<p>I think you may have given each star too many planets.  Alpha Centauri AB is a fairly close system, with a semimajor axis of 23 AU and an eccentricity of 0.52, which means the stars approach to within 11 AU of each other.  Planets aren't stable unless the binary star surrounding them is more than 3-4 times more distant, so I think your outer planets may be in trouble.  If these systems are space roughly like our own, I'd think each star could have no more than about five planets, and that would be stretching it.</p>

CC BY-SA 4.0
2021-02-18T23:59:32.490Z
This is an interesting answer, but can you cite or link to some sources that support your facts? For example, where does "more than 3-4 times" come from? 23 AU and 0.52? *Thanks!*
uhoh
CC BY-SA 4.0
2021-02-19T16:34:29.217Z
I have read several sources that gave a 1/5 distance as a maximum orbital distance for each star. After doing a hill sphere calculation for each I came to a distance which was surprisingly similar to that rough value. Then I added each planet using a mutual Hill Radii approach based on their mass and distance. Looking at one of the sources I listed. They state that a tight orbital setup would be around 20 hill sphere radii apart from one another. I always felt like there were too many planets but I haven't seen any conditions that say it cannot happen.
Markitect
CC BY-SA 4.0
2021-02-19T23:48:51.250Z
I'm going by the work of Robert S. Harrington at the Naval Observatory: Harrington, R.S. 1977. [Planetary orbits in binary stars.](http://adsabs.harvard.edu/full/1977AJ.....82..753H) Astron. J. 753-756.
bpl1960
CC BY-SA 4.0
2021-02-20T01:57:11.863Z
@Markitect it looks like a reply to your comment was accidentally posted in the wrong place. It says "I'm going by the work of Robert S. Harrington at the Naval Observatory: Harrington, R.S. 1977.  [Planetary orbits in binary stars.](http://adsabs.harvard.edu/full/1977AJ.....82..753H)  Astron. J. 753-756."
uhoh
CC BY-SA 4.0
2021-02-18T18:33:20.527Z
2021-02-18T18:33:20.527Z
bpl1960
<p>I originally posted this on the World Building SE, but I was suggested to post it here for a better answer. 
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.</p>

<h2>Attempt:</h2>

<ul>
<li>aCen A Planets
<a href="https://i.sstatic.net/Bqe3r.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Bqe3r.png" alt="Planet Setup for aCenA"></a></li>
<li>aCen B Planets
<a href="https://i.sstatic.net/oBJ3G.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/oBJ3G.png" alt="Planet Setup for aCenB"></a></li>
</ul>

<p>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.</p>

<p>Here are some papers that I have looked at for this:
<a href="http://adsabs.harvard.edu/full/1997AJ....113.1445W" rel="nofollow noreferrer">http://adsabs.harvard.edu/full/1997AJ....113.1445W</a>
<a href="https://arxiv.org/pdf/1801.06131" rel="nofollow noreferrer">https://arxiv.org/pdf/1801.06131</a>
<a href="https://core.ac.uk/download/pdf/25201586.pdf" rel="nofollow noreferrer">https://core.ac.uk/download/pdf/25201586.pdf</a></p>

<p>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.</p>

<p><strong>Question: Is the planetary spacing stable enough to host planets on Gigayear timescales?</strong> 
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.</p>

<p>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. <em>(There is an error in the image in Yellow that shows 148.623 and Eccentricity of 0.0910)</em>. 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).</p>

CC BY-SA 4.0
2020-03-31T06:19:40.027Z
The phrase "three body problem" comes to mind, except you've got a lot more than three bodies here. I suspect that the only way to answer this would be to simulate it, but I'm not an astronomer.
nick012000
CC BY-SA 4.0
2020-03-31T12:04:52.233Z
That's what I was thinking too; even the Mutual Hill Radii method is just a concept as far as I understand. And as for orbital resonance, it makes less sense to me because I've seen several conflicting sources on it.
Markitect
CC BY-SA 4.0
2021-02-19T16:35:42.943Z
I have a feeling I may need to rethink my orbits if this proposed planet around aCen A that was just discovered turns out to be true.
Markitect
<exoplanet><orbital-mechanics><orbital-elements><planetary-formation><orbital-resonance>
Is this a potential planetary setup for the Alpha Centauri System?
Markitect
# Is this a potential planetary setup for the Alpha Centauri System?

(Asked by: username_0 on 2020-03-30)

I originally posted this on the World Building SE, but I was suggested to post it here for a better answer.
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](https://i.sstatic.net/Bqe3r.png)](https://i.sstatic.net/Bqe3r.png)
* aCen B Planets
  [![Planet Setup for aCenB](https://i.sstatic.net/oBJ3G.png)](https://i.sstatic.net/oBJ3G.png)

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).

**Tags:** exoplanet, orbital-mechanics, orbital-elements, planetary-formation, orbital-resonance

> **Comments:**
> **username_1**: The phrase "three body problem" comes to mind, except you've got a lot more than three bodies here. I suspect that the only way to answer this would be to simulate it, but I'm not an astronomer.  
> **username_0**: That's what I was thinking too; even the Mutual Hill Radii method is just a concept as far as I understand. And as for orbital resonance, it makes less sense to me because I've seen several conflicting sources on it.  
> **username_0**: I have a feeling I may need to rethink my orbits if this proposed planet around aCen A that was just discovered turns out to be true.  

---

## 1 answers

### Answer by username_2 on 2021-02-18. Score: 1

I think you may have given each star too many planets. Alpha Centauri AB is a fairly close system, with a semimajor axis of 23 AU and an eccentricity of 0.52, which means the stars approach to within 11 AU of each other. Planets aren't stable unless the binary star surrounding them is more than 3-4 times more distant, so I think your outer planets may be in trouble. If these systems are space roughly like our own, I'd think each star could have no more than about five planets, and that would be stretching it.

> **Comments:**
> **username_3**: This is an interesting answer, but can you cite or link to some sources that support your facts? For example, where does "more than 3-4 times" come from? 23 AU and 0.52? *Thanks!*  
> **username_0**: I have read several sources that gave a 1/5 distance as a maximum orbital distance for each star. After doing a hill sphere calculation for each I came to a distance which was surprisingly similar to that rough value. Then I added each planet using a mutual Hill Radii approach based on their mass and distance. Looking at one of the sources I listed. They state that a tight orbital setup would be around 20 hill sphere radii apart from one another. I always felt like there were too many planets but I haven't seen any conditions that say it cannot happen.  
> **username_2**: I'm going by the work of Robert S. Harrington at the Naval Observatory: Harrington, R.S. 1977. [Planetary orbits in binary stars.](http://adsabs.harvard.edu/full/1977AJ.....82..753H) Astron. J. 753-756.  
> **username_3**: @username_0 it looks like a reply to your comment was accidentally posted in the wrong place. It says "I'm going by the work of Robert S. Harrington at the Naval Observatory: Harrington, R.S. 1977.  [Planetary orbits in binary stars.](http://adsabs.harvard.edu/full/1977AJ.....82..753H)  Astron. J. 753-756."  

---

