Freelance Traveller

Planetary Orbits in Binary Systems

by Ken Pick

This article originally appeared in the January/February 2025 issue, classified as “The Prep Room”.

Around a fifth of star systems are binary “double stars” or multiples (three or more); the proportion rising as the stars become more massive.

All binary/multiple systems tend to have less and/or smaller planets than a solo star; this is due to much of the matter in the protostellar cloud ending up in the two suns during formation and the dueling stellar gravity wells throwing much of the remaining protoplanetary matter out of the system.

Glossary

• ACCRETE System: System generated by the ACCRETE program.
• AU (Astronomical Unit): Earth-Sun Distance, the main unit of measure for planetary systems. Approximately 150,000,000 km.
• Earth-equivalent distance: The distance from its sun where a planet receives the same solar energy as Earth. Distance (in AU) = square root of star’s luminosity (in Sols [1 Sol is the luminosity of Earth’s sun]).
• Frost Line: The distance where volatiles remain solid (ices) and Gas Giants can form. Inside the Frost Line, solid planets and moons will be rockballs; outside, iceballs. Usually considered to be about 4.85×Earth-equivalent distance.
• Habitable Zone: The range of orbits where liquid water can exist on-surface. Sometimes called ‘Goldilocks Orbits’; usually considered to be 0.9 to 1.5×Earth-equivalent distance.
• Orbit (capitalized) or Traveller Orbit: Traveller nomenclature, an artifact of Book 6: Scouts where planetary orbits are in numbered zones based on the spacing of Sol System.
• “-bis Orbit”: Expansion of Traveller nomenclature; Orbits intermediate between the whole-number Traveller Orbits. From “System Generation/Adaptation from ACCRETE”, Freelance Traveller #78, Nov/Dec 2016.
• Torch Orbit: Ultra-close star-grazing orbit with an orbital period (year) of only a few days at most; the planet’s bright face will be red-hot. For Traveller purposes, inside an arbitrary boundary of around 0.25×Earth-equivalent distance (16×Earth’s solar flux). In Sol System, Orbit 1 (Mercury) is not a torch orbit, but Orbit 0 (hypothetical Vulcan) would be.
• Close Binary: A binary system whose two stars orbit each other at a distance of Traveller Orbit 1 or less (usually Orbit 0 or Close) in a low-eccentricity (near-circular) orbit.
• P-Type Binary Systems are those where the two stars are close together and all the planets orbit the pair; all planetary systems of Close Binaries will be of this type. The twin suns’ orbit around each other tends to be low- or zero-eccentricity; destabilizing orbital resonances between the suns create gaps in the planetary orbits and any asteroid belts. (These systems may also be called “Tatooine Systems”.)
• Very Large Gas Giant (VLGG): Gas Giant of more than 600 Earth masses (two Jupiter masses), the size where surface gravity (5-6 gees) makes fuel skimming impossible.
• Wide Binary: A binary whose stars are farther apart then a Close Binary; the separation averages 18 to 26 AU (Traveller Orbit 8 to 9) with an eccentricity averaging 0.5 (1½ Traveller Orbits between perihelion and aphelion distances).
• Far Binary: a Wide Binary so widely-spaced that the two gravity wells do not interfere with each other while still being gravitationally bound; “two stars flying in formation”, each with its own solo-star planetary system.
• S-Type Binary Systems are Wide Binary systems with planets orbiting one star or the other – effectively two planetary systems in one. Each stellar component can have its own system with its own mainworld – two mainworlds for the price of one. Might take a week to get from one to the other with a “Jump-0” or a couple weeks with a burn/turn/burn, but it doubles the number of Jump Destinations in a hex.

Minimum Planetary Orbits in P-Type Binary Systems

In Book 6: Scouts, the minimum planetary Orbit around both stars is two Orbits beyond the binary companion’s Orbit. (Count Close Orbit as if Orbit -1 or -0bis.)

This compares well with the Real-Life limit of around five times the companion’s apastron (maximum separation between the two suns). Since P-Type Close Binaries have low-eccentricity (near-circular) orbits, there is little or no difference between periastron (minimum separation) and apastron (maximum separation).

The two suns in an S-Type (Wide) Binary have more eccentric orbits; in this case, measure minimum P-type orbits from the Orbit Number at maximum separation.

Adjusting Maximum Planetary Orbits in S-Type Binary Systems

In Book 6: Scouts, the maximum planetary Orbit for a star in a wide binary is half the minimum/periastron distance of the other star. If a wide binary’s two components vary in size (which translates into spectral class), the larger will have a larger gravity well. Which will tend to extend its maximum planetary Orbit compared to the smaller. This is resolved in the following manner:

Each alphabetic spectral class has ten numeric sub-classes, numbered from 0 to 9. From largest/brightest to smallest/dimmest, F0 thru F9, G0 thru G9, K0 thru K9, M0 thru M9, Brown Dwarf. For every five sub-classes between the spectral class of the two stars, adjust the maximum planetary Orbit of the larger up by ½ (one “-bis Orbit”) and of the smaller down by the same amount.

Example: Hamilton’s Star (“Jump Destination: Geolan/Wasphome”, Freelance Traveller #79, Jan/Feb 2017) is a K4/K7 wide binary, distance at perihelion Orbit 8 (20 AU – about average for a wide binary). Straight Scouts maximum Orbit 4 (1.6 AU) for both components. Only three subclasses between K4 and K7, no adjustments. The K7v has moderate-eccentricity orbit for a companion, Orbit 8-9 (20-40 AU, again average for a wide binary).

Example: Cathai (“Jump Destination: Cathai”, Freelance Traveller #64/65, Apr/May 2015) is a K3/M6 wide binary, distance at perihelion Orbit 7 (10 AU). Straight Scouts maximum Orbit 3bis (1.3 AU) for both components. Thirteen sub-classes between K3 and M6 (rounded down to 10), adjust the K3’s max Orbit up by 1 and the M6’s down by 1. Result: K3v orange dwarf has max orbit of Orbit 4bis (2.2 AU), M6v red dwarf of Orbit 2bis (.85 AU). M6 red dwarf has low-eccentricity orbit for a companion, Orbit 7-7bis (10-16 AU).

“Breaking” an ACCRETE System into a Wide Binary

In Dole’s 1969 paper, ACCRETE generates planetary masses (in Earth-masses) and distance (in AU). This is normally diagrammed with the planets sized according to the cube root of their mass and orbital distances arranged on a logarithmic scale of 0.1 to 100 AU.

ACC 107 is an ACCRETE system from Fig.9 of Dole’s paper:

Table 1 and Figure 1 are presented in Modified ACCRETE format: distance from sun is on a grid of Traveller Orbit numbers; size is proportional to the cube root of the planet’s mass. Rockballs are solid, gas giants are outlined.

Measuring the Frost Line from the gas dwarf indicates a late G sun, with Planet III in the outer hab zone and IV well into the outer zone.

First, Planet VI (a “Triple Jupiter” VLGG) dominates the system. Since a VLGG’s gravity well clears out two Orbits inward and one outward, Planets V and VII would normally go away, their masses merged with the VLGG; Planets VIII and IX would probably also go away, as they now orbit at or outside the maximum Orbit for that size of star. This makes ACC107 a “Failed Binary”, as the VLGG is now the entire outer system (except for a possible iceball in Orbit 9).

With Planet V gone, the sun can be adjusted up to an early or mid-G, keeping VI behind the Frost Line, III in the inner habitable zone as the main world, and IV (the Super-Earth) around Mars-equivalent distance outside the habitable zone where its Dense atmosphere’s greenhouse effect could allow liquid water on-surface and possible settlement.

That is if ACC107 was a solo star. Now let's turn it into a wide binary with a red dwarf companion:

The easiest place to “break” the planetary system between the two is Traveller Orbit 7, the VLGG’s aphelion. Everything beyond this point goes to the companion star. To convert the Orbits to the new sun, subtract 8 (7 + 1) from the original Orbit, with any result less than 0 becoming Close. (7bis – 8 = Close Orbit, 8bis – 8 = Orbit 0bis, 9 – 8 = Orbit 1.)

This gives us the following system:

Now to calculate Sun B’s perihelion and maximum Orbit of each component’s planetary system.

• We already know the maximum size of Sun A’s system is Orbit 7 (10 AU), the aphelion of its farthest planet. According to straight Book 6: Scouts, this gives a minimum separation of Orbit 14 (1200 AU), a Far Binary.
• But A is larger than B with a deeper gravity well, so it would be able to hold onto a larger system than in straight Book 6: Scouts. Assuming A is a G4V yellow dwarf (noticeably larger than B), B’s minimum Orbit and maximum system size would be less than this. This would vary with B’s exact size/spectral sub-class:
• Sun A is G4, Sun B is M4 to M9: Sun B’s class/sub-class is 20 steps from A’s, rounded down. At an adjustment of one Orbit for 10 sub-classes, the unadjusted maximum planetary orbit of A’s system would be 7 -2 = Orbit 5. The minimum separation would be Orbit 10 (75-80 AU), and Sun B’s max planetary Orbit would be 5 – 2 = Orbit 3.
• Sun A is G4, Sun B is K9 to M3: Sun B’s class/sub-class is 15 steps from A’s, rounded down. At an adjustment of one Orbit for 10 sub-classes, the unadjusted max planetary orbit of A’s system would be 7 – 1bis = Orbit 5bis. The minimum separation would be Orbit 11 (150-160 AU), and Sun B’s max planetary Orbit would be 5 – 1bis = Orbit 3bis.
• Both the above separations exceed the minimum separation (from Scouts) of 7 + 2 = Orbit 9 (30-40 AU) and the Real-Life limit of 5× the distance of the outermost planet of each component (50 AU = Orbit 9bis). Eccentricity could add anywhere from a bis to 2 for the maximum separation.
• Sun B’s outermost Orbit of 1 is well within the maximum of 2bis to 3. Optionally, the former Planet V (the Gas Dwarf) could be restored to the system as a fourth planet of Sun B.

Result: a very plausible S-type G/M Binary whose A component is a Failed Binary with a Sol-type inner system and whose B companion is a plausible standalone red dwarf system. At 8g surface gravity, A’s only Gas Giant is too large for fuel-skimming and B’s Hot Neptune is too far away and too close to its sun. So despite having two GGs, the system would be cataloged as “No (skimmable) Gas Giants”.