# Would a 'space elevator'/sling on a rotating asteroid work?

It is possible to find numerous studies of space elevators, for Earth, Luna, Mars and even Phobos. But would a 'space elevator' work on an asteroid? I use scare quotes because typically the point of a space elevator is to escape from the gravity well of the planet, but in this case the second function of a space elevator is relevant - the ability to launch (or catch) objects at high velocities, acting as a momentum exchanger between the planet and spaceships.

The concept is simple enough, find a rapidly rotating asteroid, one which rotates in hours or minutes would be ideal, it doesn't matter too much how big it is as long as it's not so large that it has significant gravity. It also doesn't matter how small it is, as long as it's big enough to make the venture worthwhile.

A cable is anchored to the asteroid (ideally to a solid iron core) and a counterweight is flung or launched off into space, so that the rotation of the asteroid causes the cable to maintain it's extension.

The cable could then be extended further, until it reaches off as far into space as is desirable. Crawlers would bring objects up the cable and release them from the top. If the cable is long enough then the objects could be released with sufficient velocity to reach Earth.

If this scheme worked, then packets of material mined from the asteroid could be launched without the use of rocket fuel, requiring only the electricity for climbing the cable (which would not be great, as there is no real gravity to climb against - in fact mainly it would be braking which would be required as the cable would try to fling the crawlers off prematurely). Essentially the cable would transfer angular momentum from the asteroid to packet launches. The asteroid would slow down over time, but the cable could be extended to maintain launch velocities.

Furthermore, higher up the cable there would be increasing apparent gravity due to centripetal force, this would permit the construction of a station with comfortable gravity for human habitation. The cable could then also be used to catch incoming spaceships.

Are there problems with space elevator physics that would make the system hopelessly unstable in the absence of gravity? If it did work, how would the construction difficulty/cost compare with a space elevator on Luna or Mars?

• The problem is that you can achieve escape velocity from an asteroid by simply jumping. No need to invest in a space elevator, which is restricted to launches from the equator of the asteroid, and only one at a time in a logistical nightmare. The space elevator solves a problem which is already solved: Just jump! – LocalFluff Nov 18 '14 at 10:10
• @LocalFluff: "the second function of a space elevator is relevant - the ability to launch (or catch) objects at high velocities, acting as a momentum exchanger between the planet and spaceships." – SF. Nov 18 '14 at 10:34
• The gravity can't be entirely irrelevant. Too fast rotation, and the light asteroid can't hold to its own matter around equator. Also, space elevator works at cost of rotary speed of the body it's anchored to. Too light the asteroid, and it will just stop after several launches. – SF. Nov 18 '14 at 10:40
• @SF How would we make the velocities of the spacecraft to be catched, to match the speed and position of the "elevator"? Why not have the cable rotate freely in space instead of tethering it to an asteroid? – LocalFluff Nov 18 '14 at 13:09
• @LocalFluff: For the first, most vehicles will travel in the plane of ecliptic, so that should be the plane of rotation of the lift; I can imagine a hook and rubber band, the style used for stopping fighter planes on aircraft carrier for final docking. Matching the speed and phase would take some fancy mathematics and rocket science but is quite possible. As for rotating freely, you need a significant mass to provide counter-balance to the ship, halve the necessary cable length, and a big rotating mass to leech the rotary momentum off for launch. – SF. Nov 18 '14 at 13:20

Shallow gravity wells with a healthy angular velocity are much more amenable to space elevators. The elevators can be be much shorter. The stress is much less so the tether could be an ordinary material like Kevlar.

P. K. Aravind outlined the equations for an elevator's length and taper ratio: The physics of the space elevator.

I attempted to incorporate his equations into a spreadsheet. Plugging in body radius, mass and angular velocity for various bodies I got these numbers:

Stationary altitude is the distance above body surface at which a circular orbit would have the same angular velocity as the body.

Top altitude is the tether length needed to hold the tether taut and vertical. To balance the length below synchronous orbit, a length above is needed. If a counterweight is employed, it doesn't need to be this tall.

Taper ratio is the ratio of tether thickness at synchronous orbit vs the tether thickness at body surface. When the tether endures a lot of stress, the taper ratio is high.

As you can see Vesta and Ceres have lengths and taper ratios far less challenging than Mars or Earth elevators.

If we ever make it to the main belt, I believe Ceres will be an important resource body. There is some reason to believe it has lots of water beneath it's surface. Hopefully we will know more about Ceres when Dawn arrives there April, 2015.

As you say, an elevator can fling payloads and thus provide velocity for injection to a transfer orbit. The ~2000 km Ceres elevator mentioned above could only provide ~.5 km/s. Possibly enough to reach neighboring asteroids but not enough to fling a payload earthward. A Ceres elevator 26,000 kilometers tall could provide about 5 km/s, enough for Trans Earth Injection.

There are other advantages as well.

For larger asteroids, surface gravity precludes ion engines. While ion engines have great ISP, they have very meager thrust. Even on bodies like Ceres or Vesta, a spacecraft's weight would exceed the tiny thrust of an ion engine. When thrust to weight ratio is less than one, a spacecraft can't get off the ground. However an ion engine could dock with an asteroid elevator.

I have more info on space elevators at my blog post: Beanstalks, Elevators, Clarke Towers

• Nice blog post, I particularly like the comparison of the Mars and Phobos elevators. The 8 hour rotation of Phobos results in a much shorter elevator than the 25 hour rotation of Mars. – Blake Walsh Nov 18 '14 at 21:53
• By the way would it be possible to add an analysis on apparent gravity, my calculations suggest around 10% g for a Ceres elevator at 26000km. – Blake Walsh Nov 18 '14 at 22:30
• Let's see… $\omega*r^2$ in this case would be $(2*\pi/3300 seconds)^2*26,000,000$ meters. Yes, that about .9 meters/sec^2 or a 1/10 of a g as you say. Most of the asteroids I've look at have $\omega$ on the order of 2 pi radians/10 hours or so. So it'd take a mighty long elevator to give a good fraction of a g. – HopDavid Nov 18 '14 at 22:40

There is a big problem with the proposal as-stated in the OP, and I don't believe anyone else has sufficiently hit this point. I'm quoting, with emphasis my own here:

If this scheme worked, then packets of material mined from the asteroid could be launched without the use of rocket fuel, requiring only the electricity for climbing the cable (which would not be great, as there is no real gravity to climb against - in fact mainly it would be braking which would be required as the cable would try to fling the crawlers off prematurely). Essentially the cable would transfer angular momentum from the asteroid to packet launches.

A cable is not a rigid member. It has tensile strength but it can bend. It can often be coiled. Cables are structurally very useful, but they only have one specific role to play. In this case, the proposal is attempting to over-use cables.

I looked at such a scheme a while ago, and here is a really brief mockup of what we're looking at:

You'll note that the darker line along which the payload moves corresponds to the conventional notion of a space elevator. Others have already pointed out that the gravity will be overcome very easily. However, the "swing" in the tether is not so easy to deal with.

An Earth space elevator would be aligned directly with Earth's center when there is no payloads traveling up or down. Start moving lots of material into space (after all, that's the point) and the tether will be dragged along the direction of Earth's rotation. The tether will then be off-center. You can entertain this concept for an asteroid by either drawing the main elevator off-center, or add additional cables as I have done for the "Coriolis Supports" above. I like the above scheme because the system will reliably not swing and move about. Mathematically it doesn't matter.

You easily find that the time to climb the tether is constrained by the radius of the asteroid. Also the rate of rotation. This follows directly from the simple triangle in the diagram.

Where would we find such a slingshot useful? Well, Eros is one of the largest asteroids in the inner solar system. Very few large asteroids have a semimajor axis within Martian territory and Eros is a bit of an exception to the rule. The minimum useful requirement we might expect from it is a Hohmann transfer to/from Earth orbit. I did the calculations before, but you could easily put them together yourself if you want. Even being maximally generous, the time to climb the tether is on the order of months. Since these transfers should only take something like 8 months in the first place this is a huge logistical problem!

What about larger asteroids? For Ceres, Vesta, etc. it could absolutely work. You might have very few constraints on the limit of climbing rate. For these few giants it might be practical to toss things around the asteroid belt.

For a more practical approach on an asteroid like Eros, you might need a wacky structure kind of like this:

Here, we're adding additional members which are not cables. For an asteroid sling shot these would need to be fully rigid, or it would need to combine compressive strength with enough mass that it's weight on the asteroid is enough to hold it in place. Kind of like that suspension bridge on Earth. By doing this, you're increasing the radius at which you are pulling the climbing payload, which is one way of increasing the torque (force x radius).

However, once you've added all these elements, you have almost everything you need for a space trebuchet anyway. It is true that a powered sling would need its own power source (unlike using the asteroid's spin), but doing this would massively reduce the total mass of the structure. For this reason, I think that using the rotation of asteroids for transport is unlikely except for a few very select cases.

• Thanks for this answer, this is the kind of analysis I'm interested in. I would think that increasing the mass of the counterweight (or adding one), and thus increasing the tension on the cable, would allow a higher climb rate. Of course that'd mean a heavier cable, and maybe coriolis supports would be cheaper and in this case they don't exactly 'weigh' anything, but would need a good anchor. – Blake Walsh Nov 20 '14 at 20:09
• @BhanteNandiya Increasing the mass of the counterweight could indeed increase climb rate. Doing so would actually negate the use of the coriolis supports. The line would have to bow in the direction opposite of rotation. It would be difficult to prevent the payload-counterweight from having excess angular momentum, in which case it would all roll up like a yo-yo. The counterweight itself would have to have substantial angular momentum, which could be slowly transferred to the asteroid like a massive gyroscope stabilizer. The problem with more mass is specifically manufacturing cost. – AlanSE Nov 20 '14 at 20:33
• +1. I am upvoting this as coriolis force is an important consideration. One that I neglected to talk about in my answer. – HopDavid Nov 21 '14 at 2:45
• I believe a massive counter-balance at the end of the tether would allow launching smaller masses on a much nicer time-scale. (so that the mass of the elevator is much larger than mass of the launch vehicles). – SF. Nov 21 '14 at 12:27
• There are ways to deal with coriolis induced oscillations. Traveling up pushes the tether a retrograde direction, traveling down pushes in a prograde direction. By timing ascent and descents, osciallations could be dampened. – HopDavid Nov 21 '14 at 15:42

What you are describing is not a space elevator, the point of one of those is to get to an orbit where there is a significant gravity well. Your idea is more of an angular momentum sling. It's not a bad idea, however there are considerations:

• Although the crawlers would not need much energy to go out on the sling, they'd need a great deal to get back as they are fighting the outward force developed by the spin
• You will lose the spin the more you launch from the sling. Nothing is for free - the energy you impart to the cargo you launch will come out of the asteroid's spin. This may not be much but for smaller asteroids it may be a factor over time. You could regain momentum by capturing spacecraft or other objects in order to balance things out
• The sling would have to be very strong to contain the forces involved, and it would need a strong anchor, so it's not a simple bit of engineering. The technology is way beyond what we have now
• If your asteroid is spinning fast enough simply remaining on the surface is going to be a challenge, your mining operations would have to deal with this
• Finding an asteroid that is the right size, with the right spin, and in a location which would make it suitable for mining may not actually be possible
• It may not actually be worth it. The sling will have to be strong, and probably cannot be built on the asteroid from materials sourced there, so will likely have to be sent. The cost involved in building the sling, transporting it, mounting it, maintaining it, providing energy to the crawlers, and dealing with the spin's adverse effects on mining operations may not be worth the fuel savings
• I differ with the first sentence. An elevator can have more uses than just getting stuff off the ground. – HopDavid Nov 18 '14 at 20:35

A space elevator can't be built without gravity--for the system to be stable you must have more tension on the cable than the greatest force exerted by all climbers on the cable at any one instant.

While the weight of the climbers is not a realistic problem inertia is another matter if you have a cable on something that's really small--you could end up pulling the cable down a bit as your mass accelerated.

In practice there's no reason for an elevator per se on really small objects--you can just throw stuff off anyway. The only reason one would be built is as a sling--if the object has enough rotation a long enough cable would be turning pretty fast at the outer end

• I believe the part about gravity is nonsensical, with an Earth elevator gravity would anchor the cable, but it is centripetal force which maintains tension - that's why a space elevator couldn't (realistically) be built on Venus - not enough rotation. And a sling is exactly what the question is about, but the technology would be the same as an elevator - except that it is anchored mechnically to the core of the asteroid. – Blake Walsh Nov 18 '14 at 6:31

It's a realistic sci-fi. Something that technically could be done but is unlikely to be done.

The primary problem is a split between economy and safety:

• If you're aiming at a lonely asteroid, finding one with enough resources to make such construction worthwhile, and rotating in the right plane at the right speed will be exceedingly hard - in particular the first part, resources worth mining, in amounts that make the whole concept economically viable. Doing this for several hundred tons of iron - I don't think we'd find that economically viable in half a millennium.

• Now the matter is different if we're working in a swarm of meteorites. Finding ones that would contain rare, expensive resources would be viable, and delivering these resources to the "launch station", the specific asteroid with the elevator (or calling it a "sling" would be more apt), slowly, only to sling them towards Earth at high speed would be quite nice... except, acting in a swarm of meteorites, the rapidly turning lift would be at constant risk of damage, vastly higher than in open space.

So, these two are the the big roadblocks that make it unlikely.

Now for various obstacles along the way...

• the material for the tether. Currently, only buckytubes, which are insanely expensive in such amounts. Delivering them from Earth (you'd have a hard time finding enough carbon in space). It would have to be similar to currently planned space elevator tether, obviously much shorter, so the gain on length/durability could be exploited to fling heavier masses. Nevertheless, currently this is the absolute (if hopefully short-term) show-stopper. Until we can produce buckytube tethers, no space elevators for us.

• anchoring. Asteroids, due to lack of gravity, are far less packed than Earth's native rock. You'll have some mining equipment on site, but the anchor tunnel network would need to be quite extensive.

• mass, speed and plane of rotation. In this case the situation isn't quite as bad. There's a lot of asteroids. Finding ones to fit the bill should be perfectly possible. Finding ones that fit the bill and are located in a worthwhile place or have valuable resources - well, much trickier.

• unless you launch more than land (likely in the mining scenario; even with delivery from other asteroids, you'd crash the raw materials into the asteroid at fairly low speeds before lifting them) you'd have to provide energy. The crawlers could provide energy when lifting, but would consume when used as catch/dock for speedy arrivals. In a pinch, you could manufacture energy by flinging any native rock at random, e.g. crawlers never travel up empty.

• Mining operations and delivery (drops) of raw materials would need to happen in polar regions, where the gravity of the asteroid would be much higher than counteracting centripetal forces. Luckily, with gravity generally low, transport of even very heavy loads shouldn't be that hard.

• as for depleting the rotational energy - picking a bigger asteroid resolves most headaches. The stored kinetic energy scales with square of rotary speed, and fifth power of its radius. $E = {{4 }\over{15}} \pi \rho r^5 \omega ^2$

• Shallow gravity wells and high angular velocity make for an elevator that doesn't suffer as much stress. In many cases Kevlar could suffice. So no, lack of bucky tubes isn't a show stopper – HopDavid Nov 18 '14 at 20:49
• @HopDavid: How does kevlar behave in void, extremely low temperatures? – SF. Nov 19 '14 at 9:44
• (Googling...) Looks like Kevlar is okay down to about 196º C which is about 80 K. en.wikipedia.org/wiki/Kevlar#Thermal_properties At the moment I can't find the albedo for Kevlar so I will guesstimate this yellow material has albedo .8. At Ceres' distance from the sun I get a black body temp of 111 K. – HopDavid Nov 20 '14 at 15:04
• And, given the much lower stress, it is even possible to run a power cord throughout the tether length. Not only does this make temperature regulation possible, it could be a power source for climbers. – HopDavid Nov 20 '14 at 15:09