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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