Status Report (14 September 2018)

Status Report (14 September 2018)

Just a quick note, since it’s been a few days since I’ve posted anything here. Been rather distracted by finally picking up the video game Shadow of War, which is iffy from the standpoint of a Tolkien scholar but quite entertaining from a gameplay perspective.

I was about ready to wrap up my modeling of galactic history and drill down to the structure of the Khedai Hegemony (the interstellar polity that conquers and rules Earth in my Human Destiny setting). Then I had a sudden realization that caused me to re-think a lot of the chain of reasoning. To wit: stars move.

Okay, yes, that isn’t a great revelation. We all know that stars have proper motion in the sky; over long periods of time the configuration of stars around Sol (for example) will change dramatically. What I realized is that the time-scale on which this is significant is well within the periods of time I was working with for the Human Destiny setting. Interstellar civilizations can’t be treated as nice, compact, spherical volumes of space – not if they last long enough that their colony worlds are going to scatter across dozens or even hundreds of light-years.

So I’ve made a few tweaks to the chain of logic, and in the process have improved it somewhat. I can now model different interstellar civilizations based on the strategy they select as to which new cultures they choose to “uplift” into the galactic community. I also now have a solid chain of reasoning that indicates why any given interstellar culture might have neighbors, to serve as enemies or at least competitors. I believe I’m now in a position to publish my revised model here, and work on a larger-scale map of the entire Hegemony that I can use as reference when writing stories. Look for that over the next few days, so long as I can tear myself away from mowing through hordes of Sauron’s orcs.

Modeling Galactic History (Part II)

Modeling Galactic History (Part II)

So far, I’ve gotten through some of the chain of logic that sets up the structure of galactic civilization in the Human Destiny setting. Today I’m going to work through a few more steps.

Assumption #7: On the average, one Synarchy proxy can manage a volume containing about 100 subordinate cultures.

Commentary: This is a remarkable span of control. No empire in human history has managed to survive for long with a 100-to-1 disparity between the subordinate populations and the metropole. I’ll assume that the Synarchy chooses its proxies carefully, supports them effectively, and permits them a little more expansionism than the client species. Also, the Synarchy’s normal methods probably involve guiding client civilizations into a quietist lifestyle, thus discouraging rebellion.

I’ll assume that no proxy ever grows much larger than this, no matter how long it remains stable.

If the typical proxy can manage 100 subordinate civilizations, that implies that it will govern a volume containing about 40,000 habitable worlds. In the solar neighborhood, that implies a volume of about 192 million cubic light-years, or a sphere about 360 light-years in radius.

At this point, I should be able to place an upper bound on the rate at which interstellar-capable civilizations appear in the galaxy.

Consider that for all the 4.6-billion-year history of Earth, there has been a population of the 10,000 habitable worlds “closest” to Sol. Here, “closest” is in the sense that if an interstellar civilization appeared on any of those worlds, it would have been recruited by the Synarchy as a proxy, and Earth would soon have been terraformed and colonized by one of the proxy’s client civilizations.

Now, across 10,000 habitable worlds and during 4.6 billion years, we expect 92,000 tool-using civilizations to have arisen (number of habitable worlds, multiplied by the time, divided by 500 million years). If we want the expected number of interstellar civilizations to be less than one-half, then only one in about 184,000 tool-using civilizations will attain interstellar capability on their own. Let’s round that up to 200,000. That’s a very strict Great Filter (or, more likely, a very strict set of several Slightly Lesser Filters).

Assumption #8: Faster-than-light travel has three modes, which tend to limit the reach of any one interstellar culture.

Commentary: Based on the lore I’ve already established in completed stories, the primary interstellar mechanism is a relatively slow Alcubierre-like warp drive. Under the GURPS definitions, this functions as a “hyperdrive” (see p. 37-38 of GURPS Space). Ships can enter FTL anywhere, so long as they’re a safe distance away from any large mass (say, a few AU away from a star or solar mass). While in FTL, a ship is entirely isolated from the rest of the universe – all it can do is wait until it emerges at the pre-planned point. Emergence from FTL can also be done anywhere in open space, although navigation to a point of emergence tends to be rather inexact. The machinery for the FTL drive is carried on board the starship itself, and it’s the only means available for a ship to travel FTL independently. The warp drive provides variable interstellar speed, but most ships can manage up to about 90c, or about one light-year in four days. It’s available at GURPS TL10 to all interstellar cultures.

The second method of FTL travel is by wormhole bridge. Wormhole bridges are built between pairs of stellar systems, usually placed in orbit around a gas giant planet or some other convenient gravitational anchor. They are very expensive, but once built they permit almost instantaneous travel between their endpoints. Synarchy proxies build wormhole bridges between major worlds in their space, to facilitate trade and military movement. The technology for wormhole construction is available at GURPS TL11 to Synarchy proxies.

The Synarchy is believed to have a third FTL method, its operating principles mysterious, which appears capable of transiting the entire galaxy at will. This method is inferred only by those who have witnessed the Synarchy itself in direct action. Fleets appear, carry out their missions, and then vanish, never to be seen again. This method would seem to be available at GURPS TL12 to the Synarchy alone.

This combination of FTL methods has implications for the physical layout of space controlled by a Synarchy proxy culture. There’s probably a dense inner core, where the member civilizations are packed as tightly as they can go, connected by a network of wormhole bridges. On the edges of this core, there may be a middle region that’s more loosely packed, where the proxy doesn’t bother to uplift all the candidate civilizations that appear. Beyond the last outposts of the wormhole network, there’s probably a frontier zone, where the proxy keeps an eye on things but is very unlikely to uplift any civilizations that appear.

Working through some back-of-the-envelope calculations:

  • If 80% of a proxy’s member cultures are within the packed inner zone, that should be about 80 subordinate civilizations, packed into a compact volume containing about 32,000 habitable worlds. In the solar neighborhood, that implies a sphere about 335 light-years in radius.
  • Suppose the remaining 20% of the member cultures are in the middle zone, and that zone is about one year’s travel by slow FTL deep (90 light-years). That shell has inner radius 335 light-years and outer radius 425 light-years, for a total volume of about 164 million cubic light-years. That implies about 34,170 habitable worlds, of which only about 2,000 are occupied, or about 6% as opposed to the 25% or so in the inner zone.

Some Corrections

After writing the section I published here on 1 September, I became more and more uneasy with one of my assumptions – the wild-guess estimate that the first interstellar-capable civilization would appear about 6 billion years after the formation of the first stars. Instead of continuing to press forward with that guess, I went back and did some modeling of the history of star formation in the Milky Way galaxy.

With a little digging, I located a recent paper which yielded a reasonably clear profile of the galaxy’s star-formation rate throughout its history:

  • Starting at the beginning, and running for about a billion years, the galaxy formed stars at a little higher than the present-day rate. At this point, the galaxy had little shape – stars forming in this era were in the galactic halo.
  • Starting about 12.5 billion years before present, the galaxy began to form the “thick disk” of stars, forming stars at about three times the rate we see today. This burst of star formation seems to have lasted about 2.7 billion years.
  • Once the thick disk had formed, about 9.8 billion years ago, star formation fell off to about its original rate, slightly higher than today. This period lasted about 1.3 billion years.
  • From about 8.5 billion years before present, to about 7 billion years before present, star formation in the Milky Way almost stopped. Very few stars appear to have formed in this period, which marks a clear deficit in the age distribution of stars to the present day. This period seems to bracket the era during which the “thin disk” was forming. This probably isn’t a coincidence. The compression of the interstellar medium into the thin disk would have heated it, slowing down star formation.
  • Star formation from about 7 billion years ago to the present day seems to have been happening at a reasonably constant rate.

Okay, so given this profile, and a few wild-guess assumptions about the rate of stellar deaths and the rate of enrichment of the galactic medium with metals, I built a rough model of the number of stars, the number of habitable worlds, and the number of civilizations that might have existed in the galaxy throughout its history. I ended up with the following charts:

Looking at these data and applying the natural rate of appearance of interstellar cultures derived above, I found that the first interstellar culture in the Milky Way – the Precursors discussed above – probably appeared about 9.6 billion years ago. Their home stellar system was probably a halo star, remarkably rich in metals for its time, and their home planet likely reached the stage of complex ecologies much more quickly than the norm. Mildly surprising . . . but here’s the thing: the galaxy is big, and even rare cases are likely to occur somewhere.

As we’ve seen, the Precursors would have filled the galaxy in the blink of a cosmic eye. By about 9.2 billion years ago, the Precursors would have had to deal with a dozen or so local civilizations that managed to reach interstellar capability on their own. I’ll pin the era of galactic conflicts to about this time, and the foundation of the Synarchy within 50 million years or so after that.

At about this time, my spreadsheet tells me that new interstellar civilizations were appearing in the galaxy about once every 50 million years. That would have given the Synarchy plenty of time to place the whole galaxy under monitoring, so that it could begin recruiting any new interstellar cultures as its proxies.

While the galaxy’s thin disk and spiral arms formed, the Synarchy would have remained in control, “cultivating” the galaxy and preventing any new episodes of chaos such as had occurred under the Precursors. By the time Sol formed in some obscure corner of the galaxy, Earth would have been well-protected from being overrun many times over by undisciplined interstellar cultures.

With the Fermi Paradox secure, I think I’m ready to build an outline of galactic history, and to sketch out the shape of the Synarchy proxy that conquers Earth in the Human Destiny setting. All that will be for next time.

 

Modeling Galactic History (Part I)

Modeling Galactic History (Part I)

Over the next two or three posts, I’m going to be going through my reasoning for some of the background assumptions of the Human Destiny setting. This is probably going to come across as being a little stream-of-consciousness. I’m trying to work my way through a logic chain without necessarily knowing where it will need to go before I’m done.

Incidentally, although I’m not going to make any specific references to GURPS in these next few posts, I’ll continue to tag them that way – this kind of thought process is an extension of a few items in the last GURPS Space edition. I’m thinking specifically of the section titled Mapping the Galaxy, on pages 67-72. GURPS referees might find this process of some interest as a worked example.

So let’s get started.

Assumption #1: In the solar neighborhood, there exists about one stellar system for every 300 cubic light-years of space.

Commentary: The usual figure given for the stellar density in the solar neighborhood is about 0.004 stars per cubic light-year. Applying this to the 10-parsec-radius neighborhood of my map, we would predict the presence of about 580 stars. Clearly, the HIPPARCOS data set I work from is missing a lot of stars, since it only has 327 stars in that space (about 56% of the predicted number). As a cross-check, a 5-parsec radius should have about 72.5 stars, but the HIPPARCOS data set shows 64 in that space (about 88% of the predicted number). As expected, we’re missing more and more stars as we get further away from Sol.

On the other hand, we can expect that most “missing” stars are among the smallest and least luminous red dwarfs, increasingly difficult to observe with any significant distance. Even in the HIPPARCOS data set, there’s plenty of evidence that our data on individual red dwarfs becomes very poor well within the 10-parsec radius. Many stars have no other catalog designation, their spectral class isn’t at all certain, and so on. While proceeding through this analysis, I’ll bear in mind that very few of the “missing” stars are likely to have habitable planets.

Close to Sol, stellar systems seem to have an average of 1.2 stars each. This gives us an average density of about one stellar system for every 300 cubic light-years. That indicates about 480 stellar systems in the 10-parsec solar neighborhood.

Assumption #2: Within 10 parsecs of Sol, there exist about 30 habitable worlds.

Commentary: Applying the Architect of Worlds design sequence, I ended up with 28 habitable worlds in that space. Twenty of these (about 70%) appeared in stellar systems that included at least one K-class or more luminous star. None of them had a primary star of less than about 0.15 solar masses (about an M4 or M5). That suggests that habitable worlds circling the very dimmest red dwarfs – the ones by far most likely to be “missing” from the HIPPARCOS data set – are going to be very rare. I therefore assume that there might be one or two habitable worlds that I’ve overlooked, but no more than that.

Combining this assumption with the implications of Assumption #1, we get about one habitable world for every 4800 cubic light-years, or about one habitable world for every 16 stellar systems. We can apply this as a rough estimate for most regions of the galaxy.

Assumption #3: Habitable worlds that currently carry native tool-using civilizations (defined as capable of basic cultivation agriculture at a minimum) are very rare, about one in 40,000 habitable worlds.

This assumption breaks into two sub-assumptions:

  • Assumption #3A: A world will give rise to a tool-using civilization about once in every 500 million years of its habitable lifespan.
  • Assumption #3B: Almost all tool-using civilizations have a finite lifespan averaging about 12,500 years, after which they succumb to natural or sentient-made disaster, without ever developing interstellar capability.

Commentary: The computation is straightforward – divide the average lifespan of a typical civilization into the rate of their occurrence.

Naturally, both parameters are taken from the history of Earth. It should be noted that we have a very limited capability to identify other tool-using civilizations that may have occurred on Earth in the distant path. Still, we’ve never seen any evidence of prior non-human civilizations here, since the post-Cambrian appearance of complex land-based ecologies roughly 500 million years ago.

Meanwhile, humans have engaged in basic agriculture for about 11,500 years at this point. A more dramatic way of stating #3B is that, left to our own devices, we humans will drive ourselves into barbarism and extinction within another millennium or so. That gives us a total lifespan of about 12,500 years, which I’ll take as an average.

Combining this assumption with the others, we determine that at any given time in the natural steady state, tool-using civilizations appear about once in every 192 million cubic light-years, or once for every 640,000 stellar systems. That suggests the average distance between neighboring civilizations (using one of the formulae on page 72 of GURPS Space) is well over 600 light-years!

The natural state of the galaxy is many thousands of primitive cultures in existence at any given time, separated from each other by gulfs of hundreds of light-years, unable ever to see the slightest sign of each other’s presence.

Now, that assumes that no civilization ever attains interstellar capability. What happens if a few of them do?

Assumption #4: Given the possibility of interstellar (FTL) travel, as soon as one interstellar-capable civilization appears, it will no longer be subject to quick extinction and will fill the galaxy in a trivial amount of time.

Commentary: It seems reasonable to assume that an FTL civilization will no longer be subject to all the forces which drive a planet-bound culture to extinction. Only the very largest-scale natural disasters (enormous gamma-ray bursters, galactic core explosions, and so on) could destroy an FTL-capable culture. Such a culture might conceivably destroy itself through internecine warfare, but it seems reasonable to assume any culture likely to do such a thing would have done it before attaining FTL.

Meanwhile, an FTL-capable culture whose numbers expanded at even a modest rate would fill up the galaxy in a short time. Assume an annual rate of expansion as low as 0.01% – very slow, given FTL – then the Milky Way is filled up in as little as 250,000 years.

The question arises, then: given this event occurred, when?

The oldest stars in the galaxy formed about 13.5 billion years ago, but the environment for high-technology civilizations in such an early galaxy was probably very poor. Assume a minimum of four billion years for the first life-bearing planets to give rise to complex land-based ecologies. Then assume a further delay of about two billion years, for early civilizations to overcome the disadvantages of a metal-poor environment, and for more high-technology civilizations to appear at any given time. Then the first FTL-capable cultures may have appeared about 7.5 billion years in the past.

As it happens, this is after the formation of the galactic disk and spiral arms, and after a lengthy period of relatively slow star formation. If we assume one or more FTL-capable cultures appeared about then, they would have had a newly formed spiral galaxy to expand into, and a new flood of young stars to explore and colonize. These Precursor cultures might have hurried the process along, engaging in large-scale terraforming projects to create more habitable worlds.

(By an odd coincidence, the current Architect of Worlds design sequence yields that any potentially habitable world that is at least 7.6 billion years old, if its primary is not a class-IV subgiant, is guaranteed to have a complex biosphere. I didn’t plan that, but it fits! We can imagine that lots of small, cool stars that have been around since before the Precursor era were seeded with their favored ecologies back then.)

Any new FTL-capable cultures that arose during this period would have found the galaxy already full and busy. The Precursors may have been benevolent toward newcomers, or they may have been cruel and aggressive. In either case, newcomers would have had little chance to repeat the Precursors’ success. They would have been forced to survive in the margins of the elder galactic cultures.

We probably can set aside any concept of a unified Galactic Empire. Even with FTL, the natural unit of government is going to be no larger than the single star system. Such a system, if densely populated and developed, is likely to be economically self-sufficient and almost impossible to conquer.

The Precursor era was likely one of many millions of local civilizations, all in constant contact with one another, all of them rising and falling over time. Many single-system cultures may well have collapsed back into barbarism from time to time. Even whole regions of the galaxy might have fallen victim to some disaster or another. Alistair Reynolds’s concept of the “churn” (from his novel, House of Suns) seems likely to be appropriate here. Even so, the galactic association of cultures would have endured, possibly for a very long time.

Now, clearly this isn’t the situation we see now. The galaxy appears to be a wilderness. Something brought this Precursor era to an end, and something is preventing the galaxy from returning to that state today.

Assumption #5: The Precursor era was the only point in galactic history at which nearly every habitable world was occupied by high-technology civilization. Since then, the expansion of new FTL-capable cultures has been strictly limited.

Commentary: I choose to assume that in this setting, the galactic Precursor culture eventually fell victim to a massive conflict, driven by disagreements over several major issues. Among others:

  • Many local civilizations came under the domination of powerful AI, becoming machine cultures. These tended to replace their biological antecedents, through benevolent “mandatory pampering,” through non-violent competition, or through violent extermination. Naturally, civilizations which remained largely biological often regarded this development with alarm.
  • Some local civilizations found ways to “ascend” to new styles of life, often esoteric and incomprehensible to those who remained. Often this was associated with a shift to machine-culture status, as the “ascending” biological sentients abandoned their machine servants and guardians. Such “ascension” meant effectively dropping out of the galactic churn, often vanishing entirely to leave behind apparently empty worlds. Some cultural movements asserted that such “ascension” was the natural outcome and implied purpose of any sentient community. Other cultures rejected any such idea with horror.
  • Some local civilizations became concerned that the galactic community suffered from a lack of variety. They argued that ever since a single original civilization had given rise to the galactic community, all newcomers had been crippled, forced into an unnatural accommodation with that one dominant society. Over time, this became regarded as a fundamental question of justice.

Over millions of years, disputes over these issues gave rise to an epic series of wars. While a star-system community was a difficult thing to conquer, a sustained effort could sometimes do the trick. Of course, such a community was much easier to destroy. A barrage of relativistic kinetic-kill missiles, directed at every inhabited planet and space habitat in the target system, was one of the less destructive methods applied. Over time, the Precursor community collapsed across most of the galaxy, and high-technology culture was nearly eradicated.

Near the end of the conflict, an alliance of local cultures formed to defend what remained of the community, and to impose a specific solution on the galaxy:

  • Certain forms of “ascension” were accepted as the ultimate end of any sentient culture. One of the galactic community’s goals was to facilitate safe methods for such evolution, and to protect elder cultures as they proceeded toward it.
  • As elder cultures “ascended,” this would naturally make room for new biological cultures to arise, thus providing the galactic community with much-needed variety it needed. A second goal for the community was to protect such newcomers, helping them to survive the transition to FTL-capable status, and integrating them into galactic society. This specifically required leaving large volumes of space “fallow,” preventing any one culture from expanding too quickly or too far at the expense of others.
  • Powerful AI, and the machine cultures they tended to create, had a clear role in the galactic community, but they could not be permitted to harm or crowd out organically evolved cultures. Strict limits were placed on the use of AI by non-ascended civilizations. The creation of self-replicating AI was specifically forbidden.

This post-war settlement remains in effect, down to the present. Somewhere in the galaxy, very far from the solar neighborhood, a very powerful network of beings still works tirelessly to manage the galaxy, as if it were a vast garden. This network is called the Synarchy.

The Synarchy manages the galaxy by:

  • Intervening at certain points in the history of developing civilizations, helping them to avoid self-destruction and move toward readiness for participation in the interstellar community. This intervention is usually subtle but may involve overt conquest if necessary.
  • Enforcing certain foundational laws designed to prevent any one culture from overrunning the galaxy. Notably, no one civilization may claim or occupy more than a small fraction of the galaxy, and no civilization may build independent or self-replicating AI. Civilizations which break these laws may be brought into line by force.
  • Preserving knowledge and making it available to all participants in good standing in the galactic community, through the promulgation of a galactic Library. The evolutionary pathways that end with “ascension” are specifically revealed to all interstellar cultures at a certain level of maturity.

Much of the Synarchy’s work is done through proxies. These “mature interstellar empires” have generally been in existence for at least a few million years, have a good record of adherence to the Synarchy’s law, and have exhibited the ability to coexist smoothly with younger civilizations. The Synarchy deputizes such cultures to manage their areas of the galaxy, generally concealing its own existence from less mature civilizations.

So, what does an area of the galaxy overseen by one of the Synarchy’s proxies look like?

Assumption #6: In an area of space currently governed by a Synarchy proxy civilization, habitable worlds that currently serve as the home-worlds of native tool-using civilizations are much more common, about one in 400 habitable worlds.

This assumption derives from Assumption #3A, and from the following sub-assumptions:

  • Assumption #6A: About one in four tool-using civilizations survives long enough to develop a high-technology culture that will require intervention.
  • Assumption #6B: After intervention and emergence into the galactic community, civilizations have a finite lifespan averaging about 5 million years, after which they either voluntarily die out, or they “ascend” to the Synarchy and beyond.

Commentary: These assumptions imply that the average lifespan of a tool-using civilization is about 1.25 million years. Dividing this into the rate of occurrence of new civilizations (about once in 500 million years per habitable planet) gives us about one civilization per 400 habitable planets.

It should be noted that a Synarchy proxy could apply a different strategy, giving rise to a much higher density of high-tech civilizations. For example, a proxy could locate and intervene in the development of even pre-industrial cultures. Or it could even seek out promising pre-sentient species for “uplift” and civilization. I’ll assume that the Synarchy discourages such intense interventionism, possibly because it would lead the intervening civilization to force its clients into too restrictive a cultural mold. This would lead to a loss in the variety that the Synarchy values.

Without assuming anything (yet) about the shape or configuration of any volume of space governed by a Synarchy proxy, let’s examine how that space might be populated. If a given proxy governs space that includes N habitable worlds, then:

  • On the average, a new tool-using civilization will appear in that space every 500 million divided by N years.
  • On the average, a new high-technology civilization will appear, ready for intervention, every 2 billion divided by N years. This is also the rate at which established civilizations within the proxy’s sphere of influence will vanish into voluntary extinction or “ascension,” maintaining a steady state.
  • The current population of that space at any given time will be about N divided by 400 FTL-capable civilizations.

Suppose each FTL-capable civilization is allocated about 100 habitable worlds to colonize and occupy throughout its lifespan. If the space containing these worlds is compact, that implies a volume of about 480,000 cubic light-years, or a sphere with radius of about 48.5 light-years.

About 75% of the habitable worlds in a proxy’s volume will be left “fallow” at any given time. This should allow plenty of space for likely candidate species that might give rise to high-technology civilizations over the next million years or so. Potential colony worlds can be allocated to minimize the probability that a new civilization will appear on a world that’s already occupied.

The question arises: just how much space will a given Synarchy proxy be able to govern? Suppose a proxy can last much longer than the average of 5 million years for a full FTL-capable culture? Does it continue to grow, accepting responsibility for more and more space? Will the collective of all the Synarchy’s proxies fill the galaxy, or will there be “empty” space?

These questions are important, since we’re modeling a setting that needs to be consistent with what we’ve seen so far of the real universe. Results which indicate that Sol and Earth should have been visited and colonized many times in the past will mean that something has gone wrong.

I’ll examine some of these questions in the next post.

Human Destiny Reference Map Complete!

Human Destiny Reference Map Complete!

Okay, after several weeks of effort, I’ve finished my project to use the Architect of Worlds design sequence and place habitable worlds throughout the “solar neighborhood.” I’ve also finished producing a map of the region, based on those data.

The Human Destiny setting ended up with 28 more-or-less habitable worlds, and two colonized star systems without habitable worlds, in that ten-parsec radius from Sol. That’s out of roughly 328 stars that make up 265 star systems, indicating an average of one habitable planet for every nine or ten star systems. A bit more than I expected when I got started, but it’s a figure I can work with.

Here’s a thumbnail for the final draft map:

It’s a pretty huge file, so you might do better to download it and view it locally. Alternatively, here’s a link to the map’s page in my DeviantArt gallery.

At this point, I have a couple of things to publish here over the next few days. One is a review of the large-scale galactic situation in the Human Destiny setting (how common interstellar civilizations are, how they are likely to be structured and so on). Now that I have a plausible count of Earth-like worlds, I can finish those notes.

It also occurs to me that I now have a list of interesting worlds from the new map – I should draw up some capsule descriptions for those. I seem to be converging toward being able to publish a mini-worldbook in GURPS terms for this setting.

More long-term projects: now that I’ve given the Architect of Worlds system a thorough test drive, I need to go ahead and polish up and upload the working draft of the planetary-system design chapter. I also have a whole sheaf of case studies with which to develop and test a new section, on the design of individual worlds. I think I’m also prepared to produce a new draft of the next Aminata Ndoye story, a novella titled In the House of War, which will be the next item to get published. Busy, busy – but at least I’m continuing to work through my Gantt chart.

Status Report (21 August 2018)

Status Report (21 August 2018)

Still slogging along through the HIPPARCOS catalog – every day, I work through a dozen or so stars (and find myself wishing I had just written a C program for this already). At the moment I seem to have gotten through 276 entries in the database, out of a total of 327 reaching to the ten-parsec radius. Out of those stars, 23 have at least one planet with a complex biosphere, and at least a few systems have two each. It’s looking like a trend of about one in ten to twelve stars will have a more-or-less-Earthlike. I’m not bothering to count the “pre-garden” worlds, with liquid-water oceans but too young to have developed a post-Cambrian biosphere. There are quite a few of those.

Today I sat down for a few hours and started drawing a map of nearby space, including all stars of K class and above, and those few M-class stars that have Earthlike worlds. I’m using the same techniques that I once applied to this map of the solar neighborhood, and I imagine the end result will look similar.

I’m using a galactic coordinate system this time, rather than the usual equatorial coordinates, so a lot of stars will look like they’re in the wrong place if you’re accustomed to the maps from (e.g.) the 2300 AD or Universe tabletop games. I’m planning to include the appropriate coordinate transform in the Architect of Worlds draft, when I get around to writing the “using real astronomical data” section.

I’m also marking down tentative names for Earthlike worlds, instead of an abstract “resource value.” My vision for the Human Destiny setting has evolved quite a bit over the past few years. Today I’m assuming that the dominant interstellar civilizations won’t spend all that much time or effort exploiting star systems that don’t host complex biospheres. So the systems of greatest interest are going to be the ones that humans (eventually) settle.

If anyone’s interested in glancing at the work in progress, here’s a link to the appropriate entry in my Scraps folder. Only about twenty or so stars placed so far, or a little under one-third of the way through my data set. This is slow work, but it’s starting to come together.

Meanwhile, I’ve been working on a revision to my old notes about the density and structure of interstellar civilizations. Here’s a link to an article I wrote a few years ago, which lays out an argument about the limits to an interstellar civilization’s growth. (That article is also one of my few contributions to Winchell Chung’s Atomic Rockets website, in fact.) The Human Destiny setting incorporates that notion into its basic assumptions. I’ll probably publish those notes here within a few days.

Status Report (11 August 2018)

Status Report (11 August 2018)

Still working through my data pull from the HIPPARCOS data set. I haven’t found any more planetary systems that the draft Architect of Worlds model simply won’t fit, although the famous Gliese 667 C system came close.

One thing I have discovered is that my assumption about red dwarf stars seems to have been premature. A little further research tells me that the photosynthesis problem isn’t an absolute deal-breaker. The problem isn’t that photosynthesis is impossible under red-dwarf starlight, it’s that an early photosynthetic organism would have to adapt to long periods of visible-light scarcity, punctuated by the nasty stellar flares young red dwarfs tend to generate. One might imagine mats or colonies of photosynthetic microbes that drift to the surface of a planet’s ocean to take in the sunlight, then submerge to ride it out when flare weather sets in. Eventually, most red dwarf stars seem to settle in and stop producing major flares, so if their planets can give rise to life at all, evolution to complex biospheres seems at least possible.

So, rather than forbid red dwarfs from having garden worlds at all, I’ve decided to impose a penalty, requiring them to take a lot longer to develop complex biospheres. Even so, since red dwarfs burn so steadily over many billions of years, an ocean planet has plenty of time to work on the problem. Red dwarfs that are at least as old as Sol, certainly the ones that are a few billion years older, are possible candidates.

I worked out a set of criteria to determine whether I should work out a red dwarf star’s planetary system at all: at least as old as Sol, bright enough that the habitable zone falls out where the inner planets are likely to orbit, and with metallicity high enough to permit terrestrial planets at least one-quarter as massive as Earth. I’d say maybe one out of three red dwarfs in the solar neighborhood have fit the criteria well enough for me to break out the calculator, spreadsheet, and dice.

Now another facet of the new model comes into play. The draft model often generates systems of planets whose orbits are more tightly packed than one would expect, just looking at our own system. Which in turn significantly increases the probability that at least one planet will sit in the liquid-water habitable zone. In fact, sometimes I’m getting two planets in the zone in the same system. That’s not a result that the GURPS Space 4/e model would have produced very often, if ever.

The upshot is that although any given red dwarf is unlikely to host a garden world, there are so many red dwarfs that I’m getting a significant number of them. Lots of “eyeball planets” out there, it seems; possibly as many as the more Earth-like worlds with reasonable day-night cycles.

So far, I’ve worked out planetary systems to about 25 light-years from Sol, including all the K-class and hotter stars, now also including all the red dwarfs that seem to be plausible hosts for garden worlds. 168 lines in the HIPPARCOS database, although a handful of those aren’t actual stars, and 16 stars that have complex biospheres present. Looks like roughly one out of ten stars is giving me at least one garden world. More than I expected, actually, but it’s a result I can live with.

Status Report (5 August 2018)

Status Report (5 August 2018)

Most of my effort over the last few days has been directed toward two tasks. First, continuing to test the Architect of Worlds model for planetary systems by generating collections of worlds for stars close to Sol. Second, using those results to motivate the first definitions for the next stage of the design sequence: determining the physical properties of an individual world.

The first is going as well as can be expected. So far, I’ve only found one star system that I flatly can’t model properly (the HR 8832 system, about 21 light-years from here, which is believed to have an even stranger collection of super-Earths and close-in gas giants than usual). Otherwise, I’m getting a very plausible set of planetary systems, a significant improvement over the results I would have gotten from the old GURPS Space 4/e design sequence.

As far as the second task goes, I’ve had something of a breakthrough: I’ve found a model I can live with to help the user decide whether a given planet is tide-locked to its primary star or not. It’s a horrible kludge – but the question of how long it takes a planet to tide-lock is very complex, and there’s no consensus in the literature about it. If a planet could be modeled as a uniform and perfectly elastic body, the math simplifies pretty well, but planets just aren’t like that. The equation I’ve come up with seems at least plausible, in the forty or so star systems for which I’ve generated data so far.

Right now, I’m wrestling with how to decide whether a given planet (or moon) has a substantial atmosphere or not, and whether it has oceans or not.

In GURPS Space 4/e, I kind of took a backwards approach – I had the user decide which of several categories a world fell into, and then he generated the world’s mass, density, and so on to fit. I think that was slightly more useful for the gaming context, but the math was kind of annoying (not least because SJG editorial policy forbade me from using SI units, so I tried scaling everything to Earth and the Sun, with weird outcomes). The math is a bit more straightforward doing it the other way – define a planet’s mass and density, then figure out what its surface environment will be like.

Of course, now I have to wrestle with questions like why Mars has almost no atmosphere despite being massive enough to retain molecular nitrogen and carbon dioxide (and it can’t just be because Mars has no magnetic field to speak of, because Venus doesn’t either, and it has a very thick atmosphere). Or, say, why Titan has a substantial atmosphere when the almost identical Ganymede has none.

Slowly, a classification scheme is emerging, but it will probably be a few more days before I’m happy with it.

Meanwhile, the upcoming week is going to be unusually busy at the office. I’m teaching one course, taking a second course, and facing impending deadlines on writing two more courses after that. Generally, my life is not quite that full! I may or may not have a lot of time to play with my worldbuilding over the next few days. We’ll see how things go.

Architect of Worlds – Some Initial Results

Architect of Worlds – Some Initial Results

Over the past couple of weeks, I’ve been applying the star-system and planetary-system design sequences from the Architect of Worlds draft to generate planetary systems for nearby stars. In a number of cases, this has involved tweaking the parameters of the model to fit strong exoplanet candidates that we already know are there. In other cases, it also involved tweaking the parameters to avoid creating exoplanets that we would reasonably have detected by now, if they were there.

So far, the model has held up surprisingly well. I’ve had to make a few adjustments to make the results more plausible, and to allow for some of the real-world cases. That’s to be expected, but by and large I haven’t had to do any major redesign.

Let me summarize some of the results thus far.

Alpha Centauri

We know of two strong exoplanet candidates for this trinary star system – one close-in planet for each of Alpha Centauri B and Proxima Centauri. I had no difficulty at all fitting either of these candidates to the model. The result was five planets for Alpha Centauri A, nine for Alpha Centauri B, and twelve planets for Proxima. The tight or loose packing of planetary orbits makes a big difference, and of course Proxima has no close companion to block off the outer system for planetary formation. Thus the little red-dwarf companion gets the most extensive family of planets.

The mass of the known candidate for the B-component suggested a lighter protoplanetary disk than usual, but this still yielded two Earth-likes in the habitable zone, generously defined. One of these is the best candidate I’ve generated so far for a habitable world. The mass of Proxima’s known companion suggests a denser than usual protoplanetary disk, so Proxima ended up with a few gas giants up to Saturn size, at fairly wide orbital radii.

Barnard’s Star

Low-mass star, very low metallicity, not much material with which to build massive planets. The system ends up with nine planets, all packed well within one astronomical unit of the star, all but the last of them little Mars-likes. This turns out to be fairly typical of red-dwarf stars, given the assumptions of the model.

Wolf 359

Very small and dim red dwarf, although the metallicity is high and that might help form planets. We end up with ten planets this time, several of them cold super-Earths. The innermost planet is in the habitable zone, but is too small to retain much atmosphere.

Lalande 21185

Another small red dwarf. Interesting in that we have a strong exoplanet candidate here, a super-Earth very close in. The problem is that we don’t seem to see any more heavy planets or super-Jovians further out.

This star caused me to make the first adjustment to the model: I added a rule that permitted a massive, volatiles-heavy “failed core” to appear close to the star in rare cases. This makes sense, given that some of our known exoplanets are both massive and not very dense, suggesting that they’re not rocky “terrestrial” planets, but something rich in water and other light compounds instead. If a gas giant can migrate inward, perhaps a smaller planet can form out past the snow line and barrel in close to the star as well.

Placing the exoplanet candidate as a “failed core” rather than a “terrestrial planet” permitted me to keep the assumed density of the protoplanetary disk to a reasonable value. The rest of the planets turned out to be quite small close in, leading to a few modest-sized gas giants on the outskirts, safely under our current detection level. Ten planets in all, two of them within the generous habitable zone, both of those probably too low-mass to be truly Earth-like.

Luyten 726-8

Two very low-mass red dwarf stars, co-orbiting at a close distance that probably forbids either from having many planets. The model gave me two planets for the A component, one for the B component, all cold “failed cores.”

Sirius

A very hostile star system. The bright A component ended up with nine planets, all packed close in, a mix of gas giants up to sub-Jovian size and a few rocky super-Earths. All of the planets are far too hot for human comfort, the coolest of them running a blackbody temperature over 400 K.

I didn’t bother to generate planets for the white dwarf B component – I need to work out rules for applying the model to white dwarf stars, and in any case there’s no possibility of an Earth-like world in such a planetary system anyway.

Ross 154 and Ross 248

These two red dwarf systems each turned out to be barren, with four and five planets respectively. I’m not going to report on any more red-dwarf systems, as they’re all going to be similarly uninteresting.

In fact, my research tells me that the probability of any red dwarf giving rise to an Earth-like world is going to be very low. Any world that’s warm enough will almost certainly be tide-locked, with all the problems that implies. Not to mention that red dwarf stars put out most of their radiation in the infrared range. That means a world that’s warm enough to live on is likely to get so little visible-light insolation that photosynthesis is going to be problematic.

Epsilon Eridani

This was an interesting case – we have at least one strong exoplanet candidate here, a super-Jovian, with a strong indication of a dense asteroid belt just inside that candidate’s orbit. None of this was a problem for my model. The mass of the known gas giant, together with the known density of the current debris disks, suggested a high-density protoplanetary nebula. I was able to generate the rest of the planetary system to match.

I ended up with nine planets, one of them a super-Earth squarely in the middle of the habitable zone. The star system is quite young, well under a billion years old, so that planet is almost certainly a heavily oceanic “pre-garden” world, lacking complex life or a human-breathable atmosphere. Still, maybe a terraforming candidate? Meanwhile, the asteroid belt is in place and I would be comfortable marking that as a rich resource zone. This looks like a star system that people would come to visit, even if there isn’t an Earth-analogue there.

61 Cygni

No surprises here. I got thirteen planets for the A-component, due to tight packing of planetary orbits, and only seven for the B-component. Nothing so massive as to be detectable from Earth, so there’s no sign of Mesklin, alas. Each star ended up with a planet in the habitable zone, but both were too low-mass to be good Earth-like candidates.

Procyon

As expected, this system ended up like Sirius A, but not quite so extreme. Eight planets, all of them rocky worlds, no “failed cores” or gas giants in the mix. The outermost might almost be cool enough for habitability, but it’s far too small, so it’s more like a baked-dry Mars than anything else.

Epsilon Indi

This star gave me a little trouble, and caused me to tweak the model again slightly. The problem is that we have an exoplanet candidate here, but it’s simultaneously very massive (about 2.5 Jupiter masses) and very distant from the primary.

As written when I got to this point, my model permitted massive gas giants to form, but that would tend to require a dense protoplanetary disk, which would in turn force the gas giant to form close in and migrate closer. A gas giant forming much further out would suggest a lighter disk, which would render the planet less massive. A paradox. I solved the problem by adding another size category for gas giants – in rare cases, even a fairly light disk can now give rise to a super-Jupiter. Which makes sense, as this isn’t the only massive gas giant we’ve detected in the cold outer reaches of a star system.

Final result was nine planets, the innermost of which wouldn’t be a bad Earth-like candidate, except that the system is fairly young. Probably another “pre-garden” world here.

Tau Ceti

We have several strong exoplanet candidates here, all of them super-Earths fairly close in to the star. I computed the most likely disk density and proceeded, adding Mars-sized mini-worlds to fill in two gaps left by the known exoplanets. Final result was nine planets, none of them further out than about 6 AU, which gives us room for this star system’s apparently very wide and rich Kuiper belt.

Two of the known super-Earths are close to the habitable zone, but one of them is probably too hot, and the other one is probably only habitable if it’s running a very aggressive greenhouse effect. Probably interesting places to visit, but not somewhere anyone would want to live.

Summing Up

Twenty-seven stars so far, in twenty star systems, and so far I’ve only generated one strong candidate for Earth-like conditions (Alpha Centauri B-V). I’ve also concluded (or, rather, verified for myself) that red dwarf stars are very unlikely to give us Earth-likes. Depending on one’s assumptions, this may mean that such stars are best ignored when building a star map for fictional purposes.

I’m going to continue with this, probably saving myself a bunch of time by skipping over most or all of the M-class stars. Meanwhile, this is enough for me to start building a new version of my solar-neighborhood map. Stay tuned.

“Published Work” Page Now Available

“Published Work” Page Now Available

Long overdue, but I’ve created a “Published Work for Sale” page, which is linked from the sidebar to the right. At the moment that includes only the two novelettes I’ve self-published, but I’ll probably add links to some of the other work I’ve done that’s still in print. Also, as I release more work it will be added to that list. Links from there to the appropriate pages on Amazon. Hint, hint.

Architect of Worlds – Step Fourteen: Place Natural Satellites

Architect of Worlds – Step Fourteen: Place Natural Satellites

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 Rmin is the minimum distance from the planet to the primary star (in AUs), MP is the mass of the planet (in Earth-masses), and MS 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, MS is the mass of a major satellite in Earth-masses, MP 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, MS is the mass of the major satellite, and MP 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.