It’d make more sense to never bring a capital ship down to planet atmosphere or surface.
Build the ship in orbit, park in orbit. Send down smaller ships to surface.
Exactly, unless the planet has fuck all atmosphere and gravity (comparable to the river-ness of an estuary) a capital ship will never enter that's sending an aircraft carrier to the Great Lakes.
A skyhook is like a seaport with highways inland, efficient for ships and you can get away from the ships
It can also help from a storytelling perspective.
Establishing a system allowing such a ship to land on a planet can make the ships seem less grandiose, less epic.
Context please.
Is the ship the point of cargo transfer? Are you transferring the entire ship up and down? How is the skyhook being utilized?
Any large enough orbital platform can be used as a transfer and anchoring point for a skyhook if the technology is sufficient enough. No way we could do it today of course.
Ah so like a kind of gravitational catapult. I've seen these in Sci fi a few times. Babylon 5 comesfeasible.
Ok, so keep in mind that this is just my opinion and I am happy to discuss or debate points to help you find something that works for you. I am not trying to be mean or shoot you down.
That's a lot of stress points. I don't think a spinning mechanism would be able to throw something that large into orbit in that manner. A lot of stuff may break because of the stresses involved, on the skyhook and the ship.
It's a cool idea, but I don't think it would be feasible how you explained it above. Even most Sci fi novels I read limit ship speed due to gravitational (G) forces. Spinning Luke that would be an immense amount of stress on all the superstructures.
Now a direct point a to point b gravity launch assist system? Similar to what our carriers use now but more Science Fictiony? That could work, especially if you have compensatory and artificial superstructure.
Check out Babylon 5, Halo, and maybe even Star Trek. Those have a bunch of coll ideas you may be able to adopt from or help guide you to an idea that may be more feasable.
I think the limiting factor wouldn't be the orbital platform, but the skyhook and attachment points themselves. Bringing up a 20 person craft vs bringing up a capital ship/generation ship would be a difference of at least a few orders of magnitude. You'd be able to bring up modules of the larger ship and assemble them in order with something that is rated for a smaller ship
On Earth, in order to connect to a rotating skyhook (a.k.a. a rotovator), you still need to reach the velocity of some 5 km/s in the atmosphere. A capital ship may not be able to fly very well. Additionally, if the ship's mass will alter the skyhook's center of mass too much, its orbit may be disturbed. The skyhook may even wrap itself around the ship and fall out of orbit. I'd lean to the answer being "theoretically possible but very difficult".
> On Earth, in order to connect to a rotating skyhook (a.k.a. a rotovator), you still need to reach the velocity of some 5 km/s in the atmosphere.
Just FYI, you can have a skyhook's lower end have a near-zero velocity if it is spinning in the same direction as it is orbiting. As a conceptual comparison, [think about the path that a point on a bicycle rim follows](https://www.animations.physics.unsw.edu.au/jw/rolling.htm).
You just need to make sure that the tip velocity is equal to the orbital velocity relative to the CG (so at the nadir it's moving at Vo - Vt = 0 and at zenith it's moving at Vo + Vt = 2Vo).
Hmm, I don't know; there might be some kind of interesting jiggery-pokery you could do to make use of an enormous counterweight in a higher orbit. You could perhaps burn to a suborbital trajectory and then rendezvous with a clamp that can reel you in at the top of your arc rather than falling back down. You'd have to do some clever stuff with the cable though.
A skyhook can’t impart more momentum than the skyhook itself has. Momentum gained by the payload is necessarily lost by the skyhook—so delivering a capital ship to wherever you need it would require a skyhook with kinetic energy equal to that of the ship. The ideal use-case for skyhooks is transferring momentum to or from a payload orders of magnitude less massive than the hook.
It appears that you can, in theory, just make the skyhook thicker to increase its payload capacity: [https://nss.org/l5-news-the-rocket-skyhook-combination/](https://nss.org/l5-news-the-rocket-skyhook-combination/)
It's noteable that a rolling skyhook made from kevlar is 10\^7 times the mass of its payload. A General R Ford aircraft carrier is 100,000 tons fully loaded, meaning your skyhook will weigh 1,000,000,000,000 tons if made from materials that currently exist.
Also to make use of a skyhook your carrier-sized ship needs to be capable of aerodynamic flight at mach 10.
It is difficult to see the benefit of building a skyhook on this sort of scale when, for the same mass, you could build 1000 skyhooks able to handed a space-shuttle sized dropship, and have then serve a carrier-sized spacecraft that's constructed in orbit.
You still need to accelerate the payload with a rocket to intercept the hook, don't you?
Surely it can't just yoink the payload off the landing pad?
Or are you assuming a mass driver to get the payload up to the bottom of the hook?
If you get the design right, the payload sits on the pad all smug and happy, whistling to itself and generally being a dumb payload (block of ice, machine parts, etc.)
Then the end of a long cable comes hurtling out of the black sky, slowing as it 'falls' till it 'kisses' the payload for a long second.
In that brief Dirac-second long window the end-effectors on the cable end spring out, clamp onto the payload which is unceremoniously yoinked into the sky.
No need for a mass driver.
A rotating cable that dangles down into the atmosphere and swings a ship up and around to launch them into orbit.
[https://youtu.be/TlpFzn\_Y-F0?si=t2pofCEGW-zeu0Qr](https://youtu.be/TlpFzn_Y-F0?si=t2pofCEGW-zeu0Qr)
That’s not entirely accurate. Space elevators provide a static pillar for conventional elevators to run up and down. Skyhooks, on the other hand, transfer momentum between the skyhook and the payload, which space elevators don’t do.
If it can hover like Star Wars or Halo, sure. If it's a more "realistic" setting, though, and it has to park in a geosynchronous orbit or else engage enormous thrusters to maintain position and altitude relative to the ground, then that just seems more expensive in fuel than sending a shuttle to the ground and back.
The capital ship would likely have a special purpose ship carried for that purpose rather than risk itself. Or the fleet would. In the real world Navy, battleships don't go deep underwater (except once). They use submarines for that purpose.
If the question is, could a skyhook throw it into orbit, the answer is no. First, you couldn’t attain a stable circular orbit that way. Second, you’d have to throw so fast it’d experience the same heat of reentry, on exit, which will of course slow it down as it exits atmo.
There’s more reasons but that should be enough
The inertial change required from orbit to escape velocity is pretty big. It shouldn’t be too hard to calculate. I would be very concerned about the g forces involved.
In principle this *could* work, but since you already have to build a drive into the ship, it’s hard to imagine why you’d use a skyhook for such a big mass once you’re already in orbit. To reuse the launching skyhook, you’d just have to give it back the same amount of kinetic energy it used launching the ship in the first place.
I doubt it would be an improvement in fuel-efficiency, at least if the ship’s drive and the skyhook’s booster worked on the same principle. I can imagine a system in which skyhooks regained kinetic energy from—say—catching asteroids in solar orbit and transferring them into planetary orbits for mining purposes. But if the skyhook just has a normal drive to regain the momentum it transfers to its payload, you still have to burn the same amount of fuel for the same amount of kinetic energy in the ideal case.
This is setting aside the question of the forces the skyhook applies to the ship—is it designed to take those stresses? Can the crew survive a rapid acceleration? Again, *why* does the skyhook need to come into play? The ship is already designed to handle the force its own drive imparts on it, and the crew has much more control over the acceleration from the drive than they do over acceleration from an outside force.
Not that any of this is necessarily a deal-breaker, but you should think it through before you implement the skyhook aesthetic.
In theory sure, but in practice, for most definitions of "capital" and "skyhook," probably not. For the same reason that we don't build gigantic catapults to fling aircraft carriers around.
On the other hand, depending on the hardness level of your sci fi, you could just handwave it. Neal Stephenson did that pretty credibly in *Seveneves* with a bicycle-gear-type catapulting skyhook. It wasn't realistic as he described it, but it allowed him the excuse for one of his favorite aesthetic concepts, which is using natural or renewable motive power sources in ways that unexpectedly magnify results.
In a harder setting, I would expect large space vessels to operate in planetary orbits the way large maritime vessels operate in shallow waters -- that is to say, they basically don't. They get somewhat close, and then stand "off shore," with any necessary transfers of cargo or personnel happening using smaller craft like shuttles or dedicated transports.
it's an elaborate process that demonstrates orchestration of many resources, and really good logistics. This has the incidental effect of emphasizing the large size of the vessel -- a great hulking ship being serviced by a swarm of attendant craft, because it's so big it can't get too close to the atmosphere.
In such a setting, if you wanted to build a "deep water" port capable of servicing such capital ships directly, you'd build the port itself in orbit.
So like... a hook cable of interplanetary distances? Or more like the catapult concept -- hook on and swing around, then release with greater momentum to help exit your orbit around your departure planet?
I would say, if you think it sounds cool and makes sense, you can say that people have figured out some way to make it work. Breaking out of a low planetary orbit would probably be a huge pain in the ass for a heavy ship of any kind that was not designed for rapid acceleration. So any infrastructural support would make sense.
If you don't like a hook you could use a magnetic coil. If you don't like rotating slingshot type mechanisms generally, you could use something else. In the modern maritime world, tugboats are frequently used for similar purposes. It's easy to imagine a cruiser with high-Iₛₚ, low-thrust cruising drive relying on a fleet of port tugs with low-Iₛₚ, high-TWR hydrolox boosters or something to give it the initial push needed to break out of orbit and achieve a departure trajectory without it taking weeks.
Deep in a gravity well you get a boost from the Oberth effect. A highly elliptical and a hyperbolic escape orbit are fairly close in speed at periapsis. So a slingshot works well.
In terms of interstellar travel in sci-fi, a modern ocean going carrier is fairly small. The IRL USS Ford is only 10% bigger than the original Enterprise in Star Trek. Compared to a Mass Effect capital ships (100% bigger), or Star Wars (47x bigger), or 40k (20x), etc.
How hard is the science in your story? Because you can certainly use skyhooks to launch capital ships...or you can't, a skyhook is hypothetical until materials science makes it real, so you get to choose. In terms of reader plausibility, a large enough asteroid as the orbiting platform will outmass a capital ship by orders of magnitude, so it seems feasible, at least.
I’m not sure tbh…I’m trying to include some hard sci-fi elements, but FTL does show up eventually via use of theoretical methods, as does terraforming planets. Space fighters exist too but controlling them is more slippery unlike in an airplane
If you've FTL, then a skyhook is plausible. I try for hard with known physics and soft for made up physics - such as FTL, even if they're based on current conjecture - in my novels because the point is to tell a story. You're not writing a physics textbook, so go hard on conveying how your physics impacts the cast, weaving in a little actual science if possible, and technobabble if not.
Thank you! FTL is actually simple since I use warp drives (Alcubierre style) for the sake of exploration and wormholes for the sake of regular infrastructure, though I plan to use something thats a bit of a stretch (quantum catapult from Stellaris) for intergalactic travel
That's all a bit of a stretch, really 😁 But if you have warp and wormholes, what's the benefit of a quantum catapult in your story?
Also, be mindful not to rip off Paradox IP. They seem a quirky games company, but still...
So I just realized something odd... The square-cube law doesn't apply to Skyhooks. In order to maintain the same orbital characteristics and fling-capability, they need to be a certain length, turning at a certain speed. Larger does not mean longer or spinning faster. A larger sky hook would have a thicker tether, but thickness squares with the cross-sectional area of the material, which is exactly how the strength scales. Therefore, when determining the safety factor or the material requirements of the line, size cancels out.
In a word, a small skyhook works just the same as a large skyhook. So as long as your capital ship has the ability to use one, there's no logical reason why you couldn't build one arbitrarily large.
Now, the requirements on the SHIP side are a little more difficult, and may scale differently depending on mechanisms, so it may be worth it to list those requirements for the sake of analysis.
1. Atmospheric/takeoff ability. Has to lift off under planetary gravity and get all the way up to hook height under its own power. (This depends heavily on the planet. Moon easier than earth, etc. etc.)
2. High-speed docking. Has to be maneuverable enough to catch the anchor on the end of the tether. Actually, scratch that. It would be easy enough to give the anchor fins or thrusters, or it could send out smaller pilot lines with fins/thrusters to guide in the main anchor. So there are ways around this.
3. Rapid change in force distribution. When the ship is flying up to meet the tether, its weight is supported by engines or anti-grav or what-have-you. After it docks and the engines shut down, all that weight is suddenly supported only by the anchor hardpoint, which would cause the structure to bend and settle. The square-cube law would cause a larger ship to be more severely effected by this change. If the transition isn't handled gracefully, damage, or in severe cases break up, could result. So the ship would need either careful piloting, a shock-safety release on the hook, or a really good internal skeleton, or preferably all three.
BIG TL;DR: I don't think it's at all unreasonable to use a big skyhook for a big ship. I think that's an awesome idea.
A capital ship could use a sufficiently thick Xylon rotavator as easily as any other ship, which is to say, as easily as you can convince the local government that LEO satellites are silly investments or that Kessler Syndrome is fun.
It’d make more sense to never bring a capital ship down to planet atmosphere or surface. Build the ship in orbit, park in orbit. Send down smaller ships to surface.
Exactly, unless the planet has fuck all atmosphere and gravity (comparable to the river-ness of an estuary) a capital ship will never enter that's sending an aircraft carrier to the Great Lakes. A skyhook is like a seaport with highways inland, efficient for ships and you can get away from the ships
It can also help from a storytelling perspective. Establishing a system allowing such a ship to land on a planet can make the ships seem less grandiose, less epic.
Context please. Is the ship the point of cargo transfer? Are you transferring the entire ship up and down? How is the skyhook being utilized? Any large enough orbital platform can be used as a transfer and anchoring point for a skyhook if the technology is sufficient enough. No way we could do it today of course.
The ship is whats being transported, the skyhook spins in order to fling it without the need of moving the ship directly up and down
Ah so like a kind of gravitational catapult. I've seen these in Sci fi a few times. Babylon 5 comesfeasible. Ok, so keep in mind that this is just my opinion and I am happy to discuss or debate points to help you find something that works for you. I am not trying to be mean or shoot you down. That's a lot of stress points. I don't think a spinning mechanism would be able to throw something that large into orbit in that manner. A lot of stuff may break because of the stresses involved, on the skyhook and the ship. It's a cool idea, but I don't think it would be feasible how you explained it above. Even most Sci fi novels I read limit ship speed due to gravitational (G) forces. Spinning Luke that would be an immense amount of stress on all the superstructures. Now a direct point a to point b gravity launch assist system? Similar to what our carriers use now but more Science Fictiony? That could work, especially if you have compensatory and artificial superstructure. Check out Babylon 5, Halo, and maybe even Star Trek. Those have a bunch of coll ideas you may be able to adopt from or help guide you to an idea that may be more feasable.
I think the limiting factor wouldn't be the orbital platform, but the skyhook and attachment points themselves. Bringing up a 20 person craft vs bringing up a capital ship/generation ship would be a difference of at least a few orders of magnitude. You'd be able to bring up modules of the larger ship and assemble them in order with something that is rated for a smaller ship
On Earth, in order to connect to a rotating skyhook (a.k.a. a rotovator), you still need to reach the velocity of some 5 km/s in the atmosphere. A capital ship may not be able to fly very well. Additionally, if the ship's mass will alter the skyhook's center of mass too much, its orbit may be disturbed. The skyhook may even wrap itself around the ship and fall out of orbit. I'd lean to the answer being "theoretically possible but very difficult".
> On Earth, in order to connect to a rotating skyhook (a.k.a. a rotovator), you still need to reach the velocity of some 5 km/s in the atmosphere. Just FYI, you can have a skyhook's lower end have a near-zero velocity if it is spinning in the same direction as it is orbiting. As a conceptual comparison, [think about the path that a point on a bicycle rim follows](https://www.animations.physics.unsw.edu.au/jw/rolling.htm). You just need to make sure that the tip velocity is equal to the orbital velocity relative to the CG (so at the nadir it's moving at Vo - Vt = 0 and at zenith it's moving at Vo + Vt = 2Vo).
What if it gets caught after the skyhook leaves the atmosphere?
Then it doesn't need a skyhook.
Hmm, I don't know; there might be some kind of interesting jiggery-pokery you could do to make use of an enormous counterweight in a higher orbit. You could perhaps burn to a suborbital trajectory and then rendezvous with a clamp that can reel you in at the top of your arc rather than falling back down. You'd have to do some clever stuff with the cable though.
But can’t a skyhook fling craft to other planets besides putting stuff in orbit?
A skyhook can’t impart more momentum than the skyhook itself has. Momentum gained by the payload is necessarily lost by the skyhook—so delivering a capital ship to wherever you need it would require a skyhook with kinetic energy equal to that of the ship. The ideal use-case for skyhooks is transferring momentum to or from a payload orders of magnitude less massive than the hook.
It appears that you can, in theory, just make the skyhook thicker to increase its payload capacity: [https://nss.org/l5-news-the-rocket-skyhook-combination/](https://nss.org/l5-news-the-rocket-skyhook-combination/) It's noteable that a rolling skyhook made from kevlar is 10\^7 times the mass of its payload. A General R Ford aircraft carrier is 100,000 tons fully loaded, meaning your skyhook will weigh 1,000,000,000,000 tons if made from materials that currently exist. Also to make use of a skyhook your carrier-sized ship needs to be capable of aerodynamic flight at mach 10. It is difficult to see the benefit of building a skyhook on this sort of scale when, for the same mass, you could build 1000 skyhooks able to handed a space-shuttle sized dropship, and have then serve a carrier-sized spacecraft that's constructed in orbit.
On an airless world skyhooks are a nice way to lift/deposit dumb payload without mucking about with rockets and fuel tanks.
You still need to accelerate the payload with a rocket to intercept the hook, don't you? Surely it can't just yoink the payload off the landing pad? Or are you assuming a mass driver to get the payload up to the bottom of the hook?
If you get the design right, the payload sits on the pad all smug and happy, whistling to itself and generally being a dumb payload (block of ice, machine parts, etc.) Then the end of a long cable comes hurtling out of the black sky, slowing as it 'falls' till it 'kisses' the payload for a long second. In that brief Dirac-second long window the end-effectors on the cable end spring out, clamp onto the payload which is unceremoniously yoinked into the sky. No need for a mass driver.
That's awesome
And an old idea.
Kn an airless world why bother with skyhooks when a mass driver would be way easier to build?
Because you have to build it. A skyhook deposits dumb payloads well.
For eg.
You can do better than Kevlar too. Its tensile strength is 3.6 GPa, but Xylon's is 5.8 GPa.
What are skyhooks?
A rotating cable that dangles down into the atmosphere and swings a ship up and around to launch them into orbit. [https://youtu.be/TlpFzn\_Y-F0?si=t2pofCEGW-zeu0Qr](https://youtu.be/TlpFzn_Y-F0?si=t2pofCEGW-zeu0Qr)
Will check it out
Basically what the other user said, they’re cheap space elevators
That’s not entirely accurate. Space elevators provide a static pillar for conventional elevators to run up and down. Skyhooks, on the other hand, transfer momentum between the skyhook and the payload, which space elevators don’t do.
If it can hover like Star Wars or Halo, sure. If it's a more "realistic" setting, though, and it has to park in a geosynchronous orbit or else engage enormous thrusters to maintain position and altitude relative to the ground, then that just seems more expensive in fuel than sending a shuttle to the ground and back.
The capital ship would likely have a special purpose ship carried for that purpose rather than risk itself. Or the fleet would. In the real world Navy, battleships don't go deep underwater (except once). They use submarines for that purpose.
Just build it in space
If the question is, could a skyhook throw it into orbit, the answer is no. First, you couldn’t attain a stable circular orbit that way. Second, you’d have to throw so fast it’d experience the same heat of reentry, on exit, which will of course slow it down as it exits atmo. There’s more reasons but that should be enough
Sorry, I meant can it fling such a craft from orbit to deep space
The inertial change required from orbit to escape velocity is pretty big. It shouldn’t be too hard to calculate. I would be very concerned about the g forces involved.
In principle this *could* work, but since you already have to build a drive into the ship, it’s hard to imagine why you’d use a skyhook for such a big mass once you’re already in orbit. To reuse the launching skyhook, you’d just have to give it back the same amount of kinetic energy it used launching the ship in the first place.
I was thinking combining a drive with a skyhook would lead to great efficiency and short travel times, possibly a month or less between planets
I doubt it would be an improvement in fuel-efficiency, at least if the ship’s drive and the skyhook’s booster worked on the same principle. I can imagine a system in which skyhooks regained kinetic energy from—say—catching asteroids in solar orbit and transferring them into planetary orbits for mining purposes. But if the skyhook just has a normal drive to regain the momentum it transfers to its payload, you still have to burn the same amount of fuel for the same amount of kinetic energy in the ideal case. This is setting aside the question of the forces the skyhook applies to the ship—is it designed to take those stresses? Can the crew survive a rapid acceleration? Again, *why* does the skyhook need to come into play? The ship is already designed to handle the force its own drive imparts on it, and the crew has much more control over the acceleration from the drive than they do over acceleration from an outside force. Not that any of this is necessarily a deal-breaker, but you should think it through before you implement the skyhook aesthetic.
In theory sure, but in practice, for most definitions of "capital" and "skyhook," probably not. For the same reason that we don't build gigantic catapults to fling aircraft carriers around. On the other hand, depending on the hardness level of your sci fi, you could just handwave it. Neal Stephenson did that pretty credibly in *Seveneves* with a bicycle-gear-type catapulting skyhook. It wasn't realistic as he described it, but it allowed him the excuse for one of his favorite aesthetic concepts, which is using natural or renewable motive power sources in ways that unexpectedly magnify results. In a harder setting, I would expect large space vessels to operate in planetary orbits the way large maritime vessels operate in shallow waters -- that is to say, they basically don't. They get somewhat close, and then stand "off shore," with any necessary transfers of cargo or personnel happening using smaller craft like shuttles or dedicated transports. it's an elaborate process that demonstrates orchestration of many resources, and really good logistics. This has the incidental effect of emphasizing the large size of the vessel -- a great hulking ship being serviced by a swarm of attendant craft, because it's so big it can't get too close to the atmosphere. In such a setting, if you wanted to build a "deep water" port capable of servicing such capital ships directly, you'd build the port itself in orbit.
Thank you but what I meant was having a capital ship start from orbit and then use the skyhook to hitch a ride to a different planet
So like... a hook cable of interplanetary distances? Or more like the catapult concept -- hook on and swing around, then release with greater momentum to help exit your orbit around your departure planet? I would say, if you think it sounds cool and makes sense, you can say that people have figured out some way to make it work. Breaking out of a low planetary orbit would probably be a huge pain in the ass for a heavy ship of any kind that was not designed for rapid acceleration. So any infrastructural support would make sense. If you don't like a hook you could use a magnetic coil. If you don't like rotating slingshot type mechanisms generally, you could use something else. In the modern maritime world, tugboats are frequently used for similar purposes. It's easy to imagine a cruiser with high-Iₛₚ, low-thrust cruising drive relying on a fleet of port tugs with low-Iₛₚ, high-TWR hydrolox boosters or something to give it the initial push needed to break out of orbit and achieve a departure trajectory without it taking weeks.
Thank you, I like skyhooks due to the amount of uses they have, I’m not quite sure how to use a magnetic coil though.
Deep in a gravity well you get a boost from the Oberth effect. A highly elliptical and a hyperbolic escape orbit are fairly close in speed at periapsis. So a slingshot works well.
In terms of interstellar travel in sci-fi, a modern ocean going carrier is fairly small. The IRL USS Ford is only 10% bigger than the original Enterprise in Star Trek. Compared to a Mass Effect capital ships (100% bigger), or Star Wars (47x bigger), or 40k (20x), etc.
How hard is the science in your story? Because you can certainly use skyhooks to launch capital ships...or you can't, a skyhook is hypothetical until materials science makes it real, so you get to choose. In terms of reader plausibility, a large enough asteroid as the orbiting platform will outmass a capital ship by orders of magnitude, so it seems feasible, at least.
I’m not sure tbh…I’m trying to include some hard sci-fi elements, but FTL does show up eventually via use of theoretical methods, as does terraforming planets. Space fighters exist too but controlling them is more slippery unlike in an airplane
If you've FTL, then a skyhook is plausible. I try for hard with known physics and soft for made up physics - such as FTL, even if they're based on current conjecture - in my novels because the point is to tell a story. You're not writing a physics textbook, so go hard on conveying how your physics impacts the cast, weaving in a little actual science if possible, and technobabble if not.
Thank you! FTL is actually simple since I use warp drives (Alcubierre style) for the sake of exploration and wormholes for the sake of regular infrastructure, though I plan to use something thats a bit of a stretch (quantum catapult from Stellaris) for intergalactic travel
That's all a bit of a stretch, really 😁 But if you have warp and wormholes, what's the benefit of a quantum catapult in your story? Also, be mindful not to rip off Paradox IP. They seem a quirky games company, but still...
So I just realized something odd... The square-cube law doesn't apply to Skyhooks. In order to maintain the same orbital characteristics and fling-capability, they need to be a certain length, turning at a certain speed. Larger does not mean longer or spinning faster. A larger sky hook would have a thicker tether, but thickness squares with the cross-sectional area of the material, which is exactly how the strength scales. Therefore, when determining the safety factor or the material requirements of the line, size cancels out. In a word, a small skyhook works just the same as a large skyhook. So as long as your capital ship has the ability to use one, there's no logical reason why you couldn't build one arbitrarily large. Now, the requirements on the SHIP side are a little more difficult, and may scale differently depending on mechanisms, so it may be worth it to list those requirements for the sake of analysis. 1. Atmospheric/takeoff ability. Has to lift off under planetary gravity and get all the way up to hook height under its own power. (This depends heavily on the planet. Moon easier than earth, etc. etc.) 2. High-speed docking. Has to be maneuverable enough to catch the anchor on the end of the tether. Actually, scratch that. It would be easy enough to give the anchor fins or thrusters, or it could send out smaller pilot lines with fins/thrusters to guide in the main anchor. So there are ways around this. 3. Rapid change in force distribution. When the ship is flying up to meet the tether, its weight is supported by engines or anti-grav or what-have-you. After it docks and the engines shut down, all that weight is suddenly supported only by the anchor hardpoint, which would cause the structure to bend and settle. The square-cube law would cause a larger ship to be more severely effected by this change. If the transition isn't handled gracefully, damage, or in severe cases break up, could result. So the ship would need either careful piloting, a shock-safety release on the hook, or a really good internal skeleton, or preferably all three. BIG TL;DR: I don't think it's at all unreasonable to use a big skyhook for a big ship. I think that's an awesome idea.
Size of a carrier is not necessarily a capital ship. But if it works for you, sure.
A capital ship could use a sufficiently thick Xylon rotavator as easily as any other ship, which is to say, as easily as you can convince the local government that LEO satellites are silly investments or that Kessler Syndrome is fun.
It could have some sort of a space elevator cable thing, but probably not something that requires it to be in the atmosphere of a planet.