Worldbuilding For Writers Number Five: Size, Gravity, Mass and Density
Every week in Worldbuilding For Writers, Gamers and Other Creatives, we take another step toward building an Earth-like planet as a setting for your storyworld and story franchise. Throughout, we use my own storyworld setting, The Shaper's World, as an example.
So far, we've worked out the length of the year and the length of the day for Gundifai, which is what the natives call the Shaper's World. Now it's time to figure out the more tangible physical properties of the planet, including its size, gravity, mass and density.
How Big?
Our goal is to create a realistic representation of an Earth-like planet — that is, a world that will support creatures with biological demands similar to those of Earth life. Given that a planet's size, mass, density and gravity are all interdependent qualities, we have to consider them all in concert. We have to start somewhere, though, so let's look at the planet's size and mass.
If your planet is too small, its weaker gravity will make it less likely to maintain an atmosphere rich in the molecular gasses necessary to support Earth-like life. A relatively thick atmosphere also serves to bring a measure of long-term equilibrium to the world's climate as well. Too thin an atmosphere could result in wide variation from too hot to too cold.
Larger planets are friendlier to the development and sustaining of Earth-like life. A large planet, especially if it has a fairly swift rotation period, is more likely to have a magnetic field, which serves as a shield against radiation from the primary star. Larger planets tend to maintain their internal heat, which sparks the engine of convection that drives volcanic and tectonic activity. A constantly changing planetary crust perpetually stirs up the essential minerals and elements necessary to fuel life. The constantly changing land masses are thought to be essential to driving diversity and evolution. Of course, a large planet usually possesses a stronger gravity, and this helps maintain a rich and complex atmosphere. Too much atmosphere, though, and a runaway greenhouse could result, driving surface temperatures past the point of support for Earth-like life.
Given all the variables, a range of about 0.75 to 1.25 times to radius of the Earth has been suggested as suitable for Earth-like life. The Shaper's World is 0.9788 Earth radi, or 6,243.2 kilometers (3,879.3446 miles) in radius.
Calculating Horizon Distance
One nifty result of knowing the radius of your storyworld planet setting is the ability to calculate the distance to the horizon on a uniform surface, like a vast plain or desert or the surface of the ocean. For something at approximately human eye level height, the horizon is the square root of (height * radius of the planet.) So on the Shaper's World, the distance to the horizon is:
0.0016764 * 6,243.2 = 10.4661
Square root of 10.4661 = 3.2351 kilometers (2.0101 miles)
Similarly, we can determine the maximum distance at which an object of a certain elevation can be seen by taking the square root of (radius * elevation). This is handy for knowing just how close you have to be before those mountains show up. So a mountain 0.9144 kilometers (3,000 feet) high would be seen at a distance of 75.5564 kilometers (46.9486 miles).
How Massive?
Regardless of the size of the world, its chemical composition will have a strong bearing on its gravity. The ratio of heavy elements like iron and uranium to lighter elements like calcium and carbon has a direct relationship to your world's tectonic activity and, by extension, ecological diversity. Even technology is affected: a planet where metals are very rare will likely never support an industrial society, and that, in turn, has implications for scientific understanding and social sophistication.
Mass and density are inter-related. A massive (large) planet might be poor in heavy metals and therefore be less dense (and have a weaker relative gravity) than a similar planet rich in heavy metals. An extreme example is the planet Jupiter, which is eleven times larger than Earth and 300 times more massive, but because it's composed entirely of light elements, Jupiter's density is just 25% that of the Earth's.
It's suggested that a range of mass between 0.4 and 2.35 Earth masses is acceptable for an Earth-like planet. The Shaper's World has a mass 0.92 that of the Earth.
Finding Density
Your planet's density can be calculated once you know the radius and mass. The formula, expressed with Earth values equaling "one", is mass divided by (radius to the third power.) For the Shaper's World, we find:
0.92 / (0.9788 ^3 = 0.9377) = 0.981 Earth density
Gravity
Gravity is an expression of the planet's size and mass or density. If you know the radius of the world and either the mass or the density, you can calculate the gravity. Here's how it works:
Gravity = density * radius or Gravity = mass / (radius ^2)
The gravity of the Shaper's World of Gundifai is therefore:
0.981 * 0.9788 = 0.96 Earth's gravity or 0.92 / (0.9788 ^2 = 0.958) = 0.96 Earth's gravity
Gravity is an interesting story element if your storyworld's planet is visited by folks from other worlds. If your storyworld is, perhaps, a fantasy setting with no "offworld" visitors to offer a different perspective, then for your characters it's irrelevant if their local gravity is greater or less than that of the Earth. However, knowing the gravity of your world helps you calculate a variety of other things, most notably the likely composition of your world's atmosphere, the density of that atmosphere (and how rapidly that density thins with elevation) and the escape velocity of your world.
We'll talk about your planet's atmosphere… next!
Matthew Wayne Selznick - Telling stories with words, music, pictures and people.
