orbital ring in slow decay, what's the fallout?

Question

An orbital ring was just bombed by a terrorist group, causing just enough damage to push the ring out of orbit too far for a readjustment to save it. Assuming that all escape craft have already launched from the ring and stranded people onboard, the space elevators are destroyed, and that it will eventually impact earth, what would the damage be to earth? would we have another mass extinction like the dinosaurs? would the ring kill everything on earth? would spaceships be able to get in and out of atmosphere to evacuate survivors(as long as the atmosphere isn't on fire or filled with flying debris or something like that, rescue ships should be able to land)? would earth still be habitable afterwards?
The orbital ring is made out of steel, a very strong version of concrete, some glass, and a bunch of boosters and rocket equipment. probably best compared to a hollow cross section of the death star large enough to encircle the earth.

James McLellan · Accepted Answer

An orbital ring is visualized as a solid body that transfers any potential energy drop to the whole structure (raising the potential energy on the opposite side). In that way, the ring converts gravitational forces into structural forces inside the ring.
The ring is generally visualized as stationary, relative to the ground. Each segment is held by ground anchors and rope/tether from floating off (and thus, holding the opposing side from falling down).
As a result, the ring is not in orbit.

What does this mean?
There are only two ways to bring a ring down : shear a piece off completely or break enough tethers that the whole thing is coming down.
If a Piece is Sheared Off
Since it has no orbital velocity, sheared-off components will begin to fall immediately. At space station-like altitudes of 400 kilometers, each falling piece has $ 1 times 9.8 times 400,000 approx $ 4 megajoule of potential energy. Scaling up, each ton has about 4 gigajoule of energy.
The component is initially at rest, so frictional protection by the atmospheric heating is going to be significantly reduced. It will take $sqrt{} 400 - 100 km times 1,000 {m over {km}} times 2 div 9.8$ = 247 seconds to hit the Karman line. In that time, the falling load will have built up a velocity of 2,424 meters per second.
I'm ripping off my calculator for Saturn, so this is low, but the frictional heating should be a few hundred degrees (about 700 K). Not enough to melt steel.
When the fragment hits the atmosphere, ${1 over 2} rho v^2 A$ of force will be bleeding away potential energy.
For a 1-ton steel cylinder-shaped piece of debris, about 1 millimeter thick, 3 meters wide, and $1,000 div 5,000 {{kg} over {m^3}} div 3 pi div {1 over 1,000} approx $ 21 meters long, the terminal velocity of the fragment is $   sqrt{} [1,000,000 kg times 9.8] div [21 times 3 times 1.2 {{kg} over {m^3}} times {1 over 2}]$ = 509 meters per second / 1,832 kph. And carrying 129 megajoules of energy.
That's really not so bad. A typical airplane crash has 3658 megajoules of energy.
What If The Whole Thing Comes Down?
To figure this out, I think I need to understand the structure of the orbital ring. The only way I can think of constructing one (and I see it's mentioned this way in other implementations) is to build the whole ring on the ground, and add links, lifting the whole ring with each extension to the circumference.
How much does the ring weigh while resting on the ground. Still sticking with steel 3 meters in diameter, 0.001 meters thick, and 39,940 kilometers long and made of steel at a density of ~5,000 ${kg} over {m^3}$ $approx$ 599 million kilograms. The stress is carried by the walls : about 587 gigapascals. This is way above the compressive strength of steel -- so we'll need to assume some kind of exotic material.
However, it makes sense that after the first part hits, the remainder of the falling ring will be partly supported by the ring structure.
The destruction will be in a 3-meter ring around the planet, and because of shakiness as the thing rattles apart and falls the area that is subject to falling debris or made unsafe to fly (or walk) will be much broader, but I don't think the devastation will be close to civilization-ending.

LSerni · Answer

Such a ring would certainly have some kind of "fail safe"; it is even possible that what the terrorists managed to do is to (partially) activate the fail safe.
The last ditch fail safe would be engineered to destroy the ring and avoid a Kessler catastrophe; probably, some kind of slow explosive designed to transfer momentum between sections of the ring. Two thirds of the sections would be accelerated, ensuring they end up very far away. The remaining third would be decelerated, deorbiting quickly. Those sections would also be designed to self-destruct in smaller pieces as soon as they hit the atmosphere; this could be done by using materials that have little heat resistance, and burn or melt at reentry temperatures.
The whole catastrophe would be a serious hit to orbiting satellites and would likely trigger a small Kessler cascade anyway. Plus, the reentry shrapnel would wreak measurable damage: Central Africa, Indonesia, Malaysia, north Brazil, Colombia, Venezuela would all be hit (this assuming that the ring is in equatorial orbit. It would rotate at more or less orbital velocity, to balance compressive forces from Earth gravity, and possibly rotate on its axis to generate spin gravity).
But, all in all, the damage would be comparatively small. No extinction event, no fire and brimstone from the heavens.

Andrew Brēza · Answer

You have a lot of options
I'll tackle your two questions separately.
1. How long will it take for the ring to crash down to earth?
It's really hard to generalize how long a given object will take to descend from orbit. NASA has useful information:

The higher the altitude, the longer the orbital debris will typically
remain in Earth orbit. Debris left in orbits below 370 miles (600 km)
normally fall back to Earth within several years. At altitudes of 500
miles (800 km), the time for orbital decay is often measured in
decades. Above 620 miles (1,000 km), orbital debris normally will
continue circling Earth for a century or more.

I'll assume that your ring is operating in Low Earth Orbit (LEO). The answers to this question go more in-depth with the science of how long something will take to fall from LEO. You could write your story with the descent taking weeks or years. It's up to you as an author.
2. What happens to the Earth when it crashes?
I doubt that your ring was designed to survive reentry, so it would break up as it passed through the atmosphere. It's up to you how large each piece should be. Play with this calculator and see what level of devastation you want. Do you want to punch a bunch of holes in the planet that are each a few miles across? Then you'll want the ring to break into a ton of relatively small pieces, many of which completely burn up on reentry. Do you want to absolutely demolish the planet? Then keep it in a few massive chucks.

orbital ring in slow decay, what's the fallout?

3 Answers

What does this mean?

If a Piece is Sheared Off

What If The Whole Thing Comes Down?

You have a lot of options

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