# How would gravity affect a structure that completely encircled the earth

If a circular structure could be built that would wrap around the entire earth, but was of a larger radius, would it 'float' above the earths surface or would it somehow fall onto the surface at some points and be pushed further away at others? In particular, could the ring be stable without moving, or would it need to orbit at the same speed as if it were a satellite.

This construct would be similar to a dyson sphere but only a band rather than a completely enclosing sphere. However, differences and similarities between the structures would be great to know about!

I'm more interested in how it would theoretically act than its feasibility, so feel free to explain materials/stresses etc but "it's the future" can be used to explain away those kind of issues.

• This concept was discussed in some detail in Arthur C. Clarke's book 3001. Jun 24 '18 at 12:29
• A proper Dyson sphere is not a solid shell but a swarm of orbiting satellites. There are many reasons why a solid shell wouldn't work (including: it could never hold up its own weight; it wouldn't be gravitationally stable; the inside would heat up higher than the melting point of any substance; it would take far more mass than a swarm of satellites that can accomplish essentially the same thing). The swarm is what Dyson proposed, and it's only in science fiction that it mutated into a solid shell. Jun 24 '18 at 14:09
• @Nathaniel a Dyson sphere is a solid shell; the swarm of orbiting satellites is called Dyson swarm. Disregarding whether a solid sphere would be stable or cost-effective in real life, Dyson spheres have been featuring in sci-fi as a concept for a long time, and they are (usually) the solid sphere-kind. Jun 25 '18 at 9:29
• @RealSubtle yes, but they have very little to do with Freeman Dyson, so the name is incorrect. Jun 25 '18 at 9:42
• That said, I've never read the original paper and could be wrong. I will check that. Jun 25 '18 at 9:44

This remembers of Larry Niven's Ringworld series, except by the fact that in Ringworld the structure is circling a star, not a planet. The basic idea is that, by being in the center, the gravity force is simmetrical and cancels itself, so the object does not move.

The issues are:

• There are external objects that will have a gravitational effect on such structure, most notably the Moon and the Sun, but other planets will probably count, too.

• The gravity field around Earth is not uniform, there are zones with higher than average gravity potential. Wikipedia gives us a nice image:

• Even if you magically solve/compensate for the above effects, the equilibrium is unstable. The moment the ring gets, say, one meter outside its position, the part of it that has become closer to the Earth will have an increased attraction compared to the other side, which will further destabilize the orbit.

So, you can do without escape velocity, but you need some system to stabilize the structure or it will fall down on those Earthlings (but do not worry, they had it coming).

• Could explain which unit is the gals I see in the image? I knew gals can be attractive, but never saw them as units for gravity...
– L.Dutch
Jun 24 '18 at 9:59
• @GeoffreyBrent yeah, sorry. I got things mixed up. Jun 24 '18 at 13:21
• @L.Dutch en.wikipedia.org/wiki/Gal_(unit) Jun 24 '18 at 14:15
• @SJuan76 -- The gravity anomalies shown in the map are dwarfed by the gravity variations caused by the earth's rotation: either directly, as centrifugal force; or indirectly, by the variation in the distance from the center of the earth to the earth's surface, from the equator to the poles. Jul 26 '18 at 6:15

In particular, could the ring be stable without moving, or would it need to orbit at the same speed as if it were a satellite.

If the ring is made of a solid material then no, it couldn't be stable without moving - it would have to orbit. This is for two reasons: firstly because a non-orbiting solid ring would have to hold itself up by compressive strength, like an arch. Each section of the ring is trying to fall towards the Earth, and the only thing stopping it is that it's pressing sideways against the two neighbouring parts of the structure. This would require a material of far greater compressive strength than could possibly ever be made out of atoms, or any other form of matter that we can plausibly imagine - it's completely out of the realm of feasibility.

The second reason is that even if you could make a solid ring out of magical future-tech force fields it would not be gravitationally stable - whichever part of the ring is slightly closer to the Earth will experience more gravitational force, pulling it even closer to the ground and setting up a feedback loop that will cause one side of it to fall out of orbit while the other moves away from the planet.1 (That said, if you have the tech to make such a material you can probably put some thrusters on it to stabilise it. Just be aware that making the ring in the first place is far beyond plausibly imaginable science.)

However, all is not lost: if you don't mind your ring having moving parts it's quite possible to have a solid, apparently non-rotating structure that encircles the Earth, even with present-day tech, if you put enough resources into building it.

The idea is called an orbital ring. It consists, essentially, of a solid loop of wire that's moving slightly faster than orbital velocity, but surrounding it is a non-moving solid structure that repels it using magnets. The solid structure is trying to fall to Earth, but the centrifugal force from the moving wire balances it, so it stays in place. Attach a few space elevators and linear accelerators and you have a very plausible way to escape Earth's gravity well.

If you're interested in the idea I highly recommend this video by futurist Isaac Arthur, which goes into the concept in quite some depth. It's really required watching if you intend to use the concept in a science-based context.

1note to Newtonian mechanics geeks: the spherical shell theorem doesn't apply here, because it's a ring and not a sphere.

If you make a couple of assumptions the system might be easier to control.

First that the ring spins, not necessarily to escape velocity, but enough to transfer destabilizing effects along the ring - i.e. whatever would affect the ring from a fixed frame of reference would, from a rotational frame of reference, amount to an oscillation rather than a constant destabilizing force.

Second, assuming that the rate of rotation is much less than escape velocity, then you would not be dealing with tensile forces, but rather compression forces. Consider that gravity, for all intents and purposes, is acting equally over the ring. This means that gravity is pulling the ring toward the center, trying to compress the ring against its natural radius, or effectively, reduce it's circumference - if you will. So the greater concern in terms of structural engineering in this case would be to try to make the ring rigid along it's circumference - so you'd need to keep it from crumpling or bending, rather than keep it from flying apart.

Now, given that we understand that we are dealing with rigidity and oscillations, this allows an engineer to develop a control system with fewer outputs ( any kind of motor or thruster ) and perhaps even fewer inputs ( sensors which measure stability ).

As a loose analogy, machine learning systems which control quadcopters have been trained to recover when propulsion systems get damaged in flight. A system which normally flies on 4 rotors, can still be stabilized in a rotational axis with only 3 or even only 2 or 1 rotor(s). This works because the destabilizing feature of the flight - a constant force in a fixed orientation - translates into an oscillation in a rotational system - which can then be overcome or minimized by stabilizing the axis of the oscillation. In other words, counter the complex ( cone shaped ) rotation until it becomes as close to a linear axis as possible ( focus the cone into a line ) - at which point the control oscillation ( to counter the destabilizing feature of the out of control rotation ) minimizes into a constant control ( a stable spin ) in a rotational frame.

• A ringworld is gravitationally unstable, even if you spin it. Spinning it just makes it more dangerous when it collides with the Earth, and it will. Assuming that the ringworld is rotating in the x-y plane around the earth and that it is thin enough in the z-direction, then it will ignore gravitational effects in the plane of rotation, and wobble up and down the z-axis. By ignoring the gravitational effects, I mean that each bit of mass pulls on each side of the ring with the same pull. Jun 24 '18 at 14:47
• @NomadMaker I was not implying that there are no concerns to with gravitational or orbital stability, only that it would perhaps be mechanically simpler to address those concerns if the ring is rotating/orbiting. :-)
– Nolo
Jun 24 '18 at 14:55
• 4, the trouble is that it isn't orbiting. Because it's a single object, it can't orbit. And spinning makes some of the problems much worse, and some of them easier. Unlike Larry Nivens' creation (The Ringworld) this doesn't have to spin fast enough to produce gravity on the inside and it's smaller. The Ringworld not only would have crashed into the sun without rockets, but it's rotational velocity would have torn it apart. Jun 24 '18 at 19:08

If you build enough pillars, your structure will be hold in place by the them. Of course this will limit the maximum height you can reach above the surface.

If you place no pillars, the thing will fall.

In this case, if you give the thing enough velocity, it will be in a continuous fall, without ever reaching the surface, more or less like satellite in orbit do.

However, you cannot practically have such orbiting structure lower than LEO, for the simple reason that atmospheric drag at those high speed (and we are talking about km/s) would:

• generate a sheer amount of heat, damaging the structure and whatever happens to be close to it
• quickly dissipate the kinetic energy, unless you constantly replenish it
• Re: pillars: no, there is no material that can be made that has enough compressive strength to hold its own weight when built that tall, let alone hold up a structure. Jun 24 '18 at 13:48
• @Nathaniel, isn't that what I stated with "this will limit the maximum height"?
– L.Dutch
Jun 24 '18 at 14:11
• Hmm, I was assuming the ring would be in space, but reading the question again it doesn't actually say that. If the ring is only a few hundred feet up then sure, it could be held up with pillars! Jun 24 '18 at 14:18
• I'm imagining a the highest possibility would be something like the monorail in seattle, encircling the globe. Much higher and you would need many more pillars. Jun 24 '18 at 16:19

What you describe is a Ringworld, they're much harder to build than Dyson-shells, there are a lot more stresses involved, there's no material known to man with enough tensile strength to actually build one but you're handwaving that; here's what you can't handwave, they're seriously unstable (so are Dyson-shells, hard Dyson spheres, by the way). Regardless of what they're put around Ringworlds wobble horribly and that's without any other bodies in the same star system as them. If you keep Earth's moon and try to build a ring around the planet it won't last to completion, gravitational resonances will keep tearing it apart. Then you have the effect of the sun which would do the same, the other planets in the solar system would take longer but the result would be that the ring eventually wandered and crashed into the earth. The varying "background" gravity of the galaxy is enough to cause a Ringworld to eventually wobble of into whatever it's orbiting, if it's stationary the effect is accelerated. How do you stabilise a Ringworld? Put massive Bussard Ramjet style fusion drives along both edges of the ring that use the solar wind as fuel to push the ring back into position; at least that was the theory when we thought Bussard Ramjets worked now we know better I'm not sure if the Ringworld is a feasible structure or not. It certainly has a severely limited lifespan in a star system that hasn't been emptied of everything else.

Yes, this could be done. The structure would be a very thick band (from a construction point of view), or a very narrow disk (from an astronomical point of view).

Mild steel has a yield strength of about 250 MPa, and a density of about 8,000 kg / m³. For a structure close to the earth, the weight is about 80 kN / m³, or 80 kPa / m of the band's vertical thickness.

The band needs to resist a hoop stress of (the band's weight converted to a pressure) times (the radius of the hoop) divided by (the thickness of the band). The previous paragraph shows that mild steel can handle this stress if the radius of the hoop is less than 3,000 times the vertical thickness of the band. Extra band thickness will provide a margin of safety. The earth's diameter is about 12,800 km at the equator, so the band's vertical thickness should be about 2,200 meters times the margin of safety.

The band would have to be fairly wide horizontally, in order to prevent buckling. If the band were just one meter wide, the top would flop down, and it would no longer be tall enough to hold up its own weight. I have not done the calculations, but I expect that if the width were at least 1/6 of the height, vertical buckling would not be a problem. Waves along the length of the band might be entertaining, though.

Cyclic loading and stress-corrosion fatigue would also be issues. I have not done these calculations either.

So a belt of mild steel that was 1 kilometer wide by 6 kilometers tall by 80,450 kilometers around would probably suffice. That is about 500,000 cubic kilometers, or 4 million billion metric tons. Nearly all of that material is iron, which is fortunately abundant on Earth. About 0.3 percent of that material is carbon, or 12,000 billion metric tons.

Mass of earth's atmosphere: about 500 million million square meters times 10,000 kg per square meter, or 5 million billion metric tons. Thus, even extracting all of the carbon from the atmosphere would yield only about 800 billion metric tons of carbon. Extracting all of the world's proven coal reserves would only yield another 800 billion metric tons of carbon.

If we reduce the band size to 3,000 meters tall by 200 meters wide, and use ridges to prevent buckling, we reduce the material requirements to 30,000 cubic kilometers. This consists of 250,000 billion metric tons of iron and 750 billion metric tons of carbon.

Stronger materials would allow using less material, but would make fatigue issues more worrisome. Unfortunately, the alternative materials might be even harder to find than carbon.

As the MITSFS pointed out, "The Ringworld is unstable". This problem can be dealt with by leaving some of the jacks used to raise the ring in place. Unfortunately, we run into the problem of supporting the weight of the jacks. If the jacks are made of mild steel, they must either be only 3,000 meters tall, or must grow exponentially at the base. Alternative materials would be very useful for the jacks.