Penzo’s tether lengths are similar to the lengths I found when looking for a Zero Relative Velocity Transfer Orbit ZRVTO between Deimos and Phobos tethers. I wonder if Penzo used a similar process. Here’s a pic showing my math.

This method could be used to find ZRVTOs between any pair of tethers whose anchors are in coplanar circular orbits.

To the best of my knowledge, that was first proposed by Dr. Paul Penzo of JPL back in 1984. You can read about it in the Tethers in Space Handbook on page 70. And yes, it is great idea that will eventually be part of a transportation system that will help make travel between Earth and Mars affordable to everyone. It will also be important for making travel to the asteroid belt affordable.

In my observation, when big money is involved politics become a never ending issue. One example of this is the never ending price increases for launching astronauts to the ISS on the Soyuz since the Space Shuttle was retired.

As to how the system expands. The initial skyhook will be built in modules that can be launched on existing launch vehicles. Once a basic skyhook is in place, it will only be necessary to launch additional modules to lengthen and strengthen the cable. As the cable is made longer it will be necessary to increase the altitude of the skyhook. The onboard ion propulsion system will be used to do that. To increase the flight rate it will be necessary to launch additional solar power modules and additional ion propulsion modules. Since these additions will be launched into orbit using the skyhook, the launch cost for these additions will be less than using conventional launch vehicles without the skyhook. As a result, it will always be cheaper to expand an existing skyhook than to start from nothing to build a second one.

Regarding a second skyhook. It is possible to build and operate a second skyhook. To do so it will be necessary for both of them to operate in such a manner as not to interfere with each other. That will restrict the operations and profitability of both. If these skyhooks are owned by different countries or different companies there will always be tensions between them regarding those restrictions due to their not being able to operate at their maximum potential.
In short, for a given amount of investment, it will always be more cost effective to have one longer skyhook that operates without restriction than 2 shorter ones that are restricted.

It does seem like the political issues could be solved relatively easily due to all the benefits that the skyhook would provide. And I suppose it might not be too different from the ISS in a political sense.

There is one final thing that I was curious about reading through this site. As launch costs go down, how does this system expand? Do we make more skyhooks? Do we just make the one larger and larger? Or do we use the skyhook to build another system like a space elevator or orbital ring?

Yes, a high speed elevator system of some sort will be possible as the cable is made longer and stronger. As the cable is made longer, the tension on the cable increases. This allows for a higher rate of acceleration/deceleration by the elevator. Also, as the cable is made longer it becomes more massive and as a result the relative mass of the elevator relative to the cable mass becomes less. This means that high-speed elevators moving up and down the cable will have less of an impact on the overall orbit of the skyhook due to pumping.

As to the need for heavy rails like a maglev system. Since the elevator is moving up and down and not horizontally, there is no need for heavy rails to support the weight of the elevator on the cable. There will be a need for guide rails but those can be light.

As to to the best orbit. An equatorial orbit with a due East mountain side ground accelerator will give the highest flight rate for the least investment. The main problem with this will be the politics of the country where the ground accelerator is located as well as the politics of the country where the reusable stages might land. How much of an issue this might be is currently unknown. Putting the skyhook in an inclined orbit like the plane of the planets and using an air launched launch vehicle is a close second that avoids all the political issues.

Regarding the possibility that someone would use a skyhook to monopolize access to space. There are many ways to answer this. 1) It could be said that access to space is already monopolized by the current high price of getting to orbit. 2) A similar problem existed in the beginning of the railroad era when some of the railroad companies attempted to monopolize trade by controlling who could use them. This lead to a number of laws that made the railroads into common carriers such that they could not limit access. If necessary, the same could be done with a skyhook should the owners of the skyhook try to limit access.

Ah, I used the wrong word “reel”. I was thinking of what you described, that the station would pull the cable up through it and out the other side. I can see how a pulley or wheels on the station could be relatively easily designed, since it’s basically like an elevator cable. Would a maglev system be possible? Or would its rails be too heavy along the length of the cable? I suppose spending a few hours traveling up the cable might be considered a small price to pay for the reduced costs in any case.

So the best accelerator depends on the skyhook orbit. What would you say the best orbit would be? I remember reading somewhere (I’m pretty sure it was on this site) that only one skyhook could be built because different inclinations would lead to inevitable collision. So the group that built the first one would essentially monopolize space. Is this true, though? At the very least more than one skyhook could be built in the same orbital path, right?

With a basic skyhook, the space station does not reel up the cable, it travels up and down the cable while the cable remains fully extended. And yes, this is a relatively slow process. The time this takes depends on the length of the cable and the speed of the station or elevator. I have assumed that the top speed for this would be similar to the top speed of an elevator in a tall building which is about 50 MPH. The other issue is the maximum amount of acceleration or deceleration the station or elevator could use to get to that speed. The longer the cable is, the greater the tension on the cable due to the gravity gradient and the mass of the endpoint stations. The greater that tension is, the faster the space station or elevator car can accelerate or decelerate on the cable. If the station or elevator car attempts to accelerate or decelerate with a greater force than the tension on the cable, the cable will buckle. This is not something you want to have happen.

As to which is best, a vertical ground accelerator, a horizontal ground accelerator, an inclined ground accelerator, or an air launch.
That depends on a number of issues. If the skyhook is in an equatorial orbit, an inclined ground accelerator up the side of a mountain would be best. The problem with this is who owns the mountain and who owns the ground accelerator? If the company that owns the ground accelerator is from a different country than the country that owns the mountain, it could become a serious political issue.
Another issue is your customer base. If the majority of you launches are to a skyhook, an inclined ground accelerator that points East is best. If you have a number of customers who want to go to other orbits beside the skyhook, a vertical ground accelerator is best.

If the skyhook is in an inclined orbit then it becomes possible to launch from a wide range of places. For this situation an air launch is the best solution.
Another possibility occurs when the launch vehicle that is used to fly to the skyhook is powered by a combination rocket/ramjet/scramjet propulsion system. Due to the higher performance of this propulsion system it becomes possible to use a horizontal ground accelerator that is located next to the runway at an airport to get the launch vehicle up to ramjet speed. Once this is done, the launch vehicle would fly to the proper location for the boost to the skyhook on ramjet power, and then boost to the bottom of the skyhook.
Another significant issue has to do with whether this is a commercial system or a military system. A military system will be concerned about being able to survive an attack by an enemy. In this situation it would be best to use rocket/ramjet/scramjet powered launch vehicles that can be both air launched and ground accelerator launched. It would also be smart to have horizontal ground accelerators locate along side the runways at a number of different airports.