Binary Star System Build - Alpha Centauri

I'm not sure if this site or Astronomy would be better, but I figured I would try here instead. I am attempting to create a [semi]plausible star system in Alpha Centauri for a series. The system was originally intended to have 1 habitable planet per star, but after my first couple of attempts I noticed that it might be possible to get at least 3 planets to be habitable. The latest attempt actually shows 5 potentially habitable planets (2 of which are a binary[That is another SE question]). Ultimately, I would like this to be the case as it allows a much more diverse universe for the series.

Attempt:

• aCen A Planets
• aCen B Planets

I don't have access to, or knowledge how to use, any form of software like Universe Sandbox. I have read several reports on planet orbits and I think I did an "ok" job with this.

My main concern is that the planets might orbit too closely. I have attempted to find a formula (that I could understand) that could aid in spacing the planets. The nearest I could manage is using the Mutual Hill Radii. There are conflicting reports where one says that 10 - 12 MHR (Delta-H) is good or a tightly packed system. Earth and Venus have around a 25 MHR value. One of the reports that I linked mentioned up to 25 MHR for aCenA, but it also shows several other numbers and after trying to comprehend everything my brain reached orbital velocity.

Question: Is the planetary spacing stable enough to host planets on Gigayear timescales? They don't necessarily need to be able to have spawned life, but they should be able to support life with little to no human intervention.

Note and Bonus, aCen V is a binary planet that orbits with a Semi-Major axis of 750,589km with an eccentricity of 0.01204. (There is an error in the image in Yellow that shows 148.623 and Eccentricity of 0.0910). The inclination should be 0 as both planets should be on the same plane. Last note: The Semi-Major Axis distance is in Megameters (1 million meters).

• Oh, wow. Brain meltdown too. The most recent article is the one on arxiv - 2018, the other two are actually the same from 1997. I'd trust the more recent one, both of them rely on computer simulation and 20 years+ makes an eternity in terms of computing power. Second, I'd suggest you to post the question in Astronomy too - the Q is quite precise, admits very little (if at all) handwaving and there are better chances the guys there are either better prepared to answer or know articles that bear relevance. Not saying the Q is inappropriate on WB.SE, just that chances are better on Astronomy. Mar 27, 2020 at 6:23
• I'm just using Titian-Bode's law. I know it's pseudoscience, but it gives spacing that looks vaguely Solar-system-like. Apr 26, 2020 at 20:08
• Those outer two large planets around A would definitely be unstable, unless you get them into some self-stabilizing resonance with the stars themselves. Your planet a-viii is 470Mm from A, it could potentially get as close as 1210Mm from B, at B's closest approach. At this time the gravitational influence from B is a full 12.5% as much as gravity from A. This is problematic even on the short term, much less gigayear scales. Mar 13, 2021 at 12:15
• @PcMan the outer planet in each system is on a 15:1 and 20:1 orbital resonance with the orbit of the binary stars. In one of the papers I looked at they mentioned that the 15:1 and 20:1 resonances could be stable. I initially started with these orbits then added the planets going inwards. The part I found interesting with that claim was that it kept the stars withing the stable hill sphere of each star. Mar 14, 2021 at 16:39
• @Markitect yikes. I must have miscalculated. Yes, if in resonance, with the right tuning, they will not only be stable but quite solidly locked in. That does change everything. (does odd integer resonace work right? I vaguely recall that it needs to be even, for any ratio > 3:1 )? Mar 14, 2021 at 17:52

I am also trying to figure out plausibility for planets in the Alpha Centauri system for a sci fi game design... I'll share some of my initial research.

One thing about the system is how binary stars interact. Centauri actually has 3 stars, but only A and B happen to come quite close to each other. This causes major disruptions to all the orbiting bodies except those closest to each star:

From https://en.wikipedia.org/wiki/Habitability_of_binary_star_systems "In non-circumbinary planets, if a planet's distance to its primary exceeds about one fifth of the closest approach of the other star, orbital stability is not guaranteed. Studies of Alpha Centauri, the nearest star system to the Sun, suggested that binaries need not be discounted in the search for habitable planets. Centauri A and B have an 11 au distance at closest approach (23 au mean), and both have stable habitable zones. A study of long-term orbital stability for simulated planets within the system shows that planets within approximately three au of either star may remain stable (i.e. the semi-major axis deviating by less than 5%). The habitable zone for Alpha Centauri A extends, conservatively estimated, from 1.37 to 1.76 au[2] and that of Alpha Centauri B from 0.77 to 1.14 au[2]—well within the stable region in both cases."

That's good news for the habitable planets, which I care most about for my game.

But you've got 8 planets for aCenA and 7 for B, and your outer planets would surely get knocked out of stable orbits about every 80 years:

From https://en.wikipedia.org/wiki/Alpha_Centauri "Alpha Centauri A has 1.1 times the mass and 1.519 times the luminosity of the Sun, while Alpha Centauri B is smaller and cooler, at 0.907 times the Sun's mass and 0.445 times its luminosity.[16] The pair orbit around a common centre with an orbital period of 79.91 years.[17] Their elliptical orbit is eccentric, so that the distance between A and B varies from 35.6 AU (astronomical units), or about the distance between Pluto and the Sun, to 11.2 AU, or about the distance between Saturn and the Sun." "Alpha Centauri C is about 13,000 AU away from Alpha Centauri AB." [wont disrupt A or B’s planets]

So your inner planets would be stable, but not the outer ones. Luckily the habitable ones should be stable! Although they may get bombarded by meteorites when the stars get close and things get mixed up a lot.

I don't know if what I have to say will help you or if you already know it.

I have the impression that the minimum stable spacing of planetary orbits depends on the masses of the star and the planets and the distances of the orbits..

If the mass of the star is changed, it may change the minimum stable spacing of the planets.

If the planets are less massive, they should be able to have closer stable orbits. For example, tiny asteroids can have orbits with semi major axes which are very close. Hundreds and thousands of asteroids can orbit in a region where only one planet could have a stable orbit.

You also have to consider the width of the circumstellar habitable zones around Alpha Centauri A and Alpha Centauri B.

There have been many attempts in the last 60 years to calculate inner or outer edges, or both, of the Sun's habitable zone. If we know the inner and outer edges, and width, of the Sun's habitable zone, we can multiply or divide it by another star's luminosity relative to the Sun to get the size of that star's habitable zone.

Here is a link to a table with various scientific estimates of the inner or outer edges, or both, of the Sun's habitable zone.

https://en.wikipedia.org/wiki/Circumstellar_habitable_zone#Solar_System_estimates[1]

Note how greatly some estimates and calculations vary from others.

The estimate by Dole in 1964 was for planets habitable for humans. I suspect that many other estimates in the list are for planets habitable by carbon based liquid water using life forms, and that some of the inner and outer limits in some estimates may require atmospheres that humans could not breath in to get liquid water temperatures. That is a factor which science fiction writers should research.

So obviously researching the various estimates and calculations and deciding which ones seem most plausible may be a good idea for some writers.

By now astronomers have discovered a number of stars systems with two or more detected planets in stable orbits.

According to one table, the smallest semi-major axis difference between the orbits of consecutive exoplanets is 0.0016 AU or 240,000 kilometers or 149,129 miles, between Kepler-70b and Kepler-70c.

https://en.wikipedia.org/wiki/List_of_exoplanet_extremes#Orbital_characteristics[2]

There is so some evidence for a third planet in the Kepler-70 system, orbiting between B and c, which would make the difference between orbits even smaller, if confirmed. But:

If these planets exist, then the orbits of Kepler-70b and Kepler-70c have 7:10 orbital resonance and have the closest approach between planets of any known planetary system. However, later research3 suggested that what had been detected was not in fact the reflection of light from exoplanets, but star pulsation "visible beyond the cut-off frequency of the star." Further research8 indicated that star pulsation modes were indeed the more likely explanation for the signals found in 2011, and that the two exoplanets probably did not exist.

https://en.wikipedia.org/wiki/Kepler-70[4]

the smallest semi-major axis difference between the orbits of consecutive exoplanets is about 11 percent between Kepler-36b and Kepler-36c. But the absolute distance between their orbits is larger than in Kepler-70.

Kepler-36b and c have semi-major axes of 0.1153 AU and 0.1283 AU respectively, c is 11% further from star than b.

https://en.wikipedia.org/wiki/List_of_exoplanet_extremes#Orbital_characteristics[2]

The difference between the orbits of b and c is 0.013 AU or 1,944,772.3 kilometers, or 1,208,425.5 miles.

among exoplanets known to orbit in the conservative habitable zones of their stars, the smallest differences in orbits are in TRAPPIST-1 d, e, f, & g.

https://en.wikipedia.org/wiki/List_of_potentially_habitable_exoplanets[5]

The orbits of the TRAPPIST-1 planetary system are very flat and compact. All seven of TRAPPIST-1's planets orbit much closer than Mercury orbits the Sun. Except for b, they orbit farther than the Galilean satellites do around Jupiter,[41] but closer than most of the other moons of Jupiter. The distance between the orbits of b and c is only 1.6 times the distance between the Earth and the Moon. The planets should appear prominently in each other's skies, in some cases appearing several times larger than the Moon appears from Earth.[40] A year on the closest planet passes in only 1.5 Earth days, while the seventh planet's year passes in only 18.8 days.[38][35]

https://en.wikipedia.org/wiki/TRAPPIST-1[6]

TRAPPIST-1d has an orbit with a semi-major axis of 0.02228038 AU, or 3,330,000 kilometers, or 2,069,166 miles.

TRAPPIST-1e has an orbit with a semi-major axis of 0.02928285 AU, or 4.380,000 kilometers, or 2,721,605 miles. Its orbit is 1,050,000 kilometers wider than that of d, or 31.5 percent wider.

TRAPPIST-1f has an orbit with a semi-major axis of 0.03853361 AU, or 5,760,000 kilometers, or 3,769,098 miles. Its orbit is 1,380,000 kilometers wider than that of e, or 31.5 percent wider.

TRAPPIST-1g has an orbit with a semi-major axis of 0.04687692 AU, or 7,010,000 kilometers, or 4,355,812 miles. Its orbit is 1,250,000 kilometers wider than that of f, or 21.7 percent wider.

https://en.wikipedia.org/wiki/TRAPPIST-1[6]

Of course the star TRAPPIST-1 has a much different mass than that of Alpha Centauri A or Alpha Centauri B, and that may affect how closely it is possible to space planetary orbits.

The PlanetPlanet blog has a section, the Ultimate Solar System, about imaginary solar systems with large numbers of planets in the habitable zones.

https://planetplanet.net/the-ultimate-solar-system/[7]

In one post it is suggested that 4 planetary orbits would fit into the habitable zone of a star if all planets orbited in the same direction, while 8 planetary orbits would fit in the habitable zone if the planets alternated their orbital directions between prograde and retrograde.