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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 Planet Setup for aCenA
  • aCen B Planets Planet Setup for aCenB

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.

Here are some papers that I have looked at for this: http://adsabs.harvard.edu/full/1997AJ....113.1445W https://arxiv.org/pdf/1801.06131 https://core.ac.uk/download/pdf/25201586.pdf

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).

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  • $\begingroup$ 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. $\endgroup$ – Adrian Colomitchi Mar 27 at 6:23
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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_estimates1

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_characteristics2

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-704

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_characteristics2

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_exoplanets5

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-16

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 e, or 21.7 percent wider.

https://en.wikipedia.org/wiki/TRAPPIST-16

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.

https://planetplanet.net/2017/05/01/the-ultimate-retrograde-solar-system/8

I note that one planet has been confirmed for the Alpha Centauri star system, orbiting Alpha Centauri C or Proximal Centauri. You don't have to worry about such a distant planet messing up the orbits of planets orbiting A and B.

However, it is always possible that planets might be discovered orbiting Alpha Centauri A or B that would mess up the orbits of your planets.

https://en.wikipedia.org/wiki/Alpha_Centauri#Controversial_and_hypothetical_planets3

I have heard of computer orbital simulators to calculate the orbits of spacecraft and of astronomical bodies. But I don't know if there are any available to the public that can calculate whether orbits will be stable for billions of years.

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  • $\begingroup$ Thanks for the answer, lots of good information on those other systems. The Hill Sphere Radii I used involves the mass of the star and a planet plus the succeeding planet. So it fits with what you described. As for the stable range, many reports say it is around 3.5 AU; when I did a hill sphere for each star with the other star I got a range that was very similar to that. Basically, at their closest approach if a planet is beyond that 3.5 AU range then the other star will start to pull on it as it would be within its hill sphere. Both habitable zones are well within this range limit. $\endgroup$ – Markitect Mar 27 at 20:36

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