Worldbuilding For Writers Number Seven: M-O-O-N, That Spells Moon

So far in Worldbuilding For Writers, Gamers and other Creatives, we've covered nearly all the astrophysical aspects of creating a realistic Earth-like planet for your storyworld setting. In this installment, let's put a little bling in your world's sky with the addition of a moon.

Why A Moon?

Recall that the purpose of this series is to create a world capable of supporting life as we know it. Getting from a world with no life to one teeming with a global biosphere that actually changes the chemical composition of the planet's geographic and atmospheric properties is a long, complicated process that science still doesn't completely understand. That said, one thing we can confidently state is that life began in the sea… and if not for the moon, that life would not have been pressured — by way of natural selection — to populate the land. It's all to do with the transitory nature of tidepools… and the gravitational force of the planetary satellite that drives those tides.

Back in Worldbuilding For Writers, Gamers and Other Creatives number four, we talked a bit about the connection between a planet's speed of rotation and the long-term viability for the development and survival of life. In short, a planet that rotates too quickly will have powerful storms that wouldn't be conducive to early, burgeoning life.

Fortunately, the gravitational interaction between a large moon and its planet actually acts to gradually slow the rotation of both bodies. With the Earth and the Moon, the Earth's "drag" on the Moon has long since slowed the Moon's rotation until the time it takes to rotate on its axis is exactly the same as the time it takes to orbit the planet. The result? The Moon always shows the same face to the surface of the Earth. The Moon is slowing the Earth's rotation, too. Even though it's a much slower process, the Moon had billions of years to mellow the Earth's rotation before life emerged. It's possible life would not have developed on Earth at all without the Moon there to slow the Earth's rotation and create an environment "gentle" enough to allow those early molecules to hang together.

Bottom line? Your Earth-like planet should have a moon… or moons! Besides, a moon bequeaths fun cultural elements to your world, as well… time keeping based on the moon's phases, for example.

Orbital Considerations

There are two things that have to be worked out when creating your moon: the Roche limit, and tidal scaling.

The Roche Limit

The Roche limit is the minimum distance (measured between the centers of the planet and the moon) the moon can orbit without breaking up under gravitational / tidal forces. This will give you the absolute inner limit for your moon's orbit around the planet.

To figure the Roche limit, we need the radius and density of the primary planet and the density of the moon. We know these things for the Earth and Moon, and so know the Roche limit for the Moon in orbit around the Earth is 18,235.5949 kilometers from the center of the Earth, or 11,857.5949 kilometers from the surface of the Earth. Since the Moon currently orbits at a distance of 384,399 kilometers, it's in no danger of breaking up as a result of proximity to the Earth.

Let's work out the Roche limit for the Shaper's World's moon, Tala.

Tala is a very small satellite — it has a radius of 243.125 kilometers (about the size of the state of Texas) and a density of 2.8 grams per cubic centimeter. Given Gundi-Fai's (the Shaper's World) radius of 6,243.2 kilometers and density of 5.4102 grams per cubic centimeter, the Roche's limit for Tala orbiting Gundi-Fai is 18,841.1355 kilometers from the center of Gundi-Fai, or 12,597.9355 kilometers from the surface of Gundi-Fai.

Here's how to figure out the Roche limit for your planet and moon:

The Roche limit in kilometers = planet's radius in kilometers x the cube root of (the density of the planet / the density of the moon). The densities should be in grams per cubic centimeter.

Tidal Force and Tidal Lock

Tidal force — the effect of the difference in gravitational power across an object like your world — is the bulge on a planet's surface (especially its oceans) caused by the proximity of the planet's moon. Basically, the parts of the planet closest to the moon feel a stronger gravitational tug than the part of the planet farthest away from the moon. Given the mass of the moon and its distance from the planet, we can calculate the strength of the tidal force relative to the tidal force of the Moon on Earth.

Let's look at Tala's tidal effect on Gundi-Fai. First, we need to find Tala's mass. We know it's radius is 243.125 kilometers and its density is 2.8 grams per cubic centimeter. To find the mass of any spherical object, do the following:

Determine the volume, assuming the object is a sphere:

Volume = (4/4 * 3.141592653) * (radius^3)

For Tala: 60,166,845.267 cubic kilometers. In terms of Moon volume, that's 0.0027 of the Moon. We'll need that later.

Mass is determined by multiplying volume by density. We have to be working with the same scales, so let's convert the density from grams per cubic centimeter to kilograms per cubic meter. That gives us 2,800 kilograms per cubic meter. Now it's just simple multiplication:

Mass of Tala = 60,166,845.267 cubic kilometers * 2,800 kilograms per cubic meter = 168,467,167,000,000,000,000 kilograms. Put another way, Tala's mass is equal to 0.0022 that of the Moon.

Tala orbits at a distance of just 51,200 kilometers from Gundi-Fai. That's 0.1331 the distance of the Moon from the Earth. We now have enough information to measure Tala's tide-raising force on Gundi Fai. Here's how:

Tide raising force compared to Moon-Earth = Tala's mass in Moon masses (.0022) / (Tala's distance from Gundi-Fai as a percentage of the Moon's distance from Earth (0.1331)^3 = 0.9701.

All other things being equal, Tala creates tides on Gundi-Fai 97% as strong as the tidal force the Moon exerts on Earth.

Swap Gundi-Fai's mass (in Earth masses) for Tala's, and we see that Gundi-Fai's tidal force on Tala is 389.3737 times that of the Earth on the Moon.

The tidal force of the Earth on the Moon has resulted in the Moon's rotation slowing to exactly the same time it takes for the Moon to orbit the Earth. The result of this "tidal lock" is that the Moon always shows the same face to the Earth. If your world's tidal scaling force is anything more than 1, you can assume your moon is likewise locked to your planet.

Orbital Period

How long does it take your moon to orbit your planet? Assuming the moon and planet are not similarly sized, we can use the same formula we used to determine the orbital period of your planet around its star. We'll need to do some converting, since the orbital formula for a planet around a star uses astronomical units for distance and solar masses for mass:

First, find the distance from the moon to the planet in AU by taking the kilometers and dividing by 149,598,000. For Tala, 51,200 / 149,598,000 = 0.0003422.

Next, take the mass of the planet in kilograms and divide it into 1,988,920,000,000,000,000,000,000,000,000, or 1.98892 × 10^30. For Gundi-Fai, this is 0.000002763.

To find the orbital period of your moon, find the square root of (orbital distance of the moon in AU^3) / mass of the planet in solar masses. For Tala, it looks like this:

(0.0003422^3 = 0.00000000004007) / 0.000002763 = 0.0000145023525

Square root of 0.0000145023525 = 0.003808 Earth years, or 1.3908 Earth days, or 33.2903 Earth hours.

Note that you'll want this figure to be in local years (or days.) One Earth sidereal year is equal to 365.2563 days or 8742.2158 hours. A local sidereal year on Gundi-Fai is 358.6867 Earth days, or 8,584.9759 Earth hours. A local sidereal day on Gundi-Fai is 25.6382 Earth hours, so there are (8,584.9759 * 25.6382) 334.8509 local days in a local sidereal year.

If it takes 33.2903 Earth hours for Tala to orbit Gundi-Fai, that's the same as (33.2903 / 25.6382) 1.2984 days. Tala orbits Gundi-Fai 257.895 times in a sidereal year. It's a fast little bugger!

Your Moon From The Surface of Your World

The complicated orbital dance of your moon, as well as its size and distance, make for an interesting night sky for your planet and give your inhabitants lots of cultural fodder. Some of the things we can determine are the synodic period (the time between moonrises), the apparent size of the moon in the sky, and the phases of the moon.

Synodic Period

The time from moonrise to moonrise depends on how the planet's rotation and the orbital period of the moon interact. The synodic period is to the moon and planet as the solar period is to the planet and the star.

The formula is straightforward:

Synodic Period = 1 / ((1 / Sidereal rotation period of the planet) – (1 / Sidereal orbital period of the moon))

For Tala, the synodic period is = (1 / 25.6382 Earth hours) – (1 / 33.2903 Earth hours) = 0.008965. 1 / 0.008965 = 111.5384 Earth hours, or every 4.3504 days. A Tala-rise every four and a third days is going to make for an interesting "lunar" calendar on Gundi-Fai, and will undoubtedly have implications for the culture and science of the natives.

Phases of the Moon

The appearance of your moon in your planet's sky changes as the moon revolves around the planet. The "new moon," when the moon is practically invisible in the sky, occurs when it is between your world and its star and the side of the moon illuminated by the star is facing away from the planet. The "full moon" happens when the moon is on the opposite side of the planet from the star and is fully illuminated. The "cresent moon," when the moon appears to be half illuminated, occurs… you guessed it… at the halfway point between being fully illuminated and fully obscured.

You can calculate the time between full moons — the "month" — and by extension the times of all the other phases — with a formula very similar to that used to discover the synodic period:

((1 / sidereal orbital period of the moon) – (1 / sidereal orbital period of the planet)) = 1 / answer = month

The "month" for Tala is (1 / 1.3908 Earth days) – (1 / 358.6867 Earth days) = 0.7162 = 1 / 0.7162 = 1.3962 Earth days, or every 1.3034 local days. How this timetable mixes with a moonrise every 4.3504 days will make for an interesting calendar indeed!

The Size In The Sky

How big does the moon appear in the sky of your world? Measured in degrees (with 180 degrees across the bowl of the sky) the Moon on Earth is about .52 degrees in size. How big does your moon appear in your world's sky? Here's how to figure it out:

57.3 x (diameter / distance) = apparent size in degrees

For Tala, that would be (57.3 x (486.25 kilometers / 51,200 kilometers) = 0.54 degrees. Tala, though much smaller than Earth's moon, orbits Gundi-Fai very closely… and so appears slightly larger in the sky than the Moon does on Earth.

Next

The astronomical section of Worldbuilding for Writers, Gamers and Other Creatives wraps up with a few odds and ends. After that, we'll move down to the surface of your world and start exploring geology, climate and other fun stuff!

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