Sharrukin's Palace

Water is one of the most common substances in the universe. Its special properties will lead it to have a profound effect on the surface conditions of any world, from its initial geological development, to its eventual climate, and finally to the evolution of life. Some worlds may never have much water, others will tend to lose whatever water they begin with, and still others will retain massive amounts of water throughout their lives.

In this step, we will estimate how much water can be found on a given world. The possible cases will be sorted into five categories: Trace, Minimal, Moderate, Extensive, and Massive. These categories are defined as follows.

• Trace: No liquid water or water ice remains on the vast majority of the surface. If there is a substantial atmosphere, it may carry traces of water vapor. Small pockets of water ice may remain on the surface, in permanently shadowed craters or valleys, or on the night face of a world tide-locked to its primary star. Small deposits of water may be locked in hydrated minerals deep below the surface. Examples: Mercury, Venus, Earth’s moon, or Io.
• Minimal: Liquid water is vanishingly rare on the surface, but large deposits of water ice may exist in the form of polar caps, in sheltered craters or valleys, or on the night face of a tide-locked world. Substantial aquifers or ice deposits may exist close beneath the surface. Hydrated minerals can be found in the world’s interior. Examples: Mars.
• Moderate: A substantial portion of the world’s surface, but not a majority, is covered by some combination of liquid-water seas and water ice, depending on local temperature. The liquid-water oceans or ice deposits are up to a few kilometers in depth. Far away from the oceans or ice deposits, water becomes vanishingly rare. Hydrated minerals are common in the world’s interior. Examples: Mars a few billion years ago.
• Extensive: Most of the world’s surface is covered by some combination of liquid-water oceans and water ice, up to several kilometers in depth. Water is common in most areas of the surface, even away from the oceans or ice deposits. Hydrated minerals are plentiful far into the world’s interior. Examples: Earth, Venus a few billion years ago.
• Massive: The entire surface is covered by some combination of liquid-water oceans and water ice, up to hundreds of kilometers deep. Deeper layers of this world-ocean may be composed of higher-level crystalline forms of water (Ice II and up). Hydrated minerals are plentiful far into the world’s interior. Examples: Europa, Ganymede, Callisto, Titan, some “super-Earth” exoplanets.

The amount of water available on a given world will depend upon its M-number (Step Nineteen), its blackbody temperature (Step Nineteen), its location with respect to the protoplanetary disk (Step Nine), and (in some cases) the arrangement of any gas giant planets elsewhere in the planetary system (Steps Ten and Eleven).

Procedure

Begin by noting which of the following three cases the world being developed falls under, based on its M-number.

First Case: M-number is 2 or less

In this case, the world’s prevalence of water is automatically Massive.

Second Case: M-number is between 3 and 28

In this case, determine whether the world is outside or inside the protoplanetary nebula’s snow line, as determined in Step Nine. If the world’s orbital radius (or that of its planet, in the case of a major satellite) is exactly on the snow line, assume that it is outside.

If the world in this case is outside the snow line, then its prevalence of water is automatically Massive.

If the world in this case is inside the snow line, then roll 3d6, modified as follows:

• Subtract the world’s M-number.
• Add +6 if there exists a dominant gas giant in the planetary system, it experienced a Grand Tack event, and it is currently outside the protoplanetary nebula’s snow line.
• Add +3 if any gas giants in the planetary system are currently outside the protoplanetary nebula’s slow-accretion line.

Take the modified 3d6 roll and refer to the Initial Water Prevalence table:

Initial Water Prevalence Table
Modified Roll (3d6)	Prevalence
-5 or less	Trace
-4 to 3	Minimal
4 to 11	Moderate
12 to 19	Extensive
20 or higher	Massive

If the result on the table is Moderate or higher, and the world’s blackbody temperature is 300 K or greater, then the presence of water vapor in the world’s atmosphere has given rise to a runaway greenhouse event. Make a note of this event for later steps in the design sequence and reduce the prevalence of water to Trace.

Otherwise (the world’s blackbody temperature is less than 300 K) the prevalence of water is as indicated on the table.

Third Case: M-number is 29 or greater

In this case, determine whether any of the three following cases is true:

• The world’s blackbody temperature is 125 K or greater.
• The world is the major satellite of a Large gas giant, and its orbital radius is no more than 8 times the radius of the gas giant.
• The world is the major satellite of a Very Large gas giant, and its orbital radius is no more than 12 times the radius of the gas giant.

If any of these three cases are true, then the world’s prevalence of water is Trace. Otherwise, its prevalence of water is Massive.

Examples

Both Arcadia IV and Arcadia V fall into the second case. The Arcadia system has a dominant gas giant, which underwent a Grand Tack and ended up outside the snow line. The outermost gas giant (at 9.50 AU) is not outside the system’s slow-accretion line (at 14.0 AU). For both planets, therefore, she will roll 3d6, minus the planet’s M-number, plus 6. Her rolls are 13 for Arcadia IV and 10 for Arcadia V, so Arcadia IV has Extensive water while Arcadia V has only Moderate water.

The blackbody temperature of a world is the average surface temperature it would have if it were an ideal blackbody, a perfect absorber and radiator of heat. Real planets are not ideal blackbodies, so their surface temperatures will vary from this ideal, but the blackbody temperature is a useful tool for determining a variety of other surface conditions.

In particular, the blackbody temperature is useful in determining what atmospheric gases the world can retain over billion-year timescales. Simple thermal escape (also called Jeans escape) isn’t the only mechanism by which a world can lose atmospheric gases, but it is a strong influence on the stable mass and composition of the atmosphere.

In this step, we will compute the blackbody temperature and the M-number for the world under development. The M-number is equal to a minimum molecular weight that can be retained over long timescales.

Procedure

To determine the blackbody temperature for a world, evaluate the following:

Here, L is the current luminosity of the primary star in solar units, R is the orbital radius of a planet (or the planet that a satellite orbits) in AU, and T is the blackbody temperature in kelvins. Note that the blackbody temperature will be the same for a planet and all of its satellites.

To estimate the M-number for a world, evaluate the following:

Here, T is the blackbody temperature, K is the world’s density compared to Earth, R is the world’s radius in kilometers, and M is the M-number. Round the result up to the nearest integer.

Example

Alice computes the blackbody temperature and the M-number for Arcadia IV and Arcadia V:

World	Orbital Radius	Mass	Density	Radius	Blackbody Temperature	M-Number
Arcadia IV	0.57 AU	1.08	1.04	6450 km	281 K	5
Arcadia V	0.88 AU	0.65	0.92	5670 km	226 K	6

Comparing both planets to Earth (with a blackbody temperature of 278 K and an M-number of 5), Alice finds that both of these worlds are somewhat Earthlike. Arcadia IV is just a little warmer than Earth, while Arcadia V is significantly colder.

Both worlds seem likely to have atmospheres broadly similar to that of Earth. An M-number of 5 or 6 indicates that a planet can easily retain gases such as water vapor (molecular weight 18), nitrogen (molecular weight 28), oxygen (molecular weight 32), and carbon dioxide (molecular weight 44) against simple thermal escape. It’s possible that other factors will impact the atmospheres of these worlds, but for now, Alice is satisfied that she still has two somewhat hospitable environments to use in her stories.

In this step, we will determine elements of the local calendar on the world being developed: the length of the local day, the length of any “month” determined by a major satellite, and so on.

Length of Local Day for a Planet

To determine the length of a planet’s day – the planet’s rotation period with respect to its primary star rather than with respect to the distant stars – compute the following:

Here, P is the planet’s orbital period as determined in Step Fifteen, while R is the planet’s rotational period as determined in Step Sixteen, both in hours. T is the apparent length of the planet’s day, also in hours.

Note that this equation is undefined in cases when the orbital period and rotational period are equal (that is, the planet is in a spin-orbital resonance of 1:1 and is “tide locked”). In this case, the length of the local day is effectively infinite – the sun never moves in the sky!

At the other extreme, if the orbital period is much longer than the rotational period, then the day length and the rotational period will be very close together.

To determine the length of the local year in local days, simply divide the planet’s orbital period by the length of the local day as computed above.

Length of Apparent Orbital Period for a Satellite

To determine the length of a satellite’s orbital period, from any position on the planet’s surface, use the same equation:

Here, P is the satellite’s orbital period as determined in Step Fifteen, while R is the planet’s rotational period as determined in Step Sixteen, both in hours. T is the apparent length of the satellite’s orbital period, also in hours.

Again, this equation is undefined in cases when the satellite’s orbital period and the planet’s rotational period are equal (that is, the planet is tide-locked to its satellite, or the satellite happens to orbit at a geosynchronous distance). In this case, the length of the satellite’s apparent orbital period is effectively infinite – the satellite never moves in the sky.

At the other extreme, if the satellite’s orbital period is much longer than the planet’s rotational period, then the apparent orbital period and the rotational period will be very close together. Earth’s moon is a familiar example – its apparent motion in the sky is dominated by Earth’s rotation.

It’s possible for a satellite’s orbital period to be shorter than the planet’s rotational period. For example, a moonlet that orbits very close is likely to fall into this case. The apparent orbital period will therefore be negative, indicating that the satellite appears to move backward over time. The satellite will rise in the west and set in the east.

Length of Synodic Month for a Satellite

To determine the length of a satellite’s synodic month, use the same equation once more:

Here, P is the planet’s orbital period as determined in Step Fifteen, while R is the satellite’s orbital period as determined in Step Fifteen, both in hours. T is the length of the satellite’s synodic month.

It’s very unlikely for a satellite to have the same orbital period around its planet as the planet does around its primary star, so the undefined or negative cases almost certainly will not occur. T will indicate the period between (e.g.) one “full moon” and the next, as observed from the planet’s surface.

Examples

Arcadia IV has no satellite, so the only item of interest will be the length of its local day. Alice computes:

The local day on Arcadia IV is only slightly longer than its rotation period. Alice can also determine the length of the local year in local days, by dividing the orbital period by this day length. Arcadia IV has a local year of about 184.35 local days.

Arcadia V has a satellite, so that satellite’s apparent orbital period and synodic month might be of interest. For the apparent orbital period, Alice computes:

Arcadia V’s moonlet appears to move retrograde or “backwards” in the sky, rising in the west and setting in the east, with an apparent period of about 31.7 hours.

Meanwhile, for the synodic month, Alice computes:

The satellite’s synodic month – the period between “full moon” phases – is much shorter than its apparent orbital period. From the surface of Arcadia V, the moonlet will appear to move slowly through the sky, its phase visibly changing as it moves, passing through almost a complete cycle of phases before setting once more in the east. Very strange, for human observers accustomed to the more sedate behavior of Earth’s moon!