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Space

Surprisingly, Some Dyson Spheres and Ringworlds Can Be Stable (phys.org) 39

Posted by EditorDavid from the ringworld-engineers dept.
Slashdot reader Required Snark shared this article from Phys.org: In the realm of science fiction, [sun-energy capturing] Dyson spheres and ringworlds have been staples for decades. But it is well known that the simplest designs are unstable against gravitational forces and would thus be torn apart. Now a scientist from Scotland, UK has shown that certain configurations of these objects near a two-mass system can be stable against such fractures...

[A] rigid ring around a star or planet, as in Larry Niven's "Ringworld" series of novels, is also unstable, as it would drift under any slight gravitational differences and collide with the star. So [engineering science professor Colin] McInnes considered a restricted three-body problem where two equal masses orbit each other circularly with a uniform ring of infinitesimal mass rotating in their orbital plane. The ring could enclose both masses, just one or none... McInnes also investigated a shell-restricted three-body problem with the shell also of infinitesimal mass, again with the shell enclosing two masses, one or none.

For the restricted ring, McInnes found that there are seven equilibrium points in the orbital plane of the dual masses, on which, if the ring's center were placed, it would stay and not experience stresses, akin to the three stable Lagrange points where a small mass can reside permanently for the two-body problem... McInnes restricted this research to a planar ring (in the plane of the circularly orbiting masses) but says it can be shown that a vertical ring, normal to the plane, can also generate equilibria...

These results can aid the search for extraterrestrial intelligence, McInnes said, "If we can understand when such structures can be stable, then this could potentially help direct future SETI surveys." An important technosignature would be one bright star orbiting in tandem with an object showing a strong infrared excess. Shells around a sun-exoplanet pair or an exoplanet-exoplanet pair could also be possible. A nested set of Dyson spheres is also a feasible geometry.
In 2003 Ringworld author Larry Niven answered questions from Slashdot readers...

Surprisingly, Some Dyson Spheres and Ringworlds Can Be Stable More | Reply

Surprisingly, Some Dyson Spheres and Ringworlds Can Be Stable

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  • It seems conceivable that a ring could be stable, because the centrifugal force would be more or less consistent across the ring.

    But a sphere would always have gravity at the poles, with no centrifugal force to keep the structure from collapsing into the star.

    So how exactly would this collapse be prevented in a spherical geometry?

    • Re: (Score:2)

      by codrus ( 35604 )

      The stability question isn't about the tensile strength and other mechanical properties of the structure itself, it's about the orbital mechanics. A ringworld orbiting a single star is stable on a "peak" position, where any movement away from that position results in net gravitational forces that move it further away. In contrast, the stable lagrange points are positions where small amounts of movement away from that position result in graivtational forces moving it back towards that position -- a "valley

      • The stability question isn't about the tensile strength and other mechanical properties of the structure itself, it's about the orbital mechanics. A ringworld orbiting a single star is stable on a "peak" position, where any movement away from that position results in net gravitational forces that move it further away."

        That is the definition of the word "unstable," when any movement away from equilibrium results in a force moving it further from equilibrium.

        What you meant so say was, "A ringworld orbiting a single star is in equilibrium on a "peak" position." But it's an unstable equibrium.

        In contrast, the stable lagrange points are positions where small amounts of movement away from that position result in graivtational forces moving it back towards that position -- a "valley" by comparison.

        Yes, the two Lagrange points L4, and L5 are stable equilibria. The colinear Lagrange points, L1, L2 and L3 are unstable.

        • Re: (Score:1)

          by codrus ( 35604 )

          Yeah, sorry, typed the wrong word (I would have put 'balanced' there in retrospect), but didn't realize until after I'd hit submit.

    • Dyson swarms, or physically impossible material strength. The ring is unstable because if any one part of the ring has a higher pull/different mass that part of the ring experiences stronger gravity, and is pulled closer to the star. In an object that would result in a higher velocity, but in a ring the whole ring's speed balances out resulting in on change in speed but that part of the ring still being closer. This continues until the system collapses.

      But then most orbits need station keeping, I'm not su

      • Re: (Score:2)

        by Sique ( 173459 )
        Let's put it like this: Dyson spheres should be called Yogi Berra spheres, in theory, practice and theory are the same, in practice, they aren't. Take the Solar system as an example. If we want to build a Dyson sphere at the orbit of the Earth, we would have about 10 metric tons of building material per square meter - for anything, including the sphere itself. And most of our building material would be hydrogen from the big gas planets anyway. Even if we manage to fusion all hydrogen into heavier elements t

      • But then most orbits need station keeping,

        Orbits in a two-body system (one central body, one orbiting body) do not need station keeping. They only need station keeping if you have some perturbation.

        You need station keeping, for example, if you want to stay in an orbit of exactly 24 hours in a perfectly equatorial inclination (because of perturbations from the Earth's non-spherical shape, and perturbation from the gravity of other bodies, primarily the Sun and moon.). But even then, while the perturbations are enough to slightly change the shape and

        • Orbits in a two-body system (one central body, one orbiting body) do not need station keeping.

          If you're talking about a conventionally "interesting" system, you have at least three bodies : the primary (star, energy-emitting black hole, McGuffin, whatever), a planet (full of sexy non-humans for Captain Kirk to commit bestiality with/ upon), and a "light" test particle - your spaceship.

          In reality, galactic tides are both present, and significant. Was the tidally-induced "S"-shape of the inner Oort Cloud dis

          • In reality, galactic tides are both present, and significant. Was the tidally-induced "S"-shape of the inner Oort Cloud discussed here recently, or did I just read the paper, consider it interesting, but decide against submitting it? Whatever, there was a recent paper on Arxiv about the influence of Galactic tides on the Oort Cloud. That'd be sufficient to destabilise even a nominally stable Niven Ring.

            Well, significant because the Oort cloud is very very weakly bound. We've mostly been talking about stuff much closer to the sun.

            Don't I recognise your UID as a published SF author?

            In my spare time when I'm not working for NASA, yes, I'm a SF writer. Somewhat more active a few years back, but I still write a story every now and then.

    • Dyson spheres are inherently stable when it comes to gravity. It is a complex integral calc but if you work it out, any gravity body inside the sphere has a net 0 effect on the sphere. Now that said, that is a perfect sphere. In reality it would be an imperfect sphere and thus the calc doesn't give you a net 0, which I am guessing is what they are talking about here as it would allow the imperfections enough leeway to be truly feasible.

      • Re: (Score:2)

        by ceoyoyo ( 59147 )

        That's not true. If it were, you'd be floating around right now.

        I think what you're referring to is that the gravitation from a perfect spherical shell is cancelled out in its interior. Basically the opposite of what you said. It's called the shell theorem.

        This story is about the stability of a shell surrounding a mass like a star. That is definitely not stable with a single star inside. This story is about the discovery that there are stable configurations when two stars are involved.

        • No, that's not what I was talking about. Inside the dyson sphere, the sphere has no gravitational effect, and likewise the sun has no effect on it. Both will affect any body exterior to the sphere, but that's not relevant here. This has nothing to do with me floating, I'm not a dyson sphere, nor am I on the interior of any sphere. Again, this only true if it is a perfect sphere, which it won't be. Now if you want to live on the inside the sphere you're going to need a gravity like effect, produced by s

          • That's just not correct.

            • Yes, it is correct, and the very theorem you brought up, shell theorem, proves it. Here, directly from wikipedia: Isaac Newton proved the shell theorem[1] and stated that: 1. A spherically symmetric body affects external objects gravitationally as though all of its mass were concentrated at a point at its center. 2. If the body is a spherically symmetric shell (i.e., a hollow ball), no net gravitational force is exerted by the shell on any object inside, regardless of the object's location within the

              • Your math is correct but that's not the definition of the word "stability".

                Stability means that there is a restoring force in response to a perturbation which returns the system to the initial position. The shell theorem says there is no restoring force.

                • Okay, that's fair enough, I was just thinking of the two bodies relative to each other, not external vectors.

      • Your calculations may be right, assuming that the sphere is perfectly rigid. Since there's no such perfectly rigid substance, certainly not at that scale, the poles would implode into the star, even if the rest of the structure stayed intact. At the scale of a Dyson sphere, the "shell" would be as flexible as cellophane.

        • Yeah, the theory may work, in practice, no chance in hell. There is all kinds of issues once you start to turn that theory into reality. Even assuming you could find the perfect substance to make the sphere from that had just the right rigid properties and such, and can perfectly place every last atom to be in a perfect spherical pattern, the reality is it still wouldn't make a perfect sphere, just a series of point masses that resemble a perfect sphere, and that's not good enough for the theory to work.

          • There is all kinds of issues once you start to turn that theory into reality.

            The tidal forces from the rotation of the galaxy and irregular distribution of matter in the galactic disc will also exert appreciable (small, but non-zero) torques on the structure. Not to mention any passing 1I/`Oumuamua that doesn't pass.

      • Dyson spheres are inherently stable when it comes to gravity.

        No, they're not. They are precisely neutral. A perturbation from the centered position results in neither a restoring force nor a increasing force. So, if you perturb it with velocity v, the perturbation velocity remains constant, until it crashes into its sun (at constant velocity).

    • The inverse square law is the problem. If one part of the ring gets close to the sun the gravitational attraction goes up more than linearly, while the attraction across the diameter goes down more as as that is farther away from the sun.

      So soon the ring will be dragged way off center.

      The fictional Ringworld had attitude jets to hold it in position.

    • But a sphere would always have gravity at the poles, with no centrifugal force to keep the structure from collapsing into the star.

      Consider each meridian ("line of longitude" in terrestrial coordinate analogy) from an equatorial point, through a pole, to the antipodal equatorial point. It is a semicircular arch, whose weight at the apex (pole) is supported by compressional forces acting down the arch to the end points. At the end point, it resolves into a force along the pole --> centre-of-mass direction

      • There is a piece you are missing. An arch that supports itself through compression forces, relies on the pull of gravity coming from the bottom of the arch. Gravitational forces on the arch are parallel to each other vertically. In other words, the top of the arch presses "down" on the layers below, where "down" is always the same direction.

        The problem with a Dyson sphere "arch" is that at the feet of the arch (the poles of the sphere), gravity is pulling the feet towards each other, not "down" in terms of

        • The geometry changes in a non-parallel gravitational field, but I don't think it invalidates the analysis completely, just complicates it. You'll probably need a material of "significant" stiffness (Someone described any Dyson sphere material as being effectively "cling film", but I haven't analysed that claim.)

          Niven's scrith is retconned in recent work as a material designed for building a "beanstalk", an equator to low-orbit lift. Very much unobtanium-plated handwavium.

          • The geometry changes in a non-parallel gravitational field

            You have only your imagination to support this claim. The very nature of arch construction assumes two things: 1) the structure sits on an "immovable" surface and 2) gravitational forces pull the entire structure downward against that immovable surface. It is the opposition of these two forces--the downward force of the structure, opposed to the static force of the surface, that provides tension throughout the structure and keeps it in place.

            In a sphere, at the poles, there is nothing for the structure to "

  • The basic problem, not addressed, is the amount of mass required to build either a RingWorld or a Dyson Sphere with solid shells. But a Topopolis should be doable. It's not rigid and it can be build incrementally. It would probably need a diameter of at least 10 miles, and various segments of it would need to be separable (but that could be handled with magnetic links between the segments. This would allow some segments to be non-rotating so that, e.g., T-junctions would be possible.

    OTOH, I'm not sure there's enough matter in the asteroid belt to build one, so you might need to disassemble a few moons...after awhile.

    That said, a topopolis would never be self-maintaining. If civilization died, so would everyone living there. (OTOH, if you could build one, you could certainly build smaller habitats. And a working topopolis would make an excellent basis for an em-launcher for habitats headed for interstellar space. So it would be likely to spread a some very small fraction of the speed of light. Probably less than 0.001c for system to system spread. [This is assuming that controlled fusion is actually possible.])

    • You've either read Heaven's River (Bobiverse book 4), or you should.
    • The point of a Dyson sphere is to harness a non-trivial fraction of a stars energy output. If you can harness even a few percent of a stars output you can disassemble entire plants. The binding energy of the Earth, the amount of energy to break the earth down into individual atoms and push them apart so that they won't reform is 2.5x10^32 J or about a week of energy from our sun.
      • The point is that even if you disassembled all the planets in the solar system, you wouldn't have nearly enough mass to build a Dyson Sphere. https://www.youtube.com/shorts... [youtube.com]

      • If you can harness even a few percent of a stars output you can disassemble entire plants.

        Or even planets.

        Which would yield about 74% H2, 25% He, 0.078% O2, 0.033% carbon, 0.010% nitrogen, 0.010% neon, 0.003% magnesium, 0.003% silicon, 0.003% iron, 0.001% sulphur ... - assuming that your star system approximates to Solar composition. Which big planets do. Small "rocky" planets lose the H2 and He. (I've mixed atom counts and mass proportions shamelessly ; it doesn't affect the point.)

        There is a reason tha

  • A ring occupies every possible position in its orbit simultaneously so is roughly 3 x 10^8 times more likely to be hit by some random rock or comet in an elliptical orbit than if it was a satellite. A sphete on the other hand is guaranteed to be hit by everything that crosses its orbit. Just saying.

  • because OUR world ain't currently stable.

  • If you have the technology to build one of these structures, then keeping it from falling into the star wouldn't be a problem.

    Niven's ringworld had bussard ramjets keeping it stable.

    Actually I think what we might find is smaller ringworlds around red dwarf stars, because that type of star is more common and has a longer life.

    • Re: (Score:2)

      by ceoyoyo ( 59147 )

      There's a lot to be said for passive stability. As Niven illustrated when he had the residents of the Ringworld stealing the ramjets for spacecraft.

  • A friend and I were talking about how well it performs considering it's done with Unity.

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