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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?

z33k
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  • 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 May 10 '20 at 14:44
  • 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 May 10 '20 at 15:01
  • For information, I have raised a question on Meta about the on-topicness of "solve my n-body system"-type questions. –  May 10 '20 at 16:18
  • 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 May 11 '20 at 00:33
  • I'm only asking about orbit stability in terms of Hill sphere and Roche limit. Disregard anything else for simplicity. – z33k May 11 '20 at 05:24
  • If I'm understanding this system correctly, it contains subsatellites and sub-subsatellites. For the stability issues of subsatellites, see Do moons have moons?. Sub-subsatellites would be even less stable. –  May 18 '20 at 17:29
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    I’m voting to close this question because it is getting into off-topic territory. The general question about the feasibility of subsatellites has already been asked, the question about details of a specific hypothetical system are more suited for Worldbuilding. –  May 18 '20 at 17:32
  • I agree! Is “solve this n-body system for me” on topic here? – uhoh May 19 '20 at 06:17
  • I’m voting to close this question because as it has been discussed on meta, questions about worldbuilding are off-topic. – usernumber May 19 '20 at 07:48

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Thanks to this answer 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)).

z33k
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  • 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 May 19 '20 at 11:01
  • 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 May 19 '20 at 12:22
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    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 May 19 '20 at 12:58