Addendum, Space, thought experiment

Addendum: The Moon Cable

Reader Dan of 360 Exposure, pointed out something that I completely neglected to mention, regarding cable strength. Not only would the Moon Cable be unable to connect the Earth and Moon without breaking (either by being stretched, or by winding around the Earth and then being stretched), but it couldn’t even support its own weight.

There’s a really cool measurement used in engineering circles: specific strength. Specific strength compares the strength of a material to its weight. It’s often measured in (kilonewtons x meters) / kilograms. But there’s another measurement that I like better: breaking length. Breaking length tells you the same thing, but in a more intuitive way. Breaking length is the maximum length of a cable made of the material in question that could dangle free under 1 gee (9.80665 m/s^2) without the cable’s own weight breaking it.

Concrete’s breaking length is only 440 meters. Oak does better, at 13 kilometers (a really bizarre inverted tree. That’d make a good science-fiction story). Spider silk, which has one of the highest tensile strengths of any biological material, has a breaking length of 109 km (meaning a space-spider could drop a web from very low orbit and snag something on the ground. There’s a thought.) Kevlar, whose tensile strength and low density make it ideal for bullet-proof vests, has a breaking length of 256 kilometers. If you could ignore atmospheric effects (you can’t) and the mass of the rope (you can’t), you could tie a Kevlar rope to a satellite and have it drag along the ground. Zylon is even better. It’s a high-tensile synthetic polymer with a higher tensile strength than Kevlar, and a larger breaking length: 384 kilometers. You could attach a harpoon to a Zylon rope and use it to catch the International Space Station (no you couldn’t).

And, funnily enough, specific strength is one of those things that has a well-established upper limit. According to current physics, nothing (made of matter, magnetic fields, or anything else) can have a breaking length longer than 9.2 trillion kilometers. This is demonstrated in this paper, which I could get the gist of but which I can’t vouch for, because I understand the Einstein Field Equations about as well as I understand cricket, or dating, or the politics of Mongolian soccer. But the long and the short of it is that it’s not possible, according to current physics, to make anything stronger than this without violating one of those important conservation laws, or the speed of light, or something similar.

Not that we were ever going to get there anyway. The strongest material that has actually been produced (as of this writing, July 2016) is the colossal carbon tube. Think of a tube made of corrugated cardboard with holes in it, except that the cardboard and the corrugation is made of graphene. Colossal carbon tubes have a breaking length of something like 6,000 km (remember, this is under constant gravity, not real gravity). And that’s theoretical. So we’re not building a giant ISS-catching harpoon any time soon.

You might have noticed that I skipped over the one material that I was actually talking about in the Moon Cable post: steel. There’s a reason for that. I want to leave the big punch in the gut for the very end. For dramatic purposes. Ordinary 304 stainless steel has a pitiful breaking length of 6.4 km. Inconel (which is both surprisingly tough and amazingly heat-resistant, and is often used in things like rocket combustion chambers) only does a little better, at 15.4 km. There’s no handwaving it: you can’t attach the Moon to the Earth with a metal cable.

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5 thoughts on “Addendum: The Moon Cable

  1. Hey. Wow that was so eloquently put. It was text book. Very well written. Maybe you can help me with this one. Or maybe its just a silly thing to think about. Gravity.. In school teachers explain it by taking the class outside, fill a bucket with water, then spin around. The water stays in the bucket even when horizontal. That’s gravity apparently. I don’t totally agree and paid the price by getting bad marks in my science test. To me that was water been forced to the end of the bucket and stopped by the bottom. Centripetal force and the bottom held the water in place. How does water, trees as well as all of us act feel the force of gravity. Especially as space itself is a vacuum. Should we not all be spun away from the center outwards. Sorry if this is really silly, just thought to would be fun to ask. Dan

    • I wish to kick the shins of that science teacher. I should say, I’m nowhere near a physicist. But I do know that using centripetal/centrifugal force to explain gravity is like using a video of beetles mating to teach sex-ed.

      Here’s how I understand the bucket part: The water has mass, and therefore has inertia and momentum. Once it’s moving, it will keep moving in a straight line until it’s acted on by an outside force. The bucket it’s in, though, isn’t traveling in a straight line–it’s traveling in a circle. So, in order to keep it going in a circle, the bucket has to apply a continuous force to the water. In the rotating reference frame, that looks exactly like an ordinary acceleration (plus the Coriolis effect). Which sounds pretty much exactly like how you explained it. So I don’t know what your science teacher was on about.

      As for why we feel gravity, I’m not even close to qualified to answer that. All I can say is that, thus far, there is no instance of an object with mass not exerting a gravitational force on other objects with mass. I guess that’s why they call it a fundamental law: it’s just there, and finding out the reasons for gravity belongs to particle physicists and cosmologists.

      I *can* however explain why we aren’t all flung off the spinning Earth: it’s just not spinning fast enough. If the Earth didn’t rotate at all (and was a perfect sphere, which it isn’t), the acceleration of gravity standing on the equator would be about 9.807 meters per second per second. Centrifugal acceleration (acceleration away from the axis of rotation) is given by (radius of the circle) x (angular velocity)^2. The Earth rotates at about 0.004178074622 degrees per second, and its radius is roughly 6371 kilometers. Being on the equator of a rotating sphere is the same as being in circular motion, and the resulting centrifugal acceleration is something like 0.034 meters per second squared (3.4 centimeters per second squared). So, in a sense, the Earth is trying to fling you into space, most strongly at the equator and not at all at the poles, but the best it can do is reduce the effective acceleration to 9.773 meters per second squared. A bulky gentleman massing 100 kilos would feel a weight equivalent to 100 kilos at the pole, but only 96.6 kilos at the equator.

      If, however, the Earth rotated once every 84.4 minutes, people at the equator would feel no gravity, and the second they rose above sea level, they’d start floating upwards (according to the rotating reference frame).

      In real life, of course, planets aren’t infinitely rigid, and the Earth would either fling itself apart or deform into an oblate or scalene ellipsoid before this happened. The latter two cases would mean the equator would move farther from the center, and the math is complicated and I don’t understand it.

      I feel like I rambled like crazy and didn’t answer your question properly, but I hope that helps.

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