Architect of Worlds – Step Fifteen: Determine Orbital Period

September 8, 2020 Sharrukin Comments 0 Comment

So, for the first time in over two years, here is some new draft material from the Architect of Worlds project. First, some of the introductory text from the new section of the draft, then the first step in the next piece of the world design sequence.

The plan, for now, is to post these draft sections here, and post links to these blog entries from my Patreon page. None of this material will be presented as a charged update for my patrons yet. In fact, there may be no charged release in September, since this project is probably going to be the bulk of my creative work for the next few weeks. At most, I may post a new piece of short fiction as a free update sometime this month.

Designing Planetary Surface Conditions

Now that a planetary system has been laid out – the number of planets, their arrangement, their overall type, their number and arrangement of moons, all the items covered in Steps Nine through Fourteen – it’s possible to design the surface conditions for at least some of those many worlds.

In this section, we will determine the surface conditions for small “terrestroid” worlds. In the terms we’ve been using so far, this can be a Leftover Oligarch, a Terrestrial Planet, a Failed Core, or one of the major satellites of any of these. A world is a place where characters in a story might live, or at least a place where they can land, get out of their spacecraft, and explore.

Some of the surface conditions that we can determine in this section include:

Orbital period and rotational period, and the lengths of the local day, month, and year.
Presence and strength of the local magnetic field.
Presence, density, surface pressure, and composition of an atmosphere.
Distribution of solid and liquid surface, and the composition of any oceans.
Average surface temperature, with estimated daily and seasonal variations.
Presence and complexity of native life.

In this section, we will no longer discuss how to “cook the books” to prepare for the appearance of an Earthlike world. If you’ve been following those recommendations in the earlier sections, at least one world in your designed star system should have a chance to resemble Earth. However, we will continue to work through the extended example for Arcadia, focusing on the fourth and fifth planets in that star system.

Step Fifteen: Determine Orbital Period

The orbital period of any object is strictly determined by the total mass of the system and the radius of the object’s orbit. This is one of the earliest results in modern astronomy, dating back to Kepler’s third law of planetary motion (1619).

Procedure

For both major satellites and planets, the orbital period can be determined by evaluating a simple equation.

First Case: Satellites of Planets

To determine the orbital period of a planet’s satellite, evaluate the following:

$T\ =(2.77\ \times{10}^{-6})\ \times\sqrt{\frac{D^3}{M_P+M_S}}$

Here, T is the orbital period in hours, D is the radius of the satellite’s orbit in kilometers, and M_P and M_S are the masses of the planet and the satellite, in Earth-masses. If the satellite is a moonlet, assume its mass is negligible compared to its planet and use a value of zero for M_S.

Second Case: Planets

To determine the orbital period of a planet, evaluate the following:

$T\ =8770\ \times\sqrt{\frac{D^3}{M}}$

Here, T is the orbital period in hours, D is the radius of the planet’s orbit in AU, and M is the mass of the primary star in solar masses. Planets usually have negligible mass compared to their primary stars, at least at the degree of precision offered by this equation, and so don’t need to be included in the calculation.

Examples

The primary star in the Arcadia system has a mass of 0.82 solar masses, and the fourth and fifth planet orbit at 0.57 AU and 0.88 AU, respectively. The two planets’ orbital periods are about 4170 hours and 7990 hours. Converting to Earth-years by dividing by 8770, the two planets have orbital periods of 0.475 years and 0.911 years.

Alice has decided to generate more details for the one satellite of Arcadia V. This is a moonlet and so can be assumed to have negligible mass, while the planet itself has a mass of 0.65 Earth-masses. The moonlet’s orbital radius is about five times that of the planet, and Alice sets a value for this radius of 28400 kilometers. The moonlet’s orbital period is about 16.4 hours.

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