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Anchor one end of the cable to the side of the moon that faces the earth. Drop the other end of the cable to earth so that it drags along the ground. The earth's gravity and friction contributes a degree of tension to the cable. As the earth does its daily rotation and the moon does its monthly orbit the cable drags around, flicking over mountains and knocking over buildings.

Because the earth's rotation and moon's orbit happen on different planes with different periods, it never goes to the same place twice. Everyone within 30.12 degrees of the equator (the earth's axial tilt plus the moon's orbital inclination) eventually gets access to the space elevator whilst simultaneously having their cities destroyed.

People build carriages to intercept and attach to the rogue elevator cable and ascend into space.

Problem?

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  • $\begingroup$ Ooh..You missed the bit about because its so large (and dense to survival all that it will go through) it has its own gravitational pull, which will throw off the gravity of both the moon and earth. Probably causing the moon to be knocked out of its orbit, then god knows what will happen. I'm going with that we all die. $\endgroup$ – Necessity Nov 4 '15 at 3:52
  • $\begingroup$ I am sure you are trying to fit this question into the scope category: Effects of events or world elements, including technology and magic, on specific aspects of that world's societies, cultures, and environment. But your question fails to provide clarity on which specific societies, cultures and environment you would like answered. $\endgroup$ – FiringSquadWitness Nov 4 '15 at 4:39
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    $\begingroup$ The `drag it around the ground' is also interesting. The moon is not in a perfect circular orbit and its distance to earth (and hence its surface) varies by as much as 7%. 7% of 384400km means you can have a cable which barely touches the ground on one day, and which is dragging about 26900km over the ground at the other extreme. $\endgroup$ – Hennes Nov 5 '15 at 0:01
  • $\begingroup$ Problem? $\endgroup$ – Revetahw Sep 10 '16 at 19:53
  • $\begingroup$ Honestly that sounds like a lot of fun, though that might just be because I'm a good 20 degrees north of the danger zone. $\endgroup$ – ktyldev Sep 21 '16 at 10:56
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Problem?

Well, I think you stated the problem pretty well already in your question.

As the earth does its daily rotation and the moon does its monthly orbit the cable drags around, flicking over mountains and knocking over buildings.

and

Everyone within 30.12 degrees of the equator ... eventually ... having their cities destroyed.

Even without looking up the numbers, I can tell that this would work out to a significant fraction of the Earth's population. I wouldn't be the least bit surprised if, even with today's population and distribution, we are talking about anywhere between one billion and three billion people.

Seriously, why would anyone want to do that? And like WhatRoughBeast pointed out, the cable will be moving across the ground at approximately fighter jet aircraft speeds. Add to that the continual sonic boom produced which will wreak havoc (and drastically lower property values) in the vicinity as well.

When I saw the question title, I thought your question was "hmm, we can't build a space elevator on Earth, but maybe we could do it on the Moon, with its much lower gravity?". (The answer to that, of course, besides all the issues with, you know, actually building the thing, is that having a space elevator on the Moon wouldn't really do anything at all to make access to space from Earth any easier. We'd still have to climb out of Earth's gravity well.) But turns out that's not your question at all.

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    $\begingroup$ While this might not be the most efficient planet destroying weapon I think it has the makings of a fine alien reality TV show: The Cable!. Next week The Cable hit's Detroit! See it here first. $\endgroup$ – candied_orange Sep 21 '16 at 4:54
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For areas near the equator, the speed of the cable end is roughly $$V = \frac{2\times \pi \times 3960 \text{ miles}}{24} = 1036 \text{mph}$$ So any attempt to use the elevator would require matching speeds and transferring to the end of the cable - at Mach 1.4.

Top Gun, anyone?

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    $\begingroup$ Worse: The moon has significant eccentricity in its orbit. So either the end dips into the atmosphere periodically, or its dragging a long tail across the landscape. Talk about the Scourge of God! $\endgroup$ – Sherwood Botsford Dec 5 '15 at 23:20
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I think the problem is that people generally don't like the idea of dragging a cable like that. Most of our modern materials that can take the strain of a space elevator lack strength in other axes, so the cable may fray.

Gregory Benford wrote a science fiction story, Beyond Infinity, which had a structure like you described. Pinwheel was a giant sentient space elevator which wreaked havoc on whatever lay below its "cable."

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