Say, a civilization is thriving on an Earth-like planet. Let’s assume they have exactly the same technology as we have right now or perhaps just the next 10 years, the planet has the same elemental composition (thus same density), with the only exception being size. Which radius and mass (high) thresholds would it need to have, to enable its people the space elevator? At that size, what changes would you predict on things (climate, population, etc)?
With current or near-term human tech?
My WAG: Only a planet so small and/or fast-rotating it could not hold an atmosphere. Therefore none. In terms of size maybe something like Luna. But probably something sized more like Deimos. But much faster-rotating.
The problem is that the elevator structure needs to extend past synchronous orbit while under tension. And the materials required for that on Earth aren’t slightly stronger than we can now make; they’re hundreds of thousands of times stronger than we know how to make. Not gonna overcome that factor in a few Earth years.
So we need a lot less gravity and/or a lot closer synchronous altitude. At the obvious extreme, it’d be trivial today to build a “space elevator” installed on a baseball spinning on an axle in a vacuum chamber. Hell, you could use ordinary sewing thread for the tether.
If we are looking at planets specifically and not just solar system object, I would say Mars would be the first. Low mass and rotates fast enough so that an aresync orbit is only 13,650 km above the Martian surface.
Agreed with the last sentence here, but I read a source that the theoretical carbon nanotube is already ~77% the required tensile strength. Since material science is a fairly new branch, we can hope that it’s just a low fruit.
Yes, we’re looking at all theoretical sizes & masses possible, not limited to existing examples. The problem with Mars-sized planets is that it’s a bit too small for an internal dynamo, thus the climate would be so harsh, dry and barren a high-tech population would not even exist in the 1st place. I guess Mars’ good main purpose is just to smash into an Earth-sized one to help create the magnetic field.
That’s the theoretical strength of a single molecule of nanotube. The challenges of making, installing, and later repairing a single molecule tens of thousands of kilometers long and of tapering width are left as an exercise to the reader science fiction writer.
One should never say “never” about engineering, but it’s a bit safer to say “never” about physics.
I don’t mean to poop on your thread. It’s an interesting speculation about where humanity could build a space elevator. I just think the idea of constraining that space elevator to be on a body whose surface is naturally habitable by vaguely human-like human-scale critters is just a non-starter.
Here’s a different take on the issues:
Build one on an asteroid? Sure. We could do that with conventional tech today, limited only by our ability to transport the materials, machinery, & workers from Earth to the construction site.
But ultimately, space elevators are a clever thought experiment about a novel way to defeat a big gravity well. They’re pointless in a small gravity well. And the big gravity well is exactly what makes them impractical / impossible IMO without liberal helpings of Handwavium. Hence my “thought experiment” proviso.
All IMO, and the future is a big place wherein prior-era pundits are often proven to be wrong. Is there a crossover point in the tradeoff space where space elevators are a) possible, and b) useful? I don’t know, but that seems to be sorta what you’re asking for. Once we relax the requirement for it to be a naturally inhabitable body there might well be such a Goldilocks region. We’d need some actual calcs with actual design formulae to find out.
No known material, including carbon nanofiber, is strong enough for a constant-width tether. But that just means that you don’t make the tether constant-width. And then you get to the question of how much of a ratio of widths is practical.
IIRC, carbon nanofiber could do it, if its thickest part was about five times the cross-section of its thinnest part. Steel, meanwhile, would require a ratio in the tens or hundreds of thousands. It’s easy to say that a ratio of hundreds of thousands is impractical, and a ratio of 5 is practical… but where’s the dividing line between those?
This is also a more confusing part for me when I read literature about the SE. Isn’t the tensile force equal on all parts of the tether? Doesn’t that mean the tether must be constant-width, because making it smaller somewhere will break it?
Yeah… I have to admit, while the question sounds like it focuses on other planets, I’m actually looking at Earth the most. Based on the 77% number of carbon nanotube, I could already calculate that on a planet just a wee bit smaller than Venus, we could build an SE. I’m still young, but I can imagine a deep disappointment if until the day I die, we still haven’t figured out a way for the SE, or worse, found out that the Earth is just a little too big for the crossover point to be within grasp.
The reason I’m a bit fixated on the SE is because I think rockets can’t help us become a space-colonizing species. To create a habitable base on another planet requires a humongous amount of stuff being carried there from Earth before it can be self-sufficient. Yet by definition, most of a rocket’s propellant is used to carry its weight and the propellant’s weight into space. Could someone advise me the keyword for the ratio between the propellant’s mass and the payload’s? For now I’m assuming it as 10000:1. That’s a huge waste of material that can’t be lowered any easily. But for an SE, we could use a whole range of methods to power the lift-up, from rail gun to laser to solar panels… that don’t involve fuel having to carry itself.
I think you’re referring to
For simplicity, forget about the Space Elevator for a moment, and consider just a long (but terrestrial-scale) cable, hanging from a tall crane or the like. The bottom part of the cable only needs to support the weight of the payload, but the top part of the cable needs to support the weight of the payload plus the weight of all the rest of the cable. And for a sufficiently-long cable, the weight of the cable itself becomes much more relevant than the weight of the payload.
And I also have hope to see a space elevator constructed in my lifetime. What gives me that hope is that, by far, the material of the cable is the biggest technological hurdle to overcome… but the cable material needn’t be developed for the space elevator. Such a material would have all kinds of practical applications, here on Earth. Someone will develop it to use it in skyscrapers and suspension bridges and golf clubs and so on, even without the prospect of the space elevator. And once it’s in use in those things, then we can use it for the elevator.
A usual, @Chronos has given an excellent explanation of why tethers should taper.
Another tidbit along these lines is that any uniform cable has a parameter called “breaking length”, which is just what it sounds like: how long a continuous string of the stuff could you suspend vertically before its own weight causes it to fail in tension? A bit of thought will make it clear where such a suspended cable will fail (net of any real world manufacturing variation): right at the top where that particular inch of cable is carrying the greatest weight.
In the case of an SE, all the cable below GEO should taper from wide at GEO for maximum strength to narrow near the planet surface for minimum weight and strength. But wait, there’s more!
For an SE to sit there orbiting instead of falling, there has to be a bunch more cable and counterweight above GEO in what are effectively higher orbits. The tether and counterweight above are orbiting too fast for their altitude and are therefore pulling the whole shebang upwards, which is what keeps the entire assembly from falling. That tether ought to taper too, getting ever wider as it goes upwards.
With enough upper tether length you wouldn’t need a counterweight; the upper tether is the counterweight. But it’s probably simpler / cheaper to install a big rock ~1000 miles above GEO than to string another 10,000 miles of extremely expensive mono-molecular tether.
Thanks, but it seems not the term.
I agree. Tks, @Chronos ! That means my initial supposition is wrong, that tensile forces are actually not equal on every part of the long tether… right?
Wait. Now that I think about it, what makes the counterweight orbit too fast in the 1st place? The way we install and connect the rock to the tether?
No. It’s at a higher altitude than geosynch which means a slower orbital speed. Yet it’s being forced to orbit at geosynch orbital speed by being attached to the tether.
As to equal tension, that would be true for a tether connecting two pickup trucks horizontally pulling in opposite directions. The weight of the tether is immaterial, we’re just feeling how hard the trucks are pulling. That would, by definition, have equal tension everywhere along the length of the tether.
But the situation is totally different when the tether is hanging vertically. Now weight gets into the calcs. Specifically the weight of all the tether below some point X is pulling down on X. At some other height Y, the weight of all the tether below Y is pulling down. If X is not equal to Y, neither is the weight hanging from X or from Y. That changes everything.
At every altitude from just above the ocean all the way to the Moon there is a characteristic time that the orbit must take. Anything going too slow at that altitude spirals in or falls. Anything orbitting faster spirals out.
At a relatively low altitude where e.g. the International Space Station sits, the orbital period takes 90 minutes. If it was going any slower than one obit per 90 minutes it would spiral in towards the atmosphere & eventually reenter and crash. If it was going any faster it would spiral out. Up at GEO the orbital period is 24 hours. That’s what makes satellites at that distance appear to hover over one spot. They’re orbiting in 24 hours and the earth below is rotating in 24 hours so the satellite stays above one spot. [Presupposing it’s orbiting directly along the equator]. The Moon is even farther out, and at that great distance the proper orbital speed is one orbit per 28 days.
Whe whole idea behind a space tether is bolt one end to the ground, stick the other end way up past GEO, and force teh whole assembly to orbit at one orbit / 24 hours. Everything below GEO attached to the tether, and the tether itself, is orbitting too slow for that low altitude and if any bit fell off the tether it would immediately spiral inwards towards Earth. And if inside or close enough to the atmosphere, reenter & crash. In other words the balance of gravity pulling down is greater than the centrifugal force pulling up from the other end of the tether.
Out past GEO, the opposite balance obtains. The outer end of the tether still takes 24 hours to make one orbit, but out there at that great altitude the correct orbital period might be 48 hours. The tether is going 2x too fast. So it wants to spiral out. But the other end is anchored to the ground so it can’t. Instead it hold up the weight of the whole assembly. That’s the magic that gives us a skyhook supported by nothing. It’s supported by centrifugal force.
And of course, right at GEO the two forces balance. Iiagine we built a station there. You’d feel no gravity. If the two tethers leading in opposite directions became detached, the lower tether would fall to Earth because every inch of it weighs something (gravity > centrifugal force everywhere along the lower tether) and nothing is holding it up. Conversely, the upper tether would immediately launch itself away from earth toward higher orbit because every inch of it weighs less than zero (centrifugal force > gravity everywhere along the upper tether) and nothing is holding it down.
And meanwhile after the two cable departed the station itself would orbit serenely along, since it’s at the correct altitude for its orbital speed and gravity = centrifugal force.
Tks, I have a related question about rockets. Why do they (almost) always tilt early and then fly around the Earth’s curvature, i.e. “parallel” to the ground right at the escape velocity? In theory, if they just keep pointing their noses nearly all the way up before turning 90 degrees in the very last minute, wouldn’t it be more efficient and economical? As I read the book Rocket Men, the only explanation I can find for now is that the crew needs orbiting time to check all the equipment and the craft, which makes sense. But suppose that in (future Moon & beyond) missions, everything is done by automated sensors and goes well, then will we see more straight-up maneuvers?
Yes, I can see that we’re calculating stuff from the perspective of a completed SE. But how about during the construction of it? Let’s say we want to tether an asteroid at 36+2=38000 km away, and at that distance the orbiting time is 25h (not really accurate). How would you do it? I can imagine 2 scenarios:
A/ Attach rockets to the asteroid to keep it at ~38k orbit, build a 2k km tether from a station at GEO. When the cable is nearly done, fire the rockets to ‘rendezvous’ and ‘weld’ the connection.
B/ Have the asteroid at GEO next to the station in the 1st place. Then use the already attached tether to ‘push’ the rock 2000 km away.
Which option is nearer to your line of thinking, or are there other methods? In any case, it seems to me that we need to provide the initial speed before the whole shebang can work according to plan. Man, it’s really hard to put into precise words due to my lack of proper education in this field, but it’s somewhat similar to the “egg or chicken” problem… you know?
I can’t really speak to your second question: how to build it.
As to the first, why rockets lean over:
It helps to start with “What is an orbit?”.
A horizontally-thrown baseball or fired bullet immediately starts falling below the straight line represented by its initial motion. And eventually it falls enough to hit the surface below. Said another way, over time gravity adds ever more vertical velocity to the original purely horizontal velocity. This is true in a vacuum or in an atmosphere. An atmosphere changes some of the numbers; it doesn’t change what’s fundamentally happening.
Now an orbit is a coasting path in a vacuum that’s fast enough that centrifugal force balances gravity. Said another way, you’re going forward parallel to the surface so fast that even though gravity makes you fall towards the planet center just as it does the baseball or bullet, the ground under you is “falling” away at the same rate due to the curvature of the planet. Everything balances and you’re continuously falling in a big circle, never “catching up” to the planet’s surface falling away in front of you. Hence the term “freefall”
On a completely smooth no-atmosphere planet you could fire a gun 3 inches above the surface and if you got the aim right, exactly tangent to the surface, and if you got the speed right, then centrifugal force & gravity would cancel and your bullet would happily orbit your planet at 3 inches of altitude. Theoretically forever, but nothing is perfect in the real world. Something would eventually disturb the balance.
You need the speed to orbit and you need the vacuum to coast. Nothing coasts for long in an atmosphere; drag quickly turns your velocity into heat.
So with that background …
Going fast isn’t enough. To orbit, the vehicle needs to be going fast parallel to the surface. In the absence of an atmosphere you’d launch at a much flatter angle and just gain speed in the direction you really want to go: horizontally.
Our thick atmosphere is a big obstacle to space flight. It greatly interferes with the kinds of speeds you need to orbit. Being as the atmosphere is very roughly 100 miles tall you can’t orbit anywhere below there. Even at 100 miles you’ll only be able to coast a few hours or days before being slowed enough by atmospheric drag to begin spiralling in. Every bit of altitude you lose puts you in thicker air which slows you more aggressively which makes you spiral in faster which … and then pretty darn soon you reenter & burn up or impact the surface shortly thereafter. On Earth 120 miles up is near the lower limit where you don’t need to be expending propellant regularly to offset atmospheric drag. The ISS orbits at ~250 miles altitude and needs to be reboosted every few months to offset cumulative orbital drag. The drag is small, but it’s relentless.
Note also that the atmosphere may be ~100 miles tall, but it’s not equally thick/dense at every altitude. Roughly one third of the total air is in the bottom 2 miles and one half in the bottom 3 miles. By a mere 7 miles up where jets fly you’re already above 80% of it. The remaining 93 miles to the “top” contains just 20% of the air and drag.
Finally getting to the chase here … In the thick lower part of an atmosphere it’s important to get not going too fast to minimze drag, but also to get through it quickly in time to minimize fuel consumption while the vehicle is at its heaviest and therefore least fuel efficient. The best way to do that is pretty much straight up for the first 2 or 3 miles.
But once you’re past that, every bit of additional speed you gain going upwards is useless; you’ll eventually need to convert that into speed going horizontally. So real quickly the rocket leans over to start flying more horizontally. Notice that as it flies away from the launch point pretty quickly the earth starts dropping away from under it due to curvature. So its climb angle compared to the launch point is less than it’s climb angle compared to the ground directly underneath it.
Pretty soon, like a few minutes, you’re up to orbiting speed and traveling entirely horizontally compared to the surface straight down below you. While simultaneously traveling in a circle compared to the entire planet below. That’s an orbit.
Nitpick: Not spirals, ellipses. Something going too slow will be in an ellipse with the furthest point at the starting point, it’ll go down for half an orbit, and then come back up. Something going too fast will be in an ellipse with the closest point at the starting point, it’ll go up for half an orbit, and then come back down. Though the difference between “spiraling in” and an ellipse is largely academic if, before you reach the lowest point of your ellipse, you reach the surface of the planet and undergo what’s referred to as lithobraking.
First of all, “escape speed”, not “escape velocity”. If your goal is completely escaping a planet immediately, then direction doesn’t matter, and if the planet has an atmosphere, then straight up would indeed be easier, because less atmosphere.
But escaping the planet isn’t usually the goal for space missions. Usually, you want to be in orbit, which requires a speed only about 71% (\frac{1} {\sqrt{2}} ) of escape speed. But direction does matter for an orbit: If you’re at the right speed for an orbit, but pointed diagonally, then you’ll be in an elliptical orbit that goes between a point higher than your current position and a point lower than your current position. And for a low orbit, that “point lower than your current position” is likely to lead to lithobraking.
So there’s a tradeoff, between wanting to get above the atmosphere as quickly as possible so you don’t have to deal with air resistance any more, and wanting to get your velocity horizontal as quickly as possible so you can get into orbit and don’t have to continue fighting gravity any more.
The most important thing about constructing a space elevator is to keep the center of mass at GEO. To do that, you’d have to release both the ingoing and outgoing tethers at the same time and at the same rate. Initially, they would need rockets at their tips to get them away from GEO. It wouldn’t need much rockets, a small ion engine would do the trick. Or maybe not even rockets. Attach relatively small weights to each end and get them going by springs or something. Once they’re well aways from the geosynch station, they’ll naturally move further away as the tethers are played out.
Anyway, so you have a tether going out from the Geosynch station in each direction. At some point the big counterweight will need to be attached to the upper tether. That’s the tricky part, since adding that weight will immediately and rather dramatically change the center of mass of the entire system. I don’t know how this is to be accomplished. Perhaps someone else has an idea.
You start with the counterweight already attached, and just unspool the two ends at different rates. You’d need to do them at different rates, anyway, because the potential (more precisely, pseudopotential) isn’t symmetric.
I think the upward speed will contribute to a more elliptical orbit, as Chronos has pointed out if I understand it correctly. And since the farther away from a gravity well, the slower (average) speed an orbit is, if a mission is designed like this it’ll need less propellant.
lol ::
Yay! So my intuition was correct when I wrote future missions to the Moon and beyond could use this approach. But now that I thought more about it, even future missions would unlikely employ such plans, because if some mistakes happen, a near-circular orbit would provide more and easier solutions to problems. So as long as there are humans among the payload, rockets will fly orbits first. Machine-only missions might use the straight-up plan, but only not-very-important ones at that, too.
Hmm… now my interest is really piqued. Why is the difference between escaping and orbiting is a nice \frac{1} {\sqrt{2}} number? The beauty of math must be involved. If it’s not too complicated, could you enlighten me?
I agree, and thus see @Chronos ’ method much more feasible. I wonder if something like an abandoned ISS could be a sufficient counterweight. And how high on Earth can we build a tether tower, provided that carbon nanotube can be produced in mass quantity?
The larger problem is that, assuming you want to get back to Earth, you primarily need to accelerate retrograde relative to the Moon’s orbit around Earth. Since the Moon is tidally locked, there’s only a very small patch of the Moon where the direction of straight up coincides with this desired acceleration vector, namely the right-hand edge of the Moon as viewed from the northern hemisphere. Anywhere else and straight up to lunar escape velocity will put you in various weird eccentric orbits around Earth that never get close to Earth and eventually will probably rendevous with the Moon again, sooner or later, assuming they don’t send you off into interplanetary space.
Much better to lift off from the Moon and establish a lunar orbit where your ultimate desired vector is a tangent of some portion of your orbit. Then accelerate at that point of your orbit and you haven’t wasted the delta-V used to get into lunar orbit.
In all seriousness, if you want to understand basic orbital mechanics just play Kerbal Space Program. It simplifies various things, but it makes all the weird stuff like slowing down to catch up to something ahead of you in your orbit make intuitive sense.