Worldbuilding For Writers Number Six: Planetary Atmosphere

In the blog series Worldbuilding for Writers, Gamers and Other Creatives, we're building a realistic Earth-like planet, step by step, for your storyworld and story franchise. We're working from the top down, starting with large scale considerations like the star, the orbit and rotation details, and so on. Last time around, we covered the relationship between gravity, mass, density and size. This time, we'll look at the world's atmosphere. Throughout, we use my own storyworld setting, the Shaper's World, as an example.

Atmospheric Conditions

Since we're building an Earth-like world — a planetary setting where the environment is at least marginally hospitable to "life as we know it" — we can assume the atmospheric composition will be similar to that of the Earth. That means a composition of around 75% to 80% molecular nitrogen, about 20% molecular oxygen, about 1% argon, 1% to 5% water vapor, and a balance of trace gases like carbon dioxide, neon, methane and others in quantities far less than one percent. There's room for variation, especially if your storyworld doesn't have any off-world visitors to contend with air that tastes funny or doesn't adequately replenish their respiratory systems.

We can calculate some interesting qualities of your world's atmosphere — such as the height at which it thins out to nothing, the atmospheric pressure at sea level (and other elevations) and so on. First, we need to decide on the atmospheric composition and the corresponding average atomic weight and scale height.

Average Atomic Weight

The average atomic weight is a kind of standard measurement for each molecular gas in your atmosphere. One unit of atomic weight is equal to 1/2 the mass of a carbon-12 atom.

Here are the atomic weights for some common elements you would find in the atmosphere of an Earth-like planet:

Nitrogen
28.0134


Oxygen
31.9988


Argon
39.948


Carbon Dioxide
44.01


Neon
20.179


Helium
4.02


Methane
16.044


Krypton
83.8


Hydrogen
2.016


Nitrous Oxide
44.012


Carbon Monoxide
28.011


Xenon
131.3


Ozone
47.998


Nitric Oxide
30.006

To find the average atomic weight of your atmosphere, multiply the percentage of the atmosphere for each element times the atomic weight of that element, and add each one together. For example, the primary ingredients of the Shaper's World's atmosphere are nitrogen (72.7%), oxygen (21.2%) and carbon dioxide (1%) so the average atomic weight is:

Nitrogen (.727 * 28.0134 = 20.3657) + oxygen (.212 * 31.9988 = 6.7837) + carbon dioxide (.01 * 44.01 = 0.4401) = 27.5895

For comparison, the average atomic weight of Earth's atmosphere is 29.

Scale Height

The scale height measures the rate at which your atmosphere thins with altitude. This is helpful for knowing just how high your planet's atmosphere extends above the surface. Once we know the scale height, we can compute the atmospheric pressure at various altitudes above and below sea level.

Earth's scale height is approximately 7,400 meters. To determine our own planet's scale height, the formula is:

Earth's scale height * (Earth's atomic weight / your planet's atomic weight)

The scale height of the Shaper's World is:

7,400 * (29 / 27.5895) = 7778.3214 meters

Atmospheric Pressure

The atmospheric pressure at sea level is not directly tied to a planet's mass, density or gravity. Rather, it's a result of a complicated combination of processes over long (geologically long) periods. Atmospheric pressure is a reflection of how much atmosphere has been retained by the planet and is, essentially, up to you. Depending on your intentions, though, you might want to play with this. For example, a planet with a lower gravity and higher surface atmospheric pressure (relative to Earth) would be more conducive to natural flight. Also, note that the range of acceptable breathable atmospheric pressure for humans is suggested to be between .5 and as much as 5 times Earth atmospheric pressure at sea level. For the purposes of our Earth-like planet, let's assume the atmospheric pressure at sea level is equivalent to 1.

Given our planet's scale height and surface gravity, we can determine the atmospheric pressure at any height. This lets us know how high an average human being could climb without the assistance of a breathing apparatus. Of course, if you decide your sea level pressure is different than 1, you'll want to adjust for your natives. The formula is:

sea level pressure exp(-(surface gravity*height)/scale height)

So, the atmospheric pressure 1000 meters above sea level on the Shaper's World would be:

1 exp(-(.96*1000) / 7778.3214) = 0.8838 atmospheres.

Normal humans wouldn't be able to breath without assistance at about 5,500 meters above sea level.

Another useful calculation is the height at which atmospheric pressure diminishes by half:

Your planet's scale height * (the natural logarithm of 2, or .693147)

On Earth, this is about 5129.2891 meters above sea level. On the Shaper's World, the atmospheric pressure is halved at:

7778.3214 * .693147 = 5391.5215 meters above sea level.

The elevation on the Shaper's World where the atmosphere thins to next to nothing — essentially the edge of space — is approximately 70,000 meters (70 kilometers or 43.5 miles) above sea level.

Atmosphere and Planetary Temperature

The basic mean surface temperature of a planet is dependent on a great many factors. Principally, the figure depends on the amount of energy received from its parent body (usually its star) and the planet's albedo (reflectivity) and greenhouse effect. A planet with an Earth-like atmosphere will almost certainly have some degree of greenhouse effect.

Heat Energy Received

We use the star's total luminosity and distance to determine how much heat energy reaches the planet. Recall that Tah, the star of the Shaper's World, has a luminosity of .9086 and orbits at a distance of 0.979 AU. The heat energy received at the distance of the Shaper's World, or insolation, relative to Earth/Sun numbers, is determined like so:

Stellar luminosity / distance^2 = insolation

For the Shaper's World, this works out to:

.9086 / (0.979^2 = 0.958441) = 0.9479

Albedo

A planet's albedo determines how much of that heat energy is absorbed and how much is reflected back into space. For a baseline, consider that the albedo of the Earth is about 0.3 — it reflects back 30% of the energy it receives.

In very general terms, a planet's albedo will be higher if the proportion of lighter areas is greater than darker areas. A planet covered in snow will have an albedo approaching .9, for example.

Greenhouse Effect

Any world with an atmosphere will have some degree of greenhouse effect. Atmospheres — especially atmospheres with some percentage of carbon dioxide and water vapor — act to hold in heat received from the star. Since we're dealing with Earth-like planets in Worldbuilding for Writers, Gamers and Other Creatives, it's safe to say your planet will have both carbon dioxide and water vapor in its atmosphere, and a greenhouse effect will be a factor in the planet's mean temperature.

The greenhouse effect factor of an Earth-like planet is thought to be around 1.1.

Your World's Average Temperature

The formula to determine a planet's average surface temperature is:

374 * (Greenhouse Effect * (1 – Albedo)) * Insolation^.25

Let's plug in the numbers for the Earth:

374 * (1.1 * (1 – .3)) * 1^.25 = 287.98 Kelvin or 14.83 Celsius or 58.694 Fahrenheit

If we assume the same greenhouse effect and albedo for the Shaper's World, we get:

374 * 1.1 – (1 – .3)) * 0.9479^.25 = 11.0034 Kelvin or 51.80612 Fahrenheit

That's colder than the Earth, and could have a drastic impact on the planet's extremes of climate. Consider that the range of temperatures on the Earth is as cold as -89 Celsius (-128.2 Fahrenheit) and as hot as 58 Celsius (136.4 Fahrenheit), we might find that it's unsuitably cold across too great a range of the Shaper's World's latitudes and altitudes. When we address climate and weather later in this blog series, we'll tinker with the albedo and greenhouse effect to get a range that matches our intention.

Next

In the next Worldbuilding for Writers, Gamers and Other Creatives, we'll begin rounding out the astronomy-based elements in our worldbuilding… starting with a satellite for your world!

Matthew Wayne Selznick - Telling stories with words, music, pictures and people.