<blockquote>
  <p>What I'm asking here is that can a large system of 6 or 7 rogue planets and other planetary bodies orbit each other and remain stable; basically like a tiny open cluster or huge multiple star system, just comprised of planets instead of stars?</p>
</blockquote>

<h2>Sure! (but...)</h2>

<p><s>If you have a half-dozen bodies in a group, and the total energy (kinetic plus potential) is less than the energy it would take to move any of them to infinity, then they are a gravitationally bound system and they'll stay together forever.</s>†</p>

<p><sup>†</sup><strong>This is probably not true</strong>; @RobJeffries' comments (<a href="https://astronomy.stackexchange.com/questions/29592/can-rogue-nomad-planets-and-other-starless-planetary-bodies-orbit-each-other-in/29594?noredirect=1#comment53527_29594">1</a>, <a href="https://astronomy.stackexchange.com/questions/29592/can-rogue-nomad-planets-and-other-starless-planetary-bodies-orbit-each-other-in/29594?noredirect=1#comment53539_29594">2</a>) bring up <em>pairings</em>, and so even in a situation where moving "any one of them" was energetically possible, it could might for example be possible for a bound pair. I'll update this soon...</p>

<p>An extreme example would be a cluster that are touching and at rest, a second extreme example would be that cluster given a bit of a "kick" to start it jostling.</p>

<p>A good question might be "Given a half-dozen bodies of equal mass <span class="math-container">$m$</span> what is the farthest one can be from it's nearest neighbor while the system is still energetically bound?" A follow-up might be the same except remove the "equal mass <span class="math-container">$m$</span>" part. I don't know the answer to that question, perhaps someone else will post an answer here with it.</p>

<p>Without a "Sun" or particularly large central body, their motion will be chaotic, and any apparent organization (pairings or higher) will sooner or later be disturbed by another body.</p>

<p>Actually there is chaos in (probably) all real-work n-body system, but in cases like our solar system this would take quite a long time to show up.</p>

<p>If you have a particular configuration in mind, you can calculate if the system is bound or not with a little math. Here the total energy <span class="math-container">$E$</span> is the sum of potential energy <span class="math-container">$U$</span> and kinetic energy <span class="math-container">$T$</span>:</p>

<p><span class="math-container">$$E = U + T = \sum_{i\neq j} -G\frac{m_i m_j}{|\mathbf{r_i}-\mathbf{r_j}|} + \sum_{i} \frac{1}{2}m_i v_i^2 $$</span></p>

<p>Where <span class="math-container">$|\mathbf{r_i}-\mathbf{r_j}|$</span> is the distance between each pair of objects with masses <span class="math-container">$m_i$</span> and <span class="math-container">$m_j$</span>, <span class="math-container">$v_i^2$</span> is the square of the speed, and <span class="math-container">$G$</span> is the <a href="https://en.wikipedia.org/wiki/Gravitational_constant" rel="nofollow noreferrer">Gravitatinal constant</a>.</p>

<h2>but...</h2>

<p>Systems are never isolated in the real world, so for example
 - another body could pass by and disturb the system and eject one or more members. 
 - two bodies could collied and exchange mass, momentum, and energy, allowing one or more <em>fragment</em> to escape.
 - other things...</p>

CC BY-SA 4.0
2019-02-14T20:35:38.903Z
What do the variables represent in the equation?
Nirvana
CC BY-SA 4.0
2019-02-14T22:50:31.497Z
@Nirvana actually I was going to write a longer answer then ran out of time yesterday. I'll add a description now, then come back and add a few simulations and references tomorrow. Great question by the way!
uhoh
CC BY-SA 4.0
2019-02-15T07:14:15.200Z
"they are a gravitationally bound system and they'll stay together forever." This is incorrect. This is not how a small group of objects behave unless they are arranged in a specific hierarchical way.
ProfRob
CC BY-SA 4.0
2019-02-15T15:34:03.160Z
@RobJeffries Please double check the whole sentence. "f you have a half-dozen bodies in a group, *and the total energy (kinetic plus potential) is less than the energy it would take to move any of them to infinity*..."
uhoh
CC BY-SA 4.0
2019-02-15T18:27:16.360Z
What happens is that two of the objects form a hard binary and the others are given sufficient energy to escape. This happens very quickly in a small, non-hierarchical group. For example, Leigh et al. (2018) https://arxiv.org/abs/1603.07731 show that most small groups of 6 bodies are disrupted in 10,000 crossing times. Putting real numbers in - 6 Jupiters with an au of each other, disrupt in 60,000 years. Even for systems with zero initial kinetic energy.
ProfRob
CC BY-SA 4.0
2019-02-16T00:45:16.557Z
@RobJeffries **Yes you are of course right!** I was practicing conservation of energy without a license. I've struck through the offending sentence, linked to your comments, and I'll get back to work improving this answer as soon as I can. I've also asked the OP to un-accept it. In the mean time, please consider posting an additional answer, I think that paper really hits the nail on the head!
uhoh
CC BY-SA 4.0
2019-02-14T06:58:56.820Z
2019-02-16T00:28:50.503Z
2019-02-16T00:28:50.503Z
uhoh
<p>One of the main hypotheses for the formation of rogue planets is ejection from a preexisting planetary system. This is an unlikely scenario for the formation of a <em>cluster</em> of rogue planets, because it doesn't seem feasible for a whole bunch of bodies to be ejected together and remain in a stable system. If multiple planets were ejected from a planetary system, I would expect them to exit randomly and separately.</p>

<p>That said, a couple sub-brown dwarfs have been observed to host what may be protoplanetary disks (although that term may not be applicable in these cases). The important objects here are <a href="https://en.wikipedia.org/wiki/Cha_110913-773444" rel="nofollow noreferrer">Cha 110913-773444</a> (<span class="math-container">$\sim8M_J$</span>) and <a href="https://en.wikipedia.org/wiki/OTS_44" rel="nofollow noreferrer">OTS 44</a> (<span class="math-container">$\sim11M_J$</span>). These objects have not been classified yet; they could be considered rogue planets or sub-brown dwarfs (or even brown dwarfs, honestly). Assuming the normal processes active in protoplanetary disks take place - collisions, accretion and the like - then in the future, additional bodies could form.</p>

<p>OTS 44 is thought to have a disk of around 30 Earth masses (<a href="http://adsabs.harvard.edu/abs/2013A&amp;A...558L...7J" rel="nofollow noreferrer">Joergens et al. 2013</a>); depending on the efficiency of planet formation, we might see bodies similar in mass to terrestrial planets (note that this also depends on disk composition; much of it is likely to be hydrogen and helium, not silicates). Giant planets seem unlikely, as the disks mass is comparable to those of Uranus and Neptune, within a factor of two, and it is highly unlikely that the entire disk would coalesce into one planet.</p>

<p>If a rogue planet formed <em>in situ</em>, rather than being ejected from a system, we do have a different picture to consider. In this case, it seems more likely for binary rogue planets to form. At this point, of course, the label "sub-brown dwarf" is more appropriate than "rogue planet".</p>

CC BY-SA 4.0
2019-02-14T06:38:53.660Z
2019-02-14T06:38:53.660Z
HDE 226868
<p><a href="https://en.wikipedia.org/wiki/Rogue_planet" rel="nofollow noreferrer">Nomad planets</a> (also called planemos or rogues planets) which drift in space without  a star or substellar object to orbit. The majority of such planets we have discovered are gas planets with thick atmospheres and no landmass, although some of them could be frozen deserts with rocky surfaces like Earth's. </p>

<p>Most nomad planets we have found are alone/solitary, and do not orbit any other companion objects. We have only discovered <strong>1</strong> (as in 1.0) binary planemo called <a href="https://www.centauri-dreams.org/2017/07/12/a-binary-rogue-planet/" rel="nofollow noreferrer">2MASS J11193254–1137466</a>.</p>

<p>What I'm asking here is that can a large system of 6 or 7 rogue planets and other planetary bodies orbit each other and remain stable; basically like a tiny open cluster or huge multiple star system, just comprised of planets instead of stars?</p>

CC BY-SA 4.0
2019-02-14T17:41:48.297Z
Are you asking *is such a theoretical system stable* or are you asking *do such systems come together and exist  out there*.
Fattie
CC BY-SA 4.0
2019-02-14T20:22:13.417Z
@Fattie I am asking Option A "Is such a theoretical system stable?" to answer your question.
Nirvana
CC BY-SA 4.0
2019-02-14T20:33:05.527Z
gotchya.  the answer is "generally speaking yes".   but the math is too hard for us and our computers to really work out.
Fattie
CC BY-SA 4.0
2019-02-16T00:38:46.270Z
Hi @Nirvana it looks like I need to do some more work on my answer, see the comments below it and the edit. I recommend you un-accept my answer and wait for me to do some more work on it and to see if still other answers are posted. Once again, a *great question!*
uhoh
<rogue-planet>
Can rogue/nomad planets and other starless planetary bodies orbit each other in a stable system?
Nirvana
# Can rogue/nomad planets and other starless planetary bodies orbit each other in a stable system?

(Asked by: username_0 on 2019-02-14)

[Nomad planets](https://en.wikipedia.org/wiki/Rogue_planet) (also called planemos or rogues planets) which drift in space without a star or substellar object to orbit. The majority of such planets we have discovered are gas planets with thick atmospheres and no landmass, although some of them could be frozen deserts with rocky surfaces like Earth's.

Most nomad planets we have found are alone/solitary, and do not orbit any other companion objects. We have only discovered **1** (as in 1.0) binary planemo called [2MASS J11193254–1137466](https://www.centauri-dreams.org/2017/07/12/a-binary-rogue-planet/).

What I'm asking here is that can a large system of 6 or 7 rogue planets and other planetary bodies orbit each other and remain stable; basically like a tiny open cluster or huge multiple star system, just comprised of planets instead of stars?

**Tags:** rogue-planet
> **Comments:**
> **username_1**: Are you asking *is such a theoretical system stable* or are you asking *do such systems come together and exist  out there*.  
> **username_0**: @Fattie I am asking Option A "Is such a theoretical system stable?" to answer your question.  
> **username_1**: gotchya.  the answer is "generally speaking yes".   but the math is too hard for us and our computers to really work out.  
> **username_2**: Hi @Nirvana it looks like I need to do some more work on my answer, see the comments below it and the edit. I recommend you un-accept my answer and wait for me to do some more work on it and to see if still other answers are posted. Once again, a *great question!*  

---

## 2 answers

### Answer by username_2 on 2019-02-14. Score: 2 | Accepted answer

> What I'm asking here is that can a large system of 6 or 7 rogue planets and other planetary bodies orbit each other and remain stable; basically like a tiny open cluster or huge multiple star system, just comprised of planets instead of stars?

## Sure! (but...)

~~If you have a half-dozen bodies in a group, and the total energy (kinetic plus potential) is less than the energy it would take to move any of them to infinity, then they are a gravitationally bound system and they'll stay together forever.~~†

†**This is probably not true**; @RobJeffries' comments ([1](https://astronomy.stackexchange.com/questions/29592/can-rogue-nomad-planets-and-other-starless-planetary-bodies-orbit-each-other-in/29594?noredirect=1#comment53527_29594), [2](https://astronomy.stackexchange.com/questions/29592/can-rogue-nomad-planets-and-other-starless-planetary-bodies-orbit-each-other-in/29594?noredirect=1#comment53539_29594)) bring up *pairings*, and so even in a situation where moving "any one of them" was energetically possible, it could might for example be possible for a bound pair. I'll update this soon...

An extreme example would be a cluster that are touching and at rest, a second extreme example would be that cluster given a bit of a "kick" to start it jostling.

A good question might be "Given a half-dozen bodies of equal mass $m$ what is the farthest one can be from it's nearest neighbor while the system is still energetically bound?" A follow-up might be the same except remove the "equal mass $m$" part. I don't know the answer to that question, perhaps someone else will post an answer here with it.

Without a "Sun" or particularly large central body, their motion will be chaotic, and any apparent organization (pairings or higher) will sooner or later be disturbed by another body.

Actually there is chaos in (probably) all real-work n-body system, but in cases like our solar system this would take quite a long time to show up.

If you have a particular configuration in mind, you can calculate if the system is bound or not with a little math. Here the total energy $E$ is the sum of potential energy $U$ and kinetic energy $T$:

$$E = U + T = \sum\_{i\neq j} -G\frac{m\_i m\_j}{|\mathbf{r\_i}-\mathbf{r\_j}|} + \sum\_{i} \frac{1}{2}m\_i v\_i^2 $$

Where $|\mathbf{r\_i}-\mathbf{r\_j}|$ is the distance between each pair of objects with masses $m\_i$ and $m\_j$, $v\_i^2$ is the square of the speed, and $G$ is the [Gravitatinal constant](https://en.wikipedia.org/wiki/Gravitational_constant).

## but...

Systems are never isolated in the real world, so for example
- another body could pass by and disturb the system and eject one or more members.
- two bodies could collied and exchange mass, momentum, and energy, allowing one or more *fragment* to escape.
- other things...

> **Comments:**
> **username_0**: What do the variables represent in the equation?  
> **username_2**: @Nirvana actually I was going to write a longer answer then ran out of time yesterday. I'll add a description now, then come back and add a few simulations and references tomorrow. Great question by the way!  
> **username_3**: "they are a gravitationally bound system and they'll stay together forever." This is incorrect. This is not how a small group of objects behave unless they are arranged in a specific hierarchical way.  
> **username_2**: @RobJeffries Please double check the whole sentence. "f you have a half-dozen bodies in a group, *and the total energy (kinetic plus potential) is less than the energy it would take to move any of them to infinity*..."  
> **username_3**: What happens is that two of the objects form a hard binary and the others are given sufficient energy to escape. This happens very quickly in a small, non-hierarchical group. For example, Leigh et al. (2018) https://arxiv.org/abs/1603.07731 show that most small groups of 6 bodies are disrupted in 10,000 crossing times. Putting real numbers in - 6 Jupiters with an au of each other, disrupt in 60,000 years. Even for systems with zero initial kinetic energy.  
> **username_2**: @RobJeffries **Yes you are of course right!** I was practicing conservation of energy without a license. I've struck through the offending sentence, linked to your comments, and I'll get back to work improving this answer as soon as I can. I've also asked the OP to un-accept it. In the mean time, please consider posting an additional answer, I think that paper really hits the nail on the head!  

---

### Answer by username_4 on 2019-02-14. Score: 2

One of the main hypotheses for the formation of rogue planets is ejection from a preexisting planetary system. This is an unlikely scenario for the formation of a *cluster* of rogue planets, because it doesn't seem feasible for a whole bunch of bodies to be ejected together and remain in a stable system. If multiple planets were ejected from a planetary system, I would expect them to exit randomly and separately.

That said, a couple sub-brown dwarfs have been observed to host what may be protoplanetary disks (although that term may not be applicable in these cases). The important objects here are [Cha 110913-773444](https://en.wikipedia.org/wiki/Cha_110913-773444) ($\sim8M\_J$) and [OTS 44](https://en.wikipedia.org/wiki/OTS_44) ($\sim11M\_J$). These objects have not been classified yet; they could be considered rogue planets or sub-brown dwarfs (or even brown dwarfs, honestly). Assuming the normal processes active in protoplanetary disks take place - collisions, accretion and the like - then in the future, additional bodies could form.

OTS 44 is thought to have a disk of around 30 Earth masses ([Joergens et al. 2013](http://adsabs.harvard.edu/abs/2013A&A...558L...7J)); depending on the efficiency of planet formation, we might see bodies similar in mass to terrestrial planets (note that this also depends on disk composition; much of it is likely to be hydrogen and helium, not silicates). Giant planets seem unlikely, as the disks mass is comparable to those of Uranus and Neptune, within a factor of two, and it is highly unlikely that the entire disk would coalesce into one planet.

If a rogue planet formed *in situ*, rather than being ejected from a system, we do have a different picture to consider. In this case, it seems more likely for binary rogue planets to form. At this point, of course, the label "sub-brown dwarf" is more appropriate than "rogue planet".


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