It is the skyhooks that allow ships to move around the solar system using a tiny fraction of the fuel that would otherwise be needed. The skyhooks that greatly reduce the time needed to move between worlds, and extend the launch windows when launches can happen so much, that if the spatial relationship between worlds is really unfavorable some fuel can be burned and they can be reached anyhow, making it possible to launch almost any time. The Earths's skyhook turns launching to orbit from here into a job that, compared to rockets today, can be done by a ship both giant and robust that can make the trip thousands of times, without needing to take off with such fury it is like carpet-bombing the launch pad, and shaking anyone in it to near unconsciousness[?]. The Moon's skyhooks allow shuttles to move between any two points on its surface for about a quarter of the fuel otherwise needed. Each of the worlds where skyhooks are built receive this same benefit. Skyhooks change everything. They are the future, and the sooner we really understand that, the sooner we can move towards that future.
The sort of skyhooks we are talking about here are vertical skyhooks. Think of them as junior space elevators. They have a lower tether hanging down towards the surface of the body they orbit from a large anchor mass, the same as space elevators do. They just aren't attached to its surface. The platform at the bottom of their cable (the foot) instead moves above the surface at some suitably low altitude. Ships launched from the surface need to catch up to the foot, and to brake to return to the surface. The advantage is the delta v required is much less than what is needed to get to orbit, because the foot is moving much slower than orbital speed. For the first skyhook planned for the virtual colonies, it takes 1/5th of the normal delta v. That is the case if the foot hangs to 20 km above the surface and the anchor mass at the center of gravity orbits 5000 km up.
Skyhooks also have an upper tether extending upwards from the anchor mass deeper into space. The tip of this tether experiences the opposite effect from the foot - it is moving faster than orbital speed at its altitude. The effect is that objects holding onto the tip feel a force pulling outwards, like if you twirled a ball on a string above your head. The amount of that force depends on how much faster they are moving than orbital speed. As things climb the tether from the anchor towards the tip, that force appears and slowly grows. Again the opposite effect is felt climbing from the foot towards the anchor. At the foot, the pull of gravity is almost as much as on the surface. At the anchor, gravity is imperceptible because it is moving at orbital velocity. The closer you are to the anchor as you climb the tether, the closer your velocity is to orbital velocity, and you feel gravity less and less.
Essentially there are two things that have to be managed for skyhooks to work - angular momentum and cable strength. Angular momentum is how fast a skyhook is moving in its orbit. As payloads arrive and move along the tethers, the momentum of the whole skyhook is changed. It will slow down, which will cause its orbit to drop, or it will speed up, causing its orbit to rise.
There are several options for correcting this, explained in the expanding section below. It's pretty detailed. The short version is that to minimize the amount of fuel engines on the anchor and at the tip of the skyhook use, payloads travelling down the tethers need to be balanced by payloads travelling up them. When this isn't enough, dummy masses can be moved up or down from the anchor and released such that they enter elliptical orbits that accompany the skyhook. Later they can be retrieved and returned to the anchor. Both activities will affect the skyhook's angular momentum and can be carried out when convenient. The essential thing is to increase the mass of the anchor over time until it is thousands of times as massive as any payload that moves along the tethers. Then its angular momentum is affected so little by those movements that it takes a long time for changes to accumulate to the point where it affects operations. Thus there is lots of time to make changes with passive techniques instead of using engines.
The speed of a skyhook's foot is determined by the altitude of its orbit, which is located near its anchor mass. The pull of gravity decreases as something gets farther from a world, so orbital velocity is slower for the anchor mass than for something 20 km above the surface. Plus, the foot is always aligned vertically under the anchor mass - it's hanging from it. So, it takes the same amount of time to orbit the Moon once as the anchor mass does, but the distance it covers is far less, because it is travelling along a much smaller circular path. The animation in the sidebar gets this across.
So now think about this - as something moves down from the tip, it feels less and less of a force pulling up, and as something moves up from the foot, it feels less and less of a force pulling down. Where does that energy go? Energy doesn't just disappear, any more than mass does. The motion of the whole skyhook changes so the energy remains the same. When a car climbs to the anchor, as it feels less downward pull, a pull to the side is experienced by the tether. That pull is in the direction opposite its orbital motion around the Moon (which is called the retrograde direction, and the direction of orbit is called prograde). That's because the car started out moving much more slowly prograde, when it was at the foot. So, the tether is dragging it prograde as the tether's prograde speed increases. The end result is that the anchor mass experiences a net pull retrograde, which slows it down. The amount it is slowed down depends on how much more it masses than the car does.
Managing a skyhook is far easier if you have a nice, heavy anchor mass so big that the momentum it has dwarfs the momentum changes caused by cars moving up and down the tethers. The nice circular orbit it needs to have then moves very little as cars ferry things along the tethers. The feet of the skyhooks in the lunar constellation travel only 20 km above the surface, and there is 5000 km between them and the anchor station. If the anchor mass slows by only a few meters per second, in a few hours the foot platform will slam into the ground and be destroyed. If the situation is not quickly corrected the whole skyhook could be dragged down and crash.
The anchor of a skyhook must have engines on it (or even better, the skyhook tip must have engines) to speed up the anchor to compensate for the cars slowing it down (or speeding it up, as happens when a car descends from the skyhook's tip - that's a problem too). But, there are other ways to manage a skyhook's momentum budget that use no fuel at all. The first step is to try to balance incoming and outgoing payloads.
Just as a car climbing from the foot to the anchor slows the skyhook down, a car descending from the tip to the anchor speeds it up. And each of these processes in reverse does the opposite thing - when a car goes from the anchor to the foot, or the anchor to the tip. So, the best time to have a car descending from the tip, is when there is a car climbing from the foot, and that way they balance each other out.
The ships coming in from other worlds are far larger than the shuttles coming to the foot platform. So, to keep things balanced, you need to ferry the cargo on the interplanetary ship downwards bit by bit, while many shuttles bring cargo to the foot and bit by bit that gets ferried up. With the really huge ships at the end of the timeline, it could take weeks to complete this operation. It takes so long, it's best to slowly ferry the interplanetary ships that dock with the skyhook tip down to the anchor mass, even as they are also being unloaded, so that other ships will be able to dock with the tip or launch from it sooner.
This reduces a lot the need to use rocket engines to correct the skyhooks' orbits, but it won't do it all. There are lots of reasons why the traffic won't always balance in a timely manner. Also, in Phase 4 of the timeline the skyhooks are turned into specialized pairs of skyhooks, one the launch skyhook that mostly handles interplanetary ships, and the other the surface skyhook that mostly handles traffic to and from the surface. Loads can still be balanced as the cargo moves between the two skyhooks in each of these pairs on ships called hoppers, but it adds another layer of complexity to the job. It is a good thing that the cars on the tethers and the hoppers are completely robotic and take direction only from the anchor's navigation computers, short of some human override. Those computers constantly monitor orbit closely and calculate when and where all the cars and hoppers need to be based on that, and the schedule of ships arriving and departing.
Those computers have other tricks up their sleeves when all this orchestration isn't enough. If there isn't a ship or a car in a good place to move in some way to balance things, then a simple rock will do. A suitable supply of really big boulders massing many tons is stored on the anchors of the skyhooks, which have to be as heavy as possible anyhow, and don't have a direct effect on the loads being borne by the tethers themselves, as they are at orbital altitude and aren't being pulled in any direction by the forces we're talking about.
The rocks do need to be ferried by cars to where they do their work, but at least there doesn't need to be any actual payload with a destination involved. And they don't need to move all the way to the tip or the foot - that would complicate traffic of actual goods and be much slower. They are just ferried up or down by up to a fifth of the length of a given tether (which can mean up to 7000 km on the longest tether), and then released. A rock released from below the anchor has been pulling the tether prograde as it descends, causing a small net increase in the orbital speed of its skyhook. At the altitude it is released, it enters an orbit around the skyhook's world. That orbit will be an ellipse that comes closest to its world a quarter orbit after it was released. As it gets closer, it speeds up, and as it gets farther away, it slows down. Eventually it comes back to the point at which it was released, and can be easily captured. It will come back with the same speed at which it was released, which is to say, no speed relative to the skyhook tether at that point, and it will brush by it nice and close. If it isn't convenient to grab it at that moment, it will continue to return like that, and it can be caught on another pass[?]. Then it is ferried back to the anchor to be reused another time. The same effect happens when a rock is released from above the anchor station, except that makes the skyhook slow down.
A variant on this trick is occasionally tossing rocks between skyhooks, especially between the skyhooks of the Moon and Earth. The skyhook that throws one loses some momentum, and the one that catches it gains some. Really, the main thing is to keep building up the mass of the anchors over time, whenever possible. When asteroid mining grows to a major industry, this is easy. The more momentum is stored up in a giant anchor mass, the less a skyhook's speed is affected by the puny ships travelling up and down.
The most promising materials for early skyhooks in lunar orbit are aramid (Technora or Kevlar) and PBO (Zylon). Thorough tests of the behaviour of the material under load in orbit would need to be done before construction of the first skyhook and would necessarily take a few years. That could be done at the new space station built for the Moon settlement program. Without those tests, it's necessary to estimate some important qualities of the two materials. Actual properties may show the mass and complexity of the skyhooks will need to be greater, or less. The main point, though, is that skyhooks for the Moon can be built of either material. No new material needs to be invented.
Zylon, the strongest of these materials, has an ultimate tensile strength (UTS) of 5.8 GPa, and a density of 1.56 g/cm3. That means it can support a maximum of 5800 Newtons of force for each square millimeter of its cross-sectional area. A thread with a thickness similar to a sewing needle can support 590 kg, or about 8 adults (on Earth). However, loading a material like that weakens it. It stretches under the strain and will break in short order. Testing of how cables of these materials slowly stretch until they break shows that as the fraction of a cable's UTS being supported diminishes, the time it can sustain that load before failure lengthens on a log scale. Toyobo, the manufacturer of Zylon, tested a series of cables until they broke, and found that a cable loaded with 85% of its UTS will fail in only a minute, while one loaded with 60% of its UTS will take approximately 8 years to fail (based on extrapolation). Considering this result, and all the other factors the skyhook cables will be subjected to, a safety factor of 3 is used for the lunar skyhooks. That is the same as saying they are never loaded beyond one third of their UTS. Fortunately, Zylon is strong enough that even though increasing the safety factor causes the mass of a skyhook to multiply by much more than than that, it doesn't cause the mass of the cables to balloon too much in the mild gravity field of the Moon. With a safety factor of 3, the cable for the whole skyhook only needs to mass about 20 times what the total payload will mass [?].
A study done through Cambridge University, Creep and Strength Retention of Aramid Fibres, did a series of tests on both Technora and Kevlar for up to a year. Those tests showed that even though both Kevlar and Technora have formulas in the aramid family, Kevlar's ability to bear a load falls off sharply after a year, while Technora seems able to continue to bear a load that is 70% of its UTS for a century. Clearly extrapolation was also involved here, but the result is still promising. If nothing else, it shows that slight adjustments to formula and manufacturing technique can make a big difference to such properties in materials of this kind.
Since most of the mass of a skyhook's cables is there to support the cable itself, for most of its length, it can be considered to have something close to a constant static load. The cables slowly narrow as they get farther from the anchor mass because at the top, they need to support all the mass of all the cable below, and also the payload, while at the foot and the tip, they are only supporting the payload (which here means a fully loaded shuttle, the platform where it docks, and the climber car its cargo is loaded onto). Between the foot and the anchor, the way the cable hanging below a point keeps getting heavier the further from the foot it is, means the cable needed to carry that mass increases in an exponential relationship.
A safety factor that high is necessary due to the other factors acting on the cables besides the loads they are bearing. Both Zylon and aramids break down quickly in sunlight, so they will need to be protected by a sheath that blocks out the light. That sheath will also need to keep their temperature in a comfortable range by transmitting only a small portion of the heat of the sun to them, while preventing most of the heat of the cables from escaping. It also forms a protective layer, reducing wear on the cables from deformation and friction when cars pass by, pressing the cables between their wheels.
Micrometeoroid strikes should be quite rare, but the cables need to be able to sustain them without risk to the skyhooks. The cables will be an open mesh weave that redistributes loads around any broken ropes in the weave. This weave was designed by Robert Hoyt at Tethers Unlimited. New ropes can be woven into the mesh by maintenance cars. Individual sections of mesh can be only a few hundred meters long, their ends looping through the ends of the mesh sections above and below at reinforced points. The mesh system also allows an entire cable to be slowly replaced over time, rope by rope, section by section, until none of it is the original material.
Carbon nanotube (CNT) cable remains far in the future. Advances towards that goal remain slow. Developing a large amount of infrastructure in space is itself likely to speed the pace of progress on this. CNTs are one of the materials that can be created by vapor deposition on a carefully prepared substrate. Performing such work in the hard vacuum and microgravity of orbit is likely to permit approaches that yield larger quantities and superior quality. It's also easier to create and sustain higher processing temperatures in space. Temperature control can be energy intensive but quite precise and repeatable too. Different levels of gravity can be imitated on different levels of the rotating sections of the space station. All of these factors create opportunities for new approaches to materials production.
The timeline doesn't make use of CNTs until 35 years after it starts. At that date, a skyhook for Earth is built using cable with tensile strength of 30 GPa. This is a reasonable estimation of the strength the first such cables could have. A material like that produced on industrial scales permits skyhooks to be built from Mercury to Titan.
Research into polymers and carbon materials may lead to unexpected finds that provide new solutions, too. Such a possibility is colossal carbon tubes (CCT), discovered through a collaboration among several research institutes and universities in China and America in 2008. They are made purely of a hexagonal mesh of carbon atoms, just like CNTs and graphene, but are double-walled tubes around 50 micrometers wide (which is colossal compared to CNTs) and have already been produced in lengths of several centimeters (which is enough to spin them into thread). Oddly, aside from that initial paper, nothing has been published about them. They display great promise if they could be produced in bulk. Their strength isn't that much higher than Zylon (UTS of 6.9 GPa) but they are extraordinarily light (about 0.12 g/cm3). As most of the mass of a tether is cable that is just there to support the mass of the cable itself, that makes a tremendous difference. If a way could be found to bind the CCT fibers together strongly enough, they could potentially outperform the carbon nanotube cable posited above.
|Mass, kt (xP)||31 (5.16)||51.1 (17.0)||54 (18.0)||22.8 (1.14)||275 (2.75)||5.7 (0.57)||77 (0.08)|
|Foot Speed, m/s||263||2352||2798[?]||151||785||329||227|
|Mass, kt (xP)||249 (2.49)||287 (2.87)||296 (2.96)||52 (0.52)||327 (3.27)||29 (0.29)||7.7 (0.077)|
|Total Mass, kt||152.5||338.1||350||74.8||602||34.7||84.7|
|Mass, kt||47 (0.47)||30 (0.25)||97 (0.23)||11(0.11)||29 (0.13)||3.9 (0.04)||5.2 (0.05)|
|Foot Station Mass,[?] kt||90||110||400||80||200||90||90|
|Mass, kt||551[?](5.51)||522 (17.4)||2190 (21.9)||606 (20.2)||1200 (20.0)||184 (6.13)||297(2.97)|
|Total Mass, kt||688||662||2687||697||1429||278||392|
The first skyhook built in lunar orbit gets its anchor mass from material slowly lifted from the surface over many trips. More payload will be heading down the tether to the surface than will be heading from the surface to go back to Earth, so there is room in the mass budget to send mass for the anchor up the tether. Ships arrive from Earth infrequently enough that the time necessary to move loads in a balanced manner is available. Still, to allow the anchor to be built up as quickly as possible, it is worth putting a large set of high-efficiency engines at the skyhook tip (most likely VASIMR or Neumann drives) and running them pretty much all the time, so whenever they are free the shuttles can bring loads of regolith to the foot, which get ferried up and added to the anchor.
Once asteroids are being brought into lunar orbit for study and then for mining, their mass is added to the anchors and that increases anchor mass much more quickly. After the first two skyhooks, most get their anchor mass entirely from asteroid material. In the Earth-Moon system, asteroid mining, skyhook development, and space settlement all benefit each other.
The skyhook's orbits are made far more stable by the addition of mass from asteroids to their anchors. The presence of skyhooks allows delivery of machinery to turn the asteroid material into products for a fraction of the fuel otherwise required. The ships that go retrieve the asteroids can be in the ideal place to be quickly launched at high speed when new targets are detected, using almost no fuel. Such detection is aided by placing telescopes devoted to the search on skyhook tips. Teleoperation of equipment proceeds more efficiently because the skyhooks allow the colonies to be home to lots of people, meaning operators have to deal with only a very brief signal delay because they are close by - some are actually on stations built into the anchors. Industry in space is aided by how the skyhooks lower the price of shipping high volumes of material. This especially aids the Moon. Materials more easily obtained and refined on the Moon, like aluminum and titanium, can be obtained there, and materials better acquired from asteroids, like carbon, can be obtained from them.