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 , 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:

• 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:

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:

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

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:

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

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

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

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
Small Gas Giant
Medium Gas Giant
Large Gas Giant

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.