Skyhooks

From the first lunar skyhook to the Skyhook Interplanetary Transport Hubs

Skyhooks - A Really Big Deal

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.

Yes, that is really what the SpaceX BFR would be like. I mean, things can be done to manage that... nothing cheap or easy... I can't see how the ride would ever be pleasant. The humungous launch complex would need to be like 15 km out to sea. Launches would kill a lot of fish and birds, unless they were thoroughly scared away well before each launch by something they really wouldn't like. The only viable techniques for controlling the gigantic explosion that is the engines firing as designed would be to elevate the launch platform several storeys (so think for a moment about how heavy that rocket is) and channel the flames sideways with a scoop-shaped metal thing under the launch base (the tongue of flame would be hundreds of meters long and have the diameter of a baseball field), or pump basically a ring of waterfalls under it that absorb the life-threatening thunder of it and dissipate some of the heat. Seriously.

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.


Maintaining Skyhook Orbits

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.

What this would look like from the perspective of the skyhook, is that the rock first drops downwards, because it isn't going fast enough for orbit where it is. As it drops it gains speed. Long before it hits the ground, it has acquired orbital speed. To the skyhook, it is moving faster than the tether at its altitude, and it pulls out in front of it. It is moving fastest when it is 90° beyond the point in its orbit where it was dropped, and is also at its lowest altitude. The orbital dynamics add up to the rock moving in a circle aligned edge-on to the tether, a few thousand kilometers across, to observers on the skyhook. Its orbit around the Moon is an ellipse. It takes the same time for it to go around the Moon as the skyhook does, but it moves fastest when closest to the Moon, slowest when furthest away, in accordance with Kepler's 2nd Law.

There could often be a small swarm of such rocks accompanying a skyhook, gently looping around and almost kissing it each time they pass by. That means they are navigation hazards. They will need lights and radio beacons. Also thrusters sufficient for emergency collision avoidance maneuvers (rarely necessary), and to line them up properly with the skyhook (which might be necessary if they have been looping around for weeks - there are always little factors that perturb orbits).

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.

Tether Cable Strength

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 [?].

The calculation for this has to consider the changing force of gravity and angular momentum at all points on a cable, as well as the tensile strength and density of the cable material and the exponential growth of its cross-sectional area as it gets further from its end point. The safety factor multiplies the exponent in this situation. The complexity of the calculation means the results found on the Tether Tool page are only a good approximation, that is a bit on the heavy side.
More about Cable Loading

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.

Future Cable Materials

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.

The Skyhook Interplanetary Transport Hubs

Also shown in the Timeline, with many further explanations, in addition to the table explanation below.
Table Details

In the rows that show tether mass, this is the mass of just the CNT cable. Those numbers show the mass first in metric kilotons, and then in the brackets, as what multiple it is of the payload mass. Really the payload mass should be multiplied by 1.05 to account for the mass of the climber, the foot platform, and all the infrastructure on the tether for maintenance and power transmission. It also doesn't count the mass of the shaft that joins the two tethers together, around which the anchor mass is built up. That probably adds another 1% or so to the total cable mass. These things aren't included for the sake of simplicity. The grand total of both skyhooks also includes the mass of the foot station on the launch skyhook. As that mass directly bears on the mass of the cables and the strain on them, it is included there. Anchor mass uninvolved with bearing the weight on the cables has little relevance to the overall structure, other than it affects the center of gravity of the whole thing. It goes up and down over time, mostly up, and adds stability in general as it grows.

Tether figures use a safety factor of 2. That factor accounts for what a tether needs to operate safely even despite wear and tear, manufacturing defects, and damage due to any micrometeoroid strikes. Early skyhooks made of Zylon need a safety factor of 3, but because CNTs are much stiffer, can handle a wider range of temperatures, and don't degrade in sunlight, SF of 2 is enough. It means these cables never bear more than 50% of the maximum load they could theoretically sustain according to their ultimate tensile strength.

All skyhooks are made of an open weave of cables known as a 'Hoytether' weave, after Robert Hoyt of Tethers Unlimited. That design makes it easy for maintenance carts to weave in new cables when they detect a weakness on a cable. This may mean that a safety factor somewhat less than 2 would be fine. Because tethers must taper so the top of the tether can sustain the mass of all the cable below it, a change in safety factor affects the total mass of a tether in an exponential relationship. Being able to safely reduce the safety factor can drastically reduce the mass of cable that must be fabricated and delivered to build a skyhook. Thus bear in mind that as in all things here, this number is estimated somewhat on the conservative side.

lolololololol Mercury[?] Venus[?] Earth Moon Mars Callisto Titan
Surface Skyhook
Foot, km 20 100 100 20 50[?] 20 800[?]
Anchor, km 10000 7000 6500 7000 5980[?] 4900 10000
Tip, km 45000 15500 14000 30000 23000 15000 20000
Lower Tether
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)
Payload, kt 6 3 3 20 100 10 100
Foot Speed, m/s 263 2352 2798[?] 151 785 329 227
Upper Tether
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)
Payload, kt 100 100 100 100 100 100 100
V(inf), m/s 4983[?] 6142[?] 6200[?] 2664[?] 5746[?] 2179[?] 1227[?]
Total Mass, kt 152.5 338.1 350 74.8 602 34.7 84.7
Launch Skyhook
Foot, km 50 100 100 20 50 20 800
Anchor, km 1714 1000 929 1000 854 700 2000
Tip, km 10000 6500 6350 15000 9000 11000 20000
Lower Tether
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
Payload, kt 10 10 20 20 20 10 10
Upper Tether
Mass, kt 551[?](5.51) 522 (17.4) 2190 (21.9) 606 (20.2) 1200 (20.0) 184 (6.13) 297(2.97)
Payload, kt 100 30 100 30 60 30 100
V(inf), m/s 6635[?] 9705[?] 10146[?] 8150[?] 8895[?] 6469[?] 5285[?]
Total Mass, kt 688 662 2687 697 1429 278 392
The Mercury colony will be at the north pole, so the surface skyhook has a polar orbit. The launch skyhook needs to have an orbit inclined 7° from the equator or it is rarely aligned for launches to other planets. So, ships coming and going are all going to have to deal with an 83° plane changes when moving between skyhooks. Being able to do the plane change between two upper tethers should reduce the fuel needed compared to plane changes without that assistance.
Because the surface skyhook has a polar orbit, it can't be used to handle launch of Chukwas. The launch skyhook has to do it all. It has to be able to bear 100 kt at its tip.
A skyhook that combined the tasks of launch and surface ops, and had similar capacity to the skyhook pair shown here, would need to mass about 1008 kt, making it 145 kt heavier than the two skyhooks. Even then, its lower tether would only be able to support 3 kt, while the lower tether of the launch skyhook can bear 10 kt, albeit its foot is moving much faster and likely there are few cases where it makes sense to use that tether. Not only does a skyhook pair take less material, a spacecraft going up from the anchor station to launch from the launch skyhook only needs to travel half as far. There are twice as many berths, and 8 times as many launch opportunities. It might be a bit tricky to hop from the surface skyhook to the launch skyhook and vice versa, and it takes a little fuel. Overall though, a big plus to have skyhook pairs instead of one that does it all.
The Earth spins at a velocity of about 450 m/s at the equator, so a launcher would only have to gain speed of 2.35 km/s to reach the foot platform.
Actually, the average distance of this foot is 192 km, and at apoapsis it is 334 km. Which is a pain, but worth it. This is because its anchor is Phobos. See note below.
The anchor in this case is actually the moon Phobos, which orbits at an average distance of 5980 km from the equator of Mars. But its orbit is rather eccentric, so sometimes it is as close as 5838 km. This is why the foot of these skyhooks can only come down to 50 km, even though since Mars has such a thin atmosphere, and Phobos is such a giant reservoir of momentum there is no need to think about performing orbital corrections to compensate for drag. In fact, the orbit of the launch skyhook will be matched in eccentricity, to make it easier to keep them far apart with little orbital maintenance. However, as the orbit of Phobos is inclined 26° to the ecliptic, a plane change of 26° will be needed to hop to the launch skyhook, as it is best for it to be aligned to the ecliptic to minimize the energy spacecraft launched from it need for plane changes.
Titan's atmosphere is so dense (1.45 times Earth's at its surface), and its gravity so low (0.14 g, similar to the Moon), that it extends to a great height. Even at this altitude, the foot platform will experience measurable drag that will occasionally need to be corrected for. Vehicles from the surface headed for the foot platform will be able to use lift to get most of the way and require little fuel to cover the remaining distance.
To place the center of gravity of the launch skyhooks where it needs to be - at the anchor station - the most mass efficient method is to add mass at the foot. If this isn't done, the much greater mass of the upper tether puts the center of gravity inside that tether. A very heavy anchor station goes a long way to fixing this issue, but it isn't enough, and at any rate a solution is needed while that anchor mass is being accumulated. Making a cable capable of sustaining the heavy mass of a large foot station is cheap, it takes only a fraction of a ton for each ton of payload. And then a great facility can be created at the foot, that takes advantage of the proximity to the surface for a great view and reduced radiation shielding needs.

The figures in this row show a rough estimate of how massive the foot station would need to be to place the center of gravity between the upper and lower tethers. The analysis needed to properly estimate this is far beyond my math abilities and will need to wait for a time when someone else can give the question the attention it needs. A precise solution for this is impossible due to the nature of the calculation. Experimentation with an actual system will be necessary to derive a functional formula that gives a really good approximate solution (but not an exact one).
This isn't enough to get to any other world. It's about 2/3 what's needed to get to Venus, but would rarely be used for that, as this skyhook is in a polar orbit. Venus would rarely be properly aligned with it for a good trajectory to result from a launch from this skyhook. (Mercury's orbit is quite eccentric for a planet, and when it is at aphelion it would be able to launch to much closer to the orbit of Venus, but Venus is unlikely to be there when that ship arrives.) This upper tether exists to assist with transfers between skyhooks, and to give the sailing ships an initial boost.
This is a bit more than is needed to reach Mercury and Mars, and plenty to reach Earth.
Plenty for going to Mars or Venus, almost enough for Ceres
Three times what is needed for Earth, lots of extra going to Venus or Mars
Twice what's needed for Earth, Vesta, and Ceres, plenty for Venus, almost enough for Jupiter
Double what's needed for Ganymede, almost enough for Europa
Twice what's needed for Hyperion, just enough for Iapetus and Rhea
Gets you most of the way to Venus. Everything coming and going from Mercury will need to make use of the sailing ships.
Twice the speed needed for Earth, Mercury, or Mars. Vesta or Ceres with speed to spare.
Earth is of course the hub of everything, and Anshar's sister skyhook fits that role. It throws things so hard, you can launch for Venus, Mars, or Mercury anytime and have a short trip, get to Jupiter anytime and shave some months off transit , and just reach Saturn.
The sister skyhook of Gagarin throws hard to Venus or Mars any time. Ceres is also a short trip, though sometimes a little fuel will be needed to maintain the schedule. Mercury is in easy reach, Jupiter is just in range.
Really fast trips to Earth any time. Almost the same for Ceres. Twice the speed needed for Venus and Jupiter. Mercury just in range.
All Jupiter's moons in reach. (Because Jupiter's gravity is so strong, this actually takes a lot of speed to achieve. This skyhook can throw to Jupiter itself, but it is on the edge of its range.) Twice the speed needed for Mars. Earth and Venus with plenty to spare, not much margin for Mercury.
All Saturn's moons in range. Twice the speed needed to reach Saturn. Throws hard to anything closer to the sun. Laughably overpowered for reaching Earth.

Asteroid Anchors

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.

Advantages of Skyhooks over Space Elevators

  • For Earth's first skyhook, the climb to the anchor is less than a fifth of the distance to an anchor in geosynchronous orbit. As cars on the cable can only go so fast, the time savings in the trip is helpful. Beaming the power the car needs for the climb from the anchor is also easier.
  • The cross-section of the cable is much less than that of a space elevator because the loads it must bear are much lower. Many skyhooks can be made with the amount of material needed for one space elevator
  • If there is a grave accident and the cable is cut, the debris is far less dangerous. The bottom part of the cable of a severed space elevator, for the first 150 km or so above where it is connected to the ground, will crash to Earth without disintegrating and can do damage on impact. A severed skyhook cable enters the atmosphere fast enough to mostly disintegrate due to friction heating, and what doesn't is slowed to a gentle speed by the time it reaches the ground.
  • The security needed to protect an installation that starts 100 km above the Earth is much less than what is needed to protect something that reaches the ground
  • There is no need to deal with Earth's atmosphere, whereas a space elevator has to solve the problems of lightening strikes and the effects of weather on the cable.
  • The launch boost the spaceward tether can provide is more, over a shorter distance, than a space elevator can provide, because it is deeper in Earth's gravitational well.
  • Because satellites can be shifted over time to orbits that don't interfere with the skyhook, the demands of collision avoidance are minimal. A space elevator would always cut through all orbital elevations below geosynchronous.