Table of Contents

Acknowledgements

What Is Meant By "Earth-like Planet"

Selecting A Star

Too Hot, Too Cold, Too Quick, Too Old

The Best Star For Your World

The Habitable Zone

Gathering Data

Mass and Luminosity

Finding the Habitable Zone

Inner Limit

The Outer Limit

The Earth Twin Distance

Reviewing The Habitable Zone

The Orbital Period

Determining The Orbital Period

Why The Orbital Period Is Important

What About Eccentricity?

The Rotation Period

How Fast Should It Be?

The Coriolis Effect

The Impact On Life

Size, Gravity, Mass and Density

Calculating Horizon Distance

How Massive?

Finding Density

Gravity

Planetary Atmosphere

Average Molecular Weight

Scale Height

Atmospheric Pressure

Atmosphere and Planetary Temperature

Heat Energy Received

Albedo

Greenhouse Effect

Your World’s Average Temperature

The Moon

Orbital Considerations

The Roche Limit

Tidal Force and Tidal Lock

Orbital Period

Your Moon From The Surface of Your World

Synodic Period

Phases of the Moon

The Size In The Sky

The Shaper's World: Star, Planet, Moon

What's Next?

About The Author

More From Matthew Wayne Selznick and MWS Media

The Sovereign Era Storyworld

The Protector Storyworld

The Daikaiju Universe Storyworld

Music

Worldbuilding For Writers, Gamers and Other Creators

Volume One: Star, Planet, Moon

by

Matthew Wayne Selznick

Mathematical Review: Jafsica, Steven Rehn

~

Copyright 2010, 2011 Matthew Wayne Selznick. Unauthorized duplication in any media is a violation of international intellectual property laws and will be prosecuted.

Cover designed by Matthew Wayne Selznick featuring photographic elements from the National Aeronautical and Space Administration.

Press inquiries:

MWS Media

mwsmedia@gmail.com

http://www.mattselznick.com

Worldbuilding For Writers, Gamers and Other Creatives Volume One: Star, Planet, Moon appeared in a slightly different form on mattselznick.com in 2010.

Approximately 8,000 words.

Acknowledgements

This e-book was written in several installments, in public, on my blog at http://www.mattselznick.com. The science and math I rely on to describe how to "model" a realistic, Earth-like setting for use in the storyworlds of creators was culled from a wide variety of mostly online sources, including (get your Google fingers ready) NASA, Wikipedia, and, to my delight, the website of my one-time astronomy instructor Courtney Seligman.

Very special thanks to Jafsica and to Steven Rehn for their gracious review of the math in this book. If there are mistakes in what follows, the fault is entirely mine. Thanks also to Jim Ryan, Jonny D and the other folks who commented on the original posts.

Finally, thanks to you, dear reader, for purchasing this resource! Share the worlds you create with me by writing mwsmedia@gmail.com, and I'll see you for volume two!

Introduction

Worldbuilding — sometimes called sub-creation or secondary world creation — is the task / art / craft of designing and representing an internally consistent and realistic setting for use in fiction, video or tabletop role playing games, movies, comics, a transmedia experience… really any type of storyworld.

In each concise volume of "Worldbuilding for Writers, Gamers and Other Creators," and in the omnibus edition, you'll find explanations, tools and resources to give your setting a level of verisimilitude that inspires the willing suspension of disbelief on the part of your audience.

We'll work with a "top down" approach both literally and in terms of the subjects we cover. As we select an appropriate star, muse on the size, mass, and orbit of your world, its geography, climate, weather, biomes and habitats for life (including the sentient variety!) and more, I’ll use one of my own storyworld settings, the Shaper's World, to provide examples.

Since the ultimate goal is to create a fictional representation of an Earth-like planet, we're going to keep a broad focus by necessity… but you're strongly encouraged to delve deeply into each topic via Wikipedia (http://www.wikipedia.org/ ), Wolfram Alpha (http://www.wolframalpha.com/ ) and other Internet resources.

Yes, there will be math, but what's required is more basic than you might expect, and there are lots of tools (hello, again, Internet) to help us in that regard. It's worth it!

What Is Meant By "Earth-like Planet"

For the purposes of Worldbuilding for Writers, "Earth-like" means the following:

- Size and density close to that of the Earth to allow for a gravity suitable for an ecosystem similar to Earth's

- Orbiting in the "habitable zone" of a star and having appropriate orbital characteristics to allow for a climate similar to that of Earth

- Having an active, self-replenishing crust to allow for geologic processes similar to Earth

- Having an atmosphere similar in composition and density to the Earth

- Being an age sufficient to allow for the development of complex organisms, including at least one sentient species

If you're interested in creating a setting that is anything but Earth-like, you'll still find the information in Worldbuilding for Writers, Gamers and Other Creators useful — it's important to understand what's normal before you push beyond!

Selecting A Star

The first step in creating an imaginary Earth-like planet is to assign an appropriate star to orbit.

Creators of science fiction and fantasy worlds in books, movies, television and comics love to present an exotic setting with plenty of unusual and stunning details to convey a sense of the alien or fantastic. It's not uncommon to start with the sun... or suns... up in the sky. Nothing says "another world" like a lurid, balefully glowing red ball smoldering in the sky, or perhaps a pair of blistering white stars hovering above the horizon.

Unfortunately, a creator's choices when thinking about their milieu's star very often simply don't make good sense when you take into account the features of the world orbiting that star. When it comes to building a planetary system that includes an Earth-like planet (including a diverse ecosystem that features sentient native life) our choices may be rather limited.

Too Hot, Too Cold, Too Quick, Too Old

Stars, generally, are classified from hot and bright to cool and dim. While all the particulars of stellar classification are beyond the scope of this e-book, it's enough to understand that spectral classes are designated O, B, A, F, G, K and M, with each letter being further divided by numbers from zero to nine and the entire sequence ranging from hot and bright to dim and cool.

Hot, bright stars – O2 through F4, perhaps – burn themselves out in less than two billion years. If we consider the timescale of life's development here on Earth to be typical, that's probably too short a time for complex life to develop.

Even though stars from the upper K range through M-class exist for billions of years, they may not produce enough energy at a distance appropriate to place a planet and still consider it Earth-like.

The Best Star For Your World

The most likely stars for your Earth-like planet? Stellar classes F5 through K5. These include stars roughly +/- 20% the temperature of Earth's Sun that exist in a stable state for three to fifteen billion years or longer. Many scientists think these stars are excellent candidates for Earth-like planets.

Our own Earth orbits Sol, a G2 star with a surface temperature of about 5,770 Kelvin and a predicted lifespan of approximately ten billion years. My creation, The Shaper's World, orbits Tah, a G3 star with a temperature of about 5,690 K and an even longer predicted stable lifespan than Sol.

What about your world? Here are some stars and their approximate temperatures to get you started:

Spectral Class

Temperature (Kelvins)

F5

6767

F6

6600

F7

6433

F8

6267

F9

6100

G0

6000

G1

5885

G2

5770

G3

5703

G4

5636

G5

5569

G6

5501

G7

5434

G8

5367

G9

5300

K0

5200

K1

5056

K2

4911

K3

4767

K4

4622

K5

4478

The Habitable Zone

The habitable zone represents the minimum and maximum distance a planet should orbit its star in order to be most hospitable for life as we know it.

For our purposes, it's the orbital distance from the star that will permit an Earth-like planet. In particular, the planet should receive enough heat energy from its star to allow for the presence of liquid water. The opinions of astronomers vary on just what this "Goldilocks zone" should be for any given star, but many agree that the habitable zone of Sol is between 0.725 to 1.24 astronomical units from the Sun – that is, about three-quarters to one and a quarter times the distance of the Earth from the Sun.

It's important to recognize that this is an estimation drawn from science-based extrapolation. There are many, many factors that contribute to making a world suitable for Earth-like life, but for the purposes of building our worlds, we're going to go with this range and play with it.

Gathering Data

Given the acceptance of a range of distances determining the habitable zone around Sol, we can determine the habitable zones of other stars. Since it all comes down to the amount of heat received from the star at a given distance, we need to know a little bit more about the star our world orbits.

Mass and Luminosity

Specifically, we need to determine the star's luminosity and temperature. For stars between F5 and K5 on the main sequence, we can determine both of those attributes from the star's mass. Here are approximate masses (relative to Sol) for our eligible stars:

Spectral Class

Mass

F5

1.201

F6

1.161

F7

1.121

F8

1.081

F9

1.041

G0

1.039

G1

1.020

G2

1.000

G3

0.973

G4

0.946

G5

0.919

G6

0.891

G7

0.864

G8

0.837

G9

0.810

K0

0.790

K1

0.752

K2

0.714

K3

0.677

K4

0.639

K5

0.601

From this, we can determine the luminosity of the star by taking the mass and raising it by a power of 3.5.

The Shaper's World's star, Tah, is a G3 star, which gives it a mass of .973.

.973^3.5 = .9086

So, Tah has a luminosity of .9086 relative to Sol.

Finding the Habitable Zone

Now that we have the star's luminosity and know the suggested upper (closest to the star) and lower (farthest from the star) limits of the habitable zone, we can find the range of the habitable zone in astronomical units (AU) within which our planet must orbit to have a chance at being Earth-like. Here's how it works:

Inner Limit

The inner limit of the habitable zone of our own solar system is suggested to be 0.725 AU. At that point in space, a planet would receive 1.9 times the energy (or insolation) received by the Earth. We figure that out by dividing luminosity by the distance of the planet squared, or

1 / .725^2 = 1.9024

We can turn that around to see how the insolation can reveal the distance by dividing the luminosity by the insolation and taking the square root of the result:

1 / 1.9024 = 0.5256. The square root of 0.5256 = 0.725

Given that, we can now determine the inner limit of the habitable zone of Tah, the star of the Shaper's World. Remember that Tah is a G3 star with a luminosity of .9086.

0.9086 / 1.9024 = 0.4776. The square root of 0.4776 = 0.6911

The inner limit of Tah's habitable zone is 0.6911 AU.

The Outer Limit

For the outer limit, we figure the insolation at the maximum suggested distance for Sol's habitable zone, which is 0.6503:

1 / 1.24^2 = 0.6503

From that, we can see that the outer limit of the habitable zone of Tah is 1.1820 AU:

0.9086 / 0.6503 = 1.3972. The square root of 1.3972 = 1.1820

The Earth Twin Distance

Let's say you want to determine the distance a planet needs to be from your star in order receive the same amount of energy the Earth receives from Sol. This is an easy one – take the square root of your star's luminosity and you have the distance in AU!

For the Shaper's World, the Earth Twin distance is 0.9532 AU.

Reviewing The Habitable Zone

The habitable zone of Sol is between .725 and 1.24 astronomical units from the sun, with the Earth sitting pretty at 1 AU.

The habitable zone around the Shaper's World's star is between 0.6911 and 1.1820 astronomical units from Tah, with the "Earth Twin" distance – the distance where the Shaper's World would receive the same energy the Earth does from Sol – at 0.9532 AU.

What is the habitable zone of your world?

The Orbital Period

There are several ways to measure a planet's orbital period around its star. For now, we’re going to consider the sidereal orbit, which is the time the planet takes complete a circuit around its star as seen from outside of the planetary system. A bit later, we’ll explore ways to calculate the synodic period, which is a measure of how long it takes for a specific object in the planet’s sky – say, a moon – to return to the same spot in the sky. Depending on cultural sophistication on your world, either measure, or both, might be significant.

Determining The Orbital Period

We've worked out the habitable zone surrounding our star: the distance (closest to, through farthest from, the star) a planet can orbit and still have a chance to have Earth-like qualities. For the Shaper's World, our example setting, that equals between 0.6911 and 1.1820 AU, with the “Earth twin” distance being 0.9532 AU. We also know that our central star of the Shaper's World, Tah, has a mass of about 0.973 solar masses.

With distance from the star and the mass of the star expressed in terms relative to Sol, we have everything we need to calculate the orbital period of our Earth-like planet in Earth years. To do so, divide the distance from the star, cubed, by the mass of the star, then find the square root of the result. For the Shaper’s World, we get following:

At the inner limit of the habitable zone:

(0.6911^3 = 0.3300) / 0.973 = 0.3392

The square root of 0.3392 = 0.5824 Earth years. Since one Earth year is equal to 365.2563 Earth days, the orbital period at the inner limit of the Tah’s habitable zone is 212.7417 Earth days.

At the “Earth twin” distance of 0.9532 AU:

(0.9532^3 = 0.8660) / 0.973 = 0.8901

The square root of 0.8901 = 0.9434 Earth years, or 344.6016 Earth days.

At the outer limit of the habitable zone:

(1.1820^3 = 1.651400568) / 0.973 = 1.6972

The square root of 1.6972 = 1.3027 Earth years, or 475.8471 Earth days.

Note that the length of your planet’s year in Earth days is useful as a comparative figure, but your planet will have its own day length – the time it takes to revolve once around its axis – and that will be a more important metric to your planet’s natives. We’ll work that out a little later.

The orbital distance of the Shaper’s World is 0.979 AU, giving the planet an orbital period of 358.6867 Earth days.

Why The Orbital Period Is Important

Beyond simply knowing the length of the year, the orbital period – and the attendant distance of the planet from the star – is essential in determining the base surface temperature of your world. Depending on your creative preferences, you might not want an especially warm or cold world… or that might be exactly what you want. While factors like orbital eccentricity, axial tilt, volcanism and atmospheric conditions will play a role, it all starts with how much energy the planet receives from the star, and that’s directly related to the distance between the two.

What About Eccentricity?

Not every orbit is a perfect circle. Most are slightly flattened – very subtle ovals. The amount of flattening is the eccentricity. For example, the orbit of the Earth has an eccentricity of 0.0167.

Orbital eccentricity less than one percent will have negligible impact on the climate of a world, but a large degree of eccentricity would have essentially the same effect as the planet’s degree of axial tilt, except the whole planet will experience “winter” or “summer” at the same time. To belabor the obvious, the world will be colder when the planet is farthest from the star and, at the opposite end of the year, when the planet is closest to the star, much warmer.

I recommend you keep the eccentricity of your orbit to a minimum if you want to make it realistically conducive to Earth-like life. We’ll explore the specifics of the variations when we talk about climate in future volumes of this series.

By the way, while it might seem counter-intuitive, the degree of eccentricity does not have a meaningful effect on the total length of the year. The planet travels faster when it’s closer to the star and slower when it’s far, and the differences cancel each other out.

The Shaper’s World has an orbital eccentricity of 0.0192 — very nearly a circular orbit.

The Rotation Period

Put simply, the period of rotation is the time it takes for a planet to revolve around its axis. In fact, we commonly refer to two different kinds of rotation: Sidereal and solar.

Sidereal rotation is the time it takes any point on the planet to revolve around its axis relative to a distant point of reference, like the planet’s star. When we speak about the rotation period of planets, we usually mean sidereal rotation. However, the rotation period that usually matters more to inhabitants of the planet is the solar rotation, which is simply the time between sunrises.

Why the difference? As a planet orbits its star, it has to rotate slightly farther to directly face the star. In other words, the solar day has to take both solar and sidereal rotation into effect. For planets with a fairly fast rotation period, the difference isn’t all that much – on Earth, the sidereal rotation is about four minutes less than the solar rotation.

Figuring out the difference is fairly simple, and depends on the following formula:

solar day = sidereal day in Earth hours / (1 – (sidereal day in Earth hours / orbit period in Earth hours))

Let’s plug some real numbers into that formula. Our example storyworld setting, The Shaper's World, has a sidereal day of 25.6382 Earth hours and an orbital period of 8608.4808 Earth hours. So:

1 – (25.6382 / 8608.4808) = 0.9970

25.6382 / 0.9970 = 25.7153

The solar day of the Shaper’s World is 25.7153 Earth hours.

How Fast Should It Be?

The rotational speed of a planet is affected by many different factors over time. Collisions with other bodies could change the speed of rotation in much the same way a billiard ball’s spin is changed by the strike of the cue ball. The close orbit of a large satellite could mutually affect both bodies. Even the gravitational interaction with other planets could make a difference.

What does that means for your worldbuilding effort?

There’s no clean and easy way to calculate what your planet’s rotation period should be. You have some creative leeway here, but keep these things in mind:

The Coriolis Effect

The atmosphere of your world moves along with the planet as it rotates. At the equator, the rotational velocity of the atmosphere is roughly the same as the planet. As you move farther north or south from toward the poles, the ground below the atmosphere moves slower while the atmosphere itself retains most of its original velocity. That excess speed pulls the atmosphere to the side, which results in the whirling patterns (gyres) that we see as air currents... and can grow into hurricanes or typhoons.

All things being equal, a world roughly the same size of the Earth with a rotation period twice as fast will have twice the Coriolis effect. Storms will spin twice as tightly and contain more energy. This rapid distribution of warm energy from the equator to the poles (and cold energy back down from the poles to the equator) will have a profound impact on a planet’s weather system.

On the other side of the spectrum, a very slowly rotating world will also have violent weather as warm air and cold air clash in convection along the terminator line between day and night.

The Coriolis effect also influences the ocean currents close to the surface. A swiftly spinning planet will have faster, churning, currents compared to a world with a slower rotation period. This could have an impact on climate and on the capabilities of sea-going vessels.

The Impact On Life

Consider the influence the length of the day / night cycle might have on your planet’s ecosystem, life forms and cultures. The circadian rhythms – the body clocks, if you will – of your life forms will reflect the relative speed of the day. Perhaps metabolisms are faster on swiftly spinning planets..? It’s something to think about when designing your storyworld.

Size, Gravity, Mass and Density

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.

Since we have to start somewhere, let’s begin with 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. 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, scientists suggest a range of about 0.75 to 1.25 times to radius of the Earth as suitable for Earth-like life. The Shaper’s World, our example setting, is 0.9788 Earth radii, 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 approximately at human eye level, the horizon is the square root of (height * radius of the planet.) Make sure you use the same units of measurement in your equation!

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. Even though it's eleven times larger than Earth and 300 times more massive, 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 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 required to escape the gravitational hold of your world.

Planetary Atmosphere

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 molecular weight and scale height.

Average Molecular Weight

The average molecular weight is a kind of standard measurement for each molecular gas in your atmosphere. For those of you keeping score, one unit of molecular weight is equal to 1/2 the mass of a carbon-12 atom.

Here are the molecular 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 molecular weight of your atmosphere, multiply the percentage of the atmosphere for each element times the molecular 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 molecular 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 molecular 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 molecular weight / your planet’s molecular weight)

The scale height of the Shaper’s World is:

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

Atmospheric Pressure

Atmospheric pressure is a reflection of how much atmosphere has been retained by the planet.

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. Because of the functionally infinite number of variables involved, the atmospheric pressure of your planet is pretty much 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.

On the Shaper's World, normal humans are not 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, 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 = 284.1534 Kelvin 11 Celsius 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 the Shaper's World is unsuitably cold across too great a range of latitudes and altitudes.

Later in this series we'll address climate and weather at the surface level, and we'll tinker with the albedo and greenhouse effect of the Shaper's World to get a range that matches our intention.

The Moon

The purpose of Worldbuilding For Writers, Gamers and Other Creators is to create a world capable of supporting life as we know it. Taking 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.

One thing we can confidently state is that life began in the sea… and if not for the moon, that life may not have been pressured – by way of natural selection – to populate the land. It’s all to do with the transitory nature of tide pools… and the gravitational force of the planetary satellite that drives those tides.

We've already mentioned 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 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 also slowing the Earth’s rotation. 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 the Shaper’s World's 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. 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 = (4/3 * 3.141592653) * (radius^3)

For Tala: 60,197,362.753 cubic kilometers, or 6.0197 x 10^16 cubic meters. That’s 0.027 of the volume of the Moon. We’ll need that later.

Mass is determined by multiplying volume by density. We have to work 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 = (6.0197 × 10^16) cubic meters * 2,800 kilograms per cubic meter = 1.68 * 10^20 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 1.98892 * 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 = 4.007 * 10^-11) / 0.000002763 = 1.45 * 10^-5

Square root of (1.45 * 10^-5) = 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) for it to be meaningful.

One Earth sidereal year is equal to 365.2563 days or 8742.2158 hours. A local sidereal year on the Shaper's World is 358.6867 Earth days, or 8,584.9759 Earth hours. A local sidereal day on the Shaper's World 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 you lots of cultural fodder. Some of the things we can determine are the synodic period (the time between moon rises), 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 world'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 “crescent 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.

The Shaper's World: Star, Planet, Moon

Let's take everything we've determined about the Shaper's World and put it all together.

The Shaper's World orbits Tah, a G3 star with a temperature of about 5,690 Kelvin. Tah is slightly less massive that Earth's star: .973 of Sol. Tah's luminosity – the amount of heat energy it radiates – is .9086 compared to Sol.

Tah's habitable zone is between .6911 and 1.1820 astronomical units from the star. The Shaper's World orbits at an average distance of .979 astronomical units. From this, we know that it takes 358.6867 Earth days for the Shaper's World to orbit Tah. Since the orbital eccentricity of the Shaper's World is very small (.0192) it has no meaningful impact on the planet's temperature through the year.

The Shaper's World rotates on its axis once every 25.6382 Earth hours. The average time from sunrise to sunrise is slightly longer: 25.7153 earth hours.

The Shaper's World is slightly smaller than Earth: 6,243.2 kilometers (3,879.3446 miles) in radius. For a human standing in a relatively flat environment on the Shaper's World, the horizon appears to be 3.2351 kilometers (2.0101 miles) away.

The Shaper's World is a little less massive (.92) and less dense (.981) than Earth, which leads the planet's gravity to be likewise less (.96 the gravity of the Earth.)

The atmosphere of the Shaper's World is similar to the Earth's: 72.7% nitrogen, 21.2% oxygen, around 1% carbon dioxide and a variety of trace elements. Humans (of a sort) can and do live there comfortably up to about 5,500 meters above sea level.

The Shaper's World seems to be, overall, a colder planet than the Earth – about 11 Celsius (52 degrees Fahrenheit.) Since this could make for an environment too far from our creative intentinos, it's likely we'll play with both the albedo and greenhouse effect numbers of the Shaper's World in the volume of “Worldbuilding For Writers, Gamers and Other Creators” dealing with climate and weather.

The Shaper's World has a single moon, the tiny satellite Tala.  Tala is just 243.125 kilometers in radius (a tiny fraction of the size of the Earth's Moon), with a density of 2.8 grams per cubic centimeter.  Tidal forces have “locked” Tala's rotation period long ago – it appears to always show the same face to the planet.

Tala is tiny (and because of that size it's unlikely that its a spherical object) but it orbits very close to the Shaper's World.  Because of that, it takes up as much as .54 degrees in the sky, and would look larger than Earth's moon in the sky.

Tala orbits the Shaper's World every 1.2984 local days, or 257.895 times per local year.  The dance between the orbit of Tala around the Shaper's World, and the Shaper's World's orbit around Tah, results in a Tala “moonrise” every 4.3504 days and a “full” Tala every 1.3034 days.

What's Next?

In the next volume of “Worldbuilding for Writers, Gamers and Other Creators,” we'll learn how to build a realistic geography for our world. Get updates, be the first to learn when its available, and more from Matthew Wayne Selznick and MWS Media at http://www.mattselznick.com.

~ The End of Volume One of Worldbuilding For Writers, Gamers and Other Creators ~

August 17, 2011 ~ February 28, 2012

Revision: May 30, 2012

Long Beach, California

About The Author

Matthew Wayne Selznick is a creator working with words, music, video, pictures, and people. His creations, and a wide range of creative services for independent creators, are available through MWS Media. He lives in Long Beach, California. Find him on the web and subscribe to his email newsletter at http://www.mattselznick.com.

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