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If the ground end of a space elevator was severed, what would the unfolding event look like from the ground? What would the movement(s) look like, and over what period of time?

I’m assuming that it’s a “standard” space elevator: situated <= 20 degrees of the equator; diamond nanothread construction; “top” of the elevator in geostationary orbit; tethered weight at 62,000 miles above the Earth’s surface.

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    $\begingroup$ Would the elevator have enough tension to act like a snapped rubber band? $\endgroup$ – CaM Feb 14 '17 at 16:09
  • $\begingroup$ It's both stiffer and stronger than any known material, including carbon nanotubes. If you'd like, here are the numbers - which, I freely admit, are a tad beyond my own comprehension: stiffness = 850 GPa; strength = 26.4 nN; extension = 14.9%; bending rigidity = 5.35 × 10–28 N·m2; tenacity = 4.1 × 107 N·m/kg. $\endgroup$ – Ozymandias Feb 14 '17 at 21:32
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    $\begingroup$ gassend.net/spaceelevator/breaks $\endgroup$ – Dan Piponi Feb 14 '17 at 23:36
  • $\begingroup$ Have you ever heard about Tiphares? $\endgroup$ – Paula_plus_plus Feb 15 '17 at 8:02
  • $\begingroup$ Wouldn't a space elevator need to extend beyond geostationary orbit? My understanding is that it would need it's centre of mass there, otherwise the mass below geostationary would pull it down. The mass above geostationary would be moving at a higher angular velocity, providing tension for the elevator. $\endgroup$ – Baldrickk Feb 15 '17 at 14:06
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http://www.spaceward.org/elevator-whatif

Where it breaks is fairly important.

First and foremost, if the tether breaks, everything above the break-point will "fall" upwards, escaping into space. Since most of the dangerous environments are near the bottom of the tether, only a short bit will collapse back down to Earth.

A space elevator needs to be fairly light by necessity.

The nominal (20 ton) Space Elevator tether weighs about 10 grams (a third of an ounce) per meter, and so over any square kilometer, the amount of material will be miniscule.

You definitely don't want to be climbing it when it happens though.

Finally, there will 4-5 climbers on the tether. While the top ones may be able to remain in orbit, the rest will start falling towards the Earth. Manned climbers will of course have the ability to soft-land, and cargo climber might be allowed to simply splash down.

Above the break the counterweight would "fall" away from earth into a higher orbit.

It probably wouldn't be terribly spectacular with a break near the ground.

If you want something which is likely to fail in a really spectacular and devastating fashion (while also having an advantage over a space elevator that we could actually build one using known materials ) then you might want to look into a space fountain:

https://en.wikipedia.org/wiki/Space_fountain

I decided to try to work out the energy involved if there was a break very far up and most of the elevator fell to earth:

In theory a space elevator might weight anything between 20 and 750 tons.

I can't do the math for the real case where the mass is spread out all the way up it's length but I'll err on the side of "more disastrous" and do the math for all the mass being higher up near geo.

Velocity at Geo = 3.07 km/s.

(kinetic energy of 750 tons at 3.07 km/s) = 3.206×10^12 J (joules)

which is about 95% of the maximum fuel energy of an Airbus A330-300 (97,530 liters of Jet A-1) or 1/20 of a little boy bomb.

The potential energy of 750 tons falling from 35000km is larger but still only in the range of .05 megatons and most of that would be lost to friction with the atmosphere.

Imagine spreading .05 megatons of TNT along a line 20,000 km long (still erring on the side of "more disaster"), that gives you 2.5 tons of TNT per km or put another way, 2.5 kg of TNT per meter.

Imagine a stick of dynamite about 5.6 cm's thick that's 20,000 km long. That's the total energy of the falling space elevator.

You wouldn't actually want that hitting you but if you were 50 yards away from the line you'd probably be fine. Again, that's even pretending no loss of energy to the atmosphere as it falls.

A falling space elevator wouldn't be great but more along the lines of "it's bad to be hit by things falling on you" rather than "everyone nearby is very dead"

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    $\begingroup$ If it is severed at the ground wouldn't it, from the POV of folks on the ground, just disappear as it takes off into space? The space tether would just leave for higher orbit since the tension with the ground is what holds it in place, right? I guess if the tether is sufficiently large in a stable geosynchronous orbit and the elevator itself isn't under tension then the elevator would just drag through the upper atmosphere. $\endgroup$ – Jason K Feb 14 '17 at 16:49
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    $\begingroup$ @PatJ if it hits something it would damage it but try throwing a marble from europe at a rope floating in the indian ocean. It's a long tether but it's still got a tiny cross section. You'd be a tad unlucky if it happened to hit the ISS or something. $\endgroup$ – Murphy Feb 14 '17 at 16:55
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    $\begingroup$ I'm not sure it would go into a higher orbit. wouldn't the air friction along the line of the tether slow the orbital velocity such that eventually the top of the elevator would fall? Further the line top would accelerate and increase the release energy in a whip effect? $\endgroup$ – Frank Cedeno Feb 14 '17 at 18:28
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    $\begingroup$ I can't remember the source but I remember someone theorizing that virtually any kind of tether would encounter enough other factors like air resistance during its collapse that the damage to the ground would be negligible. Not sure how accurate that is but it makes sense intuitively. After all, a long cable is going to have a lot of surface area relative to its mass, so its terminal velocity would be limited. $\endgroup$ – thanby Feb 15 '17 at 0:04
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    $\begingroup$ @Ozymandias if the break is near the ground then not really. Only 0.2% of the cable in in atmosphere and that is the lightest thinnest part.The counterweight needs to be slightly beyond GEO to maintain tension so from a POV on the ground the cable would probably just disappear upwards. It might flap around but do so while rapidly heading upwards so it wouldn't do much to the ground. Bad for anyone climbing it though. $\endgroup$ – Murphy Feb 15 '17 at 11:51
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In Kim Stanley Robinson's book Green Mars (I think) he handled this in a lot of detail. The counterweight was explosively severed, and flew off, entering a solar orbit. The planet rotates, drawing the cable into a spiral. At first the cable touches down pretty softly, but soon it is being whipped into the ground at faster and faster rates. The shockwave from the first lap around the world did some damage, but the second wrap comes down at hypersonic velocities, killing everything a few kilometers north and south of the impact line.

Whether this is representative of what would happen, or artistic license is unknown to me. But his books are well researched and contain a lot of hard science, so I assume it's been well thought through.

edit sorry, I missed the bit where the OP said its the ground end being severed.

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    $\begingroup$ Add those high velocities won't air friction just rip/burn the tether apart before it reached landfall? $\endgroup$ – John Feb 14 '17 at 17:06
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    $\begingroup$ That was mostly an example of what would happen if it was severed at the top. If it was severed at the bottom then it would be a different story. $\endgroup$ – AndyD273 Feb 14 '17 at 17:14
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    $\begingroup$ I think Kim Stanley Robinsons may not be correct on the power of the impacts. Imagine spreading .05 megatons of TNT along a line 20,000 km long (still erring in kms favor), that gives you 2.5 tons of TNT per km or put another way, 2.5 kg of TNT per meter. You wouldn't actually want that hitting you but if you were 50 yards away from the line you'd probably be fine. Again, that's even pretending no loss of energy to the atmosphere as it falls. $\endgroup$ – Murphy Feb 14 '17 at 17:16
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    $\begingroup$ @Murphy I think KSR's elevator was very thick and heavy. IIRC where it had landed softly they had to dig underpasses because it was too large to drive over. $\endgroup$ – AndyD273 Feb 14 '17 at 17:50
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    $\begingroup$ This does not appear to answer the question "If the ground end of a space elevator was severed". $\endgroup$ – DaaaahWhoosh Feb 14 '17 at 20:20
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Obligatory xkcd cartoon.

Note that the space elevator does not need huge tension and ground anchors! Wikipedia indicates modern designs call for floating barges: hardly a substantial weight at the end. If you cut it near the ground, it would flutter around but not snap away.

This is the right fail safe design.

There are even sky hooks that don’t reach the ground at all. So this is a non-issue.

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    $\begingroup$ There can be little tension at the ground end (but it's still substantial to make it taut - you don't want it to wiggle around as the climbers pass), but there's plenty of tension over the tens of thousands of kilometers of length of the tether. So even a fail-safe design like yours would snap, it just wouldn't snap violently at ground-level. Also note that just because it's a "floating barge" doesn't mean it's light - we're talking about a barge that's also a deep sea port, more like an oil rig than a boat. It could easily mass a million tons. $\endgroup$ – Luaan Feb 15 '17 at 8:44
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Let's say there say an explosion at the ground base and the tether was severed. Theoretically, it would just hang there. The simplest elevator doesn't really even have to be attached, it could just hang there, a couple of meters from the ground.

However, most designs include the aforementioned counter weight to compensate for large climbing masses. Because of the counter weight, a ground level break would cause the whole system to shoot up away from the earth. Unless the counter weight was huge and tethered under tremendous strain (which I doubt) it couldn't leave orbit. The whole thing would just move into a slightly higher orbit then stabilize. Because this new orbit wouldn't be geostationary the bottom could conceivably crash into a mountain. But otherwise, it would be mostly harmless, the climbers on route could complete their journey (up) and not feel a thing. I'd like to think the engineers would be aware of this possibility and would have the ability to jettison some of the counter weight and hopefully have some thrust available to allow for them to reposition and reattach. Even if just left alone, atmospheric drag should pull the whole system back to nearly geostationary orbit (risking that dreadful mountain strike again). If the bottom of the tether is out of the atmosphere then, obviously, drag isn't a problem.

Unlike Kim Stanley Robinson's novel, a break near ground level is a best case scenario.

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    $\begingroup$ It definitely wouldn't "just hang there", especially on a planet with an atmosphere. The tension is a necessary part of the concept, and the counter-weight is there to keep the tension (though of course, for bigger load-bearing capacity, you'd want a bigger counter-weight, or one farther away). If you had a tether that was not designed for any cargo, it might slowly float away with the wind - but that already assumes the wind direction is the same in all layers of the atmosphere, which simply isn't true. But more importantly, the tension of the tether would be released, leading to vibration. $\endgroup$ – Luaan Feb 15 '17 at 8:32
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    $\begingroup$ Adding to what Luaan said: If there was no tension, and you tried to climb it, then instead of you pulling yourself up, you would be pulling the space station down. Not good. $\endgroup$ – Solomon Slow Feb 15 '17 at 16:29

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