Updated Rules for Planetary Creation

[AlexanderHowl]

In the past quarter century, we have discovered thousands of planets around thousands of stars, and none of them particularly resemble our star system (or any star system in fiction). While the limits of our technology prevent us from finding planets beyond the distance of Jupiter except by accident, we have confirmed multiple planets around hundreds of stars, some of which have planets so close together that they make the old Buck Rogers comics seem conservative by comparison. It is because of this that I think that we need new rules for planetary creation that reflect reality.

I propose a change in planetary placement in order to reflect multiple planet systems like Kepler-11, Kepler-70, or TRAPPIST-1. The Inner Limit should change to 0.001 AU * (Square Root of Absolute Luminosity) the Snow Line should change to 4.85 * (Square Root of Absolute Luminosity), and the Outer Limit should change to 50 AU * (Square Root of Absolute Luminosity). The minimum separation of orbits should change to 0.001 AU * (Square Root of Absolute Luminosity). Within the Sol System, there would exist more than a dozen empty orbits within the orbit of Mercury and the Kuiper Belt would become a second Asteroid Belt within the tenth filled orbit of the Sol System.

What do you think? Do you have any changes to the planet creation rules that would reflect reality more accurately? If so, please feel free to share them.

[Humabout]

According to The First Planets: the Critical Metallicity for Planet Formation by Jarrett L. Johnson (DOI 10.1088/0004-637X/751/2/81), planetary formation can occur out to about [Fe/H]_crit > -1.5 * log (r), where [Fe/H]_crit is the Fe/H metallicity of the star and r is the distance from the star in AU. This can be rearranged and interpreted as 10^([Fe/H]+1.5) = r_outer.

[AlexanderHowl]

We have observational data that disproves that formula even though the star systems that we have found tend to be quite dense (with a few very weird exceptions). Now, the majority of the exceptions seem to be captured rogue planets, so we can ignore them for now, but there are oddities that cannot be rogue planets. In particular, planets around a component star of a binary or multiple star system (rather than around the center of mass of the star system) are highly unlikely to be captured rogue planets due to issues of gravitational interactions between component stars.

For example, Formalhalt b orbits 177 AU from a star within a multiple star system with a Fe/H of -0.03 and an L of 16.63. According to my model, the outer limit is 204 AU, so Formalhalt b is well within my model. According to the formula within the journal, however, the outer limit is 30 AU, so Formalhalt b breaks the journal model (the formula is obviously biased to describe our solar system as the 'correct' one, if you do not include the orbit of the Kuiper Belt).

When it comes to captured rogue planets, whether or not a star system possesses them is a trial detail for most campaigns. Rogue planets may outnumber stars in the Milky Way by 100,000:1, so rogue planet capture should be a common event. I would suggest rolling 6d6 for rogue gas giants per system, with a '6' indicating a captured rogue gas giant, and 3d6-3 for the number of captured rogue terrestrial planets (rogue terrestrial planets are probably much more common than rogue gas giants). Each orbit would be 2d6 × 500 AU.

[Humabout]

Originally Posted by AlexanderHowl

We have observational data that disproves that formula even though the star systems that we have found tend to be quite dense (with a few very weird exceptions). Now, the majority of the exceptions seem to be captured rogue planets, so we can ignore them for now, but there are oddities that cannot be rogue planets.

Note: That formula is for planetary formation, not the capture of rogue planets or migration of planets that have already formed. Both of those instances could theoretically result in planets literally anywhere within a star's sphere of influence. Of course, saying a planet can be any distance from its primary isn't exactly what you're asking for. It also disproves your formula, as well.

Originally Posted by AlexanderHowl

In particular, planets around a component star of a binary or multiple star system (rather than around the center of mass of the star system) are highly unlikely to be captured rogue planets due to issues of gravitational interactions between component stars.

While they may not be captured, they have certainly been perturbed from their original orbits. A great example is likely to be Formalhalt b. It's orbit is horrifically eccentric which suggests it has migrated to where it is currently observed. Again, "Anywhere between here and where the next star's influence begins to dominate" is pretty inclusive...

Originally Posted by AlexanderHowl

For example, Formalhalt b orbits 177 AU from a star within a multiple star system with a Fe/H of -0.03

Fe/H cannot be negative. it is the ratio of iron to helium; it must fall between 0 and 1.

Originally Posted by AlexanderHowl

When it comes to captured rogue planets, whether or not a star system possesses them is a trial detail for most campaigns. Rogue planets may outnumber stars in the Milky Way by 100,000:1, so rogue planet capture should be a common event. I would suggest rolling 6d6 for rogue gas giants per system, with a '6' indicating a captured rogue gas giant, and 3d6-3 for the number of captured rogue terrestrial planets (rogue terrestrial planets are probably much more common than rogue gas giants). Each orbit would be 2d6 × 500 AU.

In the absence of actual data, any formula can be used, so sure.

On another note, you should probably consider the Roche limit for the inner limit radius

[AlexanderHowl]

Fe/H is the log(10) of the relative metallicity of a star compared to Sol, so it most definitely can be negative. FE/H of 1 would have 10 times the metallicity of Sol, 0 would have the same metallicity of Sol, and -1 would have 0.1 the metallicity of Sol (https://en.m.wikipedia.org/wiki/Metallicity). For example, Fomalhaut possesses a maximum metallicity of -0.03 and a minimum metallicity of -0.34, meaning that it has between 45% to 93% the metals of Sol (https://en.m.wikipedia.org/wiki/Fomalhaut).

[Daigoro]

You could try PMing the author of GURPS Space, Jon F. Ziegler. I don't know about his progress, but he did mention an update to the planetary creation rules a little while ago. He's a sometime poster here.

ETA: More on his project here. Includes a free pdf of the draft system rules.

[Anthony]

The big problem doesn't seem to be the position of the snow line, it's that the snow line means a lot less than we thought it did because apparently planets don't just stay where they formed.

[AlexanderHowl]

Originally Posted by Daigoro

You could try PMing the author of GURPS Space, Jon F. Ziegler. I don't know about his progress, but he did mention an update to the planetary creation rules a little while ago. He's a sometime poster here.

ETA: More on his project here. Includes a free pdf of the draft system rules.

Interesting, though he uses an unconventional definition of metallicity. The normal range is '-1' to '1', which is a log10 scale with '0' representing Sol, while he seems to be using a straight ratio, which would be '0.1' to '10', with '1' representing Sol. It is easy enough to convert his scale to the standard scale and visa versa though.

[Flyndaran]

Originally Posted by Anthony

The big problem doesn't seem to be the position of the snow line, it's that the snow line means a lot less than we thought it did because apparently planets don't just stay where they formed.

I think some theories have our own systems as likely being shaken up just like that. Possibly with another gas giant that was shot out during the jostling according to some computer models.

Our methods of planet discovery are still best suited to finding the weird ones though, so the exact ratio of them to classic model systems isn't clear, I think.

[AlexanderHowl]

I agree, there is a question of how much we are seeing is a reflection of observational bias due to primitive technology. Even so, a comprehensive planet creation system should reflect everything that we have already observed.