# Building a (solid) ring around the earth

Could you build a ring around the earth, so that it would just sit in the sky? I'm not talking a geostationary orbit of rubble like the rings around Saturn, but a solid structure just high enough to clear Mt Everest. As gravity would be acting equally on it from all sides it would just hover there wouldn't it?

Structurally it would be uniformly under compression as gravity would be trying to squeeze it inward, so a substance such as concrete would be perfect, and cheap too. Kind of like a giant masonry arch that keeps going right over the horizon.

Although the main reason for building such a structure would obviously be the lulz, I can think of one use: if you were to rotate it it could be used as a transporter - like a giant version of those moving footpaths they have at airports - 'travelators' I believe they're called. You could even have different rings at different heights going in other directions.

So would this be possible, physically, and economically? Should I start a Kickstarter campaign?

• Donation of 50 USD: Your name on the ring – Pavel Janicek Dec 19 '14 at 12:26
• Donation of 1000000 USD, we promise not to build it directly over your house. Because we're almost 99.9% sure it won't fall down, maybe. – stib Dec 19 '14 at 12:28
• Upvoted because I love this kind of concept but I cant help you on the "would be possible" question. Consider that if it rotates you could have many rails for cranes/hoist on the bottom of it, and then its just a matter of lifting cargo, rotating ring +up and down rails for delivering cargo everywhere. – mcbecker Dec 19 '14 at 12:28
• With Earth's gravitational variances and the moon's gravity pulling it slightly, that might set up some interesting mechanical resonance in the loop, making for a wild ride. – GrandmasterB Dec 19 '14 at 18:21
• @stib 60% of the time, the giant sky-ring stays up... every time. – corsiKa Dec 19 '14 at 22:34

Structurally, if my math is correct, no, it cannot hold together if made of concrete.

We can consider the ring as being analogous to a thin-walled cylindrical pressure vessel with a negative pressure. We start by describing the pressure:

$$P = F/A$$

Here, $A$ is the area of a given portion of the ring and $F$ is the force on the area. The force is equal to $\text{ gravity} \times \text{ density} \times \text{ volume}$, where the volume is the area of the portion of the ring times its thickness, or

$$F = g \times \text{ density} \times V = 9.8 \times 2400 \times A \times t$$

$t$ in the above equation is the thickness of the ring. This can be plugged into our equation for pressure to yield the following value after cancelling out $A$ (area) in the numerator and denominator:

$$P = 9.8 \times 2400 \times t$$

The tensile force for a cylindrical pressure vessel is $\frac{Pr}{t}$, although we have a negative force since gravity is compressing our pressure vessel, so we'll have an equivalent compressive force on our ring. We can plug our pressure equation in to get the following, after cancelling out thickness:

$$\text{ stress} = \frac{Pr}{t} = 9.8 \times 2400 \times r$$

$r$ in this case is the radius of the arch, which is roughly equal to the radius of the earth, or around $6370 \text{ km}$. We want this in meters to get stress in $\text{ MPa}$, so we'll convert to $2400 \times 9.8 \times 6.37 \times 10^6$, which comes out to around a total of $150 \text{ GPa}$, which is far greater than the compressive strength of concrete, which is around $800 \text{ MPa}$ for ultra-high performance concrete, and also much higher than the strength of materials such as steel or quartz. It's on the same order of magnitude as the compressive strength of diamond, but diamond is about 50% denser than concrete, so it would still probably fail. The stress is around the same point as the maximum predicted stress of nanodiamond, but this hasn't been tested in a lab.

Values used for calculations:

• Acceleration due to gravity of $9.8 \text{ m/s}^2$
• Concrete density of $2400 \text{ g/m}^3$
• Radius of $6370 \text{ km}$
• Maximum compressive stress of $800 \text{ MPa}$

All of this is under the assumption that the ring is relatively stationary with respect to the earth.

• We are going to need a loads of money to build it from diamonds... – Pavel Janicek Dec 19 '14 at 20:16
• @PavelJanicek Our planet would need to be entirely made of paper banknotes to afford that thing... – kubanczyk Dec 19 '14 at 20:41
• Awesome answer. Just added some LaTeX to improve the look; hope that's okay. – HDE 226868 Dec 19 '14 at 21:06
• They have great tensile strength, but don't do as well under compression as something like diamond. – ckersch Dec 20 '14 at 18:33
• @kubanczyk if the planet was made from/replaced with from banknotes it would have a much lower density, so lower gravity, so a thinner diamond ring would suffice. It is looking even more practical than before. – Penguino Aug 13 '19 at 0:13

Ringworlds have been around for a while in scifi. One major issue with sticking them around other objects (like planets or suns) is that they're inherently unstable in that scenario:

https://physics.stackexchange.com/questions/41254/why-is-larry-nivens-ringworld-unstable

Your object isn't really a ringworld but it would suffer from the same issue. Since gravity isn't perfectly equal all the way around, one side would fall, which destroys the integrity of the rest and would lead to it crashing to the ground.

# Build it on Space and include expansion/contraction joints

So, you mentioned concrete right?

Building it on the ground and then hoisting the pieces up sounds damn near impossible to me, many things would have to be considered: space for building, clearing whole areas for construction, activists against clearing wildlife reserves where one of the temporary pillars would stay...

I really think it should be built in space, using material found already in space. Sending the resources into orbit would be way to expensive.

That is how I see it:

1. Build it in space, using resources already out there
2. Like bridges, have built-in expansion-contraction joints, huge ones, to prevent faults in the overall extructure
3. Make it bigger (diameter wise) than it needs to be
4. Set it on place around earth
5. Contract joints to desired diameter (to make it hang lower on the sky)
6. Add rails for cranes/hoists on the bottom, rotate ring for longitudinal movement and go up and down rails for the latitude.
7. Hoist any cargo, move up and down / rotate to deliver anywhere on earth

The cranes on the bottom, like carts on rails, allow for many things to be added, like a huge lighting system, whenever a nation suffers from natural disaster you could rotate the ring so it hovers over it. Light up the night to help the rescue teams, you could pour water to extinguish fires, hoist people up for medical treatment on ring facilities...

I cant help you with the technical issues, how much it would weight, how wide/tall it should be, etc.. but I believe if such a structure would be possible, many possibilities would be open, like:

Solar panels on the outward side of the ring.

Base jump sport is the new trend?

Home for the elite class? Polution goes rampant down there, everything allright up here.

Skyport, biggest runway on top (railgun like?) or cataput to send cargo into space?

People could fly down on gliders, later the gliders are hoisted back up.

• Important thing to add. What about the ring structure being attacked by terrorists? Could their weapons reach it? Maybe planting a bomb among a cargo being hoisted? Should the ring have countermeasures against land-air missiles? Should the ring have weapons? What would the nations of the world think about it? Specially because it passes over their heads (daily?). Who would be responsible for administration of the ring? the UN? A new conglomerate of countries? – mcbecker Dec 19 '14 at 16:59
• Yes. They could reach it. They could nuke any of our GPS satellites right now. – Caleb Woodman Jan 6 '16 at 16:33

Such a ring is inside the Roche Limit, so tidal forces of the Earth's gravity would tend to tear it apart.

Also, unlike an object in orbit, where the orbital speed balances gravity, this ring is not anchored to anything. Any impetus vertically would allow the ring to drift relative to earth until one side or another collides with the ground.

• Could the ring be built on a borderline area? I mean, above the Roche Limit? Or could it be built not so high, say, 50.000m high? – mcbecker Dec 19 '14 at 18:37
• The Roche Limit only applies to bodies held together by their own gravity. If the ring is held together structurally, it wouldn't apply. – ckersch Dec 19 '14 at 18:38
• The lower it is the stronger the tidal forces. The Roche Limit is .8 to 1.53 radii for Earth. Making it thinner would help, but also make it weaker. – Oldcat Dec 19 '14 at 18:41
• @ckersch - Not quite. But for large objects the Roche Limit gives a feel for when Gravity forces start to matter. So even in this "arch", there is added strain being added by tidal forces that will try and break this arch, besides its own weight. – Oldcat Dec 19 '14 at 18:44

No, spare your reputation and your finances and the people of planet Earth--no Kickstarter for this one.

A ring satellite would be short-lived: The propagation of waves through the solid material results in nonuniform gravitation, which will generate more waves and hasten the ring's demise. Creating expansion/contraction joints would only transform the waves into more nearly inelastic collisions instead of elastic ones. If the wave propagations are elastic, they build up over time until the ring shatters due to the vibrations. If they are inelastic, they will steal energy from the ring's angular momentum and it will crash into the planet by gravity. Either way, you will be have to be putting enormous amounts of energy back into your ring to keep it "afloat" (in orbit) in order to compensate for these losses, and to damp oscillations to prevent self-destruction. This fact alone makes the economy of such a ring unsustainable.

James Clerk Maxwell found that a solid ring around a planet would be unstable and could not exist for long:

"...the stability of the motion of a solid ring depended on so delicate an adjustment, and at the same time so unsymmetrical a distribution of mass, that even if the exact condition were fulfilled, it could scarcely last long... These considerations, with others derived from the mechanical structure of so vast a body, compel us to abandon any theory of solid rings."

In this Essay Maxwell proved that the only stable configuration for a planetary ring is disconnected (fluid or solid) particles, each behaving like an isolated satellite.

In his introduction to the essay, Maxwell also wrote:

"The Saturnian system still remains an unregarded witness in heaven to some necessary, but as yet unknown, development of the laws of the universe."

https://archive.org/details/onstabilityofmot00maxw/page/66

As it turns out, the mathematical condition that Maxwell derived for the stability of Saturn's rings is the crux of automatic control systems--ultimately making computer-controlled space flight a possibility. His discovery is known as the Criterion for the Stability of a Dynamical System, and it is used in virtually every modern control system and field of research, from anti-aircraft guns to automobile cruise control to robots to medicine and epidemiology.

I write a few of the dizzying implications for posterity:

Saturn "told" us how to get there.

Much of robotics technology came from the study of Saturn.

Life itself requires a mastery of feedback and control, and must be stable in its environment in order to exist or to continue to exist.

• Thanks for the James Clark Maxwell info. He sounds like an interesting fellow. I like it when something like Saturn's rings has links to things like robotics. – stib Aug 12 '19 at 22:17