<p>Thanks to <a href="https://astronomy.stackexchange.com/a/2333/19829">this answer</a> linked by antispinwards I learned that such system most probably <strong>would not be stable</strong>, as I calculated it with proximity to upper limit of Hill sphere for each body.</p>

<p>But, if instead, I would have taken distances closer to 1/3-1/2 Hill sphere, <strong>it could be theoretically feasible.</strong></p>

<blockquote>
  <p>The orbit of a satellite's satellite will be stable if it's deep
  enough inside the Hill sphere, within the so-called true region of
  stability. The limits are a bit fuzzy, but the true region of
  stability is typically the lower 1/3 to 1/2 of the Hill sphere.</p>
</blockquote>

<p>On a personal note, if it's so, it surprises me this type of systems are not more pondered on and discussed, with maybe even some probabilities calculated. As it could have a great impact on thinking about abundance of potentially habitable worlds in the universe (imagine how great a number of earth-like satellites could live in such a system in the habitable zone of its host star (it being short-lived on cosmological time-scale notwithstanding)). </p>

CC BY-SA 4.0
2020-05-19T11:01:29.380Z
Probabilities of systems are calculated - from disk evolution models. Not by a-priori assumptions of what they should look like. A system like the one described here is not a likely solution by a huge margin of any reasonable models based on physical models
planetmaker
CC BY-SA 4.0
2020-05-19T12:22:52.190Z
Is how _reasonable_ these models are measured against vastness of space and multitude of systems? I know the chance is small, but faced with enormity of space, is it orders of magnitude too small?
z33k
CC BY-SA 4.0
2020-05-19T12:58:52.923Z
IMHO yes. Maybe not as unlikely as a stone jumping up and the room getting cooler, but it goes in that direction. It get's very difficult to reason wrt how planets form in a disk around a star - and it needs all the matter to form such planet within a larger portion of the disk. Given that, there never is enough material for another planet where another forms, or they would eventually collide - especially not given your cascade. The existing bigger moons generally are what roughly can form within the hill sphere, given available material, formed due to catastrophic collision  or were captured.
planetmaker
CC BY-SA 4.0
2020-05-19T09:24:51.493Z
2020-05-19T09:32:24.607Z
2020-05-19T09:32:24.607Z
z33k
<p>I once conducted a thought experiment and with some amateurish calculations based around Hill sphere and Roche limit came up with semi-major axis distances like this: </p>

<pre><code>Procyon-BD:  3.6 AU
BD-Jupiter:  0.7 AU
Jupiter-SE:  0.12 AU
SE-Mars:     0.02 AU
Mars-Pluto:  0.0033 AU
</code></pre>

<p>Assuming respective masses of: 496 260 earths, 15 000 earths, 313 earths, 6 earths, 0.107 earths and 0.00218 earths.</p>

<p><em>Clarification: I use names of specific bodies (Procyon, Jupiter etc) but a Procyon-like star, a Jupiter-like gas giant and so on would be more precise. Think of them only as examples of bodies with such masses.</em></p>

<p>Could such a system be possible?</p>

CC BY-SA 4.0
2020-05-10T14:44:38.900Z
You want a system with those exact distances or a system with just those bodies present? Should they all orbit the central object (thus Procyon) or should each orbit the next bigger object? The latter would certainly not work stably. A system would also be considered bound when the orbits are outside the bigger object's hill sphere.
planetmaker
CC BY-SA 4.0
2020-05-10T15:01:05.943Z
A brown dwarf orbits a Procyon-like star in the center, a Jupter-like gas giant orbits a brown dwarf, a superearth orbits a gas giant, a Mars-like planet orbits a superearth and a Pluto-like planet orbits a mars planet. So it wouldn't be stable? Why?
z33k
CC BY-SA 4.0
2020-05-11T00:33:24.257Z
Are you just asking about the orbit stability of such a system? Or are you (also) asking if it's theoretically possible for such a system to form naturally? (My guess is that it's not stable, and that it couldn't form).
PM 2Ring
CC BY-SA 4.0
2020-05-11T05:24:29.763Z
I'm only asking about orbit stability in terms of Hill sphere and Roche limit. Disregard anything else for simplicity.
z33k
CC BY-SA 4.0
2020-05-19T06:17:23.100Z
I agree! [Is “solve this n-body system for me” on topic here?](https://astronomy.meta.stackexchange.com/q/595/7982)
uhoh
CC BY-SA 4.0
2020-05-19T07:48:56.637Z
I’m voting to close this question because as it has been discussed on meta, questions about worldbuilding are off-topic.
usernumber
<natural-satellites><planetary-systems><roche-limit><hill-sphere>
Is a Procyon - brown dwarf - Jupiter - superearth - Mars - Pluto system theoretically possible?
z33k
# Is a Procyon - brown dwarf - Jupiter - superearth - Mars - Pluto system theoretically possible?

(Asked by: username_0 on 2020-05-10)

I once conducted a thought experiment and with some amateurish calculations based around Hill sphere and Roche limit came up with semi-major axis distances like this: 
Procyon-BD:  3.6 AU
BD-Jupiter:  0.7 AU
Jupiter-SE:  0.12 AU
SE-Mars:     0.02 AU
Mars-Pluto:  0.0033 AU

Assuming respective masses of: 496 260 earths, 15 000 earths, 313 earths, 6 earths, 0.107 earths and 0.00218 earths.
Clarification: I use names of specific bodies (Procyon, Jupiter etc) but a Procyon-like star, a Jupiter-like gas giant and so on would be more precise. Think of them only as examples of bodies with such masses.
Could such a system be possible?

**Tags:** natural-satellites, planetary-systems, roche-limit, hill-sphere
> **Comments:**
> **username_1**: You want a system with those exact distances or a system with just those bodies present? Should they all orbit the central object (thus Procyon) or should each orbit the next bigger object? The latter would certainly not work stably. A system would also be considered bound when the orbits are outside the bigger object's hill sphere.  
> **username_0**: A brown dwarf orbits a Procyon-like star in the center, a Jupter-like gas giant orbits a brown dwarf, a superearth orbits a gas giant, a Mars-like planet orbits a superearth and a Pluto-like planet orbits a mars planet. So it wouldn't be stable? Why?  
> **username_2**: Are you just asking about the orbit stability of such a system? Or are you (also) asking if it's theoretically possible for such a system to form naturally? (My guess is that it's not stable, and that it couldn't form).  
> **username_0**: I'm only asking about orbit stability in terms of Hill sphere and Roche limit. Disregard anything else for simplicity.  
> **username_3**: I agree! [Is “solve this n-body system for me” on topic here?](https://astronomy.meta.stackexchange.com/q/595/7982)  
> **username_4**: I’m voting to close this question because as it has been discussed on meta, questions about worldbuilding are off-topic.  

---

## 1 answers

### Answer by username_0 on 2020-05-19. Score: 1 | Accepted answer

Thanks to [this answer](https://astronomy.stackexchange.com/a/2333/19829) linked by antispinwards I learned that such system most probably **would not be stable**, as I calculated it with proximity to upper limit of Hill sphere for each body.

But, if instead, I would have taken distances closer to 1/3-1/2 Hill sphere, **it could be theoretically feasible.**

> The orbit of a satellite's satellite will be stable if it's deep
> enough inside the Hill sphere, within the so-called true region of
> stability. The limits are a bit fuzzy, but the true region of
> stability is typically the lower 1/3 to 1/2 of the Hill sphere.

On a personal note, if it's so, it surprises me this type of systems are not more pondered on and discussed, with maybe even some probabilities calculated. As it could have a great impact on thinking about abundance of potentially habitable worlds in the universe (imagine how great a number of earth-like satellites could live in such a system in the habitable zone of its host star (it being short-lived on cosmological time-scale notwithstanding)).

> **Comments:**
> **username_1**: Probabilities of systems are calculated - from disk evolution models. Not by a-priori assumptions of what they should look like. A system like the one described here is not a likely solution by a huge margin of any reasonable models based on physical models  
> **username_0**: Is how _reasonable_ these models are measured against vastness of space and multitude of systems? I know the chance is small, but faced with enormity of space, is it orders of magnitude too small?  
> **username_1**: IMHO yes. Maybe not as unlikely as a stone jumping up and the room getting cooler, but it goes in that direction. It get's very difficult to reason wrt how planets form in a disk around a star - and it needs all the matter to form such planet within a larger portion of the disk. Given that, there never is enough material for another planet where another forms, or they would eventually collide - especially not given your cascade. The existing bigger moons generally are what roughly can form within the hill sphere, given available material, formed due to catastrophic collision  or were captured.  

---

