Self-supporting 'anti-gravity' cage.

[No brains]

Suppose there was a planet. Around this planet, some people built a cage. The cage had normal supports when built, but when the cage was completed and balanced, the supports were removed. All of the cage would be pulled toward the center of the planet, but the cage was built so strong and so balanced that no one part of the cage could fall ahead of the other sections. Would the cage hold itself up in the sky so long as the gravity of the planet pulled down on all sides of the cage equally?

This might be impossible to describe without some kind of graphic, or brains, but I want to know if anyone else ever thought of this before.

[Grinner]

What is the cage shaped like?

I'd think a cube would begin to deform instantly.

[No brains]

What is the cage shaped like?

I'd think a cube would begin to deform instantly.

Let's assume a sphere or something with so many little facets it may as well be called a sphere. For that matter, a solid bubble or sphere could funnel into itself to resist gravity too, assuming the idea could ever work.

[Mando Knight]

The cage would probably need to be built out of some unbelievably strong material in order to not buckle, but ignoring that, yes, it would more-or-less float in place after it was finished.

[Fortuna]

Would it be stable, though? I'd think that any slight shift would tend to cause one side of the cage to crash into the planet below (although admittedly, that's based on intuition rather than maths - I'll have a go at some maths tonight, perhaps, if no one beats me to it.)

[Karoht]

Suppose there was a planet. Around this planet, some people built a cage. The cage had normal supports when built, but when the cage was completed and balanced, the supports were removed. All of the cage would be pulled toward the center of the planet, but the cage was built so strong and so balanced that no one part of the cage could fall ahead of the other sections. Would the cage hold itself up in the sky so long as the gravity of the planet pulled down on all sides of the cage equally?

This might be impossible to describe without some kind of graphic, or brains, but I want to know if anyone else ever thought of this before.

So kind of like a Dyson Sphere/Cage around a star, but scaled down to a planet instead?
Is the cage above the atmosphere? Keep in mind that some satellites orbiting earth are still in earths atmosphere.

I say yes, it would remain stable so long as it was self supporting. It would need something to stablize it's orbit/momentum as the planet moves in space, but that's just a guess. Depends on the orbital path and speed of the planet as well. Also, does it rotate with the planet? Since there were initially supports connecting it to the planet I'm going to say yes? Might need thrusters to maintain that inertia once in a while.

This is all operating on rudimentary knowledge of physics, and a poor memory of it at that.

[Broken Crown]

I think Random is right. If anything moves the cage even a little off-centre, the whole thing will collapse. The force of gravity is inversely proportional to the square of the distance, so the part of the cage which is closest to the planet will be attracted more strongly than the part that is further away, so it will be pulled towards the centre of the planet, making the cage even more off-centre, causing a positive feedback loop. Also, tidal forces will squash it.

As I recall, Larry Niven's Ringworld had the same problem. It's in equilibrium, but it's an unstable equilibrium, so it'll only stay up until something nudges it just a little bit.

[warty goblin]

It's worth noting a few things here. Planets are not perfect spheres, mostly because they rotate. If the planet's axis of rotation is tilted relative to its orbital plane, the action of the sun's gravity on this slight deviation from a sphere will cause the axis of rotation to wobble. It's a very slow wobble to be sure, but it is a wobble; this is why in some thousands of years Polaris will no longer be the visible star closest to polar north.

All of which boils down to the fact that unless your cage can somehow dynamically alter itself, in a couple thousand years the planet will no longer be pulling equally on it in all directions.

But I'd expect an asteroid would probably have dinged it by then, and then it's all over. Ditto if the planet has a moon.

[No brains]

Another person IRL brought up the Dyson sphere comparison, which got me thinking of some other things. Are Dyson sphere theoretically stabilized by the star's pulling with gravity as well as pushing with matter and energy? If so, is it possible to use a planet's magnetic field to stabilize the cage by making the cage so that it is repulsed by, rather than attracted by the field?

As for outer forces: yes, they really do set the idea in shambles.

[Knaight]

I think Random is right. If anything moves the cage even a little off-centre, the whole thing will collapse. The force of gravity is inversely proportional to the square of the distance, so the part of the cage which is closest to the planet will be attracted more strongly than the part that is further away, so it will be pulled towards the centre of the planet, making the cage even more off-centre, causing a positive feedback loop. Also, tidal forces will squash it.

Treating the planet as a point mass here, the of the cage which is further away also consists of a greater part of the surface, and the increased mass there operates in an opposite way than the closeness of the planet. It would be a pretty straightforward surface integral to cover the rest of this, but I'm lazy, and based off hazy memory and intuition, I'm thinking that it wouldn't actually be much of a problem. What could be a problem is the balance of forces allowing the cage to move entirely too freely around the planet, ending with one side smashed into it.

[factotum]

As he says, this problem was brought up in Niven's "Ringworld", and I believe it was a professor of astrophysics who pointed out the problem, so one would hope he knows what he's talking about. If I recall correctly, the problem is that the mass on the further side is greater by a linear degree, but the reduction in gravitational attraction goes by the inverse square law, so the greater mass does not offset the reduced attraction.

[Knaight]

As he says, this problem was brought up in Niven's "Ringworld", and I believe it was a professor of astrophysics who pointed out the problem, so one would hope he knows what he's talking about. If I recall correctly, the problem is that the mass on the further side is greater by a linear degree, but the reduction in gravitational attraction goes by the inverse square law, so the greater mass does not offset the reduced attraction.

Sure, but a ring and a sphere have dramatically different behaviors in this regard, so that doesn't really help here.

[Fortuna]

Right, that... was painful. Glad I don't have to do that kind of algebra these days, and glad I have Wolfram to assist me.

Yeah, a uniform perfect sphere of zero thickness surrounding a point mass tends to return to a coincident centre of mass, and unless I recall incorrectly that generalizes to surrounding a non-point mass and to spheres of nonzero thickness. So no compelling reason it can't work, besides the strength of the materials.

[Max™]

Hmmm, the Shell theorem says that the net gravitational force at the center of a spherical arrangement of matter is zero, similarly the net pull from a shell of matter at the center would be zero.

The problem there is that it could drift in relation to the planet and collide.

With a star you can use a statite type arrangement and "inflate" it with radiation pressure, with a planet, you would need stuff like Xeelee Construction Material, i.e. physics breaking ubermaterials, otherwise I don't see how you would be able to keep it rotating and generating pseudo-gravity on the interior, or just generally find some way to keep it in place relative to the planet.

We have portions of this structure in place with the geostationary satellites, but extending them into a shell is a bit more difficult.

Edit: Incidentally, the cube example is one of the uses described in the Xeelee stories, the humans call them Sugar Lumps, there is more about them in the short Vacuum Diagrams and I think one actually called Sugar Lump in the Vacuum Diagrams compilation.

Pools of Light has an example with a sphere of XCM around a star with "window" sections (the pools) and the sphere was rotating as I recall so there was bearable gravity near the equator but the pull from the star was unbearable as you went to higher latitudes.

[nedz]

The action of other planets and the Moon would soon cause perturbations which would destabilise the orbit of the cage — this is why geosynchronous satellites have to do constant station keeping. (Actually variations in the earth's gravitational field would do this too). Once one side of the cage is closer to the earth than the other; gravity would pull it further out of alignment. The only solution would involve continuous station keeping, which would consume a large amounts of fuel — which causes further issues.

[noparlpf]

It's hypothetically possible in a simplified system. If the Earth is a perfect sphere (or better yet, a point mass) and there's no movement or outside masses, then the bubble would stay in place. But here in real life, the Earth isn't perfectly spherical, it moves, it wobbles, it has a moon, it has a sun (I'm lazy, but I wonder how much more gravity the sun exerts on the near side of the Earth than the far side...), and a bunch of other random stuff flying around.

[Ravens_cry]

Light pressure would also have an effect I wouldn't doubt.

[ace rooster]

Another person IRL brought up the Dyson sphere comparison, which got me thinking of some other things. Are Dyson sphere theoretically stabilized by the star's pulling with gravity as well as pushing with matter and energy? If so, is it possible to use a planet's magnetic field to stabilize the cage by making the cage so that it is repulsed by, rather than attracted by the field?

As for outer forces: yes, they really do set the idea in shambles.

ohh, that is cool, but you don't go far enough. Current carrying rings that compress the planet's magnetic field would be stable with a little angular momentum, and scale favorably (ie, doubling the volume of conductor and current increases lift by more than a factor of 2 for very big machines, by which I mean machines with magnetic field comparable to the planet). You would need some alternating current components to keep the rings seperate, but you do not need any exotic materials if you support it magnetically. Superconductors would help, but are not required.

[CarpeGuitarrem]

Well, the atmosphere manages it somehow. :smallbiggrin:

[Mando Knight]

Another person IRL brought up the Dyson sphere comparison, which got me thinking of some other things. Are Dyson sphere theoretically stabilized by the star's pulling with gravity as well as pushing with matter and energy? If so, is it possible to use a planet's magnetic field to stabilize the cage by making the cage so that it is repulsed by, rather than attracted by the field?

A Dyson Sphere is stabilized by an interesting quirk in gravitational math:

At a Sphere's scale, even a star can be approximated as a point mass fairly easily. In addition, the Dyson Sphere's thickness is considered to be much thinner than its radius (since it's literally on an astronomical scale, like with the star's approximation as a point mass, this is rather valid). Inside a thin uniform shell, the net gravitational pull on any point mass is 0... at any location off-center, the added closeness to one section of the sphere is exactly counteracted by the mass of the remaining sections.

[Ravens_cry]

A Dyson sphere as originally conceived wasn't a single rigid structure either, I believe.

[factotum]

but I wonder how much more gravity the sun exerts on the near side of the Earth than the far side...)

About half as much as the Moon does, since that's what causes the tides. :smallsmile:

[Fortuna]

Hmmm, the Shell theorem says that the net gravitational force at the center of a spherical arrangement of matter is zero, similarly the net pull from a shell of matter at the center would be zero.

The problem there is that it could drift in relation to the planet and collide.

With a star you can use a statite type arrangement and "inflate" it with radiation pressure, with a planet, you would need stuff like Xeelee Construction Material, i.e. physics breaking ubermaterials, otherwise I don't see how you would be able to keep it rotating and generating pseudo-gravity on the interior, or just generally find some way to keep it in place relative to the planet.

We have portions of this structure in place with the geostationary satellites, but extending them into a shell is a bit more difficult.

Edit: Incidentally, the cube example is one of the uses described in the Xeelee stories, the humans call them Sugar Lumps, there is more about them in the short Vacuum Diagrams and I think one actually called Sugar Lump in the Vacuum Diagrams compilation.

Pools of Light has an example with a sphere of XCM around a star with "window" sections (the pools) and the sphere was rotating as I recall so there was bearable gravity near the equator but the pull from the star was unbearable as you went to higher latitudes.


The action of other planets and the Moon would soon cause perturbations which would destabilise the orbit of the cage — this is why geosynchronous satellites have to do constant station keeping. (Actually variations in the earth's gravitational field would do this too). Once one side of the cage is closer to the earth than the other; gravity would pull it further out of alignment. The only solution would involve continuous station keeping, which would consume a large amounts of fuel — which causes further issues.


It's hypothetically possible in a simplified system. If the Earth is a perfect sphere (or better yet, a point mass) and there's no movement or outside masses, then the bubble would stay in place. But here in real life, the Earth isn't perfectly spherical, it moves, it wobbles, it has a moon, it has a sun (I'm lazy, but I wonder how much more gravity the sun exerts on the near side of the Earth than the far side...), and a bunch of other random stuff flying around.

As I said above, having done the maths (with some help from Wolfram Alpha), momentary perturbations do not cause the sphere to crash - the gravitational force of the body it orbits, which is dominant, will tend to return it to its stable state.

[Max™]

I didn't ignore it, I posted before I saw your post. :P


Well, the atmosphere manages it somehow. :smallbiggrin:

If you could get the cage to float on top of the atmosphere that might work.

Kinda describes the cloud layer on Venus actually.

[Broken Crown]

Hmmm, the Shell theorem says that the net gravitational force at the center of a spherical arrangement of matter is zero, similarly the net pull from a shell of matter at the center would be zero.
Right. Shell theorem + Newton's 3rd law. Now I feel stupid.


Yeah, a uniform perfect sphere of zero thickness surrounding a point mass tends to return to a coincident centre of mass, and unless I recall incorrectly that generalizes to surrounding a non-point mass and to spheres of nonzero thickness. So no compelling reason it can't work, besides the strength of the materials.
Tidal forces could still be a problem though, could they not? A nearby moon or star would tend to make the shell non-spherical. I wonder how rigid the shell would need to be to prevent this from causing a catastrophic failure.

(I'm not asking anyone to do more math; I'll do it myself when I have the time. I need the practice.)

[factotum]

Tidal forces could still be a problem though, could they not? A nearby moon or star would tend to make the shell non-spherical.

Generally, if you're going to build a Dyson sphere, you'll probably need to use every scrap of matter in the system you build it in to construct it--even if you *didn't*, sequestering that matter or ejecting it from the system would make sense anyway, because you don't want random bits of orbiting rock punching holes in your sphere. As for a star, the only way you'd get significant tidal forces from one is if it was part of the same stellar system, and why would you choose to build your Dyson sphere there? It's not like stellar systems with only one sun are hard to find!

[Eldan]

(I'm lazy, but I wonder how much more gravity the sun exerts on the near side of the Earth than the far side...)

Well, enough to cause noticeable tides, at least.

[Max™]

Generally, if you're going to build a Dyson sphere, you'll probably need to use every scrap of matter in the system you build it in to construct it--even if you *didn't*, sequestering that matter or ejecting it from the system would make sense anyway, because you don't want random bits of orbiting rock punching holes in your sphere. As for a star, the only way you'd get significant tidal forces from one is if it was part of the same stellar system, and why would you choose to build your Dyson sphere there? It's not like stellar systems with only one sun are hard to find!

Fun fact, 16 of the closest 55 star systems are binary or trinary, and estimates range from 1/3 to 1/2 of the galaxy consists of multiple star systems.

[TuggyNE]

Well, enough to cause noticeable tides, at least.

Are the sun's tides really noticeable past the variance in the moon's tides? *goes off to check* Yes, but not nearly as much. Total solar tidal effect is only 46% of lunar effect.

[Eldan]

Are the sun's tides really noticeable past the variance in the moon's tides? *goes off to check* Yes, but not nearly as much. Total solar tidal effect is only 46% of lunar effect.

But they are still noticeable. The combination of the two tides is what causes springtides and so on.

[Tyndmyr]

Suppose there was a planet. Around this planet, some people built a cage. The cage had normal supports when built, but when the cage was completed and balanced, the supports were removed. All of the cage would be pulled toward the center of the planet, but the cage was built so strong and so balanced that no one part of the cage could fall ahead of the other sections. Would the cage hold itself up in the sky so long as the gravity of the planet pulled down on all sides of the cage equally?

This might be impossible to describe without some kind of graphic, or brains, but I want to know if anyone else ever thought of this before.

Technically yes, but it would be very instable. The slightest shift will rapidly escalate into an impact. You can roughly simulate this with a magnet and a hollow metal container.

Better to built your ringworld, dyson sphere, etc safely away from planets.

[ace rooster]

Technically yes, but it would be very instable. The slightest shift will rapidly escalate into an impact. You can roughly simulate this with a magnet and a hollow metal container.

Better to built your ringworld, dyson sphere, etc safely away from planets.

Wrong, magnetic forces drop off as the 4th power, compared to the 2nd power for gravity and electrostatics. This is very important, as it means we can use flux density as a measure of field strength. This implies that converging field lines mean a strengthening field, and diverging field lines mean a weakening field. Spherical symmetry means that all field lines have to point to or from the center, and that the field at the center is 0. As field lines converge to or diverge from the center, the maximum field has to be at the center, where it is 0, hence the field is 0 everwhere within the sphere. The system is not unstable, is is neutrally stable.