Which planet could we build a space elevator with current technology?

In My Humble Opinion
41

But then we get to the length factor. Last I heard, nanofiber has a conductivity comparable to the best metals. But you can’t make a practical power cord that’s 40 megameters long, even out of silver. A wire that long, made of anything short of a superconductor, is going to have a very high resistance.

One nitpick, though:

Most electrical devices humans make are designed to be hooked up to a power supply with a fixed voltage (and most of the power supplies we make are, at least approximately, fixed voltage). And given a fixed voltage, the lower the resistance, the more heat you’ll get. Try to make a heating element out of wood, say, or rubber, and it simply won’t work at all, because wood and rubber are both terrible conductors.

So why don’t we make oven heating elements out of copper? Two reasons. First, you don’t want too much heat, or you end up doing things like melting the heating element. Second, while you’ll get more heat from a better conductor, where the heat will be mostly produced is in the part of the circuit with the most resistance: Make an oven heating element out of copper, and the whole circuit will heat up, including the parts in your walls.

42

Well said. Our OP is showing some pretty big gaps in knowledge so I was trying to pitch it low and slow. In that case I probably pitched it too low and too slow.

Continuing in the effectivley-fixed voltage supply case, we have a practical current limit for our e.g. toaster. That limit is supplied, as you say, by the need to not overheat the supply wires in the walls. Which are protected by circuit breakers to prevent the excess current that would heat the wall wiring.

So now, with a fixed voltage and a max available current, the question becomes
“How to concentrate (almost) all the heat production just in the useful part of our toaster circuit?” And the answer is to put relatively crappier conductors in there thanelsewhere. Which will convert the electricity into heat as they relatively poorly conduct that electricity.

Yes, they’re a long way from “insulators” like wood or rubber. “Insulator” just being another word for “monumentally crappy conductor.”

43

OK, I did the calculations for the length. I quickly realized that the length needed for the siphon effect involves solving a cubic equation, which isn’t worth doing by hand, so I put everything in Desmos (all units in SI):

Summary of results:

  • Geosynch height, as we already knew, is 42.4 megameters (all heights measured from the center of the Earth)
  • The height needed for the siphon effect, which is also the height needed for a constant-thickness cable with no counterweight, is 151 megameters (so probably not practical)
  • If we did have a cable that height, the effective gravity at Topsy-Turvy Station would be about half of that on the Moon.
  • The height needed for launching payloads to escape the Earth is 53.2 megameters, or \sqrt[3]{2} times geosynch height. We’d be fools not to go for that, at least.
44

Tres cool. Thank you for spending the time!

Which raises a side question.
The esteemed @Stranger_On_A_Train is fond of saying that the atmosphere on Mars is just the wrong density. It provides all the problems of a non-vacuum approach, landing, and surface ops, with none of the benefits of useful aerobraking, reasonable wing-borne flight, effective cosmic ray shielding, etc. Accepting his contention at face value …

Applying that rubric to this situation, I’ll suggest that the ~1/2 Moon gravity (~= 0.8 ms-3) at Topsy Turvy Station (great name BTW) would be just the wrong amount.

Not zero, so people and stuff can’t float from here to there, but also so little that getting adequate traction on the floors for powered wheeled carts, or for simple human walking would be highly problematic. Big equipment would still need lifting, not just pushing and pulling, and would still be difficultly heavy for ordinary human strength. Not convenient; not convenient at all.

Comments?

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If we expand on this, what would be the easiest solar system object to build a space elevator even if only as a proof of concept meaning we don’t want one only 20 foot or so high so tall enough to prove the engineering can be done but short enough that it can practically be done.
I’ll put out Ceres with a surface gravity of 0.03g and a rotation period of 9.075 hours. A cereriansync orbit is 721km above the surface and no atmosphere to deal with. Is there a moon that would be better?

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Big thanks, @LSLGuy ! Especially the resistivity vs resistance part was very helpful.

As per my understanding, it’s strongest because of the lattice being in a particular shape, and carbon just happens to have such a shape in its arsenal of different forms. So as we learn more about how geometrical shapes make strong connections, we could possibly create (even much) stronger, novel lattices by forcing (hopefully) lighter elements into computer-generated formations. Please correct me if I’m wrong.

It sounds contradictory with itself, but after some deliberation, I want to put forth my own explanation and ask for your criticism: “more heat from better conductor” is because of U=IR. Since U is constant, a lower R leads to high I. And since P=RI^2, the square of the bigger value will more than make up for the smaller component.
“Heat is produced most in the part with most resistance”: again, using the latest formula but with small r: P=rI^2. Since I is big (and constant for this particular circuit?), a big r will boost P to a hot value. It seems like the key here is to plug different R & r into the formula, isn’t it?
On another note, how would you describe the “whole circuit” in your example? Does it reach all the way back to the turbines at the power plant?

Which leads to an observation of mine that the best conductor in this situation is something with the resistivity in the sweet spot between the wire material (copper) and rubber. Something calculated using the geometric mean?

Could you elaborate a bit for me? When “siphon” is mentioned, I can only think of 2 bodies of water connected by a pipe, and can’t expand that to anything “spacey”.

47

@Chronos introduced the siphon idea for elevators a few posts ago. Search for “siphon” in this thread and you’ll find it.

48

The total amount of heat generated depends on the total resistance in the circuit. But that heat can be generated anywhere in the circuit. In practice, wiring is usually designed to have a very, very low resistance, much lower than the resistance of any sort of appliance, so the total resistance of the circuit is very close to the resistance of the appliance, and almost all of the heat is generated in the appliance. And “the whole circuit” means “going back to the part that’s at a fixed voltage”, which is kind of a cop-out, since in real life, there isn’t actually such a thing as a fixed-voltage source, which generally becomes very apparent when you have a short circuit.

Nothing that simple, because it also depends on factors like how much heating you’re willing to tolerate in your wires (since you’ll always get some), and how much power you want your appliance to draw, and how expensive copper or other wiring material is, and so on.

OK, picture a very tall space elevator, that goes up far past geosynchronous height. Below that height, the elevator cars want to fall towards the Earth, so you’re lifting them uphill. But above that height, the cars want to “fall” away from the Earth, due to the centrifugal force, so they’re effectively going downhill. You have the top of a hill at geosynch height, and low areas on both sides of the hill.

Well, in an ordinary water siphon, you can get water over the top of a hill for free, as long as the far side is lower than the source. The water going downhill on the far side pulls the water on the near side with it. And you can make a siphon like this with more things than just liquids: Take a long chain or beaded string in a bucket, for instance, and drape it over the top of a low-friction hill, with the bottom of the chain lower than the bucket, and it’ll all pull out of the bucket. It’s the same idea with the space elevator: Let the cars above geosynch, that are falling away from the Earth, pull up the cars below geosynch height.

Except, of course, that to make that work, as I just calculated, you’d need a much longer cable. I’ll have to think of other ways to run a space elevator for nearly-free. Maybe only use the elevator to lift cargoes up a couple hundred km, above the atmosphere, and then use a skyhook from there? But operating a skyhook right next to a space elevator is probably just asking for trouble.

49

Thank you for the explanations. But in a water or chain bead siphon, I notice that 1) the ‘substance’ is connected (with itself) continuously from end to end; and 2) it moves. In the SE case, the cars are not “connected” or at least, connected by a cable made from another material, i.e. not continuously. Even though it’s quite easy to make a mental leap and consider the car-cable-car system as a whole, I doubt that all the system moves. Not to mention the tremendous weight of a cable long enough to connect 2 cars on opposite sides of the GEO will likely push the needed length for siphon effect further and further, toward infinity.

I guess what you wrote a few posts earlier, about cableA-B in some non-rotating frame is a proposed solution to that problem. I still have troubles imagining that system, so no comments. But I think something that could harvest the planet’s rotational energy to power its own is pretty cool.

OTOH, I believe the skyhook will never become a reality. Any artificial structure that requires moving a lot is prone to failures, and having something huge constantly rotating just over our heads is more than asking for troubles, with or w/o SE.