Dyson Shell and GR

[Corgon]

One of the major complaints I see about shellstyle Dyson Spheres as portrayed in SF is that the inner side should be uninhabitable - that when you run the calculus, the mass of the shell cancels itself out, and somebody standing on the inside would (very slowly) start falling into the star. Calculus beat my brain into a bloody pulp, unfortunately, so I didn't work through the proof I saw, but it sort of makes sense anyway.

However, that calculation was based just on calculus, so I'm wondering if maybe it didn't account for the space-warping of general relativity. Anybody know if that would be a factor in making the inner edge more (or less) friendly to going out for a stroll?

[Ken G]

Welcome to the forum Corgon. Newton's approach to gravity, using calculus, works to very high accuracy for this problem. The falling you describe would occur long before any general relativity corrections came into play. By the way, it wouldn't take longer than a few months to fall all the way to the star-- it wouldn't be so slow! Rotation could help, but not along the axis. I have no idea what Dyson's solution to this was, probably just using a ring not a sphere. The sphere idea seems to have overlooked something pretty basic, unless I'm missing something.

[Corgon]

Thanks for the answer! I knew the star would be too far away for its on GR curvature, but I wasn't sure about the mass of the sphere.

The solid shell is, AFAIK, a misinterpretation of Dyson's original theory - he meant something more like a network of satellites. Even going with the solid version, living on the outside of the sphere should be doable, but SF often (from what I've seen) goes with the "inside" version (most notably, one episode of Star Trek).

[antoniseb]

Among the aspects worth noting about the problems of a solid Dyson Sphere are:
1. the star is not in a stable position in the center of the sphere, and so some active mechanism is required to move the sphere so it is centered on the star.
2. the equator of the sphere could be supportd by rotating it at the right orbital velocity, but unless the sphere were light-weight enough to be held up by Solar-sail-like mechanisms, the poles would just collapse down to the star.

[selden]

Somewhat off topic: a pair of books by Jack Williamson and Fredrick Pohl described life on the outside of a spherical dyson sphere: Farthest Star (1975) & Wall Around a Star (1983)

[Mister Earl]

Ah! But wouldn't the gravity of the star itself hold the shell perfectly around it? If the shell became off-centered, wouldn't it occilate until it was centered again? I imagine there would be normal peturbations (solar wind, more output on one side than the other) but that gravity would keep it generically centered?

[Ken G]

If the shell became off-centered, wouldn't it occilate until it was centered again? I imagine there would be normal peturbations (solar wind, more output on one side than the other) but that gravity would keep it generically centered?

No, that's antoniseb's point-- gravity would pull the sphere more and more if it got slightly off center, so it would not oscillate-- it would crash. But perhaps more to the point, no internal strength of the sphere could hold it up in the first place, it would have to be in pieces orbiting in various different planes and somehow not colliding.

[Mister Earl]

But if it was off-center, wouldn't there be more mass to pull on, on the farther side?

*EDIT*
Also, wouldn't the near-side recieve more pressure from solar wind? A theoretical dyson sphere would be very, very thin, I don't think gravity would factor in as much as a gigantic solar sail, here.

[Ken G]

But if it was off-center, wouldn't there be more mass to pull on, on the farther side?

Yes, but the nearer side is closer, and that effect wins out, which is what makes it unstable.

*EDIT*
Also, wouldn't the near-side recieve more pressure from solar wind? A theoretical dyson sphere would be very, very thin, I don't think gravity would factor in as much as a gigantic solar sail, here.

That would depend on the mass of the sphere. I'm neglecting the solar wind because the whole idea is kind of preposterous, but if you want to worry about things other than gravity, the push of sunlight would be much more than that of the solar wind.

[antoniseb]

Most Dyson Sphere studies have looked at the stability gravitationally. The idea of constructing something with solar sail thickness, so that the dynamics are dominated by stellar wind and light seems like a fairly new idea. Yet, that being said, even then you would need to actively stabilize it because the forces you describe as potentially correcting things balance each other out.

I'm assuming that your thought is to construct some kind of gigantic carbon nano-tube based photovoltaic sail over the poles of the star extending from a 'Ringworld'.

I think when you look at the masses and angular momentum involved, you'll need to do this in a Solar System with a hot super-Jupiter.

[Mister Earl]

If the dyson sphere were an enclosed sphere, wouldn't solar radiation itself keep it spherical and equidistant from the sun? Even if that didn't work, I image you could construct colossal "shutters" to let out more radiation on one side than the other, shifting to the other side, though that would mean a loss in harvested energy.

[antoniseb]

I image you could construct colossal "shutters" to let out more radiation on one side than the other, shifting to the other side

That would be an example of the active system I was talking about.

[ozark1]

Biggest problem with a Type 2 Dyson sphere is runaway heating. You trap all a star's energy, then you have to get rid of it. Essentially the sphere gets very warm indeed. Oh and radiator fins etc don't work. I think that the whole thing ends up glowing brightly in the infrared.

[Andreas]

Yes, but the nearer side is closer, and that effect wins out, which is what makes it unstable.

AFAIR the inside of a uniform, hollow sphere is free of gravity. The nearer side may be closer, but that is exactly compensated by the larger part of the mass being on the other side.

I suppose it gets more complicated GR wise when you start to rotate the sphere.

[gwiz]

Biggest problem with a Type 2 Dyson sphere is runaway heating. You trap all a star's energy, then you have to get rid of it. Essentially the sphere gets very warm indeed. Oh and radiator fins etc don't work. I think that the whole thing ends up glowing brightly in the infrared.

If the outside of the shell is glowing in the infra-red, you are not trapping the star's energy, just shifting it around the spectrum. There's got to be an equilibrium temperature for the shell, and a distance from the star at which that equilibrium temperature is habitable.

[Ken G]

Biggest problem with a Type 2 Dyson sphere is runaway heating. You trap all a star's energy, then you have to get rid of it.

As gwiz said, that's not actually a problem, you only need to get the side away from the star to reach the same temperature as the side facing the star. Then a shell at 1 AU would be the same temperature as the Earth!

[Mister Earl]

Other factors come into play as far as Earth's temperature, as well. Atmosphere for the main thing... I doubt you could have atmosphere over the entire outside surface of the sphere, so you can't reasonably expect for the temperatures not to be different by a wide margin.

[Ken G]

Atmosphere for the main thing... I doubt you could have atmosphere over the entire outside surface of the sphere, so you can't reasonably expect for the temperatures not to be different by a wide margin.

That's actually a small correction, you could just put the sphere at a radius of about 0.8 AU to compensate for a lack of atmosphere on the "back side", if there was such a lack. The only planet on which I would call it a "wide margin" is Venus.

[Mister Earl]

Even a shell at 0.8au would require an enormous volume to have the same depth and density of our atmosphere. Considering the lack of density and gravity of a dyson sphere, would the atmosphere even stick, if you could import that much gas?

[Ken G]

To make the atmosphere stick, you'd first have to resolve the other structural problems we've already mentioned. Is the shell broken up into orbiting pieces, or is it supported by internal support of some kind? I think the latter would be impossible, so it'd have to be in orbit. Then you could make it so thin that it's own gravity didn't matter, and get the atmosphere to stick by virtue of also being in orbit. Would it be dense enough to breathe? I doubt it, but then, there are so many problems with this idea that it all seems pretty absurd.

[ozark1]

I quote

Its temperature becomes
T=[E/(4 pi eta sigma r^2)]^(1/4)
where eta is the emissivity (=1 for a blackbody), sigma the constant of Stefan-Bolzman's law (5.67032e-8 Wm^2K^-4)and E the total energy output of the star measured in watts.

and

at 1 AU, the energy flux is around 1.4e3 W/m^2, which calculates as around 395 K, or 122 degrees C if the sphere is a blackbody. This is a bit too hot for an earthlike biosphere (Earth is cooled by its rotation, which effectively halves the energy flux, and its spherical shape, that lowers it further), and a dyson shell need some rather impressive cooling to work.

[antoniseb]

a dyson shell need some rather impressive cooling to work.

Nice straight-forward work on calculating the temperature. Thanks.

I'm not trying to sell anyone on constructing a Dyson sphere. To me it seems both technologically out of our range, and way too expensive for now... However, there are several solutions to the above concerns. One would be to make it 40% larger. Another would be to put the habitable space outside the main collecting area. This would allow building the shell much closer to the star.

You could imagine building such a shell around a relatively stable M3 dwarf with a relatively massive orbiting ring connected to two energy collecting solar sail hemispheres which between them encompass the whole star. This sphere would only have to be a few million miles in diameter.

Going back to the OP, this has nothing to do with GR. Sorry.

[Ilya]

But if it was off-center, wouldn't there be more mass to pull on, on the farther side?

Yes, but the nearer side is closer, and that effect wins out, which is what makes it unstable.

Actually, it does not. Draw a circle (Dyson sphere) a put a dot (star) off-center. Then draw two straight lines intersecting on the dot. They will mark off a smaller arc on the closer side and a larger arc on the farther side. Arc lengths are proportional to the distance from the dot. In three dimentsions lines correspond to cones and arcs to circular cutout sections of the sphere. Diameters of this cutouts are proportional to the distance from the dot, and areas are proportional to square of the distance. IOW, if the star is 3 times closer to one side than the other, every section of Dyson sphere pulling on it at the close side is balanced by the 9 times bigger section on the other side. Since force of gravity is proportional to inverse square of the distance, the pull of these two sections is exactly equal.

The bizarre result is that the star and the sphere are gravitationally invisible to each other. Each acts as if the other did not exist. Which does not mean stability, BTW. If the sphere, for whatever reason, begins to move with respect to the star, it will continue moving, neither accelerating nor decelerating, until it hits the star. But it's not as bad as you and Anitoseb think (unstable equilibrium).

[Ken G]

at 1 AU, the energy flux is around 1.4e3 W/m^2, which calculates as around 395 K, or 122 degrees C if the sphere is a blackbody. This is a bit too hot for an earthlike biosphere (Earth is cooled by its rotation, which effectively halves the energy flux, and its spherical shape, that lowers it further), and a dyson shell need some rather impressive cooling to work.

Actually, if the Dyson sphere didn't have some rather impressive way to conduct the heat from the inside to the outside (making its outside as warm as its inside), the inside would heat up way past 400 K, up to a limit of the the Sun's surface temp of about 6000 K. If you do have a way of getting the outside as warm as the inside, then you would only need to put it at 2 AU to get back to a situation similar to the Earth's temperature. You do make the good point that such a shell at 1 AU would be hotter than the Earth even if it had no atmosphere, and as you say that is because the Earth absorbs through its pancake cross section but emits through its spherical surface (I hadn't taken that factor of 4^1/4 in T into consideration). The rotation is not crucial, the Earth's atmosphere functions fine for sharing the heat from day to night-- the spherical shape is the key issue not the rotation.

[Ken G]

The bizarre result is that the star and the sphere are gravitationally invisible to each other.

That's a good point, I was uncritically accepting the statement that it is unstable, which I've heard made elsewhere. Now I see no basis for that claim, so perhaps someone else who has asserted this instability can elaborate. Maybe the instability is meant to apply only to a ring which is "held up" by structural integrity, but that seems far-fetched because if you were going to let it be a ring you would certainly rotate it into orbit.

Which does not mean stability, BTW. If the sphere, for whatever reason, begins to move with respect to the star, it will continue moving, neither accelerating nor decelerating, until it hits the star.

That's termed "marginal stability", and counts as stable, in the sense of not-unstable. It would be easy to manage if it started to get out of kilter, or as easy as any other aspect of this impossible idea.

[Corgon]

Going back to the OP, this has nothing to do with GR. Sorry.

Hey, I got my answer - I figured if somebody had something to add to Ken G's answer, they'd have said it by now, so whatever you guys want to use this thread for is fine by me

Followup question: I've been reading a bit about "frame dragging" near rotating objects. From the outside, I presume a rotating shell would somewhat resemble a rotating solid sphere. Inside the sphere, would there be any dragging, or would that effect also be nullified by the gravitational "invisibility" of the sphere from inside?

[Ken G]

From the outside, I presume a rotating shell would somewhat resemble a rotating solid sphere. Inside the sphere, would there be any dragging, or would that effect also be nullified by the gravitational "invisibility" of the sphere from inside?

Now you are definitely pushing my GR knowledge, but I very strongly suspect that frame dragging also occurs inside the sphere. But it gets tricky-- if the sphere is rotating, the spacetime distortion makes it hard to specify what one means by a "sphere" in the first place! If you mean all points equidistant from the center, note that the distance part of the metric depends on the choice of reference frame, and it will not be the same in all directions. This gets into Mach's principle and many other real mind-bending aspects of GR, about which I have no clue at all.

[DaveC426913]

Rotation could help, but not along the axis. I have no idea what Dyson's solution to this was, probably just using a ring not a sphere. The sphere idea seems to have overlooked something pretty basic, unless I'm missing something.

Dyson's vision of his sphere did not involve a solid object. His idea was really more about small planetoid-like bodies completely gathering the sun's energy. A rigid sphere was a later modification.

Actually, if the Dyson sphere didn't have some rather impressive way to conduct the heat from the inside to the outside (making its outside as warm as its inside), the inside would heat up way past 400 K.

Sorta missing the point of a Dyson sphere here (at least, by Dyson's reasoning). The reason for creating a Dyson sphere is to capture all the energy your sun puts out because you need it to power your civilisation.

[Ken G]

Dyson's vision of his sphere did not involve a solid object. His idea was really more about small planetoid-like bodies completely gathering the sun's energy. A rigid sphere was a later modification.

But of course a rigid sphere could never possibly work, the stresses would be astronomical, no pun intended.

Sorta missing the point of a Dyson sphere here (at least, by Dyson's reasoning). The reason for creating a Dyson sphere is to capture all the energy your sun puts out because you need it to power your civilisation.

Certainly, but energy does not "go away" when used, it goes into heat. Unless you want a "gobal warming" that makes Venus seem like a refrigerator, you need to get rid of the heat you are "using". Transferring it to the outer side of the sphere and radiating it into space would seem to be the only option, and you'd have to do it quite effectively-- otherwise the inside heats up to uncomfortable temperatures. Of course, if you are living on the outside of the sphere, which may be Dyson's vision (nice starlit skies, but no daylight), then you are at a comfy temperature at about 2 AU. You can't use the Sun's gravity for weight though, it's too weak, so you still need self-gravity of your sphere. There won't be enough mass to create this. It's just a crazy idea for a host of reasons.

[peter eldergill]

ABout the Star Trek episode. The neat thing about that was the structure was there, uninhabited, huge and, as mentioned, impossible to build.

Yet, there it was anyways....instant mystery! Who built it? How? When? How old was it, etc....

Of course, on Star Trek, you just hit the console buttons #1,4 and 6 and PRESTO! All the interior heat is disspated without anyone on the outside noticing. It;s a simple matter of (insert babble lines here)

BTW I did enjoy that episode

Pete