Dyson spheres, ring worlds, and their physics (split from Re: EP262: Cruciger)

[ElectricPaladin]

For whatever it's worth (and I know this gets the "apocryphal" stamp) but I read somewhere that dyson spheres wouldn't actually work (awesome as they might be) because a hollow sphere of sufficient mass and density to have enough gravity to hold an atmosophere on its inner surface would collapse back into a solid sphere. Ringworlds have the same problem in reverse: enough spin to produce sufficient sentrifugal gravity to hang on to an atmosphere and it will fall apart. The only solution is for the worlds to be made of handwavium, and deciding not to go the route of creative physics is a totally valid narrative choice. Perhaps Globus Cassuses (Globus Cassi?) are different? I don't know.

[wintermute]

For whatever it's worth (and I know this gets the "apocryphal" stamp) but I read somewhere that dyson spheres wouldn't actually work (awesome as they might be) because a hollow sphere of sufficient mass and density to have enough gravity to hold an atmosophere on its inner surface would collapse back into a solid sphere.

The net gravity inside a hollow sphere is zero (gravity attracts in all directions equally), so you'd need to spin it to provide artificial gravity, which brings up to:

Ringworlds have the same problem in reverse: enough spin to produce sufficient sentrifugal gravity to hang on to an atmosphere and it will fall apart.

I recall Larry Niven saying in an essay that he'd invented the fictional material scrith to deal with that problem, only to have readers run the maths tell him that carbon fibre would be strong enough to withstand the necessary stresses.

[blueeyeddevil]

For whatever it's worth (and I know this gets the "apocryphal" stamp) but I read somewhere that dyson spheres wouldn't actually work (awesome as they might be) because a hollow sphere of sufficient mass and density to have enough gravity to hold an atmosophere on its inner surface would collapse back into a solid sphere.

The net gravity inside a hollow sphere is zero (gravity attracts in all directions equally), so you'd need to spin it to provide artificial gravity,

First, and very important: Balanced gravity =/= zero gravity.
Furthermore, imparting spin would create only equatorial "artificial gravity" thus causing anyone toward the poles to 'fall' toward the center. Moreover, any spin sufficient to impart "gravity" would collapse the globe into a disc (or at least a toroid) like a frisbee-ball, at least over time (think of an old time pizzaria with someone throwing the dough up and spinning it to flatten it out).

[wintermute]

First, and very important: Balanced gravity =/= zero gravity.

If you have an equal pull in all directions, the result is zero gravity. As the Shell theorem says, if the body is a spherically symmetric shell (i.e. a hollow ball), no gravitational force is exerted by the shell on any object inside, regardless of the object's location within the shell. This is pretty basic physics.

Furthermore, imparting spin would create only equatorial "artificial gravity" thus causing anyone toward the poles to 'fall' toward the center.

Assuming there's a gravity source at the centre (like maybe a star) this is true, yes. If there's no such gravity source, people will just float around. Either way, people are unlikely to live in the polar regions of a Dyson Sphere.

Moreover, any spin sufficient to impart "gravity" would collapse the globe into a disc (or at least a toroid) like a frisbee-ball, at least over time (think of an old time pizzaria with someone throwing the dough up and spinning it to flatten it out).

That would depend on the tensile strength and rigidity of the material used to construct the sphere. It's like claiming that a building more than 50 floors high wouldn't be able to support its own weight - and this is one of the many reasons why we don't build skyscrapers out of pizza dough.

To get 1G on the equator, it would need to have an orbital period of ~9 days, which means the equator is moving at around 1,200Km/s. I don't want to work out what kind of stresses that would cause, but it's certainly outside of the tolerance of almost any known material (carbon fibre being the best candidate for something that can handle it).

[Ocicat]

Dyson spheres are all about capturing the energy of the star.  Cover it completely in a sphere to harness the full power of the naturally occurring fusion reactor.

Ring worlds are about extra living space.  It would make sense to have a ring world inside a larger dyson sphere, where the ring spins and holds atmosphere, and the sphere is just a bunch of solar cells.

[wintermute]

Or you can spin the sphere and have it also serve the purpose of the ring. There would be extra engineering problems involved, but you'd need less materials, and you don't have the risk of a collision between the ring and the sphere, which would be pretty devastating.

[blueeyeddevil]

First: Yes, equal pull from a shell in all directions creates a mathematic '0' but only if the shell is an idealized form, and the only thing that exists in spacetime. Gravity, also, is non-zero for any body making actual contact with the shell, especially if held in contact with the shell through centrifugal force. Furthermore, as soon as more than one person/being began walking/swimming around the interior 'floor' of the sphere the gravitational profile would no longer perfectly equal.  Unless all the beings within this sphere walked around in some parrallellized cosmic synchronized-dance routine (which actually is in itself an interesting story idea) the equilibrium of the sphere would fail. This too is basic physics.

Second: I misspoke, by "center" I meant the central equator. Sorry.

Third: I perhaps invited the 'towers of pizza dough' with my analogy, but I was still thinking of the actual materials described in the story. Of course materials of sufficient resilience may exist for this undertaking, they simply weren't the ones described in the story.
 
I think the ring-within-a-sphere idea is great, however, and really fixes all of my quibbles within the realm of the practicable.

[wintermute]

First: Yes, equal pull from a shell in all directions creates a mathematic '0' but only if the shell is an idealized form, and the only thing that exists in spacetime.

True. Assuming that we're talking about a sphere 1AU in radius, and construction is such that area density is within 1Kg/m², then the internal gravity from the shell might be as much as 0.0000000000000000000000001G. My apologies for the imprecision.

Gravity, also, is non-zero for any body making actual contact with the shell, especially if held in contact with the shell through centrifugal force.

Also correct. But if the spin is regulated so that objects "fall" towards the surface at 9.8m/s^-1, this results in a force of 1G, even if that force is not gravitational in nature. It's the same context as when fighter pilots are exposed to "high G's" during manoeuvres.

Furthermore, as soon as more than one person/being began walking/swimming around the interior 'floor' of the sphere the gravitational profile would no longer perfectly equal.  Unless all the beings within this sphere walked around in some parrallellized cosmic synchronized-dance routine (which actually is in itself an interesting story idea) the equilibrium of the sphere would fail. This too is basic physics.

And when people walk on Earth, it changes the length of both the day and the year by some immeasurably small amount. Does that mean that planets are also unstable? Given that a Dyson Sphere would outmass the Earth by many orders of magnitude, it's not unreasonable to say that the effect would be literally unmeasurably small.

Besides, people don't need to be walk ing around in parallel loops for them to cancel each other out; they just need to be walking around at random; for everyone heading west, there's (on average) someone else with the same eastward momentum.

Second: I misspoke, by "center" I meant the central equator. Sorry.

Unless there's some thickening of the material at the equator, this would not happen. The gravitational attraction (unnoticeable as it is) is not towards the plane of rotation, but towards whatever part of the surface had a manufacturing defect that makes it thicker / more dense than the rest of the structure.[/quote]

Third: I perhaps invited the 'towers of pizza dough' with my analogy, but I was still thinking of the actual materials described in the story. Of course materials of sufficient resilience may exist for this undertaking, they simply weren't the ones described in the story.

Nor, of course, was a Dyson Sphere. If we're changing the basic structure, it seems only fair to also change the materials it's made of. The Globus Cassus is indeed flattened out, and has low enough tensions that the construction materials described would work admirably.

[Max e^{i pi}]

I'm just posting here so it shows up in my ego-search.
I find the discussion fascinating, but I only have a college freshman's knowledge of physics, so I can't really contribute.

[Planish]

Dyson spheres are all about capturing the energy of the star.  Cover it completely in a sphere to harness the full power of the naturally occurring fusion reactor.

That was my understanding too.

It makes sense for intercepting electromagnetic radiation, but what happens with the solar wind?

The solar wind is a stream of charged particles ejected from the upper atmosphere of the Sun. It mostly consists of electrons and protons with energies usually between 10 and 100 keV. The stream of particles varies in temperature and speed over time. These particles can escape the Sun's gravity because of their high kinetic energy and the high temperature of the corona.

... and plasma from coronal mass ejections? It can't be good to have it bottled up forever.