Worldbuilding For Writers Number Three: The Orbital Period
Welcome to Worldbuilding for Writers, Gamers and Other Creatives, the weekly blog series dedicated to building an Earth-like planet for use as a setting in your storyworld. Now that we've determined how to find the habitable zone of our planet's star, we'll examine orbital properties for our planet. In this installment we'll specifically learn how to work out how to determine your planet's orbital period, or year.
Defining The Orbital Period
There are several ways to measure a planet's orbital period. 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. Later in this series, 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 the sophistication of a culture, either measure, or both, might be significant.
Determining The Orbital Period
Last time around, we 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, my storyworld and 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, 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. To do so, divide the distance from the star cubed by the mass of the star and 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 it's 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 in a later installment.
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 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. The orbit of the Earth, for example, 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, much warmer when the planet is closest. It's recommended that 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 installments.
By the way, while it might seem counter-intuitive, the degree of eccentricity does not have an 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.
Next
In the next installment of Worldbuilding for Writers, Gamers and Other Creatives, we'll discuss the rotation period of the planet — the length of the local day — and learn why your planet shouldn't spin too fast or two slow.
Your Comments
I'd love to hear your thoughts on this series so far. Have you been following along and building a world of your own? Has the level of detail been too much? Not enough? What about the math? Share your feedback in the comments, with my thanks.
Matthew Wayne Selznick - Telling stories with words, music, pictures and people.
