## Dyson Sphere / Ringworld (in)stability

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### Dyson Sphere / Ringworld (in)stability

A recent topic discussed that in the center of a metal sphere / shell in the middle of the earth, gravitational forces on an object cancel out perfectly due to Gauss' Law even if the object is off center. I haven't done the math, but this made sense to me.

Thinking about this more, I took away the earth and enlarged the metal sphere into a Dyson Sphere. This brought me to the conclusion that a Dyson Sphere exerts no net gravitational force on the star in the center. It seems logical and all, but then I thought about the Ringworld, and the whole 'Ringworld is Unstable' issue.

Now, I don't know how Gauss' Law applies to a ring compared to a sphere, but it seems like the net gravitational force at the center of a ring would also be zero. As would the net gravitational force for an object that is off-center. Please correct me if I'm wrong about this assumption, but I don't see why a ring would be different than a sphere / shell.

Niven wrote in (i believe) Ringworld Engineers about how the slightest instability in the ring would result in a tiny net gravitational force that would grow and pull the ring farther off center until it hit the star. This was the point of the book - engines around the edge of the ring needed to be restored and the ring had to be re-centered using solar flares.

But if an object in the center / offcenter of a ring experiences no net gravitational force, I don't see why the ring would get pulled farther and farther off center. You would basically have a system of two independent objects flying in close formation, and to move as massive an object as the Ringworld would take incredible amounts of energy and / or time, not the 20 years given in the book.

Does anyone know what I'm getting wrong here? Is it just that the rules for a 2d Ring and 3d Sphere / Shell are different?

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### Re: Dyson Sphere / Ringworld (in)stability

It's not the gravity of the ring or sphere that's the problem; it's the gravity of the star in the middle.
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### Re: Dyson Sphere / Ringworld (in)stability

Mr_Rose wrote:It's not the gravity of the ring or sphere that's the problem; it's the gravity of the star in the middle.
Fortunately Newton's third law takes care of that.

Levelheaded wrote:Now, I don't know how Gauss' Law applies to a ring compared to a sphere, but it seems like the net gravitational force at the center of a ring would also be zero. As would the net gravitational force for an object that is off-center. Please correct me if I'm wrong about this assumption, but I don't see why a ring would be different than a sphere / shell.
You are wrong about this assumption. Go through how the fact about spheres is derived and see how it doesn't apply to a ring.
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### Re: Dyson Sphere / Ringworld (in)stability

antonfire wrote:
Levelheaded wrote:Now, I don't know how Gauss' Law applies to a ring compared to a sphere, but it seems like the net gravitational force at the center of a ring would also be zero. As would the net gravitational force for an object that is off-center. Please correct me if I'm wrong about this assumption, but I don't see why a ring would be different than a sphere / shell.
You are wrong about this assumption. Go through how the fact about spheres is derived and see how it doesn't apply to a ring.

I think that if, instead of a ring, you were inside an infinitely long cylinder, then the equivalent of Gauss' Law would apply. You'd need an infinitely large universe for that however.

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### Re: Dyson Sphere / Ringworld (in)stability

Levelheaded wrote:Now, I don't know how Gauss' Law applies to a ring compared to a sphere, but it seems like the net gravitational force at the center of a ring would also be zero.

This is true.
As would the net gravitational force for an object that is off-center.

This is false. The net gravitational force for an object that is off center is nonzero, and points towards the closest point of the ring. So the ring and the star pull each other more and more off-center, until they collide.
Please correct me if I'm wrong about this assumption, but I don't see why a ring would be different than a sphere / shell.

The difference is that gravity is a 1/r2 force, while the surface area at distance r of a 2-dimensional object inside a certain solid angle goes as r2. The fact that these exactly cancel is what balances the gravitational forces from a sphere so that they all cancel out in the interior. However, this balance doesn't happen with a ring, so the nearer parts of the ring provide more of a pull than the more distant parts, resulting in a net force towards the closest point.
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### Re: Dyson Sphere / Ringworld (in)stability

Couldnt you make it work with a ring with a variable density?

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### Re: Dyson Sphere / Ringworld (in)stability

Nope, that could only fix the stability in one direction. If you have a small perturbation 'north,' you keep getting pulled 'north.' If you fix this with some cleverness (I'm not even sure that's possible, but let's say it is) then you certainly have just made the problem worse for a small perturbation 'south.'
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### Re: Dyson Sphere / Ringworld (in)stability

What about a series of reflective sails mounted along the inside of the ring? One side gets a hair closer, and the light pressure gets a hair stronger and pushes it back. Doesn't need power or any controll systems, just maintenence.

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### Re: Dyson Sphere / Ringworld (in)stability

Only if the force from the sails is exactly equal to the gravitational force. I think it'd be safe to assume that that would not be true in practice.
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### Re: Dyson Sphere / Ringworld (in)stability

Couldn't you get away with having it be slightly stronger?

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### Re: Dyson Sphere / Ringworld (in)stability

That still seems like it could easily lead to oscillation, possibly to an arbitrary level.

Just use controllable attitude jets, like they do on the real ringworld.
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### Re: Dyson Sphere / Ringworld (in)stability

Xanthir wrote:like they do on the real ringworld.
hehe
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### Re: Dyson Sphere / Ringworld (in)stability

Just you wait, gmal. We've only got about another 850 years.
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### Re: Dyson Sphere / Ringworld (in)stability

The Ringworld is already out there, it was built by SPOILERS millions of years ago

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### Re: Dyson Sphere / Ringworld (in)stability

whereswalden90 wrote:Only if the force from the sails is exactly equal to the gravitational force. I think it'd be safe to assume that that would not be true in practice.

Possibly a series of solar sails on pistons? Large light objects can ride on solar pressure. They are known as statites, they "float" on a sea of light. Lower them closer to increase solar pressure without exacerbating the gravity problem(much).

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### Re: Dyson Sphere / Ringworld (in)stability

Or you could do the easy thing furling and unfurling the sails as needed.

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### Re: Dyson Sphere / Ringworld (in)stability

Sockmonkey wrote:Or you could do the easy thing furling and unfurling the sails as needed.

That's a bit much work for a sail that size if you're trying to do it mechanically. I'd go with something like Japan did with http://en.wikipedia.org/wiki/Ikaros Put LCD panels on the solar sails, that can adjust between transparent(which would end up reflective, due to the sail behind it) and opaque. That way, you can electrically adjust the reflectance of your sail, and thus adjust the force on it. Ikaros has them along the edges, and can control them separately of each other to turn the sail.

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### Re: Dyson Sphere / Ringworld (in)stability

whereswalden90 wrote:Only if the force from the sails is exactly equal to the gravitational force. I think it'd be safe to assume that that would not be true in practice.

No, it would stabilize the ringworld if the force from the sails were at least as strong as gravitational force, and could be any amount more. For this to work without power would require that the outward force from light pressure be less than the inward force from gravity, which puts an upper limit on the density of the ringworld, but assuming that condition were met, it would stabilize the ringworld.

Yes, a perturbation would lead to oscillations, but that's what you want. That's what it means to be stable. Consider a marble in the bottom of a bowl. It is stable, exactly because when you bump it, it oscillates near where it started.
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### Re: Dyson Sphere / Ringworld (in)stability

*Damping* oscillations = stable. Other kinds of oscillations... not so much.
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### Re: Dyson Sphere / Ringworld (in)stability

Then no orbit is stable.
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### Re: Dyson Sphere / Ringworld (in)stability

If you want to be precise... they're not. In deep time all the planets will be flung out of the solar system.
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### Re: Dyson Sphere / Ringworld (in)stability

Xanthir wrote:If you want to be precise... they're not. In deep time all the planets will be flung out of the solar system.

Explain? Conservation of energy would seem to disagree. Strongly.
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### Re: Dyson Sphere / Ringworld (in)stability

Even if that were not the case, according to your definition the orbits would be unstable. And so would the L4 and L5 Lagrange points, and so on. The word "stable" becomes pretty much useless in reference to orbital mechanics.

But hey I suppose I should just link you to the actual definitions.
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### Re: Dyson Sphere / Ringworld (in)stability

Charlie! wrote:
Xanthir wrote:If you want to be precise... they're not. In deep time all the planets will be flung out of the solar system.

Explain? Conservation of energy would seem to disagree. Strongly.

The planetary orbits aren't perfectly elliptical - they have a chaotic component which means they'll diverge from the "ideal" orbit by an arbitrary amount, given sufficient time. At some distance, they stop being gravitationally bound to the Sun (background gravitational influence from non-Solar bodies dominates).

antonfire wrote:Even if that were not the case, according to your definition the orbits would be unstable. And so would the L4 and L5 Lagrange points, and so on. The word "stable" becomes pretty much useless in reference to orbital mechanics.

But hey I suppose I should just link you to the actual definitions.

True. My original statement was somewhat incorrect, and then I had fun with diving deeply into definitions. Damping oscillations are stable, but other types of oscillations are called "stable" as well. I was trying to exclude only oscillations with positive feedback, which can happen in a system as described if you're not careful.
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### Re: Dyson Sphere / Ringworld (in)stability

Xanthir wrote:True. My original statement was somewhat incorrect. I was trying to exclude only oscillations with positive feedback, which can happen in a system as described if you're not careful is irrelevant to the situation of a reflective ringworld where the light pressure exceeds gravity.

Fixed. According to the actual definition of "stable," a ringworld could be made stable by making the interior surface of the ring reflective, provided the density is low enough that the force per unit area from reflected sunlight equals or exceeds the force per unit area from gravity. (Just as I said in my previous post.)
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### Re: Dyson Sphere / Ringworld (in)stability

I have no physics background, but wouldn't the doppler effect result in a dampening affect on the solar sales? the energy transfer from the light on the sales would be red-shifted on the side that began moving in towards the star, while the otherside would be blueshifted.
Last edited by Cyclocross4life on Sat May 07, 2011 8:14 pm UTC, edited 1 time in total.

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### Re: Dyson Sphere / Ringworld (in)stability

skeptical scientist wrote:
Levelheaded wrote:Now, I don't know how Gauss' Law applies to a ring compared to a sphere, but it seems like the net gravitational force at the center of a ring would also be zero.
The difference is that gravity is a 1/r2 force, while the surface area at distance r of a 2-dimensional object inside a certain solid angle goes as r2. The fact that these exactly cancel is what balances the gravitational forces from a sphere so that they all cancel out in the interior.

This isn't immediately obvious to me.

Left: two similar cones. Base area scales with cone height squared.

Center: the two opposing masses are non similar frustums.

For the sphere, the two opposing masses look even less similar to one another.

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### Re: Dyson Sphere / Ringworld (in)stability

Cave Wizard wrote:The Ringworld is already out there, it was built by SPOILERS millions of years ago

I am so waiting for the James Webb Space Telescope to send back an image of a star partially occluded by an artificial structure.. LOL

A partially completed dysonsphere or some such
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### Re: Dyson Sphere / Ringworld (in)stability

HopDavid wrote:For the sphere, the two opposing masses look even less similar to one another.

The key is, being closer to the smaller side, you feel a stronger attraction towards it (half the distance = 4x the attraction). There's more mass on the far side, but it's further away, and so each amount of mass has a smaller pull. From the inside of a sphere, these two factors balance each other out.

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### Re: Dyson Sphere / Ringworld (in)stability

Cyclocross4life wrote:I have no physics background, but wouldn't the doppler effect result in a dampening affect on the solar sales? the energy transpher from the light on the sales would be red-shifted on the side that began moving in towards the star, while the otherside would be blueshifted.

Except for two things--1) the radial component of motion isn't very large, so the doppler effect would quite small, and 2) the shift is in the opposite direction from what you said--that is, the side approaching the star would see its light (very slightly) blue-shifted, while the receding sail would receive red-shifted light.
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### Re: Dyson Sphere / Ringworld (in)stability

Soralin wrote:The key is, being closer to the smaller side, you feel a stronger attraction towards it (half the distance = 4x the attraction). There's more mass on the far side, but it's further away, and so each amount of mass has a smaller pull. From the inside of a sphere, these two factors balance each other out.

A high school physics teacher points a flashlight straight down at the floor forming a cone with height h and base of radius r. Area of the disk of light is pi r^2.

Then he doubles the distance of the flashlight from the floor. Now there's a similar (that is, having the same proportions) cone but h and r doubled. Now the disk of light has area 4 pi r^2.

Same number of light beams, but 4 times the area. Thus he demonstrates light falls with inverse square of the distance.

By asking his students to imagine gravity as tractor beams, he shows gravity is also inverse square.

If I understand Skeptical Scientist's argument correctly, he thinks of two directly opposing mass particles being collinear with the mass within the sphere. The lines passing through the mass form two similar cones with similar bases. If this were the case, the mass indeed the near part of the solid angle would indeed be 1/4 the mass of the opposite mass.

On the left are two opposing disks, the top having 4 times the area of the bottom disk. If mass is proportional to disk area, each disk would exert an equal tug on the grain between.

But what if the point lies between a floor and ceiling of equal thickness? Then the two opposing masses are frustums. I will leave it as an exercise to determine the volumes of frustum A and frustum B. I will say they do not differ by a factor of 4.

Now how about a spherical shell of constant thickness? In this case the opposing masses would be two bowl shapes. The nearer bowl would have smaller radius, shallower shape but the same thickness as the far bowl. Two dissimilar shapes, so it is not immediately obvious to me that Skeptical Scientists' argument is correct.

Here's a discussion of how to determine the volume of a solid of revolution. This might be a way to compare opposing bowl volumes.

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### Re: Dyson Sphere / Ringworld (in)stability

@ HopDavid: suppose you have a hollow sphere of non-negligible thinkness. You can see the gravitation of this sphere as the total gravitation of N thinner spheres exactly surrounding each other. By making N large enough, each of those thinner spheres will resemble the ideal situation of negligible thickness. The inner particle is (neutrally) stable with respect to all of those spheres, and therefore with respect to the larger sphere.

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### Re: Dyson Sphere / Ringworld (in)stability

Zamfir wrote:@ HopDavid: suppose you have a hollow sphere of non-negligible thinkness. You can see the gravitation of this sphere as the total gravitation of N thinner spheres exactly surrounding each other. By making N large enough, each of those thinner spheres will resemble the ideal situation of negligible thickness. The inner particle is (neutrally) stable with respect to all of those spheres, and therefore with respect to the larger sphere.

This seems to work in the case of a particle lying between two flat walls of equal thickness.

Slicing the two frustums into small frustums of thickness h, each thinly sliced frustum becomes more cylinder like as h goes to zero. And so its volume approaches h * pi * r^2.

Each cone base seems to have a corresponding opposing conebase on the other side of the particle.

In a sphere, if each cone is made narrow enough, the spherical shell more closely approximates a flat wall.

Okay, I'm convinced.

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### Re: Dyson Sphere / Ringworld (in)stability

EricH wrote:
Cyclocross4life wrote:I have no physics background, but wouldn't the doppler effect result in a dampening affect on the solar sales? the energy transpher from the light on the sales would be red-shifted on the side that began moving in towards the star, while the otherside would be blueshifted.

Except for two things--1) the radial component of motion isn't very large, so the doppler effect would quite small, and 2) the shift is in the opposite direction from what you said--that is, the side approaching the star would see its light (very slightly) blue-shifted, while the receding sail would receive red-shifted light.

Oops, had my light shifts backwards, thanks for pointing that out

If we found an infinitely strong material that could withstand temperatures higher than the core of a star and managed to encicrle a star in a ring of it, would it actually matter if the star pulled it offcenter? seems like it would just have one side going through the middle of a star, while the rest of it stuck out.

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### Re: Dyson Sphere / Ringworld (in)stability

Cyclocross4life wrote:If we found an infinitely strong material that could withstand temperatures higher than the core of a star and managed to encicrle a star in a ring of it, would it actually matter if the star pulled it offcenter? seems like it would just have one side going through the middle of a star, while the rest of it stuck out.

Well that would pose quite a problem if you have the ring set up as a habitable surface. After all, if the ring is still rotating, then you'll soon find your section of the ring thrust through the core of the star. And if it's not rotating, then there's no centripetal force keeping you, (or other things, for example, air), stuck to the inside surface of the ring.

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### Re: Dyson Sphere / Ringworld (in)stability

Re: Solar sail as the balancing force.

Solar sails are tremendously terrible, you basically need ~10^6 m^2 of very light material (at least 1/10th the weight of paper) to hold up a 1 tonne payload. I can imagine even a small perturbation giving a serious problem for any solar sail based solution.

Just use the thrusters

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### Re: Dyson Sphere / Ringworld (in)stability

Soralin wrote:And if it's not rotating, then there's no centripetal force keeping you, (or other things, for example, air), stuck to the inside surface of the ring.

Centripetal force does not keep you stuck to the ring. It keeps you from flying through it.

It is one thing to tell students "there is no centrifugal force" in an attempt to avoid confusion. But using it in completely the same way, only substituting centripetal is seven times more wrong.