Architect of Worlds – Step Fourteen: Place Natural Satellites

July 26, 2018 Sharrukin Comments 0 Comment

This is the last chunk of the “design planetary systems” section of the Architect of Worlds draft. Before I post it, a small status report.

One of the things I’ve been doing over the past week is applying the current draft model to some real-world data – the HIPPARCOS catalog of the nearest stars to Sol. The next major project on my Gantt chart, after all, is to draw a map of nearby space and take a census of plausible habitable worlds in our neighborhood. This effort is helping me to test out the model, and it’s giving me data to suggest how to outline the next section (on designing specific planets).

So far, the results have actually been rather encouraging. I’ve been able to apply the model and the design sequence even to nearby stars for which we have strong candidate exoplanets. In those cases, I’ve been able to demonstrate not only that the model permits the known exoplanets, but that it also plausibly extrapolates what other planets may exist in the system, as yet undetected! That’s a good check on whether the model and design sequence are actually going to hold up against the real universe.

On the other hand, I have come across a few bits of data indicating that I need to make some revisions. In particular, the current design sequence doesn’t deal with red dwarf stars very well. I’m getting crowded arrays of Mercury- or Mars-sized rocky worlds, even in cases where what I should be seeing is icy “failed cores” out past the snow line. It’s a small logic problem, mostly in Step Eleven, which makes sense since that’s the most complex step in the sequence thus far. I think I already see how to fix it – but it will take a little bit of testing and rewriting.

I know a few of you have been experimenting with the draft sections that I’ve posted. I think what I will do, when I’ve made the necessary changes to the draft, is to revise those specific posts in place. When I’ve done that, I’ll also make a new status-report post here, with links to the altered posts. Of course, once I’m satisfied with this draft section for the time being, I’ll post a PDF to the Sharrukin’s Archive site.

Okay, with that out of the way, let’s have a look at the draft Step Fourteen.

Step Fourteen: Place Natural Satellites

In this step, we will determine the number and placement of major satellites. We define a major satellite as a natural satellite which is large enough to have formed a sphere under its own gravitation. A major satellite will be at least 200 kilometers in radius if it is mostly made of ice, or at least 300 kilometers in radius if it is mostly stone.

In general, the rocky planets close to a star are unlikely to form major satellites during the process of planetary accretion. A terrestrial planet which suffers a specific kind of massive impact event may form one major satellite, as the planetary material scattered into orbit coalesces. Gas giant planets are likely to have several major satellites. For example, planets with major satellites in our own system include Earth (1), Jupiter (4), Saturn (7), Uranus (5), and Neptune (1).

Many planets will also have moonlets, much smaller satellites that are irregular in shape. Some moonlets may be remnants of the process of planetary formation. Others are likely to be captured asteroids or comets. Even very small objects may have moonlets of their own. In our system, the planet Mars has two moonlets, and many asteroids and Kuiper Belt objects have been found to have moonlets of their own. A gas giant planet will often have dozens of moonlets in a wide variety of orbits.

Procedure

To determine the number and arrangement of natural satellites for a given planet, begin by computing the planet’s Hill radius. This is the distance from the planet within which its gravitation dominates over that of the primary star. The Hill radius defines the region of space where a satellite is likely to form or be captured, and where it can maintain a stable orbit around the planet for long periods of time.

If R_min is the minimum distance from the planet to the primary star (in AUs), M_P is the mass of the planet (in Earth-masses), and M_S is the mass of the star (in solar masses), then:

$H=2170000\times R_{min}\times\sqrt[3]{\frac{M_P}{M_S}}$

Here, H is the Hill radius in kilometers. Round off to three significant figures.

First Case: Satellites Forming via Natural Accretion

To estimate how many major satellites will form with the planet, as part of the original accretion process, evaluate the following formula:

$N=\frac{H^2}{(5\times{10}^{14})\times\sqrt R}$

Here, H is the Hill radius in kilometers, and R is the average distance from the planet to its primary star in AU. Round N down to the nearest integer. If the result is greater than 0, then the planet will have one or more major satellites that formed with the planet itself. No planet is likely to have more than about 8 major satellites.

If N is greater than 0, feel free to adjust N upward or downward by up to 2, so long as the result is still greater than 0 and no greater than 8. To make this adjustment at random, roll 1d6: subtract 2 from N (minimum 1) on a result of 1, subtract 1 from N (minimum 1) on a result of 2, add 1 to N (maximum 8) on a result of 5, and add 2 to N (maximum 8) on a result of 6.

The innermost major satellite will have an orbital radius equal to about 1d+2 times the radius of the planet (feel free to adjust this by up to half the planet’s radius). Major satellites after the first can be placed using the same procedure as in Step Eleven, assuming tight orbital placement. The eccentricity of major satellite orbits will be very small (less than 0.01).

The total mass of all major satellites formed during planetary accretion will be about one ten-thousandth of the mass of the planet. The mass of each major satellite can be generated at random with a 3d6 roll:

$M_S=\frac{(3d6)\times M_P}{100000\times N}$

Here, M_S is the mass of a major satellite in Earth-masses, M_P is the mass of the planet in Earth-masses, and N is the number of major satellites. Round the satellite’s mass off to two significant figures.

To determine the density of any of these major satellites, roll 3d6:

$D=K+\frac{(3d6)}{100}$

Here, D is the satellite’s density, and K is a constant that depends on whether the planet is inside or outside the system’s snow line. Inside the snow line, use K of 0.5. Outside the snow line, use K of 0.25. The radius and surface gravity of these major satellites can be determined as in Step Thirteen.

If a planet has one or more major satellites formed during planetary accretion, it will probably also have many moonlets. We will not generate these in detail, but they may be of interest in general.

Close to the planet will be a family of inner moonlets. These can range in number from a handful up to dozens. Their orbital radii usually range from about 1.8 times the planet’s radius, out to just inside the radius of the innermost major satellite. In some cases, inner moonlets can be interspersed between the orbits of the first few major satellites as well.

If there are inner moonlets, the planet is also likely to have a ring system. A few inner moonlets usually mean a thin system of rings, not easily visible from any distance. More inner moonlets imply a thicker and more visible set of rings. Ring systems usually hug close to the planet, reaching out to about twice the planet’s radius.

To generate the ring system at random, roll 3d6. On a result of 6-9, the planet will have a thin, wispy ring system comparable to that of Jupiter or Neptune, barely visible even at close range. On a result of 10-13, the ring system will be moderate, comparable to that of Uranus, visible from a distance through a telescope. On a result of 14 or higher, the planet will have many inner moonlets, supporting a dense ring system comparable to Saturn’s: easily visible from anywhere in the star system through a telescope, and spectacular at close range.

Beyond the major satellites will be one or more families of outer moonlets. As with the inner moonlets, these can range in number from a handful up to dozens. They are usually captured planetoids or other debris, following orbits that are eccentric, strongly inclined to the planet’s equator, or even retrograde. Their orbital radii usually begin at over 100 times the planet’s radius, and continue outward to about one-fifth to one-third of the planet’s Hill radius.

Second Case: Satellites Forming via Major Impact

Leftover Oligarchs and Terrestrial Planets, late in their formation process, are subject to repeated massive impact events. The planetary material scattered into orbit by such impacts is likely to form a large natural satellite. However, that satellite is in turn likely to spiral back into collision with the parent planet, or to migrate outward and escape the planet’s Hill radius entirely. In our own planetary system, only Earth still has a major satellite because of this process. While Mercury, Venus, and Mars all appear to have suffered similar massive impacts, none of them have retained any resulting major satellite.

To determine whether a Leftover Oligarch or Terrestrial Planet can have a large natural satellite, divide the planet’s Hill radius by its own radius. If the result is 300 or greater, then the planet can retain a large natural satellite over the long term. In this case, roll 1d: on a 5 or 6 the planet will have one large natural satellite.

If it exists, the major satellite will form quite close to the planet, but will quickly move outward due to tidal interactions. Its current orbital radius will usually be between 40 and 100 times the planet’s radius. To generate an orbital radius at random, roll 3d6+7 and multiply by 4 times the planet’s radius. The eccentricity of the major satellite’s orbit will be small (no more than about 0.05).

The major satellite formed by a massive impact event will have a mass about one hundredth of the mass of the planet. The mass of the major satellite can be generated at random with a 3d6 roll:

$M_S=\frac{(3d6)\times M_P}{1000}$

Here, M_S is the mass of the major satellite, and M_P is the mass of the planet, both in Earth-masses. Round the satellite’s mass off to two significant figures.

To determine the density of the major satellite, roll 3d6:

$D=0.5+\frac{(3d6)}{100}$

The radius and surface gravity of the major satellite can be determined as in Step Thirteen.

Third Case: Terrestrial Planet Moonlets

If a Leftover Oligarch or Terrestrial Planet has no major satellite, it may acquire one or more moonlets through a variety of means. For example, in our own planetary system, Mars has two moonlets.

A Leftover Oligarch or Terrestrial Planet may have moonlets if it can have a major satellite (that is, its Hill radius is at least 300 times the planet’s own radius) but it has no such satellite. In this case, roll 1d: on a 4-6 the planet will have at least one moonlet. Roll 1d-3 (minimum 1) for the number of moonlets.

The innermost moonlet will have an orbital radius equal to about 1d+2 times the radius of the planet (feel free to adjust this by up to half the planet’s radius). Moonlets after the first can be placed using the same procedure as in Step Eleven, assuming wide orbital placement. The eccentricity of these moonlets will be very small (less than 0.02).

Examples

Arcadia: Alice adds more columns to her table and computes the Hill radius for each planet. She then selects or randomly generates the number of major moons for each.

Radius	Planet Type	Planet Mass	Radius	Eccentricity	Hill Radius	Satellites
0.09 AU	Terrestrial Planet	0.88	6280	0.03	194000	None
0.17 AU	Terrestrial Planet	1.20	6680	0.10	377000	None
0.30 AU	Terrestrial Planet	0.95	6220	0.18	561000	None
0.57 AU	Terrestrial Planet	1.08	6450	0.05	1290000	None
0.88 AU	Terrestrial Planet	0.65	5670	0.02	1730000	1 moonlet
1.58 AU	Leftover Oligarch	0.10	3380	0.38	1050000	2 moonlets
2.61 AU	Planetoid Belt	N/A	N/A	0.00	N/A	N/A
4.40 AU	Large Gas Giant	480	83000	0.00	79900000	7 major satellites
5.76 AU	Medium Gas Giant	120	70000	0.00	65900000	4 major satellites
9.50 AU	Small Gas Giant	22	30000	0.08	56800000	2 major satellites

As it happens, none of the first four inner planets can have major satellites or moonlets. In particular, the habitable-planet candidate has too small a Hill radius to permit it. Alice rolls at random for the fifth and sixth planets, and gets the results she tabulated above. She decides not to bother generating these moonlets in detail, unless her story visits one of these two planets.

With very wide Hill radii and plenty of distance between them and the primary star, the three gas giants all have extensive systems of satellites. Alice uses the formula and a random die roll to determine how many major satellites each planet has. She doesn’t bother to set up their systems of moonlets, although she does roll at random to see whether either planet has a prominent ring system. She rolls a 10, an 11, and another 10, so all three gas giants have ring systems that are visible at a distance through telescopes, but none of them have a remarkable Saturn-like set of rings.

Beta Nine: Bob computes the Hill radii for his two planets. The inner planet has a Hill radius of about 863,000 kilometers, which is only about 160 times the planet’s radius. The outer planet has a Hill radius of about 1.42 million kilometers, which is better but still comes to only about 260 times the planet’s radius. Bob concludes that neither planet has any satellites.

Architect of Worlds – Step Thirteen: Determine Planetary Density, Radius, and Surface Gravity

July 25, 2018 Sharrukin Comments 0 Comment

Step Thirteen: Determine Planetary Density, Radius, and Surface Gravity

The physical size of a planet depends on not only its mass, but its physical composition. In this step, we will determine the density of each planet, which will immediately give us its radius and surface gravity.

Procedure

The density of a planet is a measure of its mass per unit volume. We will express planetary density in comparison with Earth. Thus, a planet with a density of 1.0 is exactly as dense as Earth. To convert to the usual units, multiply by 5.52 to get grams per cubic centimeter.

Leftover Oligarchs and Terrestrial Planets which form inside the snow line are made primarily out of silicate compounds (i.e., rocks). The heat of the accretion process tends to cause heavy metals, especially nickel and iron, to separate out and settle into a planetary core. The density of the fully formed planet will largely depend on the amount of nickel-iron available, and so on the size of this metallic core. To estimate the density of a Leftover Oligarch or Terrestrial Planet, roll 3d6 and apply the following:

$D=(0.90+\frac{\left(3d6\right)}{100})\times\sqrt[5]{M}$

Here, D is the planet’s density, and M is its mass in Earth-masses. Round the density off to two significant figures.

In some cases, a rocky Leftover Oligarch may have significantly higher density due to a massive impact event late in the process of planetary formation. The impact scatters most of the lower-density rocky material out into space, leaving behind a planetary body dominated by the nickel-iron core. In our own planetary system, Mercury appears to have undergone such a process. To determine whether a rocky Leftover Oligarch has unusually high density, roll 1d: on a 5 or 6 the planet will be dominated by its metallic core. Add 0.4 to the density computed above.

Failed Cores, and Leftover Oligarchs and Terrestrial Planets that form outside the snow line, incorporate a great deal of water and other ices. The density of the fully formed planet will be significantly lower than that of a rocky planet of the same mass. Determine the density of these planets by rolling 3d6:

$D=(0.50+\frac{\left(3d6\right)}{100})\times\sqrt[5]{M}$

Again, D is the planet’s density, and M is its mass in Earth-masses. Round the density off to two significant figures.

Gas Giants are constructed almost entirely out of hydrogen and helium gas. Although a gas giant will have a solid core of stone and ice, the factor dominating its density is the degree to which its gaseous envelope is compressed under gravity. To determine the density of a gas giant, let M be its mass. Then use the appropriate formula below:

$D=\frac{1}{\sqrt M}\ \left(M\le200\right)$

$D=\frac{M^{1.27}}{11800}\ (M>200)$

Here, D is the density of the gas giant planet. Round the density off to two significant figures.

Radius

The radius of a planet (normally measured in kilometers) is dependent solely on its mass and density. If M is the planet’s mass (in Earth-masses), and D is the planet’s density, then:

$R=6370\times\sqrt[3]{\frac{M}{D}}$

Here, R is the planet’s radius in kilometers. Round off to three significant figures.

Surface Gravity

The surface gravity of a planet, measured in comparison to standard gravity at Earth’s surface, is again dependent solely on its mass and density. If M is the planet’s mass (in Earth-masses), and D is the planet’s density, then:

$G=\sqrt[3]{MD^2}$

Here, G is the planet’s surface gravity. Round off to the nearest hundredth of a gravity. Note that under our model, a Gas Giant of 200 Earth-masses or less will always have a surface gravity of exactly 1.

Examples

Arcadia: The computations here are very straightforward. Alice adds more columns to her table and generates planetary densities, adjusting these to taste and then computing planetary radius and surface gravity for each planet.

Radius	Planet Type	Planet Mass	Density	Radius	Gravity
0.09 AU	Terrestrial Planet	0.88	0.92	6280	0.91
0.17 AU	Terrestrial Planet	1.20	1.04	6680	1.09
0.30 AU	Terrestrial Planet	0.95	1.02	6220	1.00
0.57 AU	Terrestrial Planet	1.08	1.04	6450	1.05
0.88 AU	Terrestrial Planet	0.65	0.92	5670	0.82
1.58 AU	Leftover Oligarch	0.10	0.67	3380	0.36
2.61 AU	Planetoid Belt	N/A	N/A	N/A	N/A
4.40 AU	Large Gas Giant	480	0.22	83000	2.85
5.76 AU	Medium Gas Giant	120	0.091	70000	1.00
9.50 AU	Small Gas Giant	22	0.21	30000	1.00

Beta Nine: Bob also has no difficulty with the necessary computations.

Radius	Planet Type	Planet Mass	Density	Radius	Gravity
0.27 AU	Terrestrial Planet	0.63	0.98	5500	0.85
0.45 AU	Terrestrial Planet	0.59	0.89	5550	0.78

Architect of Worlds – Step Twelve: Determine Eccentricity of Planetary Orbits

July 22, 2018 Sharrukin Comments 2 comments

Step Twelve: Determine Eccentricity of Planetary Orbits

The procedures in Step Eleven will generate a stack of planetary orbits which are likely to be stable, if all of them are perfectly circular. However, few planets follow such carefully arranged orbital paths. In this step, we will assign eccentricity values to the planetary orbits generated in Step Eleven, in such a way that the whole ensemble remains stable.

Starting with the innermost planet and working outward, select an eccentricity for the planet’s orbit. Planetoid Belts will have orbital eccentricity of 0. Planetary orbits tend to have low eccentricity, averaging around 0.1 to 0.2, but cases with eccentricity up to about 0.6 are known.

After each planet’s eccentricity has been determined, the eccentricity of the next planet’s orbit will be bounded. Let R₀ and E₀ be the orbital radius and eccentricity of the planet that has just been checked, and let R₁ and E₁ be the orbital radius and eccentricity of the next planet. Then:

$\left(1+E_0\right)\frac{R_0}{R_1}-1<E_1<\left(-1+E_0\right)\frac{R_0}{R_1}+1$

If this inequality holds, then the two orbits will not cross at any point. Select eccentricity values with this requirement in mind, except for the last planetary orbit to be placed. If the last two planetary orbits are in resonance, the two orbits can cross if the outermost planet’s orbit is inclined at a significant angle. This will make no significant difference when determining the properties of that planet, but it may be of interest as a distinctive feature.

To determine an eccentricity at random, roll 3d6 on the Planetary Orbital Eccentricity Table. If the orbital spacing is tight, modify the roll by -4. If the orbital spacing is moderate, modify the roll by -2. Feel free to adjust the eccentricity by up to 0.05 in either direction. Check randomly generated eccentricity values using the inequality above, and increase or reduce eccentricity as needed.

Planetary Orbital Eccentricity Table
Roll (3d6)	Eccentricity
6 or less	0
7-9	0.1
10-12	0.2
13-14	0.3
15	0.4
16	0.5
17	0.6
18	0.7

Once the average distance and eccentricity have been established, the planet’s minimum distance and maximum distance from the primary star can be computed. As before, let R be the planet’s orbital radius in AU, and let E be the eccentricity of its orbital path. Then:

$R_{min}=R\times\left(1-E\right)$

$R_{max}=R\times\left(1+E\right)$

Here, R_min is the minimum distance, and R_max is the maximum distance.

If a planet’s minimum distance implies an approach to its primary star more closely than the inner edge of the protoplanetary disk, this is acceptable. If its maximum distance implies that the planet moves out into a forbidden zone at some point on its orbit, this is not a stable situation; reduce the planet’s eccentricity to ensure that this does not occur.

Selecting for an Earthlike world: Human-habitable worlds are not likely to have high orbital eccentricity, although a moderate value (no greater than 0.2) is probably not incompatible with Earthlike conditions.

Examples

Arcadia: Alice adds another column to her table and generates orbital eccentricities at random, adjusting each result to taste.

Radius	Planet Type	Planet Mass	Eccentricity
0.09 AU	Terrestrial Planet	0.88	0.03
0.17 AU	Terrestrial Planet	1.20	0.10
0.30 AU	Terrestrial Planet	0.95	0.18
0.57 AU	Terrestrial Planet	1.08	0.05
0.88 AU	Terrestrial Planet	0.65	0.02
1.58 AU	Leftover Oligarch	0.10	0.38
2.61 AU	Planetoid Belt	N/A	0.00
4.40 AU	Large Gas Giant	480	0.00
5.76 AU	Medium Gas Giant	120	0.00
9.50 AU	Small Gas Giant	22	0.08

Random generation yielded an eccentricity of 0.18 for the third planet, which concerned Alice, since the fourth planet was her Earthlike-world candidate. She therefore evaluated the inequality to determine how the fourth planet’s eccentricity was bounded:

$\left(1+0.18\right)\frac{0.30}{0.57}-1<E_1<\left(-1+0.18\right)\frac{0.30}{0.57}+1$

$-0.38<E_1<0.57$

Apparently, even a very large value for the fourth planet’s eccentricity would still be within bounds. Without making a random roll, she selected a small value of 0.05 (comparable to that of Earth) and proceeded.

Alice’s roll for the sixth planet (the Leftover Oligarch) was a modified 15, suggesting an eccentricity of close to 0.4. She reduced this to 0.38, checked the minimum and maximum distances for this orbit, and determined that the planet that moves from 0.98 AU out to 2.18 AU during its “year.” This did not appear to cross the orbit of the fifth planet, nor did it venture into the heart of the planetoid belt just outward. Alice decided to accept this result as a distinctive feature of the planetary system.

Beta Nine: Bob adds another column to his table. Random rolls give him an eccentricity of 0.0 each time, which he tweaks upward for variety. Both planets in the Beta Nine primary’s system have nearly circular orbits.

Radius	Planet Type	Planet Mass	Eccentricity
0.27 AU	Terrestrial Planet	0.63	0.03
0.45 AU	Terrestrial Planet	0.59	0.02

Architect of Worlds – Step Eleven: Place Planets

July 21, 2018 Sharrukin Comments 6 comments

Step Eleven: Place Planets

Beginning close to the primary star and working outward, use the following procedure to determine the orbital radius, type, and mass for each planet in the system.

Procedure

At any given point in this process, the spacing of planetary orbits will be tight, moderate, or wide. Tight orbital spacing tends to occur when the protoplanetary disk was very dense, encouraging many planets to form and migrate inward together, until they fall into a stable but closely packed arrangement. Moderate orbital spacing normally occurs when the disk is less dense, or in the outer reaches of the disk. Wide orbital spacing occurs in very thin disks, or in regions of the disk that have been disturbed by the migration of a dominant gas giant.

Each planetary system will be governed by two orbital spacing regimes, one from the inner edge of the protoplanetary disk to the final location of the dominant gas giant, and another once the dominant gas giant has been placed. Select an orbital spacing regime when beginning the process of placing planets, then choose again immediately after the dominant gas giant has been placed.

To select an orbital spacing regime at random, roll 3d6 and apply the following modifiers:

-3 if the disk mass factor is 6.0 or greater
-2 if the disk mass factor is at least 3.0 but less than 6.0
-1 if the disk mass factor is at least 1.5 but less than 3.0
+1 if the disk mass factor is greater than 0.3 but no greater than 0.6
+2 if the disk mass factor is greater than 0.15 but no greater than 0.3
+3 if the disk mass factor is 0.15 or less
+1 if there is a dominant gas giant which underwent weak inward migration
+2 if there is a dominant gas giant which underwent moderate inward migration
+3 if there is a dominant gas giant which underwent strong inward migration
+3 if outward from a dominant gas giant that did not undergo a Grand Tack

The current orbital spacing regime will be tight on a final modified roll of 7 or less, moderate on a roll of 8-13, and wide on a roll of 14 or more.

Before beginning, make a note as to how many gas giant planets must appear in this planetary system. If a dominant gas giant was generated in Step Ten, then there must be at least one gas giant; if a Grand Tack event has taken place, there must be at least two.

Selecting for an Earthlike world: To maximize the probability of an Earthlike world, select orbital placements and planetary types so that a Terrestrial Planet will fall close to the critical radius $R=\sqrt L$ , as discussed under Step Ten.

Sub-Step Eleven-A: Determine Orbital Radius

If no planets have already been placed, determine the first orbital radius as follows:

If an epistellar gas giant was generated in Step Ten, then it is automatically the first planet to be placed, and its orbital radius has already been established.
If there is no epistellar gas giant, and the spacing is currently tight, then the first orbital radius is equal to the disk inner edge radius.
If there is no epistellar gas giant, and the spacing is currently moderate, then if M is the star’s mass, the first orbital radius will be:

$R=(2d6)\times0.01\times\sqrt[3]{M}$

If there is no epistellar gas giant, and the spacing is currently wide, then if M is the star’s mass, the first orbital radius will be:

$R=(2d6)\times0.04\times\sqrt[3]{M}$

After placement of the first planet, each orbital radius will be based on the previous one. Roll 3d6, and subtract 2 if the previous orbital radius was resonant. The next orbit will be resonant if:

The spacing is currently tight, and the 3d6 roll was 14 or less.
The spacing is currently moderate, and the 3d6 roll was 10 or less.
The spacing is currently wide, and the 3d6 roll was 6 or less.

Roll 3d6 on either the Stable Resonant or the Stable Non-Resonant Orbit Spacing Table, depending on whether the next orbital radius is resonant or not. In either case, multiply the previous orbital radius by the ratio from the table to determine the new orbital radius. Round each orbital radius off to the nearest hundredth of an AU.

Stable Resonant Orbit Spacing Table
Roll (3d6)	Ratio	Resonance
3-7	1.211	4:3
8-9	1.251	7:5
10-12	1.310	3:2
13	1.368	8:5
14	1.406	5:3
15	1.452	7:4
16-18	1.587	2:1 (see Note)

Note: Immediately after one 2:1 resonance appears, the next orbit will automatically be resonant as well, and will also exhibit a 2:1 resonance. After that, determine the spacing of further orbits normally. Single 2:1 resonances are normally unstable, but a stack of two or more such resonances can be very stable; this is a special case called a Laplace resonance.

Stable Non-Resonant Orbit Spacing Table
Roll (3d6)	Ratio
3	1.34
4	1.38
5	1.42
6	1.50
7	1.55
8	1.60
9-10	1.65
11-12	1.70
13	1.75
14	1.80
15	1.85
16	1.90
17	1.95
18	2.00

When rolling on the Stable Non-Resonant Orbit Spacing Table, feel free to select a ratio between two of the values on the table, but be careful not to match any of the precise ratio values from the Stable Resonant Orbit Spacing Table.

In any case, if there exists a dominant gas giant that has not yet been placed, and the new orbital radius is at least 0.7 times the orbital radius of the dominant gas giant as established in Step Ten, then skip to the dominant gas giant instead. Select or randomly generate a new orbital spacing scheme after this point.

If the new orbital radius is greater than the radius of the inner edge of a forbidden zone, then stop placing planets and move on to Step Twelve. Any remaining planetary mass budget is lost.

Sub-Step Eleven-B: Determine Planet Type

For each planet, roll on the Planet Type Table. Refer to the Inner Planetary System column for all planets before the dominant gas giant (if any), or the appropriate Outer Planetary System column for the dominant gas giant and all subsequent planets.

If this planet is the dominant gas giant, or a Grand Tack event took place and this planet is the first one after the dominant gas giant, then roll 2d6+8 on the table. Otherwise, roll 3d6.

If the maximum possible number of gas giants for this planetary system have already been placed, then any subsequent planets will be Terrestrial Planets (inside the snow line) or Failed Cores (outside the snow line).

Planet Type Table
Roll (3d6)	Inner Planetary System	Outer Planetary System (Inside Snow Line)	Outer Planetary System (Outside Snow Line)
3-7	Leftover Oligarch	Terrestrial Planet	Failed Core
8-11	Terrestrial Planet	Small Gas Giant	Small Gas Giant
12-14		Medium Gas Giant	Medium Gas Giant
15 or higher		Large Gas Giant	Large Gas Giant

Sub-Step Eleven-C: Determine Planet Mass

The mass M_P of a Leftover Oligarch can be generated randomly as:

$M_P=(3d6)\times0.01$

The mass M_P of a Terrestrial Planet can be generated randomly as:

$M_P=(3d6)\times0.2\times M\times K\times D$

Here, M is the mass of the star in solar masses, K is the star’s metallicity, and D is the disk mass factor. Adjust this result by all the following which apply:

If there is at least one gas giant in the system, the dominant gas giant underwent at least weak migration during Step Ten, and the current orbital radius is less than 0.7 times the orbital radius of the dominant gas giant after inward migration, then multiply the Terrestrial Planet’s mass by 0.75 for weak migration, 0.5 for moderate migration, and 0.25 for strong migration.
If there is at least one gas giant in the system, the dominant gas giant underwent at least weak migration during Step Ten, and the current orbital radius is at least 0.7 times the orbital radius of the dominant gas giant after inward migration, but less than the current orbital radius of the dominant gas giant, then multiply the Terrestrial Planet’s mass by 0.1. Note that this case should only occur if a Grand Tack event took place in Step Ten.

The minimum mass for a Terrestrial Planet is 0.18 Earth-masses. If the estimated mass of a Terrestrial Planet is less than this:

If there is at least one gas giant in the system, and the current orbital radius is at least 0.5 times the current orbital radius of the dominant gas giant, then the current orbit will automatically be filled by a Planetoid Belt rather than an actual planet.
If there is a forbidden zone in the system, and the current orbital radius is at least 0.85 times the radius of the inner edge of the forbidden zone, then the current orbit will automatically be filled by a Planetoid Belt rather than an actual planet.
Otherwise, treat the planet as a Leftover Oligarch instead, and re-roll its mass as above.

The mass M_P of a Failed Core can be generated randomly as:

$M_P=(3d6)\times0.25$

The mass M_P of a Small Gas Giant can be generated randomly as:

$M_P=4+\left(3d6\right)\times0.25\times M\times D\times\sqrt R$

The mass M_P of a Medium Gas Giant can be generated randomly as:

$M_P=4+\left(3d6\right)\times3\times M\times D\times\sqrt R$

The mass M_P of a Large Gas Giant can be generated randomly as:

$M_P=4+\left(3d6\right)\times15\times M\times D\times\sqrt R$

For the last three, M is the mass of the star in solar masses and D is the disk mass factor. If this is the dominant gas giant, then R is the planet’s original orbital radius before any migration or Grand Tack. Otherwise, R is the current orbital radius, or the slow-accretion radius, whichever is less.

In all cases, feel free to adjust the result upwards or downwards by up to one-half of the amount associated with one point on the dice. Round off the planet’s mass to the nearest hundredth of an Earth-mass for Leftover Oligarchs and Terrestrial Planets, and to two significant figures for all other types.

Sub-Step Eleven-D: Adjust Planetary Mass Budget

Mass Cost Table
Planet Type	Mass Cost
Planetoid Belt	0
Leftover Oligarch Terrestrial Planet Failed Core	$M_P$
Small Gas Giant	$0.9\times M_P$
Medium Gas Giant	$0.2\times M_P$
Large Gas Giant	$0.1\times M_P$

Once the new planet’s type and mass have been determined, determine that planet’s mass cost using the appropriate formula from the Mass Cost Table. In these formulae, M_P is the mass of the planet. Round the mass cost for a given planet off to two significant figures.

Deduct the planet’s mass cost from the current planetary mass budget. “Spending” more than remains in the budget is allowed. However, if the planetary mass budget has now been exhausted, and the minimum number of gas giants has been placed, then stop placing planets and move on to Step Twelve. Otherwise, return to Sub-Step Eleven-A and continue to place planets.

Examples

Arcadia: Alice applies the looped procedure described above to place the planets of the Arcadia system. She has few preferences as to the placement of planets, other than a probably habitable world near an orbital radius of 0.58 AU. She decides to use moderate orbital spacing throughout. She has already determined that she has a planetary mass budget of 83.

Alice uses a combination of random rolls and minor adjustments to suit her taste, and builds a table of planets that looks something like the following:

Radius	Planet Type	Planet Mass	Mass Cost	Remaining Mass Budget
0.09 AU	Terrestrial Planet	0.88	0.88	82.12
0.17 AU	Terrestrial Planet	1.20	1.20	80.92
0.30 AU	Terrestrial Planet	0.95	0.95	79.97
0.57 AU	Terrestrial Planet	1.08	1.08	78.89
0.88 AU	Terrestrial Planet	0.65	0.65	78.24
1.58 AU	Leftover Oligarch	0.10	0.10	78.14
2.61 AU	Planetoid Belt	N/A	0.00	78.14
4.40 AU	Large Gas Giant	480	48.9	30.14
5.76 AU	Medium Gas Giant	120	24.0	6.14
9.50 AU	Small Gas Giant	22	19.8	-13.66

After the third planet, Alice noticed that she was approaching the critical orbital radius for the Earthlike world she wanted, so rather than roll a new orbital radius at random she simply selected a ratio of 1.90 and recorded the result. She also selected a Terrestrial Planet for that orbit, rather than rolling at random and possibly getting a Leftover Oligarch.

Recall that the dominant gas giant in the Arcadia system migrated inward to 1.7 AU before undergoing a Grand Tack, which means that the materials to build terrestrial planets are depleted from about 1.19 AU outward. For the sixth orbit, at 1.58 AU, Alice rolled a Terrestrial Planet whose mass turned out to be below the minimum of 0.18 Earth-masses. Since this orbit was not close enough to the dominant gas giant at 4.4 AU, she substituted a Leftover Oligarch instead. The same thing occurred for the orbit at 2.61 AU, but this orbital radius was greater than half that of the dominant gas giant, so that orbit acquired a Planetoid Belt instead.

The next orbital radius after the Planetoid Belt was very close to that of the dominant gas giant, so Alice skipped to that radius instead. Since the dominant gas giant went through a Grand Tack, the next planet outward was guaranteed to be another gas giant. The third gas giant exhausted the planetary mass budget, so Alice stopped generating planets at that point. Notice that even if the first gas giant had exhausted the mass budget, Alice would have been required to place the second, since there was a Grand Tack event. Also, notice that the first two gas giant planets are in a 3:2 resonance.

Alice concludes that the Arcadia planetary system somewhat resembles ours, with rocky planets close in, gas giant planets further out, and a planetoid belt in between. On the other hand, the system’s denser protoplanetary disk meant that the planets were more tightly packed, yielding more substantial rocky planets and fewer gas giants.

Beta Nine: Bob generates the Beta Nine planetary system entirely at random, curious to see what results he will get. He already knows that the system has a planetary mass budget of 5.1, and that a forbidden zone exists at 0.67 AU.

There is no gas giant in the system, and the disk mass is 0.5. Bob makes a modified 3d6 roll of 16, and determines that the planets will have wide orbital spacing. Random rolls generate the following:

Radius	Planet Type	Planet Mass	Mass Cost	Remaining Mass Budget
0.27 AU	Terrestrial Planet	0.63	0.53	4.57
0.45 AU	Terrestrial Planet	0.59	0.59	3.98

The next orbital radius turns out to be at 0.74 AU, which is beyond the edge of the forbidden zone, so no more planets will be placed, even though part of the planetary mass budget remains available.

Architect of Worlds – Step Nine: Structure of Protoplanetary Disk

July 18, 2018 Sharrukin Comments 0 Comment

Over the next few days, I’ll be posting the current draft of the next section of the Architect of Worlds project. Here, now that we’ve designed and arranged the star(s) of a given system, we can give each star its own family of attendant planets, determining their basic physical and dynamic properties along the way.

Step Nine: Structure of Protoplanetary Disk

In this step, we determine the most important properties of the star’s protoplanetary disk, which will in turn govern the size and placement of the planets that form. These properties include the location of the disk’s effective inner and outer edges, the location of the “snow line,” and the relative mass and density of the disk.

Procedure

Select or compute each of the following parameters, and record the results for later use.

Disk Inner Edge

Astronomers are not clear where the inner edge of a protoplanetary disk will normally be located. In fact, it’s possible that the disk has no inner edge, since material continues to fall onto the star’s surface throughout the period of planetary formation. Planets which migrate strongly inward do seem to stop some distance away from the primary star, but their eventual orbital period may be quite short, on the order of a few days.

Select a radius for the inner edge of the protoplanetary disk. To select a distance at random, roll 2d6:

$R=(2d6)\times0.003\times\sqrt[3]{M}$

Here, R is the radius of the disk inner edge in AU, and M is the star’s mass in solar masses. Round off to two significant figures.

Snow Line

The “snow line” represents a distance from the star where volatiles, especially water, can freeze and remain solid within the protoplanetary disk. Inside the snow line, any solid matter within the disk will tend to be dry: dust leading up to masses of stone. Outside the snow line, water and other volatiles will be present in the form of ices. Thus, crossing the snow line outward, an observer would see a sharp rise in the amount of solid material available for planetary formation. The most probable location for the formation of the system’s largest planet is at the snow line.

Determine the radius of the snow line as follows. If L₀ is the initial luminosity of the star in solar units, then:

$R=4.2\times\sqrt{L_0}$

Here, R is the radius of the snow line in AU. Round off to two significant figures.

Slow-Accretion Line

On the outer edges of a planetary system in formation, the density of available material is low and the orbital period of that material is long. Protoplanets forming in this region may have difficulty sweeping up all the material that’s theoretically available. Most of that material is likely to remain free when the period of planetary formation ends, to be swept out into interstellar space. We model this effect by establishing a “slow-accretion line,” beyond which the formation of planets is unlikely.

Determine the radius of the slow-accretion line as follows. If M is the mass of the star in solar masses, then:

$R=15\times\sqrt[3]{M}$

Here, R is the radius of the slow-accretion line in AU. Round off to two significant figures.

Disk Density

Mass available for the formation of planets will be limited, since the bulk of the protostellar nebula will have ended up in the star rather than in the protoplanetary disk. The mass in the disk is dominated by gas, primarily hydrogen and helium. Other constituents of the disk include frozen volatiles (outside the snow line) and dust.

For astronomers, measuring the mass of a protoplanetary disk is rather difficult. Most estimates indicate that a star’s protoplanetary disk will have about 1% of the star’s mass, although this can vary widely. For this design sequence, we will need to determine the disk mass factor. This is a multiplicative factor; for example, a star with mass equal to the Sun and a disk mass factor of 1.0 will have a protoplanetary disk roughly as massive as the Sun’s.

Select a disk mass factor between 0.1 and 1.0, with most protoplanetary disks having a density factor close to 1. To select a disk mass factor at random, roll 3d6 on the Disk Mass Factor Table. Feel free to select a value between two results on the table. Each component in a multiple star system can have its own disk mass factor.

Roll (3d6)	Disk Mass Factor
3	0.1
4	0.13
5	0.18
6	0.25
7	0.36
8	0.5
9	0.7
10-11	1.0
12	1.4
13	2.0
14	2.8
15	4.0
16	5.6
17	7.5
18	10.0

Selecting for an Earthlike world: The ideal disk density to produce an Earthlike world depends on many factors. To maximize the probability of an Earthlike world, multiply the selected disk mass factor by the star system’s metallicity; the result should be close to 1.

Planetary Mass Budget

The disk mass factor will determine how much material is available for the formation of planets. We will measure this material as a planetary mass budget, deducting from this budget as planets are placed. The planetary mass budget is an estimate of the metals that will end up in planets, where “metals” is used in the astronomical sense (that is, all elements heavier than helium).

To determine the planetary mass budget, let M be the mass of the star in solar masses, let K be the star’s metallicity, and let D be the disk mass factor determined above. Then:

$B=80\times M\times K\times D$

Here, B is the planetary mass budget, measured in Earth-masses. Round off to two significant figures.

Special Case: Forbidden Zone

If the star under development is a member of a multiple star system, it is possible that one of its companion stars will approach so closely as to disrupt part of the protoplanetary disk. This will give rise to a forbidden zone, a span of orbital radii in which no stable orbit is possible. As the planetary system is designed, planets will not form within the forbidden zone, and any planet that migrates into the zone will be lost.

To check for the existence of a forbidden zone, compute one-third the minimum distance for the nearest companion star. This will be the radius of the inner edge of any potential forbidden zone.

If a forbidden zone exists, and its inner edge is inside the slow-accretion line, then some of the disk material that might otherwise have formed planets has been stripped away by the companion star’s influence. Adjust the planetary mass budget as follows. If B₀ is the planetary mass budget before accounting for the forbidden zone, R_F is the radius of the inner edge of the forbidden zone, and R_A is the radius of the slow-accretion line, then:

$B=B_0\times\sqrt{\frac{R_F}{R_A}}$

Here, B is the adjusted planetary mass budget. Round off to two significant figures.

Examples

Arcadia: Alice is working with a single star with a mass of 0.82 solar masses, initial luminosity of 0.28 solar units, and metallicity of 0.63. She decides that the disk inner edge will be at about 0.025 AU. She computes that the snow line will be at about 2.2 AU and the slow-accretion line will be at about 14.0 AU.

Alice makes note of the star’s metallicity of 0.63, and selects a disk mass factor of 2.0. Multiplying the two together yields a result of 1.26, which is reasonably close to 1 and seems likely to yield an Earthlike world at the end of the design process. The planetary mass budget will be:

$80\times0.82\times0.63\times2.0\approx83$

Since the primary star is a singleton, there will be no forbidden zone, so Alice has all the information she needs to complete this step of the design process.

Beta Nine: Bob is working on the primary star of the Beta Nine system, a red dwarf with a mass of 0.18 solar masses, luminosity of 0.0045 solar units, and metallicity of 2.5. He rolls 2d6 for a result of 8, and determines that the disk inner edge will be at about 0.014 AU. He computes that the snow line will be at about 0.28 AU, and the slow-accretion line will be at about 8.5 AU.

Bob rolls 3d6 on the Disk Mass Factor Table, and gets a roll of 8. This suggests a disk mass factor of 0.5. Bob accepts this result, noticing that the product of 0.5 and the star’s metallicity of 2.5 is 1.25, not far from the value most likely to yield an Earthlike world. The initial planetary mass budget will be about 18 Earth-masses.

Beta Nine is a binary star system, with a brown dwarf companion in a close orbit. The minimum separation of the two stars is 2.0 AU. One-third of this is 0.67 AU, well within the slow-accretion line, but not within the snow line. There is a forbidden zone for this star, with its inner edge at 0.67 AU. The existence of the forbidden zone will (dramatically) reduce the available planetary mass budget:

$18\times\sqrt{\frac{0.67}{8.5}}\approx5.1$

The Beta Nine primary will have fewer planets, since the brown dwarf companion has stripped away most of the material needed to form them!

Designing the Vasota Species

July 5, 2018 Sharrukin Comments 5 comments

At this point, I’ve played through the Phil Eklund games Bios: Genesis and Bios: Megafauna, and I’ve used some of the results of those games to design the Karjann star system and its one Earth-like planet, Toswao. Now for the fun part – looking at the game results in more detail to come up with (hopefully) the design for the planet’s sole tool-using, language-using species.

Hmm. This species will need a name. A few moments paging through a random-name generator, and my brain comes up a word that sounds a little like the name of the planet. So be it: a singular member of the species will be a vaso, and the plural and collective form of the name is vasota. Today, we’re going to be designing the vasota species.

Bios: Megafauna Analysis

There’s one methodological point that I should probably make up front.

When playing Bios: Megafauna, you’re invited to think of yourself as playing the role of one or more single species. In fact, that’s not a good way to think about the situation. The game covers hundreds of millions of years, and very few single species have ever persisted over such long periods. A better way to think about it is that you’re tracing a few of the most prominent clades.

Over time, species give way to new species in the clade, many steps taking place in each game turn, at a level too fine-grained for the simulation to make explicit. The acquisition of cards and cubes for one “species” in your tableau follows the development of traits characteristic of the clade, over a long period of time. The final state of a “species” in the game may describe only one actual species in the generated world, but that’s not required.

A corollary of this is that your tableau of cards and cubes can’t be a complete description of any given species in the chain. Cards in Bios: Megafauna only appear once and never again, so only one “species” can ever hold a given trait in a game. That doesn’t make sense if you take it too literally. More likely, what the cards mark is that a given clade is notable for having that trait – maybe it was the first to evolve the trait, or many members of the clade have invested heavily in it.

Thus, if a species doesn’t have a given card, that doesn’t necessarily mean it lacks the corresponding trait, it just means its own version of the trait is unremarkable. On the other hand, if a species does have a specific card, it probably exhibits that trait to an unusual degree.

So, what do we know about the vasota, given their representation as a “species” at the end of my Bios: Megafauna game?

Well, since the species belonged to Player White, that means it is endoskeletal, analogous to the vertebrates of Earth. That doesn’t tell us much yet; it could resemble fish, amphibians, reptiles, birds, mammals, or none of the above.

At the end of the game, the species was size 3, which the rulebook informs us is approximately 20 kg in mass. Since the size scale is logarithmic by powers of 10, we could take this as indicating a typical body mass somewhere between about 6 kg and about 65 kg. Smaller than a human, but not necessarily a lot smaller.

The species had the following cube set, taking “monster” markers into account:

4 red (nervous system, reflexes, “pounce” hunting and “dash” evasion)
4 yellow (circulatory system, stamina, “chase” hunting and evasion)
6 blue (reproductive system, investment in sexual behavior and offspring)
2 green (digestive system, ability to process lots of biomass, survival in warm climates)
3 white (cold adaptations, survival in cold climates)

The preponderance of red and yellow over green and white cubes suggests the species has a strong tendency toward carnivory. On the other hand, in actual play the species (or, rather, members of the same clade) spent a lot of time in the “herbivore” position in the biomes it occupied. I suspect we can square the circle by assuming that the species is omnivorous, but prefers meat if it can get it. Earthly examples might include raccoons, or certain species of bears.

Meanwhile, wow, that’s an impressive array of blue cubes. The species still has one of the blue “monster” markers, which indicates a lot of investment. I would guess that this species comes down heavy on a K-selection strategy: finding high-quality mates, then having just a few offspring and lavishing lots of time and attention on them. This species may be more invested in sexual behavior and child-rearing than humans are, which is kind of impressive.

Let’s look at the traits that this clade has acquired over time, both in their basic and promoted forms.

Courtship Dance and Territorialism – These were the first two traits acquired, and Territorialism is what gave the clade its blue “monster” marker. It’s interesting that the first traits this clade developed, the ones which continued to define its behavior throughout its existence, were both behavioral in nature. That suggests some very deep-seated instincts toward sexual competition, display behavior, and territory defense. Whatever social groups this species naturally forms, they probably have a strong sense of in- and out-group distinctions, and a willingness to face down outsiders who trespass on their range.
Brainstem and Pituitary Gland – Early investments in a sophisticated system of nerve and hormonal control. Even from the beginning, these were smart animals.
Periodontum – Clearly, even though this clade never invested heavily in being able to process lots of plant matter, it does have a jaw apparatus, with teeth supported by specialized tissues.
Hormones and Muscle Shivering – More sophisticated biochemistry to regulate tissues and behavior. Muscle Shivering gave the clade its white “monster” marker, indicating a strongly endothermic animal that can deal well with widely varying climates. At this point, I’m comfortable calling this species pseudo-mammalian, with one exception that I’ll mention later.
Vertical Flexure – The first trait that seems relevant to the physical body plan. This clade is made up of striding walkers, whose footsteps fall under the body, as opposed to “sprawlers” which crawl along with their feet out to either side. That suggests the ability to move quickly, and possibly to develop a good bipedal stance that can free up the forelimbs for manipulation.
Pons & Medulla and Hypothalamus – Still more sophistication in the brain, giving the species good reflexes and strong regulation of homeostatic processes. I’m not seeing a lot of forebrain-like development, but a look through the Bios: Megafauna trait deck tells me that almost all the brain-development cards focus on the hindbrain. A species that has lots of brain cards is probably going to be smart regardless.
Long-Term Memory and Larder Hoarding – More brain traits! At this point I’m comfortable assuming this species will be about as intelligent as humans, but here’s an interesting indicator as to what kind of intelligence it will have. I see an emphasis on good memory, not just quick information processing or abstract reasoning.
Olfactory Organ and Smelling Nose – Here we have some indication as to what kind of sensory apparatus the species has. We can assume that it has eyes, ears, and so on, but the cards tell us that the species is remarkable for its sense of smell. The card text specifically calls out the noses of bears, which have possibly the best sense of smell of any land animal on Earth.

Finally, we can look at the Emotions held by the clade at the end of the game:

One red Emotion, representing “anger,” aggression, quick action, and the “fight” part of the fight-or-flight reflex.
Two blue Emotions, representing “jealousy,” pride and self-centeredness, and sexual attraction and desire.
One purple Emotion, representing “curiosity,” the drive to learn, the need to try new tools and techniques.

This suggests a creature that is at least somewhat human-like in psychology: aggressive, curious, strongly driven by the need to find a mate and raise offspring. Again, this species may be a bit more motivated by personal pride and sexual desire than we are, depending on whether you believe humans would have two blue Emotions in their card tableau too.

GURPS Analysis

Now for a bit more fine-grained detail, which I’ll describe by designing a character template for the vasota in GURPS terms.

The older book GURPS Uplift is actually a great source for this kind of work. It has an alien-design sequence based on algorithms that Dr. David Brin developed for his own creative work, one which considers how a species evolved to intelligence. That makes it a good fit for my current project, which is taking a different approach to do the same thing.

GURPS Uplift is a Third Edition sourcebook, but it still works very well as a set of guidelines when designing aliens. If you want something more closely tied to Fourth Edition, James Cambias built a similar system for the current edition of GURPS Space. The fact that I’m using GURPS Uplift instead is purely a matter of personal preference – I got used to that system long before James and I co-authored GURPS Space.

I’m going to work my way through the major headings in the GURPS Uplift design sequence. Rather than do everything with random dice rolls, I’m going to select options and traits to fit what I saw in the Bios: Megafauna game, and see what kind of template that gives me.

Home Environment

Thinking back to the Bios: Megafauna game, the White Archetype species spent most of its time living in forested continental biomes. Once Toswao flipped to a relatively cool climate on the last turn, those were probably temperate rather than tropical forests. We’ll run with that.

Our intelligent species evolved in a temperate forest, as “climbers” (ground-dwelling creatures that can climb trees if they need to, like bears or gorillas). Looking at suggested traits, I’ll go with +2 skill bonuses to Climbing and Jumping. Those seem to fit the large numbers of red and yellow cubes in the clade’s tableau, which suggest an agile and athletic creature.

Incidentally, recall that the surface gravity of Toswao is about 1.09 G, a bit higher than Earth’s, but not high enough to count as a “heavy world.”

Body Plan

I don’t see a lot of traits in the Bios: Megafauna tableau to suggest anything unusual here. The Vertical Flexure trait is the only body-plan item, and that doesn’t imply anything too alien.

I’ll assume that the vasota are bog-standard, bilaterally symmetrical tetrapods. They have evolved into a fully upright, bipedal stance that frees up their forelimbs for manipulation. A vaso has one pair of hands and one pair of walking paws (“feet”). That doesn’t give us any modifiers to the ST or DX scores.

I’m agnostic as to whether the vasota have any “special limbs” (e.g., tails) but a quick dice-roll on the pertinent table from GURPS Uplift says no. Moving on . . .

Diet

I’ve already established that the vasota are omnivores, who prefer meat when they can get it. GURPS Uplift calls this kind of species “hunter-browser” omnivores. Glancing at the list of suggested traits, I see the possibility of half a level of the Enhanced Move advantage. This fits the picture that’s growing in my head, and it works just as well in Fourth Edition rules, so I’ll go with that.

Metabolism

We already know the vasota are endothermic, strongly resembling Earthly mammals. GURPS Uplift simply calls this being “warm-blooded,” which doesn’t carry any advantage or disadvantage. Sounds good to me, let’s move on.

Society

This is an important item – the size and structure of their natural social group – which will strongly affect vaso psychology. GURPS Uplift would normally encourage most species to fall at the “family group” or “pack/troop” level. For the vasota, I think I’m going to do something different, a social structure that appears in the natural world but isn’t easy for the GURPS Uplift charts and tables to capture.

The idea is that the vasota are “solitary but social” in a very specific pattern. Both males and females are highly territorial in their natural state, but they express that territoriality differently.

In pre-civilized times, female vasota formed small family groups. An elderly female would live with her daughters and grand-daughters, all in the same shared range, centered on some reliable source of food. Young males stayed with their mothers for a while, but eventually they would get pushed out to fend for themselves. Mature males lived mostly solitary lives on the fringes, setting up and defending their own home ranges. A male’s range probably overlapped with at least one female clan-range, and that’s where he went to visit during mating season, but male ranges tended not to overlap with each other. This pattern is found in some Earthly primates – some lemurs and tarsiers, and (sort of) in orangutans as well.

With the appearance of tool use, language, and more complex societies, the vasota modified their age-old social pattern. As with humans, females ended up doing most of the work of foraging, and later of agriculture. Yet vasota males were never able to cooperate very well, so unlike human males, they rarely managed to force females into a subordinate role by applying coordinated violence. Matrilineal, matriarchal clans became the first villages, and later the first towns. Males continued to live a wandering and solitary life, sometimes associating themselves with a female community, offering whatever service they could in exchange for security and social contact.

A social system like that is effectively a hybrid. Vasota males fall under the “Solitary” line on the GURPS Uplift chart, whereas the female communities fall under the “Family Group” line. None of that has a direct effect on physical or mental capabilities, but it will affect the personality. Later, I’ll be looking at the possibility of different sets of Mental Disadvantages for vasota males and females.

Size

This is one area in which the GURPS Uplift tables won’t be of much use. Third Edition GURPS handled the size of objects, along with ST and HT scores and Hit Points, very differently than Fourth Edition.

I’m going to assume that adult vasota average around 40 kg in mass, well within the range implied by their Bios: Megafauna size category. If they’re not a lot thinner or blockier than humans, that suggests that they’ll be about 80% as tall as an average human, small enough to get a Size Modifier (SM) of -1. In Fourth Edition GURPS, this is a zero-point feature.

A creature that small is likely to have a lower ST score than the human average. According to the Build Table on p. B18, a human of average build who’s about 1.5 meters tall and masses about 40 kg is likely to have a ST score of about 7. Let’s bump that up a little, since the vasota do live in a stronger gravity field. I’ll set the average ST score for the vasota at 8, a 20-point disadvantage. I’ll leave their basic HT score at 10, since I don’t see anything to indicate that they’re less energetic or robust than humans.

Food Chain Position

The clade from which the vasota originated were rarely the peak predators in their environment. Only with the development of tool-use did they push to the top of their food chains. Let’s stipulate that their position on the food chain is “near the top,” which doesn’t confer any advantages or disadvantages in the GURPS Uplift charts.

Activity Cycle

I don’t have any preference for whether the vasota are naturally diurnal or nocturnal. A quick dice-roll on the pertinent table in GURPS Uplift gives me “diurnal,” which confers no unusual traits. I’ll take that, and assume the species sleeps about as much as humans do, and at the same times.

Reproduction

We already know a fair amount about vasota reproductive strategies. For example, we know they may be even more heavily invested in a K-selection strategy than humans are. I’ll assume a natural lifespan comparable to that of humans, and a “very few offspring, intense investment” strategy. GURPS Uplift suggests a Sense of Duty disadvantage directed toward young vasota, and that makes sense to me.

I’ll also assume a very high degree of neoteny, in which adult members of the species retain many of the psychological traits of the young. That suggests a high IQ score, and a higher than average level of curiosity that might lead to a Mental trait or two.

Let’s assume that the vasota have two sexes, just as humans do (the “produce lots of cheap gametes” and the “produce a few expensive gametes” genders, which we call “male” and “female”). Just to make them a little less like mammals, I’ll stipulate that the vasota are egg-layers, the females producing very small clutches. When the young hatch, they have a lot of physical growth and development to do, but they can eat bits of meat, fruit, and high-value seeds almost at once.

Natural Weapons

None of the cards in the Bios: Megafauna tableau had anything to do with natural weaponry. I’ll assume that the vasota are about as well-armed as humans (blunt teeth and nails, with no venom or other special weapon systems).

Body Covering

There were no traits in the Bios: Megafauna tableau to describe the vasota integument, either. I’ll assume they don’t have anything remarkable. Again, to reduce the resemblance to Earthly mammals, let’s assume that the vasota have a covering of thin scales, like those of a lizard or snake. This might be enough for a single point of Damage Resistance.

Senses

We did get one set of traits that had to do with the vasota senses, suggesting a superb sense of smell. I’ll assume that their senses are otherwise unremarkable:

Good vision, two eyes frontally placed, with no special visual abilities.
Average hearing with no special auditory abilities.
No electrical or magnetic senses.
Excellent senses of smell and taste, suggesting Acute Taste and Smell and Discriminatory Smell.
Average tactile and kinesthetic senses, with no special abilities.

Communications

There were no cards to suggest specific communication abilities – no pheromones, warning cries, anything of that nature. Let’s assume that the vasota communicate primarily through spoken language, in the same frequency range as the human voice. Their voices might sound a little funny to us, but with a little work we should be able to understand each other.

Mental Abilities

We did see above that the vasota might be a little more intelligent than humans, since they retain neotenous traits (such as curiosity and mental adaptability) far into their lifespan. We also got one Bios: Megafauna card suggesting unusual mental ability – Long-Term Memory, later promoted to Larder Hoarding. Rather than give the vasota higher than average IQ, I’ll give them Eidetic Memory instead, which in Fourth Edition rules is a 5-point advantage.

Personality Traits

GURPS Uplift has an elaborate system for working out a species’ personality traits. It measures each species on a set of eight numeric scales that translate into specific Advantages and Disadvantages. It’s an interesting system, although perhaps not to be taken too literally.

Instead of working through the system in detail, I simply glanced through it, thinking about how the vasota would measure up. Naturally, since the vasota have had high-tech civilization for thousands of years when we first meet them, some of their primitive psychological traits have changed to make them more suited for a complex society. Even so, male and female vasota still have different personalities.

Male vasota remain rather solitary creatures, comfortable around aliens but not very good at “reading” them, and very unhappy in large crowds. They are driven by personal ambitions and desires, and are not very altruistic. In GURPS terms, they have the Broad-Minded quirk, and moderate levels of the Loner, Oblivious, and Selfish disadvantages.

Female vasota are more human-like in their psychology, better at cooperating and living in groups. They are much less likely to wander and travel, and don’t encounter aliens as often. They have only the Proud quirk. They have no specific psychological disadvantages to keep them close to home, but individuals will often have Dependents, Duty, or Sense of Duty disadvantages that make travel and adventuring difficult.

Both males and females have the Curiosity trait.

So, let’s pull all this together, and write up a pair of GURPS racial templates:

Male Vaso (5 points)

Attribute Modifiers: ST-2 [-20].
Secondary Characteristic Modifiers: SM -1 [0].
Advantages: +2 to Climbing [4]; +2 to Jumping [4]; Acute Sense of Taste and Smell +4 [8]; Damage Resistance 1 [5]; Discriminatory Smell [15]; Eidetic Memory [5], Enhanced Move (Ground) 1/2 [10].
Disadvantages: Curiosity (12 or less) [-5]; Loner (12 or less) [-5]; Oblivious [-5]; Selfish (12 or less) [-5]; Sense of Duty (toward young) [-5].
Quirks: Broad-Minded [-1].

Female Vaso (20 points)

Attribute Modifiers: ST-2 [-20].
Secondary Characteristic Modifiers: SM -1 [0].
Advantages: +2 to Climbing [4]; +2 to Jumping [4]; Acute Sense of Taste and Smell +4 [8]; Damage Resistance 1 [5]; Discriminatory Smell [15]; Eidetic Memory [5], Enhanced Move (Ground) 1/2 [10].
Disadvantages: Curiosity (12 or less) [-5]; Sense of Duty (toward young) [-5].
Quirks: Proud [-1].

There we go! A male vaso is roughly comparable to a human character – a little smaller and less physically robust, but fast and agile, and capable of surprising feats of scent and memory. Not very sociable, to be sure, but perfectly capable of contributing to (say) a starship crew or a colonial venture. Female vasota are much the same physically, and more congenial, although we probably won’t often see them away from their home-world.

Final Comments

Let’s sum up. Over the past month, I’ve done a play-through of Bios: Genesis and Bios: Megafauna, and used the results of that to design a star system, a habitable world, and the sentient species native to that world. The results seem to work well enough for my purposes, and I can see the possibility of much more unusual outcomes in the process. This may seem to be a cumbersome approach, but I find that it pays off quite well. The game-play itself only took a few hours of time; most of the work came from documenting the results for this series of blog-posts. If I were to do this again, I suspect I could rattle off results of similar scope in a week of evenings.

At this point, I have about half of a story in the back of my mind, in which my human protagonist (Aminata Ndoye) meets and befriends a male vaso aboard her assigned ship. The two of them get involved in a political intrigue when he returns to his homeworld, and Aminata learns new lessons about dealing with non-humans in the context of the interstellar empire she serves. I think I’m going to let this story percolate in the back of my mind for a few days, and then see if I can get it down on the page. More news on that as it happens.

Building Toswao

June 28, 2018 Sharrukin Comments 0 Comment

This morning I’ll be focusing on the single Earth-like world in the Karjann star system, Toswao, the focus of my play-through of Bios: Genesis and Bios: Megafauna.

Here, I’m getting into world-design procedures that I haven’t fully documented yet. The part of the Architect of Worlds project that’s giving me the most trouble is procedures for working out the properties of individual worlds. I find that there are a lot of contingent factors, many of which have been completely ignored by the world-design systems that I’ve previously found in print, or written myself. Some of those factors are not well-understood even today, or are so complex that no simple model will really capture them. So it’s a challenge to come up with a design sequence that’s coherent, straightforward to apply, and likely to reflect a wide range of plausible results. Research continues.

Of course, for Toswao, a lot of parameters are already set and it’s just a matter of fleshing out details, while checking to make sure there’s nothing wildly implausible. That’s an easier problem.

Let’s start with what we know. Toswao is a terrestrial planet with a mass of 1.18 Earth-masses. I have a straightforward model for the density of terrestrial bodies, and with one dice roll I can compute that Toswao has an average density of 1.044 times that of Earth (5.72 g/cc). That immediately gives us a planetary radius of 6635 kilometers (1.04 times that of Earth) and a surface gravity of 1.09 G.

Here’s the first big question that most published world-design sequences would ignore: does Toswao have a strong magnetic field?

It turns out that item is important. A planetary magnetic field is critical for protecting the surface environment from solar and cosmic radiation. It’s also critical for making sure the planet can retain a significant atmosphere. Without a strong magnetic field, the solar wind comes into direct contact with the outer atmosphere, and will tend to strip away the air over fairly short time-scales. This effect turns out to be quite a bit stronger than simple thermal loss, so if you want a habitable planet, you really need to make sure compasses work there.

Toswao is nice and big and dense, so it will certainly have a liquid nickel-iron core whose rotation can create a dynamo. But that leads us to a second question that most world-design sequences probably get wrong: how quickly does Toswao rotate, and where is its rotational axis?

The world-design sequences I’ve seen (and the ones I’ve written in the past) generally assume that terrestrial planets all rotate at similar rates, their rotational axes well-behaved, modified (if at all) only by tidal effects over long periods. Yet even in our own planetary system we can see that this isn’t the case, especially when we look at Venus. Recent models for the formation of terrestrial planets suggest that the process is much more catastrophic than we once assumed. Every terrestrial planet, even Earth, has been shaped by enormous impacts and collisions, so that its final rotation axis and rate are more random than we might expect.

Then, of course, the tidal interactions between a terrestrial planet and its primary star (and any major natural satellite) turn out to be much more challenging to model than we might like. This isn’t because the physics of the situation are poorly understood – they’re not – but because the system is very sensitive to small details. If Earth was a perfect, elastic, and uniform sphere, it would be easy to determine exactly how solar and lunar tides would affect its rotation over eons. Unfortunately, terrestrial planets are quite a bit more complex and varied than that.

In the light of that, I have yet to produce a game-ready model for planetary rotation that I’m happy with. For now, let’s assume that Toswao’s rotation is similar to that of Earth (especially since the planet does have a major natural satellite like our Moon). Toswao is younger than Earth, so I’ll assume that its rotation rate is a bit faster, and that its satellite is a little closer in than the Moon. Without laying out all of my selections and computations in full, here’s some results:

Toswao

Mass: 1.18 Earth-masses
Density: 1.044 Earth (5.72 g/cc)
Radius: 6635 kilometers (1.04 Earth)
Surface Gravity: 1.09 G
Orbital Radius: 0.99 AU
Orbital Eccentricity: 0.08
Periastron: 0.91 AU
Apastron: 1.07 AU
Angular Diameter of Primary Star: 0.55 – 0.64 degrees
Orbital Period: 0.9660 standard years (352.84 standard days)
Rotation Period: 22.608 standard hours (0.9420 standard days)
Day Length: 22.669 standard hours (0.9445 standard days)
Apparent Year Length: 373.56 local days
Axial Inclination: 24°

Given these values for Toswao’s rotation, we can be confident that it has a nice, strong magnetosphere to protect the air and surface. We can proceed on the assumption that Toswao has a more or less Earth-like atmosphere.

We already know some things about that atmosphere, from the final state of the Bios: Megafauna game, and from our computations when we were determining the planet’s placement in orbit around Karjann. A quick random dice roll gives us an “atmospheric mass” for Toswao of about 1.2, noticeably greater than that of Earth. Along with the known details of composition that I generated earlier, that gives us:

Atmospheric Mass: 1.2
Surface Atmospheric Pressure: 1.3 atmospheres
Atmospheric Composition: Nitrogen 64%, oxygen 34%, argon 1.6%, carbon dioxide 0.2%, other components 0.2%. Nitrogen partial pressure about 0.83 atm. Oxygen partial pressure about 0.44 atm. Carbon dioxide partial pressure about 0.003 atm.
Hydrographics: 88% ocean coverage
Planetary Albedo: 0.5
Greenhouse Effect: 44 K
Average Surface Temperature: 292 K (19° C, or 66° F)

That atmosphere looks breathable for unmodified and unprotected humans, but just barely. The partial pressure of oxygen is approaching high enough to be toxic over long exposures, and there’s a lot of CO2 in the air too. We would probably find Toswao’s air rather invigorating in the short term, but causing some damage to our eyes and lungs in the long term. In the meantime, we might find our cognitive function a bit muddled by CO2-triggered changes in blood flow to our brains. Might want to wear a light breather mask just to keep our blood chemistry happy, if we’re going to be spending much time here.

One more set of details. We know from the Bios: Genesis game that Toswao had a “big whack” event like Earth’s, giving rise to a big, Luna-like natural satellite. I double-checked Toswao’s “Hill radius,” the distance at which Karjann’s gravitational influence overwhelms Toswao’s, and found that there’s plenty of room for the planet to retain a moon.

A random roll sets the satellite’s mass, from which I can quickly determine its density, radius, and surface gravity. I made the non-random decision to place this satellite a little closer to Toswao than Luna is to Earth, about 50 Toswao-radii rather than Luna’s distance of 60 Earth-radii. Here are the numbers:

Toswao’s Moon

Hill Radius: 2.06 million kilometers
Orbital Radius: 320,000 kilometers
Orbital Eccentricity: Negligible
Mass: 0.0165 Earth-masses
Density: 0.64 Earth (3.53 g/cc)
Radius: 1880 kilometers
Surface Gravity: 0.189 G
Orbital Period: 19.180 standard days
Apparent Lunar Cycle: 23.776 standard hours (0.9907 standard days)
Synodic Month: 20.283 standard days
Angular Diameter: 0.69 degrees (from planetary surface)

So there we go. There are a few more physical parameters we could probably generate, but this should give us enough to work with for now.

Toswao is an ocean planet, a little warmer than Earth, with lots of clouds. Visiting humans would find the local gravity heavy, but manageable even over long periods. The planet’s atmosphere is breathable for humans in the short term, although we might find it difficult under long exposures. I haven’t explicitly computed the strength of local tides, but both the primary star and the moon are more massive and closer than their counterparts on Earth, so I would expect stronger tides.

Toswao has Earth-like axial tilt and so exhibits similar seasons, although the situation is complicated by a larger orbital eccentricity. Depending on how the orbital parameters line up with the axial inclination, that might tend to either damp out or to accentuate seasonal variation.

I don’t intend to draw a world map, unless the story emerging in my head turns out to be a lot more extensive than I expect. Still, we can say a few things, based on the end state of the Bios: Megafauna game. I would expect the planet’s small continents to be heavily forested, at least in their natural state. Lots of green in the shallow seas, too, to contribute to that high oxygen concentration. I wouldn’t expect to see a lot of deserts or wastelands.

A useful exercise, not only because it gave me a world to use in my creative work, but also because it gave me a motivating example, bringing out details that I’ll need to address in upcoming sections of Architect of Worlds. In the next couple of posts, I’ll be working out a character template for the dominant sentient species native to this world, and writing up some of their back story.

Building the Karjann System

June 27, 2018 Sharrukin Comments 0 Comment

Okay, for the last few weeks I’ve been logging a play-through of the Phil Eklund games Bios: Genesis and Bios: Megafauna, in a demonstration of how those games can be used to support worldbuilding for science fiction. A quick way to review those posts would be to check out the Worldbuilding by Simulation category and look at all the posts since the beginning of June 2018.

Now it’s time to do some math, and design the star system and main habitable planet compatible with the results of the Bios games. I’ll be using the current draft design sequences from my Architect of Worlds project. In particular, the current draft of the star system design sequence can be found at Architect of Worlds: Designing Star Systems. The design sequence for designing planets hasn’t been published yet, and I need to do a fairly extensive revision pass before that happens, but its current draft should be sufficient for this purpose.

I begin by coming up with a pair of names for the habitable planet (Toswao) and its primary star (Karjann). I have absolutely no constructed language work to back those up, and probably won’t go that far for a single story. Those names simply emerged from the back of my mind under the stimulus of a random-name generator; I think they look and sound pleasant, so there we go.

Primary Star

Looking back on the Bios: Megafauna game, I recall that Toswao has spent most of its history with very warm climate, well above Earth’s present average temperature. That suggests a primary star that’s a touch more massive than Sol, and therefore probably more luminous.

Meanwhile, we also know that Toswao is quite a bit younger than Earth. With adjustments, the Bios: Genesis game covered about 3.75 billion years from planetary formation to the end of the Proterozoic period. The Bios: Megafauna game covered about 240 million years from there to the first appearance of a tool-and-language-using species. Add that up and we get 3.99 billion years, which I’m comfortable rounding off to 4.0 billion. Evolution moved fast here! That doesn’t necessarily indicate anything about Karjann, but in my mind the notion of a somewhat more energetic primary star also fits a faster pace of development. So I decide to non-randomly select a primary star mass of 1.04 solar masses.

With a dice roll, I find that Karjann is a solo star – no need to generate details for any companions. I set the star system’s age at exactly 4.0 billion years, and randomly generate the system’s metallicity, ending up with a value so close to 1.0 that I decide to round that off as well. Working through the design sequence, I end up with the following parameters:

Karjann

Mass: 1.04 solar masses
Main Sequence Lifespan: 8.6 billion years
Current Age: 4.0 billion years
Metallicity: 1.0
Current Effective Temperature: 5800 K
Current Luminosity: 1.23 sols
Radius: 0.0051 AU (767,000 km)
Spectral Class: G2V

Karjann turns out to be quite similar to Sol, a cheerful yellow star about halfway through its stable lifespan, a touch hotter and noticeably brighter.

Planetary System

Before beginning planetary system design, I need to figure out where the habitable world (Toswao) is going to be placed. Here, I have a few clues.

The final state of the Bios: Megafauna game suggested that the planet’s atmosphere had 34% free oxygen. This is pretty high, equivalent to the highest level ever seen in Earth’s atmosphere, back in the Cretaceous era. Some research tells me that such a high free oxygen level has to be supported by very high levels of carbon dioxide, several times the current value in Earth’s atmosphere. So I pin the current CO2 level as about six times Earth’s pre-industrial level, or about 1800 parts per million.

The final Bios: Megafauna state also suggests a planetary albedo of 0.8, but that isn’t at all plausible. The most reflective water-vapor clouds have about that albedo, so a long-term planetary albedo that high means that the entire planet is covered with the brightest possible cloud canopy. Unlikely over a long period, and how is anything surviving with direct sunlight cut off from the photosynthetic base of the food chain? Still, a planet with more hydrographic surface than Earth is likely to have more cloud cover, and therefore a higher overall albedo. I’ll set the planet’s albedo to 0.5, which is probably still very high, but not utterly implausible.

That albedo also suggests a lot more water vapor in the atmosphere than Earth currently sees. I’ll tentatively assume double the amount.

At low concentrations, greenhouse gases appear to affect the planetary average temperature in a logarithmic fashion: every time you double the amount of a greenhouse gas, the temperature goes up by a fixed amount. This question is hideously complex, and climate scientists don’t have any simple models for it, but for CO2 the effect seems to be about 3 K of increase for every doubling of the concentration in the atmosphere. Assuming that water vapor behaves similarly, the greenhouse effect on Toswao appears to be about 11 K more aggressive than on pre-industrial Earth. That gives us a total greenhouse effect of about 44 K.

In Bios: Megafauna, planetary climate is marked on a scale which varies up and down during the game. Next to the bottom of the scale is a space marked “Ice Age,” which I tentatively interpret as a planetary average temperature of 280 K, equivalent to the middle of the last glacial age. The top space on the scale is marked “Runaway Greenhouse,” which I’ll tentatively take as a planetary average temperature of about 350 K, high enough (assuming standard atmospheric pressure) for the equatorial oceans to start boiling. There are twelve spaces between these two points on the scale, so a rough guess of about 6 K per space makes sense. At the end of my play-through, the climate was in the higher of the two spaces in the “Cool” climate band, two spaces above the “Ice Age” point. That suggests a planetary average temperature of about 292 K, a bit warmer than present-day Earth.

If the actual surface temperature is about 292 K, then a greenhouse effect of 44 K suggests an albedo-adjusted blackbody temperature of about 248 K. The relevant formula is:

$T_B=278.8\times\sqrt[4]{\frac{\left(1-A\right)L}{R^2}}$

Here, A is the planetary albedo, L is the primary star’s luminosity in sols, and R is the planet’s orbital radius in AU. Plugging in values and solving for R, we get an orbital radius of about 0.99 AU, surprisingly quite close to the value for Earth.

Okay, now that I know where to place Toswao, I can lay out the whole planetary system. In particular, I determine that the primary gas giant (the Jupiter-analogue) engaged in moderate inward migration, but then got caught up in a “Grand Tack” event which pulled it back outward to its present position. This depleted the population of planetesimals in the inner system, leading to smaller planets, more widely spaced. Here’s the basic table of planets:

Radius	Planet Type	Planet Mass
0.41 AU	Terrestrial Planet	1.05
0.68 AU	Leftover Oligarch	0.15
0.99 AU	Terrestrial Planet (Toswao)	1.18
1.68 AU	Terrestrial Planet	0.65
2.95 AU	Terrestrial Planet	1.12
4.27 AU	Large Gas Giant	350
6.83 AU	Large Gas Giant	400

I didn’t meddle too much with the random dice rolls here, aside from ensuring that a Terrestrial Planet would appear at the right orbital radius to become Toswao. I did have two results that I wanted to ensure, given the outcome of the Bios: Genesis game.

First, I needed there to be a Mars-analogue close to Toswao, so that at least some microbial life would make the journey very early in the system’s development. The dice gave me a Leftover Oligarch in the next inward orbit, so I was happy with that. That planet was probably relatively cool and moist in the first hundred million years or so after formation, but while Karjann has heated up over the eons, the small planet has been baked dry and is now more barren than Mars.

Second, I wanted to make sure there was no “late heavy bombardment” (LHB), since that event didn’t take place in the Bios: Genesis game. The best theory we have about the LHB, assuming it happened at all, is that our gas giant planets went through a period of orbital instability that also disrupted the Kuiper Belt. Here, the outermost gas giant is still well within the “slow-accretion line” that represents the nominal start of the system’s Kuiper Belt. Hence the belt has never been disrupted, and is probably much more full and dense than ours. An analogue might be the Tau Ceti system, whose Kuiper Belt appears to be at least ten times as dense as Sol’s.

So here we go, before I head off to work this morning. The Karjann system has a solo star and seven planets, including the Earthlike world Toswao. The inner planets are likely to be a super-hot Venus type, and a very hot, dry Mars-like. Beyond Toswao we have two cold worlds unlike anything in the Sol system, probably with lots of ice, the outermost likely to have a methane-ammonia atmosphere if the temperatures are right. Then two Jovians, which apparently gathered up all the mass that might otherwise have formed ice giants on the fringes of the system. Finally, a dense Kuiper Belt that probably indicates lots of comets. No asteroid belt, although there are likely to be extensive collections of junk in the Trojan points of the two gas giants.

Next time, I’ll focus on Toswao and its major natural satellite, and work out the details of its physical environment.

Architect of Worlds – Step Eight: Stellar Orbital Parameters

April 22, 2018 Sharrukin Comments 3 comments

This is the last step in the design sequence for star systems – once the user has finished this step, she should know how many stars are in the system, what their current properties are, and how their orbital paths are arranged.

At this point, I’ve finished the current rewrite of the “Designing Star Systems” section of the book. I don’t plan to make any further mechanical changes to that section, except to correct any errors that might pop up. The instructions and other text might get revised again before the project is complete. A PDF of the current version of this section is now available at the Sharrukin’s Archive site under the Architect of Worlds project heading.

Step Eight: Stellar Orbital Parameters

This step determines the orbital parameters of components of a multiple star system. This step may be skipped if the star system is not multiple (i.e., the primary star is the only star in the system).

Procedure

The procedure for determining the orbital parameters of a multiple star system will vary, depending on the multiplicity of the system.

The important quantities for any stellar orbit are the minimum distance, average distance, and maximum distance between the two components, and the eccentricity of their orbital path. Distances will be measured in astronomical units (AU). Eccentricity is a number between 0 and 1, which acts as a measure of how far an orbital path deviates from a perfect circle. Eccentricity of 0 means that the orbital paths follow a perfect circle, while eccentricities increasing toward 1 indicate elliptical orbital paths that are increasingly long and narrow.

Binary Star Systems

To begin, select an average distance between the two stars of the binary pair.

To determine the average distance at random, roll 3d6 on the Stellar Separation Table.

Stellar Separation Table
Roll (3d6)	Separation	Base Distance
3 or less	Extremely Close	0.015 AU
4-5	Very Close	0.15 AU
6-8	Close	1.5 AU
9-12	Moderate	15 AU
13-15	Wide	150 AU
16 or more	Very Wide	1,500 AU

To determine the exact average distance, roll d% and treat the result as a number between 0 and 1. Multiply the Base Distance by 10 raised to the power of the d% result. The result will be the average distance of the pair in AU.

Feel free to adjust the result by up to 2% in either direction. You may wish to round the result off to three significant figures.

Next, select an eccentricity for the binary pair’s orbital path. Most binary stars have orbits with moderate eccentricity, averaging around 0.4 to 0.5, but cases with much larger or smaller eccentricities are known.

To determine an eccentricity at random, roll 3d6 on the Stellar Orbital Eccentricity Table. If the binary pair is at Extremely Close separation, modify the roll by -8. If at Very Close separation, modify the roll by -6. If at Close separation, modify the roll by -4. If at Moderate separation, modify the roll by -2. Feel free to adjust the eccentricity by up to 0.05 in either direction, although eccentricity cannot be less than 0.

Stellar Orbital Eccentricity Table
Roll (3d6)	Eccentricity
3 or less	0
4	0.1
5-6	0.2
7-8	0.3
9-11	0.4
12-13	0.5
14-15	0.6
16	0.7
17	0.8
18	0.9

Once the average distance and eccentricity have been established, the minimum distance and maximum distance can be computed. Let R be the average distance between the two stars in AU, and let E be the eccentricity of their orbital path. Then:

$R_{min}=R\times\left(1-E\right)$

$R_{max}=R\times\left(1+E\right)$

Here, R_min is the minimum distance between the two stars, and R_max is the maximum distance.

Trinary Star Systems

Whichever arrangement is selected, design the closely bound pair first as if it were a binary star system (see above). This binary pair is unlikely to have Wide separation, and will almost never have Very Wide separation. Select an average distance for the pair accordingly. If selecting an average distance at random, modify the 3d6 roll by -3. Select an orbital eccentricity normally, and compute the minimum and maximum distance for the binary pair.

Once the binary pair has been designed, determine the orbital path for the pair (considered as a unit) and the single component of the star system. The minimum distance for the pair and single components must be at least three times the maximum distance for the binary pair, otherwise the configuration will not be stable over long periods of time.

If selecting an average distance for the pair and single component at random, use the Stellar Separation Table normally. If the result indicates a separation in the same category as the binary pair (or a lower one), then set the separation to the next higher category. For example, if the binary pair is at Close separation, and the random roll produces Extremely Close, Very Close, or Close separation for the pair and single component, then set the separation for the pair and single component at Moderate and proceed.

Select an orbital eccentricity for the pair and single component normally, then compute the minimum distance and maximum distance. If the minimum distance for the pair and single component is not at least three times the maximum distance for the binary pair, increase the average distance for the pair and single component to fit the restriction.

Quaternary Star Systems

As in a trinary star system, design the closely bound pairs first. Each binary pair is unlikely to have Wide separation, and will almost never have Very Wide or Distant separation. Select an average distance for each pair accordingly. If selecting an average distance at random, modify the 3d6 roll by -3. Select an orbital eccentricity, and compute the minimum distance and maximum distance, for each binary pair normally.

Once the binary pairs have been designed, determine the orbital path for the two pairs around each other. The minimum distance for the two pairs must be at least three times the maximum distance for either binary pair, otherwise the configuration will not be stable.

If selecting an average distance for the two pairs at random, use the Stellar Separation Table normally. If either result indicates a separation in the same category as either binary pair (or a lower one), then set the separation to the next higher category. For example, if the two binary pairs are at Close and Moderate separation, and the random roll produces Moderate or lower separation for the two pairs, then set the separation for the two pairs at Wide and proceed.

Select an orbital eccentricity for the two pairs normally, then compute the minimum distance and maximum distance. If the minimum distance for the two pairs is not at least three times the maximum distance for both binary pairs, increase the average distance for the two pairs to fit the restriction.

Stellar Orbital Periods

Each binary pair in a multiple star system will circle in its own orbital period. The pair and singleton of a trinary system will also orbit around each other with a specific period (probably much longer). Likewise, the two pairs of a quaternary system will orbit around each other with a specific period.

Let R be the average distance between two components of the system in AU, and let M be the total mass in solar masses of all stars in both components. Then:

$P=\sqrt{\frac{R^3}{M}}$

Here, P is the orbital period for the components, measured in years. Multiply by 365.26 to get the orbital period in days.

Special Case: Close Binary Pairs

Most binary pairs are detached binaries. In such cases, the two stars orbit at a great enough distance that they do not physically interact with each other, and evolve independently. However, if two stars orbit very closely, it’s possible for one of them to fill its Roche lobe, the region in which its own gravitation dominates. A star which is larger than its own Roche lobe will tend to lose mass to its partner, giving rise to a semi-detached binary. More extreme cases give rise to contact binaries, in which both stars have filled their Roche lobes and are freely exchanging mass in a common gaseous envelope.

This situation is only possible for two main-sequence stars that have Extremely Close separation, or in cases where a subgiant or red giant star has a companion at Very Close or Close separation. If a binary pair being considered does not fit these criteria, there is no need to apply the following test.

For each star in the pair, approximate the radius of its Roche lobe as follows. Let D be the minimum distance between the two stars in AU, let M be the mass of the star being checked in solar masses, and let M´ be the mass of the other star in the pair. Then:

$R=D\times(0.38+0.2\log_{10}{\frac{M}{M^\prime}})$

Here, R is the radius of the star’s Roche lobe at the point of closest approach to its binary companion, measured in AU. Compare this to the radius of the star itself, as computed earlier. If the star is larger than its Roche lobe, then the pair is at least a semi-detached binary. If both stars in the pair are larger than their Roche lobes, then the pair is a contact binary.

The evolution of such close binary pairs is much more complicated than that of a singleton star or a detached binary. Mass will transfer from one star to the other, altering their orbital path and period, profoundly affecting the evolution of both. Predicting how such a pair will evolve goes well beyond the (relatively simple) models applied throughout this book. We suggest treating such binary pairs as simple astronomical curiosities, special cases on the galactic map that are extremely unlikely to give rise to native life or invite outside settlement. Fortunately, these cases are quite rare except among the very young, hot, massive stars found in OB associations.

One specific case that is of interest involves a semi-detached binary in which one star is a white dwarf. Hydrogen plasma will be stripped away from the other star’s outer layers, falling onto the surface of the white dwarf. Once enough hydrogen accumulates, fusion ignition takes place, triggering a massive explosion and ejecting much of the accumulated material into space. For a brief period, the white dwarf may shine with hundreds or even thousands of times the luminosity of the Sun. This is the famous phenomenon known as a nova.

Most novae are believed to be recurrent, flaring up again and again so long as the white dwarf continues to gather matter from its companion. However, for most novae the period of recurrence is very long – hundreds or thousands of years – so nova events from any given white dwarf in a close binary pair will be very rare. Astronomers estimate that a few dozen novae occur each year in our Galaxy as a whole.

Examples

Arcadia: Alice has already decided that the Arcadia star system has only the primary star, so she skips this step entirely.

Beta Nine: Bob knows that the Beta Nine system is a double star. Proceeding entirely at random, he rolls 3d6 on the Stellar Separation Table and gets a result of 7. The two components of the system are at Close separation. He takes a Base Distance of 1.5 AU and rolls d% for a result of 22. The average distance between the two stars in the system is:

$1.5\times{10}^{0.22}\approx2.489$

Bob rounds this off a bit and accepts an average distance of exactly 2.50 AU. He rolls 3d6 on the Stellar Orbital Eccentricity Table, subtracts 4 from the result since the stars are at Close separation, and gets a final total of 5. The orbital path of the two stars has a moderate eccentricity of 0.2. Bob computes that the minimum distance between the two stars will be 2.0 AU, and the maximum distance will be 3.0 AU.

Bob can now compute the orbital period of the two stars:

$P=\sqrt{\frac{{2.50}^3}{(0.18+0.06)}}\approx8.07$

The two stars in the Beta Nine system circle one another with a period of a little more than eight years.

The two components of the Beta Nine system form a binary pair, with a minimum separation of 2.0 AU. There is no possibility of the pair forming anything but a detached binary, so Bob does not bother to estimate the size of either component’s Roche lobe.

Modeling Notes

The paper by Duchêne and Kraus cited earlier describes the best available models for the distribution of separation in binary pairs. The period of a binary star appears to show a log-normal distribution with known mode and standard deviation. Generating a log-normal distribution with dice is a challenge without requiring exponentiation at some point, hence the unusual procedure for estimating separation used here.

Architect of Worlds – Step Seven: Stellar Classification

April 19, 2018 Sharrukin Comments 0 Comment

Step Seven: Stellar Classification

This step determines the classification of each star in the system being generated, according to the Morgan-Keenan scheme most often used by astronomers. This classification scheme is not strictly necessary for the complete design of a star system, but it can provide useful flavor, and many science fiction readers and players will recognize it.

The classification for any given star is composed of two components, its spectral class and its luminosity class. Spectral class is strongly dependent on the star’s effective temperature. It uses the capital letters O, B, A, F, G, K, and M, in a sequence from the hottest (O-type) to the coolest (M-type) stars. Each letter class is also divided into ten sub-categories, numbered 0 through 9. Our own Sun, for example, is a G2-type star. Luminosity class is (for most stars) marked by a Roman numeral. Almost all stars fall into class III, class IV, or class V. Under this system, a star’s complete classification is given by spectral class, then luminosity class, with no spaces in between. Hence the Sun’s complete classification is G2V.

Brown dwarfs have also been assigned spectral classes, under an extension of the Morgan-Keenan system that uses the capital letters L, T, and Y for progressively cooler objects. These assignments are more tentative, since the study of brown dwarfs is relatively new and very cold examples are hard to observe. The spectral class Y is almost hypothetical at present, with only a few objects appearing to meet the definition.

To determine the spectral class of a star other than a white dwarf, locate the Temperature value on the Spectral Class Table closest to its effective temperature, and read across to the right to find its most likely spectral class.

Spectral Class Table
Temperature	Class	Temperature	Class	Temperature	Class	Temperature	Class
9700	A0	5900	G0	3850	M0	1300	T0
9400	A1	5840	G1	3700	M1	1200	T1
9100	A2	5780	G2	3550	M2	1100	T2
8800	A3	5720	G3	3400	M3	1000	T3
8500	A4	5660	G4	3200	M4	950	T4
8200	A5	5600	G5	3000	M5	900	T5
8000	A6	5540	G6	2800	M6	850	T6
7800	A7	5480	G7	2650	M7	800	T7
7600	A8	5420	G8	2500	M8	750	T8
7400	A9	5360	G9	2400	M9	700	T9
7200	F0	5300	K0	2300	L0	600 or less	Y0
7060	F1	5130	K1	2200	L1
6920	F2	4960	K2	2100	L2
6780	F3	4790	K3	2000	L3
6640	F4	4620	K4	1900	L4
6500	F5	4450	K5	1800	L5
6380	F6	4330	K6	1700	L6
6260	F7	4210	K7	1600	L7
6140	F8	4090	K8	1500	L8
6020	F9	3970	K9	1400	L9

Main sequence stars have a luminosity class of V. Brown dwarfs also technically fall into luminosity class V, and we will record them as such. Subgiant stars have a luminosity class of IV, and red giant stars (whether on the red giant branch or the horizontal branch) have a luminosity class of III.

White dwarf stars are an exception to this system, with their own classification scheme. We will record all white dwarf stars as having the simple classification D.

Examples

Arcadia: Alice notes that the primary star of the Arcadia system has an effective temperature of 4950 kelvins. The closest value on the Spectral Class Table is 4960 kelvins, associated with a spectral class of K2. Since the star is on the main sequence, its complete classification is K2V.

Beta Nine: Bob notes that the two stars of the Beta Nine system have effective temperatures of 3200 K and 1420 K. It turns out that the two stars are a red dwarf of class M4V and a brown dwarf of class L9V.

Modeling Notes

A star’s spectral class depends on many features of its spectrum, and when it comes to the decimal subclasses, astronomers do not agree on their definitions. The same star is often given slightly different classification depending on the source. Once again, the system described here is a simplification designed for ease of use. The primary source was Mamajek’s compiled set of definitions, cited under Step Six.