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Can a Dyson Sphere and a star inside of the Dyson Sphere, both have a "stable" orbit around the barycentre of a system where they are not the most massive objects? And/Or Can they both orbit together around a larger body? These are effectively the same question but with the Barycentre Inside Sphere and the Barycentre Outside Sphere respectively.

Since I'm not expecting any of these cases to be completely stable, so where/if possible I would like to know details about the differences in how much work it would be to achieve 'active stability' for such arrangements.

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  • $\begingroup$ Welcome to Worldbuilding SE, Techdragon, you may need to edit your question to clarify its details. It seems you are overthinking the problem, The black hole, the star & the dyson sphere will all orbit the system's barycentre. Most probably inside the black hole (depending on their masses). A system like this can be stable if the distances and masses are sufficient to allow stable orbits. The question is basic orbital mechanics. Put aside the shell theorem & Lagrange points as they don't necessarily apply here. $\endgroup$ – a4android Sep 17 '17 at 7:04
  • $\begingroup$ Dyson spheres are unstable enough as it is without any external centres of gravity. Niven rings are much better. Or check out those orbital halo thingies. $\endgroup$ – Mr Lister Sep 17 '17 at 12:10
  • $\begingroup$ Solid Dyson spheres are not doable unless you have Scrith or some other NonObtainium material. More plausible is a Dyson Swarm A multitude of objects in separate orbits buzzing about the star like an opaque swarm of gnats. $\endgroup$ – HopDavid Sep 17 '17 at 23:29
  • $\begingroup$ @HopDavid Not true, a non-rotating solid sphere experiences very little in the way of structural stress, you could build it from Iron, as long as you have gravity generators. $\endgroup$ – Ash Oct 11 '17 at 12:09
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The Dyson Sphere and the star it is built around both have the same center of gravity. Thus for most multi body problems they form a single body to the outside. Every body in the system would rotate around the barycenter so that would mostly not be a problem at all.

The only time this is not the case is when the sphere would get deformed or warped by a substantial amount. That might happen if it is orbiting too close to the larger mass object. Thus if the orbit is large enough, there is no problem at all.

As for the large enough portion... think of Jupiter as a type M star rotating around our sun (about 85 times its current mass). A Dyson sphere around it would have a radius of ~ 8 million km (within the habitable zone of such an M class star). That sounds like a lot but it is actually only 1% of the distance to the sun. The barycenter would move to around the current earth orbit and would still be much much further away than the Dyson Sphere. The asteroid belt, the Jupiter trojans, basically all objects in the "vicinity" of Jupiter all would be much much further away. For every outside observer, the Dyson Sphere and Jupiter could be treated as a single object. At the barycenter the Jupiter Dyson Sphere would appear around 3 times larger than the full moon.

Also, the orbit of Jupiter around the sun is a merely 5.5 AU. There are star systems out there with multiple stars that have distances of hundreds of AU between the stars.

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  • $\begingroup$ Would you mind editing your answer to clarify and expand out the assumptions your using in the explanation of "the large enough portion" of your answer? A Dyson Sphere doesn't really have a specific size, it pretty much depends on how and why it was built. Are you size estimates for an interior habitable zone like earth? Or an exterior surface gravity of 1g? $\endgroup$ – Techdragon Oct 17 '17 at 13:38
  • $\begingroup$ @Techdragon I did mean the habitable zone of an M class star. Edited it for clarification. $\endgroup$ – Adwaenyth Oct 17 '17 at 13:41
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How much of the Dyson Sphere's living space are you willing to give up? If you spin the Dyson Sphere, and it's made of something magnetic, you can use the magnetic field to stablise the stellar primary at it's centre and then it's a matter of orbiting the Sphere since the star is now part of the same gravitational object. That shouldn't present too many issues if that orbit is stable. The atmosphere of the Dyson Sphere will of course pool around the equator under the influence of centrifugal pseudo-gravity leaving staggering areas as airless deserts.

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