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System Generation/Adaptation from ACCRETE

This article originally appeared in the November/December 2016 issue.


At age 20, I first hooked up with organized SF litfandom at my first SF convention (NASFiC 1975, Los Angeles), and met Wayne Shaw (then 19 years old; later to develop the Shavian Empire campaigna), who would be my primary FRP GM for the next few years. (NASFiC was his first, too; he was introduced to D&D and the world would never be the same.)

During his high school years, Wayne was working on a space-opera universe to write in, and had defined over 20 alien races from parahuman to AWAP (as weird as possible). I was interested in figuring out the races’ homeworlds and systems, and the current issue of Scientific American (September 1975, theme “The Solar System”) included two pages of diagrams of hypothetical planetary systems, selected for maximum variety from runs of a computer simulation called ACCRETE.


ACCRETE was apparently developed around 1969 by Stephen H Dole of RAND corporation to study solar system formation, concentrating on forming solar systems similar to our own. The SciAm article diagrams appear to be from a subsequent experiment by Richard Isaacman and Carl Sagan (yes, that Carl Sagan) at Cornell University, tweaking the various constants used in Dole’s original ACCRETE to see what would happen.

According to Dole’s original 1969 paper, ACCRETE works by simulating a protoplanetary disk of gas and dust particles in orbit around a gravity well (protostar) and injecting random “seeds” into that orbiting disk on random orbits. These “seeds” grow by sweeping in the smaller particles of the disk. These growing planets will coalesce if their orbits cross or they come too close to one another (gravity wells overlap); growth stops when a planet has cleared its orbital region.

When a growing planet becomes massive enough (Dole sets this at 3.5 Earth masses, the point of helium capture), the “seed” begins to gather in gas as well as dust. Seeds are injected until most all the dust has been swept up.

Varying the parameters of the simulation – disk mass, density gradient, density distribution over distance, orbital eccentricity of the particles and seeds, etc. – varies the architecture of the resulting system. Dole’s original paper (and most of the ACCRETE apps online) had its parameters set for maximum chance of generating a solar system similar to Sol’s. Isaacman & Sagan’s paper changes these parameters and observes the results on the systems.

Classic ACCRETE output its systems as a table of planetary masses (Earth = 1) and orbital distances (in AU) and a diagram of planets (represented as disks of varying size) distributed over a logarithmic scale of orbital distances from 0.1 to 100 AU; planet sizes in the diagram were proportional to the cube root of the mass, which was written next to the planet’s disc. Some also had orbital eccentricity ranges for each planet.

Conversion of ACCRETE-generated systems to (primarily Classic) Traveller

To “Travellerize” an ACCRETE-generated system (or a RL system), you need only the masses and orbital distance (semi-major axis) of the planets in the system. The latter can be in a table of distances or “eyeballed” from the logarithmic scale of published ACCRETE run diagrams.

Travellerizing” a system from these parameters does not require high-precision calculations. I use my father’s slide rule to do the squares and cube roots needed for these calculations. Two or three significant digits is accurate enough for these purposes, and it’s traditional—slide rules were used for starship navigation calculations in pre-1960s SF.


  1. The orbital distance of the innermost “gas planet” determines the “frost line”, the point where it is cold enough for volatiles to condense and form gas giants. The exceptions are when the innermost world (less than half an AU) is a “Hot Jupiter” or otherwise gas planet or where there are no gas planets; in such cases, arbitrarily pick a distance for Step 2 depending on the actual planetary arrangement.
  2. Divide this distance from (1) by 4.85 (approximate as 5). This distance is where the solar flux/illumination is the same as Earth.
  3. Multiply the value from (2) by .9 or .95 to get the inner edge of the Habitable Zone (HZ).c
  4. Multiply the value from (2) by 1.5 to get the outer edge of the HZ.d
  5. Square the value from (2) to get the luminosity of the sun.
  6. Stellar mass as a function of luminosity is best looked up on a table such as Table 11 in Habitable Planets for Man, “Characteristics of Main-Sequence Stars.” Taking the cube root of the luminosity is an approximation (10-15% low).e
  7. The maximum size of the system – the distance where solar gravity is normally enough to accrete planets – is given by multiplying the cube root of the luminosity by 40. Outside of this limit, there will normally be only dwarf planets and the ice asteroids of a Kuyper Belt.
  8. Translate planetary masses into Traveller Size.
  1. Translate orbital distances into Traveller orbit zones, using the following table:k
    Table of Orbit Zones
    Orbit Distance (AU) Range (AU) Stellar Class Luminosityl
    Close <0.1 <0.1 -
    0 (Vulcan)m 0.2 0.1 to 0.25 M1v or M2v 0.04
    0bis 0.3 0.25 to 0.35 K8v 0.09
    1 (Mercury) 0.4 0.35 to 0.47 K4v 0.16
    1bis 0.55 0.48 to 0.67 G9v or K0v 0.3
    2 (Venus) 0.7 0.68 to 0.77 G6v 0.49
    2bis 0.85 0.78 to 0.9 G3v 0.72
    3 (Earth) 1.0 0.9 to 1.15 G0v or G1v 1.0
    3bis 1.3 1.15 to 1.45 F6 1.7
    4 (Mars) 1.6 1.45 to 2.0 F3v or F4v 2.6
    4bis 2.2 2.0 to 2.5 A8v 4.8
    5 (Ceres) 2.8 2.5 to 3.4    
    5bis 4.0 3.4 to 4.6    
    6 (Jupiter) 5.2 4.6 to 6.5    
    6bis 7.6 6.5 to 9.0    
    7 (Saturn) 10.0 9.0 to 11.9    
    7bis 13.8 11.9 to 16.7    
    8 (Uranus) 19.6 16.7 to 24.4    
    8bis 29.2 24.4 to 34.0    
    9 (Neptune) 38.8 34.0 to 48.4    
    9bis 58.0 48.4 to 67.6    
    10 77.2 67.6 to 116    
  2. Tweak these results as needed to prevent absurdities or add variety.
  1. ACCRETE-based systems could be combined with other systems as far binaries, giving “two systems in one”. The following special considerations apply:

Example 1: Isaacman-Sagan Fig.6b

  ACCRETE Traveller
Planet Distance (AU) Mass Orbit Zone Size
I .45 AU 0.42 1 6
II 0.8 0.25 2bis 5
III 1.5 20.6 4 SGG(20)
IV 3.2 18.1 5 SGG(20)
V 7 14.7 6bis SGG(15)
VI 12 500 7bis LGG(500)
VII 20 0.09 8 3
VIII 30 0.3 8bis 5
IX 43 0.56 9 7

A typical ACCRETE system.

Result: We have a typical Traveller system, an orange dwarf sun with six planets. Planet I is the main world, small and cold, day lengthened by suntide drag, barely surface-habitable. The SGGs are ideal for fuel-skimming.

Example 2: Isaacman-Sagan Fig.10d

  ACCRETE Traveller
Planet Distance (AU) Mass Orbit Zone Size
I 0.3 0.14 0bis 4
II 0.55 0.94 1bis 8
III 0.8 0.79 2 7
IV 1.1 0.34 3 6
V 3 6.6 5 GasDwarf(7)
VI 5 22 6 SGG(20)
VII 9 449 7 LGG(450)
VIII 27 2.7 8bis 11
IX 40 0.07 9 3

Another typical ACCRETE system. This one was the first diagram in the SciAm article.

Result: Another typical Traveller system (a yellow dwarf with eight planets), except with two main worlds in the HZ. (Two for the price of one!) The inner main world will be hot and dry, probably habitable only at the poles; the outer is best cold and wet. Planet VI (the SGG) is a natural fuel-skim site.

Example 3: Mystery System

  ACCRETE Traveller
Planet Distance (AU) Mass Orbit Zone Size
I 0.21 0.05 0 3
II 0.37 3.6 1 12
III 0.85 0.62 2bis 7
IV 1.49 0.7 4 7
V 10.4 1570 7 VLGG(1600)
VI 19.2 0.24 8 5
VII 34.8 0.11 9 4

This one was listed in my 1975 notes (including exact orbital distances) but I cannot find it anywhere in either Dole’s or Isaacman & Sagan’s papers. I can only conclude it was on the missing p.32 of the Scientific American article that kicked off this whole schmeer some forty years ago.

I assume this was one of Isaacman & Sagan’s runs when investigating the effect of changing the disk density profile, with more mass distributed farther out.

Result: A dim orange dwarf with four planets; three in a compact inner system and the fourth an eccentric Super-Jupiter with an incredible ring system sweeping in and out of the outer system. Despite having a gas giant, there can be no fuel-skim site insystem; the gas giant is a deathtrap, with a surface gravity of 12G.

Alternative 3-A:

Let us keep the eccentric orbit for the VLGG and size the frost line from its periastron of Orbit 6 = about 5 AU.

Alternative 3-B:

Same as Alternative 3-A except make the VLGG’s orbit nearly circular, with a frost line around 9 AU.

Example 4: Dole Fig.17, Isaacman-Sagan Fig.5c

  ACCRETE Traveller
Planet Distance (AU) Mass Orbit Zone Size
I 0.45 1.13 1 8
II 0.8 2.33 2 11
III 1 32.8 3 SGG(30)
IV 3 5150 5 Brown Dwarf(5200)
V 9 37700 7 Red Dwarf Star
VI 20 3770 8 Brown Dwarf(3800)
VII 43 59.5 9 SGG(60)

This one appears in both Dole’s and Isaacman’s/Sagan’s papers, increasing the central density/mass of the protoplanetary disk to about four times the value of “standard” ACCRETE, pushing the program to its limits. The result was fewer but much more massive “planets”, to the point of Brown Dwarves and binary systems.

Because this is a binary system, the orbit restrictions from Classic Traveller Book 6: Scouts come into play; with the companion star at Orbit 7, everything else above Orbit 3 goes away. Let us go over the system one star at a time:

Component A (main sun):
Component B (companion):

Result: a dim M1/M5 red dwarf binary with two SGGs but no potentially-habitable worlds; all planets are in their respective stars’ Outer Zones.

Example 5: Isaacman-Sagan Fig.13b

  ACCRETE Traveller
Planet Distance (AU) Mass Orbit Zone Size
I 0.45 989 1 VLGG(1000)
II 0.9 1.04 3 8
III 1.6 0.69 4 7
IV 3.2 0.015 5 2
V 5 0.001 6 1 (Dwarf Planet)
VI 7 0.001 6bis 1 (Dwarf Planet)
Farther out several <.001 10+? 0 (Asteroids)

Also from the 1975 SciAm article, this is a “hot Jupiter” system, caused by different radial-density distributions than standard ACCRETE. Though the most-easily-detected of extrasolar systems, hot Jupiters were unknown at the time of the article, and seemed absurd – how could a gas giant form so close to a sun?

Later research theorized that planets tended to migrate towards the sun during formation, in a game of gravitic pinball. (Jupiter and Saturn formed a stable resonance when still beyond the frost line and prevented each other from migrating further in.) Planet I would probably have formed at the frost line and migrated inward, wreaking havoc on any planetary bodies in its path. Planets II-VI probably accreted from the planetisimals it left in its wake. Given that…

Result: An F-class sun with four planets: a hot Jupiter, a Super-Venus, a possible habitable (with two spectacular morning/evening stars), a small rockball (too small to be a Mars), and a very sparse asteroid belt with dwarf planets separated by a gap from a thick Kuyper belt. Though spectacular, the only gas giant insystem is not skimmable (too large and too hot).

Alternative 5-A, “The Twins”:

In 1975, systems like Example 5 were considered absurdities – hot Jupiters were unknown at the time, though IRL they are very common. My surviving notes show I swapped out the hot Jupiter for a binary companion around .2 AU (Orbit 0) and sized it so Planet I (the Size 8 in Orbit 3) was the main world (with a “Tatooine” double sun).

Result: A belter’s dream system, handicapped by not having a gas giant for fuel-skimming.

The following examples are RL extrasolar systems, which do not break cleanly into Traveller-style systemsn. Reality has a way of throwing curveballs at any neat plans, and evidence is that a “normal” solar system such as Sol’s or the default ACCRETE isn’t all that common.

With actual stars, the spectral class and luminosity will be known and calculations will go from there. Spectral class, mass, and luminosity can vary from the tables, which represent the average class/mass/luminosity relationship.

These systems probably have additional planets to the ones given. The larger the planet and the closer the orbit, the more likely it is to be detected.

Example 6: Durre Menthor (Tau Ceti)

Planet Distance (AU) Mass Orbit Zone Size
b 0.105 2 Close 10
c 0.195 3.1 0 11
d 0.374 3.6 1 12
e 0.552 4.3 1bis 13 or Gas Dwarf(4)
f 1.35 6.6 3bis Gas Dwarf(7)

3.7 parsecs from Earth, Durre is a G9v yellow dwarf with a luminosity of 0.52 Sols (unusually bright for a G9). Using the luminosity as a base:

Result: No habitables (like most RL systems). Outer system (if any) unknown; this might be a “compact system” with all the planets close-in. Which brings us to…

Alternative 6-A:

Another RL system – Ran (Epsilon Eridani, a much younger K2v orange dwarf) has an outer system detected but no known inner planets (though there is definitely room for some):

Planet Distance Mass Orbit Zone Size
- 3 Asteroids 5 0
b 3.44 492 5bis LGG(500)
- 20 Asteroids 8 0
c 40? 32 9 SGG(30)

Tacking this outer system onto Durre’s inner system gives us a full Traveller-esque system. Still no habitables, but two gas giants and asteroid belts. The outermost SGG could be moved inwards to the maximum system size of Orbit 8bis and the outer asteroid belt to Orbit 7 or 7bis.

Example 7: Gliese 676A

Planet Distance Mass Orbit Zone Size
d 0.04 4.4 Close 13
e 0.19 11.5 0 Gas Dwarf(10)
b 1.8 2130 4 VLGG(2100)
c 5.2 2160 6 VLGG(2200)

16.5 parsecs from Earth, Gliese 676 is a red dwarf binary – M0v/M3v, separation 800 AU (Far). The larger component has a massive planetary system reminiscent of the original ACCRETE runs for Example 5.

Result: Another uninhabitable system. The innermost world is probably a lava world tidally locked in a torch orbit with an atmosphere of rock and metal vapor and a molten bright face. The gas dwarf is also in the Inner Zone and with all that atmo to hold the heat will resemble a Super-Venus with a very small solid core. Then those two VLGG deathtraps in the outer system – probably both resembling “Jupiters with smallpox” from internal heat. Any Traveller action insystem will probably be on their outer moons.

Example 8: Kepler-42

Planet Distance Mass Orbit Zone Size
c 0.006 2.1 Close 10 (Super-Venus)
b 0.012 2.7 Close 11 (Super-Venus)
d 0.015 0.9 Close 8 (Super-Venus)

About 40 parsecs from Earth, Kepler-42 is a solitary M5v red dwarf with a luminosity of .002 Sol, very dim for its spectral class. It is one of the most “compact systems” known, more like something you’d expect to find around a Brown Dwarf or VLGG.

Result: Here we see where reality conflicts with any possible system generation rules. I’d recommend using this system for a Brown Dwarf companion.


“Formation of Planetary Systems by Aggregation: a Computer Simulation” by Stephen H Dole; RAND Corporation, October 1969; Icarus, November 1970.

Pages 28-35 are ACCRETE diagrams of the systems generated in Dole’s “Set 4” runs. These runs were to find conditions and constants which generated systems similar to our own.

Free PDF download at http://www.rand.org/pubs/papers/P4226.html

Habitable Planets for Man by Stephen H Dole, 1964.

The first detailed scientific study on the probability and description of a human-habitable and/or life-bearing planetology. A second edition abridged and appended to by Isaac Asimov was later published under the title Planets for Man. (Use the original version with Stephen H Dole as sole author, not the mass-market edition “by Stephen H Dole and Isaac Asimov”; the latter omits much of the detailed technical information and all of the tables and graphs.)

Free PDF download at http://www.rand.org/pubs/commercial_books/CB179-1.html

“Computer Simulations of Planetary Accretion Dynamics: Sensitivity to Initial Conditions” by Richard Isaacman and Carl Sagan, Cornell University Center for Radiophysics and Space Research, Icarus, August 1977.

Using Dole’s ACCRETE paper as a basis, Isaacman & Sagan experimented with changing the assumptions, conditions, and constants in ACCRETE to see how the resulting systems varied. Figures 1 – 13 at the end of the paper contain many variant ACCRETE systems.

Free PDF download at https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770006045.pdf

“The Solar System” by Carl Sagan; introduction to the September 1975 issue of Scientific American, pp 22-32.

Pages 31-32 are diagrams of ACCRETE runs from Isaacman & Sagan’s paper. (Page 32 was missing from the microfilm archives at Cal State Fullerton library and may contain more systems and actual mass/distance tables, as my 1975-vintage handwritten notes had detailed mass & orbital distance information not on the Page 31 diagrams, as well as two systems which did not appear on Page 31.)

ACCRETE on the Web

Dole first created and ran ACCRETE at early Tech Level 7, written in longhand on coding forms and transcribed by keypunch onto FORTRAN card decks.

At TL9, ACCRETE is available as a download or Web page app. Unfortunately, all the ACCRETE apps on the Web seem to be adjusted to Dole’s original parameters, optimized for solar systems similar to Sol’s. However, some of downloads claim to include source code, which leaves open the possibility of reverse-engineering a version with the control parameters exposed for Isaacman-Sagan-style tweaking. (Into the “fun” systems.)


This page contains several ZIPped download links, including a Java applet with source code.


This appears to be a clearinghouse page for several worldbuilding apps. ACCRETE apps are under the headings “StarGen” and “Accrete”. One ZIPped download claims to be to a C-language version of the original ACCRETE source code.


A description of StarGen, one of the more elaborate ACCRETE apps. StarGen is more elaborate than the original ACCRETE, generating random star types and a lot of planetary details; all you need for this article’s form of Travellerization is the planetary mass and orbital distance.


Online runnable StarGen interface. I prefer the “SVG Graphic File Output” option, which outputs in a classic ACCRETE diagram format, but the graphic does not seem to match the tables of mass and orbital distance below. You can eyeball orbits from the diagram (close enough for Travellerization) or from the table.

These sites appear to be clean, but I cannot vouch for the downloads. Use full virus protection just in case.


  1. http://www.freelancetraveller.com/features/othroads/shavfoib/genesis.html
  2. Note that one J-mass is within three percent of .001 S-mass. This permits easy comparison of Super-Jupiter or Brown Dwarf masses (measured in J-masses) to their parent sun (measured in S-masses).
  3. When Dole wrote Habitable Planets for Man, Earth was believed to orbit in or near the middle of Sol’s habitable zone. Later information showed Earth is actually close to the inner edge of the HZ.
  4. A world with a Dense atmosphere can orbit slightly outside of this outer edge; the increased greenhouse effect of Dense atmo and/or Hydro 9-A has the effect of stretching the outer edge. This works both ways; such a world near the inner edge would likely become Venus-like from runaway greenhouse effect.
  5. Actual proportions of main-sequence stars are 73% M-class red dwarves, 15% K-class orange dwarves, 7% G-class yellow dwarves (like Sol), 3% F-class yellow-whites, and 2% larger. Of these, Ks and Gs are considered the most likely to host habitable planets. For Traveller purposes, my rule-of-thumb is two or three Ks for every G, two Gs for every F, and Ms as “targets of opportunity”.
  6. Dole selected 3.5 T-mass as the upper limit of a potentially-habitable planet; 3.5 T-mass has a surface gravity of 1.5G, the threshold to capture helium, and helium capture would increase mass to the point of hydrogen capture and gas gianthood. This was his dividing line between solid and gas planets, but a smooth transition from a solid planet with very dense atmo and a gas planet with a solid core is more likely. Gas Dwarves are not considered suitable for fuel-skimming as their atmospheres are heavily contaminated with other gases than hydrogen and helium – treat as “Contaminated” fuel, one step below “Unrefined”.
  7. In the Inner Zone, a Gas Dwarf-mass world is much more likely to be a Super-Venus.
  8. These are now called “Ice Giants”, as they have more solid or liquid than gas in their material than a true gas giant. “Small Gas Giant” was the terminology in use during the time of Classic Traveller.
  9. 60 T-masses was chosen as the dividing line between SGG & LGG from the graph on p.34 of Habitable Planets for Man (Figure 11, “Mass-density relationship of the solar system planets”). According to this graph, 50-60 T-mass is the point of minimum density/surface gravity (less than 1G). In an SGG, adding more mass decreases the density; in an LGG, adding mass increases the density. Because of this, 50-60 T-masses is considered the optimum size for fuel-skimming; even 1G ships will have no problem.
  10. A VLGG will not be much larger in diameter than Jupiter; the high-end of them may even be smaller. At this size, any added mass is just crushed into greater and greater density by the planet’s greater gravity. Because of this near-constant diameter, surface gravity on a gas giant above 150 T-mass will be .8G for every 100 T-mass, making VLGGs too large for fuel-skimming.
  11. Whole-number orbital distances are directly from Classic Traveller, Book 6: Scouts, with the addition of intermediate “bis” orbits. The original table in Scouts was taken directly from orbital distances of Sol System extended by the Bode-Titius Rule, and ACCRETE (and RL) orbits do not break down so cleanly.
  12. For Earth-equivalent solar flux at the nominal orbit distance (center of the orbit zone range).
  13. The hypothetical planet inward of Mercury, not the one from Star Trek.
  14. For further Traveller adapations of actual systems, a list of known planetary systems is available at https://en.wikipedia.org/wiki/List_of_multiplanetary_systems. Some of these are linked to pages detailing the actual systems and planets.