Assume it’s somehow hooked to an orbiting platform in space (I don’t know all of the mechanical aspects of the space elevator idea). If it got disconnected, would it inevitably fall back to Earth (likely causing a lot of damage)? Or just drift along, with whatever unlucky passengers doomed to starvation?
Your question is perhaps not as simple as stated.
What is the space elevater made of?
What is the mode of disconnection from its orbital tether/counter weight/platform? ie material failure, sabatoge, other?
What failsafes are in place or built in to the structure to prevent such an occurrence?
Interestingly, this is actually described in one of Kim Stanley Robinson’s Mars (Blue Mars I believe). In that scenario, which takes place during a civil war and the asteroid to which the elevator is attached is blown off, the cable crashes down onto Mars and wraps itself around a couple of times, causing an obviously huge amount of damage.
Weird! A friend of mine mentioned this exact scenario to me, which sparked this very thread. I wanted to know if this was a possible outcome.
As has been said already, this gets complicated quickly, but for the simplest scenario where the tether is held by tension and “dangling” from an orbital station in geostationary orbit, the parts below the break would fall to Earth in a long line as the Earth rotates away from it, and the parts above the break would still dangle from the orbital station, which might change orbit depending on how far its center of mass shifts.
The counterweight at the upper end needs to be out well beyond geostationary orbit in order to be able to hoist anything:
A break anywhere in the cable tethering that counterweight to Earth would result in the counterweight (and anything attached to it) being set into an elliptical orbit around the earth, with its perigee being the altitude at which it was previous being held by tether. The counterweight and whatever length of cable remaining attached to it would then be a rotating system with a period of 24 hours.
If the elevator is above the break, it’s going into elliptical orbit with that counterweight. If it’s below the break, then there are a couple of possibilities:
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If the elevator is sufficiently above geostationary orbit and massive enough relative to the length of cable below it, it could serve as a new counterweight that keeps the cable below it stretched taut. But if the elevator tries to descend to Earth, the amount of tension in the cable below it will decrease until it reaches zero - and if the elevator continues descending, it will start falling. This will happen with the elevator somewhere below geostationary orbit, but exactly where it will happen depends on how much cable mass is still out there above geostationary orbit still serving as a counterweight.
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If the elevator is below geostationary orbit, then it’s coming down.
The first season of the TV series Foundation had a good depiction of a space elevator collapse, from terrorist bombings. Long story short: millions, possibly billions dead, and a massive trench across the entire planet (although the fact that the entire planet of Trantor was one single city certainly exacerbated the death toll).
Yeah, I was envisioning the SF version where a significant amount of the mass is in a station in geosynchronous orbit, but I expect that scenario a) isn’t necessarily advantageous and b) underestimates how big such a station would need to be to be significant compared to even a slim tether and its counterweight with the distances involved.
I’m imagining a situation where the elevator is low enough to assure it comes down to Earth, while the break is very high, as close to the counterweight as possible while still assuring that the distal portion of cable (beyond the elevator) can’t function as an effective counterweight. Physics doesn’t demand a specific altitude for the counterweight: it could be very massive and just above geosynchronous (~22,000-mile radius, or very light and very far above geosynchronous. To pick an arbitrary length, assume the falling length of cable is 50,000 miles long, enough to wrap twice around the earth. It would happen pretty much at the equator, and a bit of quick measuring on Google Maps shows that for the 25,000 miles of circumference at the equator, about 19,000 miles is uninhabited ocean; for the remaining 6,000 miles of each lap around the globe, most of it would fall on the Amazon or across central Africa, with some of it also landing across Sumatra and Bornei. A round-section cable is not particularly aerodynamic, so unless it’s extremely large in diameter, like a cylindrical meteor, aero drag will limit its terminal velocity to far less than 25,000 MPH. Might damage some buildings, maybe even kill some people unfortunate enough to be near the impact zone, but I don’t envision anything like a trench being laid down across the face of the earth.
Here’s the scene in question:
Anything below the break would fall, but most of it wouldn’t hit the surface. It’d burn up in the atmosphere before then. The cable would be made of carbon, and have a very high surface area, and carbon, heated very hot in a high-oxygen atmosphere, will burn.
Neither would it be a particularly great economic catastrophe, unless it’s very early in the elevator’s life. Once you have one space elevator, it’s really, really easy to use it to build another, or ten more. You might even want to put multiple elevators at different points around the equator, just for shipping from one point to another on the Earth. And that also means that if, say, terrorists manage to take out all of the infrastructure in Ecuador, there’d still be infrastructure in Kenya, and India, and China, and wherever else decides to build one.
Even 100 or 200 miles of cable hitting the ground - presumably not able to reach reentry burn-up speed - would do some interesting damage. The Foundation bit depicts a very thick cable construction, not a simple tether.
Gravity is inversely proportional to r^2, distance from the center of the earth (except inside earth itself.) So the acceleration of the near-earth cable is inhibited by the tension from the further points, depending on where the break occurs. Earth’s radius is ~4,000mi, so 22,300mi up - geosync - gravity will (If my physics memory serves me right) be pulling 1/25 as much, and centrifugal resistance will be significant extra resistance to the cable falling. This is not the same as something in low earth orbit scraping across the upper atmosphere at 17,000mph already.
I guess that’s the question - how is the tether constructed? Is it a minimal thickness of carbon fiber that a cable car type unit ascends and descends (Perhaps by gripping it), or a complex construction allowing for multiple cars to ride up and down simultaneously while providing power? So will it be a whip that leaves a narrow row of destruction that takes out a sequence of buildings and spares the neighbours, or a destructive path a hundred meters or more across? however you build it, it will require all the unobtanium you can mine.
Also occurs to me that the trip is either very long or has to be very fast. traversing over 22,000 miles with startup and slowdown requires and impressive piece of equipment; if the motors are self-contained, it need to pack a lot of energy to climb at that speed - especially with significant cargo. What’s the wear and tear on a carbon fiber cable when it’s being gripped strongly by wheels turning at 1,000mph? The engineering is more complex than the concept.
You can do it with very little energy input, by making multiple cars tethered to each other. Imagine a string of cable, shorter than the main cable by a length epsilon, with cars strung along it spaced epsilon distance apart, like a string of pearls. The bottom of the string of pearls wants to fall down, while the top wants to fall up, and the whole is very nearly in balance, so it would take almost no energy to move the string of pearls a distance epsilon (say, going from the bottom pearl being at ground level, to the top pearl being lined up with the counterweight).
Now, put a set of compartments on the main cable, that never moves, with the same spacing as the compartments on the moving cable. Start with the moving cable in its low position, and load up the bottom compartment (the others are all already loaded). Move the moving cable up one step, and transfer all of the cargo into the stationary compartments. Then move the moving cable back down, load a new load in the bottom, and transfer all of the cargo in the stationary compartments back to the moving cable, and repeat.
Having grown up with a good friend whose father owned an elevator company and told us lots of stories*, I keep thinking of things like “Well, at least nobody will be trapped in it” and “Is there a phone to call for help?”
*One such: company policy was that if someone was stuck on the cab, the tech was on top of the car when it was restarted. This came about after a rugby team beat the **** out of a tech because they were angry at having been trapped.
Why?
The tether is not entering the atmosphere at the speeds meteors arrive (45,000+ mph).
It is just dropping onto the planet. I doubt first few hundred miles of the tether could come anywhere close to the speeds needs to burn up in the atmosphere.
Also, presumably the tether is quite robust (read: massive). While the outside burns is that enough to ensure it all burns before hitting the planet?
Although the scene in Foundation is quite impressive, is there any reason for the tether to fall in a certain direction, and along a Great Circle ? Shouldn’t there be a point, early or late in the process, when the whole thing is just falling in a random pile like a fakir’s rope ? It does start off geostationary, after all.
IIRC a space elevator needs to be built on the equator. As such it has momentum in only one direction so I would think it would only fall in one direction. (Although maybe the explosion at the top pushes things in different directions…I really do not know how it would all add up.)
I would think the issue would be that without the counterweight, the cable would start to “wind” around the earth since it no longer is being pulled by the extreme end. At very least, wind would start to push it at the lower levels in one direction.
But each point would be travelling too slow for that altitude’s orbit, and start to descend. Each point would try to describe an ellipse that any satellite released at that orbit and horizontal velocity would do - basically a descending elliptical path. The higher regions would be almost circular orbit, but as pulled down would travel faster, and from that perspective I imagine it doing a “crack the whip” forward along the equator.
It’s an interesting physics problem.
Why bother - do it like a conveyor or ski chair lift. the upward units are balanced by the downward, and the cable just needs to keep going - cars can release and regrip. like Frisco cable trolleys. The only energy needed is the net weight of cargo going up vs down.
The point though is it’s 22,3000 miles to geosynchronous orbit. Either it’s a painfully slow ride, or that cable is on a wheel turning amazingly fast. A cable moving 1000mph will still take 22 hours for one way trip. Then, how do you attach to a vertical cable zipping by at 1000mph?
Stopping every 100 miles or so to swap cargo to a new car could mean a journey of weeks.
The engineering details are the most interesting problems. The devil is always in the details.
Why would the cable be moving?
I think other methods of climbing would be used. A spinning cable on a 22,300 mile tether is nuts (a 44,600 mile cable on a spinning wheel?).
If I may jump in here asking a question about this: The Wikipedia article has an animation of a hypothetical space elevator, and it shows the entire construction, including the counterweight, tight at all times, as if a stick were attached to a rotating sphere. How can that be if the counterweight is above geostationary orbit? Wouldn’t the orbital period of the counterweight be more than 24 hours, so that it would, when seen from the surface of the Earth, constantly lag behind?