can host 50 times more people for the same surface. Why this? Because there will be no deserts, no seas and no tundra. Also, being closer then the Earth will not affect the ecosystem, since humans can control the amount of light received more easily.

Spaceships

The amount of people that can be hosted by a spaceship depends on the artificial ecosystem it will carry.

Examples

The following list contains calculated values for planets and satellites inside Solar System, suppose they will become an Earth - like planet.

We will also define a new term, density constant, which varies from a planet to another. It reflects the mean population density per surface. As shown below, it is only influenced by luminosity. Density constant for a planet can be considered a percent of Earth's density constant.

Inner planets

Mercury, luminosity = 6.57, density constant = 15

Mercury, surface = 0.147, population limit = 112 million

Venus, luminosity = 1.93, density constant = 52

Venus, surface = 0.902, population limit = 2336 million

Earth, luminosity = 1.00, density constant = 100

Earth, surface = 1.000, population limit = 5000 million
Luna, surface = 0.074, population limit = 370 million

Mars, luminosity = 0.43, density constant = 43

Mars, surface = 0.275, population limit = 590 million

Ceres, luminosity = 0.130, density constant = 13

Ceres, surface = 0.054, population limit = 35 million 
(assuming an atmosphere can be kept in place)

As one can see, the inner planets offer the best conditions for colonization and can support a large population. However, Mercury, Venus, Mars and Luna together cannot host the same population that Earth hosts.

Gas giants

In case of the gas giants, their moons are small, resulting in small surfaces to be inhabited. Still, because of the low luminosity that limit plant activity and because of the high risks to break the greenhouse equilibrium, population density is extremely low, as shown by the density constant.

Jupiter, luminosity = 0.037, density constant = 3.7

Io, surface = 0.082, population limit = 15.2 million
Europa, surface = 0.061, population limit = 15.2 million
Ganymede, surface = 0.171, population limit = 31.6 million
Callisto, surface = 0.143, population limit = 26.5 million

Saturn, luminosity = 0.0109 density constant = 1.1

Tethys, surface = 0.007, population limit = 0.38 million
Dione, surface = 0.0078, population limit = 0.43 million
Rhea, surface = 0.0144, population limit = 0.79 million
Titan, surface = 0.163, population limit = 8.88 million
Iapetus, surface = 0.013, population limit = 0.71 million

Uranus, luminosity = 0.0027 density constant = 0.3

Titania, surface = 0.015, population limit = 0.20 million
Oberon, surface = 0.014, population limit = 0.19 million

Neptune, luminosity = 0.0011 density constant = 0.1

Triton, surface = 0.045, population limit = 0.25 million

Together, the 12 larger moons of the giant planets can offer a surface of only 69% of Earth's surface. So, even if they were located at Earth's orbit, they could not sustain Earth's population. Since they are so far from the Sun, their total population limit is of all these 12 moons is 100.33 million, so only 2% of Earth's population limit.

From this, one can see that population will never reach high values around the outer planets. Also, population density will be low. Large surfaces will be cultivated with plants that will use what little light reaches them.

Not only that population density will be low, but also large cities cannot exist. Suppose a huge city like Tokyo is built on the surface of Titan. The heat it produces will create warm vertical currents that can penetrate the layer of greenhouse gasses, creating a hole. Thermal radiation will escape and the city will be exposed to the extreme cold weather of space. As temperature drops, winds will occur and will create other holes in the greenhouse layer, leading to a global winter, with temperatures that can reach -70 degrees Celsius.

Kuiper Belt

When luminosity is below 0.001, in red or blue spectra, plants will find very hard to survive. So, terraforming with classic Earth-like plants is impossible. Still, using the same formulas, some calculations can be made:

Pluto: population limit = 110 000
Eris: population limit = 36 000
Sedna: population limit = 1 170

It is clear that terraforming the dwarf planets of the Kuiper Belt is not possible without an extra source of light and heat.

Local population limit

Population limit applies in two ways: on a global and on a local scale. If we concentrate all Earth's population and industry on a small area (for example in South America), this will have worse effect then if people were spread all over the globe. This is because too much pressure on a small part of the biosphere can trigger effects that the rest of the biosphere cannot cope with. In our example, if we move all humans and all human activities to South America, soil will be overrun, desertification will start, water will become too polluted and air will be too heated. The biosphere will lose a continent and the effects will be felt immediately. Toxic water will affect the oceans and will destroy plankton, allowing unwanted species to multiply. Nature will have no way to absorb the shock.

If population is spread all over the world, nature has the power to heal itself. It is the difference between having one big, lethal wound, compared to having many small wounds. In case of a big wound, all local resources are not enough and the infection will spread through the body. In case of many small wounds, they are not so deep, so that the body can work repairing them faster, using local resources.

If we look on Earth, at China and India, we see this very clear. Desertification and pollution to incredible levels are common. Soil is exploited beyond natural regeneration limits, so that desertification is inevitable. And when Chinese rivers reach the sea, they are so polluted, that the effect is felt as far as Japan. This has destroyed the plankton and as a result fish has vanished and was replaced by nature with the toxic giant jellyfish species.

Formulas

On Earth, we see giant cities with 30 million inhabitants. This is close or perhaps above the limit Earth biosphere can support without major side effects. Based on this, we can say that the population limit for a city should be 0.4% of global population limit.

Pc = P*0.004 - where Pc is max population of a city and P is the population limit

Also, on Earth, we see that in rural areas of India and East China, fields are feeding even 1000 people per square km. However, a value that should be safe for soil erosion and would not have major side effects for the biosphere, should be around 300 mouths per square km. Given Earth's population (at a safe value, or 5 billion inhabitants), the needed farmland would be 5% of planet surface, including water.

Sa = S*0.05 - where Sa is surface for agriculture and S is total planet surface.

• Ad = 300*L for outer planets,
• Ad = 300/L for inner planets.

Here, Ad is agriculture density (how many people can 1 square km of land feed) and L is the luminosity (for Earth it is 1).

Examples

Remember that on Earth we passed these numbers, but we made many ecological problems.

For the Solar System, this is the data:

Mercury:

• Largest city - 448 000 people
• Farmland production - 45 people fed from one square km

Venus:

• Largest city - 9 350 000 people
• Farmland production - 156 people fed from one square km

Earth:

• Largest city - 20 000 000 people
• Farmland production - 300 people fed from one square km

Moon:

• Largest city - 1 500 000 people
• Farmland production - 300 people fed from one square km

Mars:

• Largest city - 2 360 000 people
• Farmland production - 129 people fed from one square km

Ceres (assumed we can hold an atmosphere):

• Largest city - 140 000 people
• Farmland production - 39 people fed from one square km

Io:

• Largest city - 60 000 people
• Farmland production - 11 people fed from one square km

Europa:

• Largest city - 61 000 people
• Farmland production - 11 people fed from one square km

Ganymede:

• Largest city - 130 000 people
• Farmland production - 11 people fed from one square km

Callisto:

• Largest city - 106 000 people
• Farmland production - 11 people fed from one square km

Tethys:

• Largest city - 1 500 people
• Farmland production - 3.3 people fed from one square km

Dione:

• Largest city - 1 700 people
• Farmland production - 3.3 people fed from one square km

Rhea:

• Largest city - 3 100 people
• Farmland production - 3.3 people fed from one square km

Titan:

• Largest city - 35 000 people
• Farmland production - 3.3 people fed from one square km

Iapetus:

• Largest city - 2 800 people
• Farmland production - 3.3 people fed from one square km

Titania:

• Largest city - 800 people
• Farmland production - 0.9 people fed from one square km

Oberon:

• Largest city - 760 people
• Farmland production - 0.9 people fed from one square km

Triton:

• Largest city - 1000 people
• Farmland production - 0.3 people fed from one square km

Pluto:

• Largest city - 440 people
• Farmland production - plants might not survive

Eris:

• Largest city - 144 people
• Farmland production - plants might not survive

Sedna:

• Largest city - 4.5 people
• Farmland production - plants might not survive.

Please note that this data is only for orientation. Many known and unknown factors have to be taken into consideration. But what one can see, is that nature would not support giant cities on other planets and that the few who will settle in the outer solar system, will require huge farms.

Politics

As new terraformed worlds are created, settlers will try to move there. Local governments will be pleased to see how their population increases. However, when the population reaches dangerous levels, where the ecosystems might be threatened, new settlers will not be allowed to move in.

Another factor, linked with the population density, is Pollution that will appear, associated with the overall population.

As long as a planet has a low population density, its government should try to stimulate colonization, giving free land for settlers and developing infrastructure. When population increases close to the population limit, the government will try to increase taxes, forcing people to move to another planet. The same principles should be used to stimulate colonization in remote areas and to avoid building too large cities where environmental conditions do not allow this.

In the end

Population limit is defined by many factors:

• The parent star
  • Luminosity (visual, red, blue spectra)
  • Temperature (infrared light)
  • Dangerous radiations (ultraviolet, X-rays, particle radiations)
  • Stellar stability (flare stars)
• Planetary orbit
  • Ellipse elongation
  • Year length
  • Axis tilt
  • Day-night cycle
• Planet behavior
  • Surface
  • Gravity
  • Possibility to hold an atmosphere
  • Magnetosphere
• Atmosphere
• Ground chemistry
  • Amounts of minerals needed for life
  • Heavy metals and other toxins
• Volcanism
• Water
  • Sea water chemistry
  • Surface of oceans
• Climate
  • Surface with suitable climate
  • Surface without suitable climate (deserts, tundra)
  • Climate stability

Also, we, humans, are able to adapt and improve our environment. In the model showed above, Earth's population limit is set to 5 billion people. However, we are already more then this. It is possible to increase population above the limit, without affecting the environment. Also, with less population, but higher resource consumption, the effect on the environment can be much worse.

The values listed above, for each terraformed body, are just for orientation, since many parameters are not known yet. However, they give us an idea about how populated the solar System will be.