User:Skyhook1/sandbox

A rotating and non-rotating skyhook in orbit.

A skyhook is a proposed space transportation concept, which its promoters claim will make Earth-to-orbit and interplanetary spaceflight affordable, thereby opening the way for the commercial development of lunar mining, asteroid mining, space-based solar power stations, space colonies, and colonies on the Moon, Mars, and in the asteroids. Skyhooks are often confused with an Earth surface to geostationary orbit space elevator, but they are different. A skyhook is a much shorter version of the space elevator that does not reach down to the surface of the Earth, is much lighter in mass, and can be affordably built with existing materials and technology. It works by starting from a relatively low altitude orbit and hanging a cable down to just above the Earth’s atmosphere. Since the lower end of the cable is moving at less than orbital velocity for its altitude, a launch vehicle flying to the bottom of the skyhook can carry a larger payload than it could otherwise carry to orbit on its own. When the skyhook is long enough and the lower endpoint velocity is low enough, single stage to skyhook flight with a reusable sub-orbital launch vehicle becomes possible.

The most important difference between a skyhook and a space elevator is that a skyhook can be built with presently available materials, while a space elevator cannot.

The following is a direct quote from "Hypersonic Airplane Space Tether Orbital Launch System" (HASTOL), a NASA funded study on rotating and non-rotating skyhooks.

"The fundamental conclusion of the Phase I HASTOL study effort is that the concept is technically feasible. We have evaluated a number of alternate system configurations that will allow hypersonic air-breathing vehicle technologies to be combined with orbiting, spinning space tether technologies to provide a method of moving payloads from the surface of the Earth into Earth orbit. For more than one HASTOL architecture concept, we have developed a design solution using existing, or near-term technologies. We expect that a number of the other HASTOL architecture concepts will prove similarly technically feasible when subjected to detailed design studies. The systems are completely reusable and have the potential of drastically reducing the cost of Earth-to-orbit space access."

The following is a quote from Keith Henson, co-founder of the L-5 Society regarding space elevators.

"No current material exists with sufficiently high tensile strength and sufficiently low density out of which we could construct the cable [for a space elevator]. There’s nothing in sight that’s strong enough to do it – not even carbon nanotubes."

Skyhooks come in two types: rotating and non-rotating. While no skyhook capable of capturing an arriving spacecraft has been built so far, there have been a number of flight experiments exploring various aspects of the skyhook/space tether concept.

Affordable spaceflight and skyhooks

The three most important issues that need to be addressed if a transportation system is to be commercially affordable on a mass-market level are:

• reusability,
• a low propellant fraction, and
• a high payload fraction.

Reusability so the investment can be amortized over a large number of trips, a low propellant fraction for reduced operating costs, and a large payload fraction so that the cost of each trip can be distributed over a large amount of payload. Trains, planes, automobiles, trucks, and ships are all very good examples of this. Currently existing expendable rockets are not.

When a launch vehicle takes-off to go to Earth orbit, approximately 90% of its take-off weight is propellant, 9% is the weight of the rocket, and 1% is the weight of the payload. With numbers like these it should be fairly obvious why the currently existing expendable launch vehicles are somewhat of a failure when it comes to meeting the three main requirements for a commercially affordable mass-market transportation system. This is also why current launch vehicles cost so much.

The reasons for this failure are threefold:

• the speed the rocket needs to achieve to reach Earth orbit,
• the amount of propellant it takes to achieve that speed (which has to do with the performance of the rocket motor), and
• the lack of reusability of the launch vehicle.

The total speed that a launch vehicle needs to achieve in order to reach low Earth orbit is approximately 9,400 m/s. This includes the speed of low Earth orbit, plus additional velocity for overcoming the force of gravity that is trying to pull the rocket down, and additional velocity for the atmospheric drag as the launch vehicle climbs through the atmosphere.

A skyhook makes spaceflight affordable by reducing the speed the rocket needs to achieve in order to reach low Earth orbit. That reduction in speed means less propellant is required. The reduction in propellant allows the size of the payload to be increased. More payload and less propellant per flight means a lower cost to orbit.

In order to provide some examples of how different sized reductions in velocity translate into increased payload capacity, some simple calculations were made using the ideal rocket equation, the 90% propellant, 9% rocket, and 1% payload ratio, and the 9,400 m/s total speed for orbit value. The results of these calculations show that:

• reducing the speed required for orbit by 200 m/s increases the payload size by over 50% and reduces the cost by over 33%,
• reducing the speed required for orbit by 400 m/s more than doubles the size of the payload and reduces the cost by over 50%,
• reducing the speed required for orbit by 800 m/s more than triples the size of the payload and reduces the cost by over 67%,
• reducing the speed required for orbit by 1,600 m/s increases the payload by a factor of 6 and reduces the cost by over 84%.

This process continues as the skyhook gets longer and applies to both rotating and non-rotating skyhooks.

Reusability of the launch vehicle is the third key issue that needs to be addressed if a skyhook space transportation system is to become commercially affordable on a mass-market level. Using some the increased payload capacity that the skyhook makes possible to make the launch vehicle reusable is an idea that is used and discussed in every reference in this article that discusses either rotating or non-rotating skyhooks. The specific amount of extra weight that will be required to make a launch vehicle reusable will depend on the details of the launch vehicle design. Is it single-stage-to-orbit, two-stage-to-orbit, ground launched, air launched, catapult launched, air-breathing, all rocket, or a combination propulsion system? All of these will have different requirements in order to make the launch vehicle reusable. But regardless of the details, using some of the increased payload capacity made possible by the skyhook to go from an expendable launch vehicle to a reusable launch vehicle, will also be a very important step in the process of making spaceflight mass-market affordable: which is the whole purpose of a skyhook.

Non-rotating skyhooks

Non-rotating skyhook first proposed by E. Sarmont in 1990.

A non-rotating skyhook is a vertically oriented, gravity gradient stabilized tether whose lower endpoint does not reach the surface of the planet it is orbiting. As a result it appears to be hanging from the sky, hence the name skyhook. The idea of using a tidally stabilized tether for downward-looking Earth observation satellites was first proposed by the Italian scientist Giuseppe Colombo.

The idea of using a non-rotating skyhook as part of a space transportation system for Earth where sub-orbital launch vehicles would fly to the bottom end of the tether, and spacecraft bound for higher orbit, or returning from higher orbit, would use the upper end of the tether, was first proposed by E. Sarmont in 1990, expanded on in a second paper in 1994, and in a third paper in 2014. Other scientists and engineers, as well as NASA, Lockheed Martin, former astronaut Bruce McCandless II, and Dr. Robert Zubrin, have also investigated, validated, and added to this concept.

In addition, NASA representatives who have reviewed this concept have described it as, "The first idea we have seen that offers a believable path to $100 per pound to orbit."

Basic 200 km long non-rotating skyhook.

The non-rotating skyhook is not a space elevator. A non-rotating skyhook does not reach down to the surface of the Earth. The lower end of the non-rotating skyhook is above the upper edge of the atmosphere and requires a high-speed aircraft/sub-orbital launch vehicle to get there. Since the lower end of the skyhook is moving at less than orbital velocity for its altitude, a launch vehicle flying there can carry a larger payload than it could carry to orbit on its own. When the cable is long enough, single-stage to skyhook flight with a reusable sub-orbital launch vehicle becomes possible. In addition, unlike a space elevator that remains over the same spot on the Earth, a non-rotating skyhook circles the planet every few hours. This allows the skyhook to serve as a terminal for sub-orbital launch vehicles arriving from just about anywhere on Earth. This type of skyhook can start out as short as 200 km and grow to over 4,000 km in length using a bootstrap method that takes advantage of the reduction in launch costs that come with each increase in tether length.

At its longest, the non-rotating skyhook is approximately 1/25th the length of the 100,000 km long space elevator. As a result, it is much lighter in mass, and can be affordably built with existing commercially available carbon fiber materials. Analysis has also shown that this saving in construction cost for the non-rotating skyhook more than makes up for the additional cost of the sub-orbital launch vehicle that it requires. As a result, a mature non-rotating skyhook with reusable single stage sub-orbital launch vehicle is considered to be cost competitive with what is thought to be realistically achievable using a space elevator, assuming a space elevator can ever be built.

Another advantage of the non-rotating skyhook is that once it is long enough, the upper end of the cable as shown in figure 2, will be moving at just short of escape velocity for its altitude. This means that a spacecraft such as the Orion spacecraft could be placed on either a free-return orbit to the Moon, or on course for a near-Earth asteroid, without the need for an expensive expendable upper stage for boosting it to escape velocity. Elimination of the expendable upper stage and all the propellant it will require will also dramatically reduce the number of flights to the lower end of the non-rotating skyhook, which will further reduce the cost of such a mission.

This ability to capture sub-orbital launch vehicles coming up from the Earth at the lower end of the cable, and to launch spacecraft to higher orbits from the upper end of the cable, requires energy. Energy that comes from either a solar powered ion propulsion system or an electrodynamic propulsion system on the skyhook. The advantage of this over current launch systems is the greatly improved operating efficiency and reduced cost of either of these propulsion systems compared to conventional expendable rockets. While these high-efficiency, low-thrust propulsion systems cannot be used for a planetary surface to orbit launch system due to their low thrust, they are perfect for use on an orbiting skyhook due to their ability to gradually store up energy by raising the orbital altitude of the skyhook between arriving and departing flights.

The docking maneuver

The process of docking an arriving spacecraft at the lower end of the non-rotating skyhook starts with the skyhook in an elliptical orbit. The low point of this elliptical orbit, the perigee, is selected so that the lower end of the skyhook cable will be at an altitude of 185 km at that point in the orbit. The altitude of the high point of the elliptical orbit, the apogee, is selected based on the mass of the arriving spacecraft.

In addition to boosting the arriving spacecraft to the proper speed and altitude for rendezvous, the sub-orbital launch vehicle for this flight will also need to time its take-off so that it will rendezvous with the lower end of the skyhook when the skyhook is at the low point of its orbit.

When the arriving spacecraft docks with the lower end of the skyhook it will lower the center of gravity of the total skyhook system, thereby pulling the skyhook down into a lower more circular orbit. If the apogee altitude of the skyhook's initial elliptical orbit was properly selected, the skyhook will end up in a circular orbit after the arriving spacecraft has docked.

Upon completion of the docking maneuver, the skyhook's solar-powered ion propulsion system, or electrodynamic propulsion system, is activated so as to start raising the orbital altitude of the skyhook back to its original altitude.

What makes the skyhook concept work is energy exchange. When the skyhook is in its initial elliptical orbit it is in a higher-energy orbit than the one it ends up in after the arriving spacecraft docks with the lower end of the skyhook. What happens is that the skyhook gives the extra energy of the higher elliptical orbit to the arriving sub-orbital spacecraft; a spacecraft that doesn't have enough energy to remain in orbit on its own. The end result is that the arriving spacecraft gets an energy boost from the skyhook that allows it to remain in orbit while the skyhook gives up energy and drops to a lower energy orbit. Before another arriving spacecraft can dock at the lower end of the skyhook, the skyhook will need to use its high efficiency low thrust propulsion system to raise itself back to the original higher-energy orbit.

A non-rotating skyhook transportation system for Mars

In 1984, Paul Penzo of JPL proposed a planetary surface to escape velocity tether transportation system for Mars that consists of two non-rotating skyhooks; one attached to the Martian moon Phobos, and the other attached to the Martian moon Deimos. An illustration of this concept can be seen here.

With this system, a spacecraft arriving at Mars, either direct from Earth, or from an Earth-Mars cycler spacecraft as it swings by Mars, docks at the upper end of the non-rotating skyhook attached to the outer moon Deimos. The people and cargo on that spacecraft then transfer to an elevator on the skyhook that will take them down to the lower end of the Deimos skyhook. There they board a small orbital transfer vehicle that will take them to the upper end of the non-rotating skyhook that is attached to the inner moon Phobos. Again they transfer to an elevator that will take them to the lower end of the Phobos skyhook where they will transfer to the reusable single stage Mars Lander that will carry them to the Martian surface. Passengers and cargo from the Martian surface that are bound for either the asteroids, or for Earth, would ride the system in reverse.

One of the advantages of this concept is that neither skyhook will require a propulsion system for orbital re-boost or for orbit control, as they both will use the Martian moon they are attached to as a momentum bank to make up any discrepancies in the upward versus downward mass flow of people and cargo. This elimination of the propulsion systems for the two skyhooks also makes for a significant reduction in the cost to build, and the cost to operate. Like the non-rotating skyhook for Earth, this two-stage non-rotating skyhook system for Mars can be affordably built with existing materials and technology.

Rotating skyhooks

As the name implies, rotating skyhooks rotate end over end in the plane of their orbit such that the upper endpoint becomes the lower endpoint and the lower endpoint becomes the upper endpoint. In other words, it rotates like a wheel that has two spokes and no rim.

Earth launch assist bolo

When a rotating skyhook is placed in orbit around a planet, the rotational direction is selected so that the lower endpoint of the skyhook is moving slower than orbital velocity and the upper endpoint is moving faster than orbital velocity. When the planet being orbited has an atmosphere, the length and orbital altitude of the rotating skyhook is selected so that the lower end of the cable is above the majority of the atmosphere when it is closest to the ground. The reasons for this are to minimize heating of the cable as it passes through the upper part of the atmosphere, and so that a launch vehicle flying to the bottom end of the rotating skyhook does not have to deal with atmospheric buffeting while attempting to dock with the lower end of the skyhook. The fact that the lower end of the cable has a horizontal velocity of less than orbital velocity means that the launch vehicle will not have to go as fast as it would if it were going directly to orbit. Therefore, like the non-rotating skyhook, this reduction in velocity increases the payload capacity of the launch vehicle, thereby reducing the cost of getting into orbit. Once the payload in the suborbital launch vehicle is captured by the lower end of the rotating skyhook, it is carried up and around until the end of the cable is at the top of its rotational arc where the payload is released. When released, the payload will be moving faster than circular orbit velocity for that altitude. This rotating skyhook/sub-orbital launch vehicle combination has also been referred to as 'Tether Launch Assist'.

Like the non-rotating skyhook, the rotating skyhook known as an 'Earth launch assist bolo':

• will need to be in a higher energy elliptical orbit prior to picking up the payload from an arriving launch vehicle
• will need a solar powered ion propulsion system, or electrodynamic propulsion system, for re-boosting the rotating skyhook back to its original orbit after lifting the arriving payload to a higher orbit
• will need to be at the low point of its elliptical orbit when the payload pickup is made
• will need a sub-orbital launch vehicle for carrying cargo and passengers to and from the lower end of the cable.

In addition, the rotational position of the lower end of the cable will also need to be at the bottom of its swing when the rotating 'Earth launch assist bolo' is at the low point of its elliptical orbit.

Zero velocity rotating skyhooks

Zero Velocity Skyhook. When the skyhook rotation rate is synchronized with the skyhook's speed over the ground, the end of the skyhook moves in a cycloid, and the endpoint is momentarily stationary with respect to the ground. (Image from the cycloid article.)

Another proposed method for using a rotating skyhook that is in orbit around a small airless, or near airless body such as the Moon or Mars, is to select the length and rotation rate of the skyhook such that the lower end of the cable would have zero horizontal velocity relative to the ground so that it could pick up payloads directly from the planetary surface. These type of rotating skyhooks are called non-synchronous skyhooks, rotovators, or zero velocity rotating skyhooks.

Interplanetary skyhooks

A third type of rotating skyhook is one that is far from its parent body, that rotates in the plane of the planets, and is used for interplanetary spaceflight. An example of this would be a rotating skyhook located at L-4, the leading Earth-Moon Lagrangian point, that would be used to launch and receive small transfer spacecraft traveling to and from a Mars cycler spacecraft as it swings by the Earth on it way to Mars and the asteroid belt again. This type of rotating skyhook is sometimes referred to as a free space skyhook, bolo, interplanetary bolo, or interplanetary skyhook.

Hans Moravec

All three of these rotating skyhook concepts were first published by Dr. Hans Moravec in 1977, expanded on in follow-on papers in 1978, and again in 1986. In his first paper he states that the idea for the rotating skyhook was conceived and suggested to him by John McCarthy of Stanford University. Other scientists and engineers, as well as NASA, Boeing, Tethers Unlimited, Inc., Dr. Robert Forward and Dr. Robert P. Hoyt, have also investigated, validated, and added to the rotating skyhook concept.

Launch Vehicles

Any orbital launch vehicle can fly to the lower end of either a rotating or non-rotating skyhook, allowing it to both increase its payload capacity and reduce its launch cost compared to flying to orbit directly. This applies to all existing expendable launch systems, such as the Atlas V, Delta IV, Falcon 9, Antares, Vostok, Proton, Long March, and the Ariane V. It applies to air launch to orbit launch systems such as the Stratolaunch/Pegasus II combination. This also applies to proposed reusable launch systems such as the reusable Falcon 9, New Shepard, Skylon, DC-X, a vertical take-off horizontal landing rocket powered spaceplane, a rocket-based combined cycle powered spaceplane, or the scramjet-powered Rockwell X-30. Additional advanced launch vehicle concepts that could also benefit from using a skyhook can be seen here.

Rendezvous and capture

The following is direct quote from "Hypersonic Airplane Space Tether Orbital Launch System" (HASTOL).

"In any rotating tether transport system, one of the most challenging tasks will be to enable the rendezvous between the payload and the tether tip. For the tether to successfully capture the payload, the payload and tether grapple vehicle must come together at nearly the same place in space and time with nearly the same velocity. Because the payload is in free fall, and the tether is rotating, the payload and grapple vehicle will experience a relative acceleration equal to

a = V_t²/L

where V_t is the velocity of the tether tip relative to the tether facility’s center of mass, and L is the distance from the tether tip to the center of mass. In the HASTOL tether designs described above, V_t is approximately 3.5 km/s, and L is approximately 500 km, so this acceleration is about 2.5 g’s. If neither grapple nor payload perform any maneuvering, the two will coincide only instantaneously, providing a minimal rendezvous window. Fortunately, it is possible to extend this rendezvous window to five seconds or more by using tether deployment from the grapple vehicle."

The rendezvous and capture of a payload at the lower end of a rotating skyhook happens in five seconds or it does not happen. Compare this to the three to five minutes that are available for rendezvous and capture with the non-rotating skyhook. When using a reusable launch vehicle to fly to the bottom of either a rotating or non-rotating skyhook, a missed approach does not mean the loss of a launch vehicle or payload. However, it does mean that the mission will need to be re-flown with all the additional cost that entails. As a result, critics of the rotating skyhook concept are concerned, that due to the much shorter amount of time available for rendezvous and capture, that the rotating skyhook will likely have a much higher re-flight rate than the non-rotating skyhook. This is an additional cost that will need to be accounted for when comparing the two concepts. Fortunately this is an issue that NASA Marshall Space Flight Center and Tennessee Technological University have been working on.

Combination launch systems

In 1999, in the workshop that lead to the NASA conference paper "Space Elevators, An Advanced Earth-Space Infrastructure for the New Millennium", the idea of combining some kind of ground accelerator, rocket sled, or catapult with a non-rotating skyhook was proposed as a way of further reducing the propellant fraction of the sub-orbital launch vehicle so as to increase its payload fraction and further reduce the cost of getting to orbit. Illustrations of two of the notional ideas that were proposed at the workshop can be seen here.

In 2009, Dr. Dana Andrews of the University of Washington, went into more detail regarding a possible combination non-rotating skyhook and catapult system in pages 6 through 12 of a presentation he gave at the 'Advanced Space Technology Workshop' at NASA Langley. In addition to further reducing the propellant fraction of the sub-orbital launch vehicle, another way of taking advantage of this combination system would be to use it to reduce the startup cost of building an initial skyhook system by off-loading some of the launch vehicle velocity reduction to a cheaper to build ground accelerator which then allows for a shorter and less expensive skyhook in the beginning. The trackless ground accelerator shown in this presentation, which builds on the winch launch system used by sailplanes, is potentially one very low cost method for doing this. Another possible low cost ground accelerator idea for use with a skyhook would be a rail system like the Holloman High Speed Test Track which currently holds the land speed record for rail vehicles of Mach 8.6, or 9,465 ft/s (2,885 m/s).

The idea of adding some type of ground accelerator or catapult to a launch system is not new. The Wright brothers used a catapult to help get the Wright Flyer up to take-off speed for its first flights. The U.S. Navy uses them to launch aircraft off of aircraft carriers on a daily basis. They have also been used in a number of science fiction stories and movies for launching spacecraft into orbit. Air launch to orbit, where an airplane is used to carry the launch vehicle up to 30,000 to 40,000 feet of altitude before launch, is another launch method that could be used as part of a combination skyhook launch system.

Best orbit for a skyhook

The two most commonly proposed orbits for either a rotating or non-rotating skyhook are the plane of the equator and the plane of the planets, also known as the plane of the ecliptic.

The advantage of an equatorial orbit is that it allows for frequent revisit opportunities between a near-equatorial launch and landing site and the lower end of the skyhook. This is especially important if the ground site includes a ground accelerator or catapult for giving the sub-orbital launch vehicle its initial boost. The disadvantage of the equatorial orbit is that a spacecraft using the upper end of the skyhook for interplanetary travel will most likely require a plane change maneuver.

The advantage of the skyhook orbit being in the plane of the planets is that it avoids the need for a plane change maneuver when going interplanetary or when launching a spacecraft from the upper end of the skyhook to rendezvous with a Mars cycler as it swings by the Earth. The disadvantage of this orbit is the greatly reduced frequency of launch opportunities from a fixed ground site to the lower end of the skyhook. As a result, use of this orbit would most likely drive the design of the sub-orbital launch vehicle to an air launch to orbit system like Stratolaunch but with a single stage reusable launch vehicle.

Navigating a Skyhook

Navigating a skyhook and controlling the location of the low point of its orbit, its orbital eccentricity, and its average orbital altitude will be very different from any other Earth orbiting satellite or spacecraft that has been put in orbit before. The primary difference between a skyhook and previous orbital vehicles is that the skyhook will be under almost continuous acceleration and as a result its perigee location, eccentricity, and average altitude will be in a near-constant state of change. This applies to both rotating and non-rotating skyhooks regardless of their overall length and inclination of orbit. For a skyhook in an orbit that is inclined to the plane of the equator there will also be the additional issue of nodal precession and how to manage the change in the orbital plane this causes so that the skyhook will be in the desired orbital plane at the right time for launching a vehicle from the upper end of the skyhook. Another significant issue regarding the navigation of a skyhook is the low thrust to weight ratio of the skyhook propulsion system and the resulting low rate of acceleration. It is due to this low rate of acceleration that every spacecraft arrival at the lower end of the skyhook, every return to Earth from the lower end of the skyhook, and every launch to a higher orbit from the upper end will need to be planned many months in advance and coordinated with other planned arrivals, departures, and upper endpoint launches in order to make sure the skyhook is in the right place at the right time so as to fulfill each specific mission and to maximize the utilization of the skyhook.

Control of all these factors is made possible by the skyhook's propulsion system and by planning in advance so as to minimize the total change in velocity required by the skyhook to accomplish the various missions. Some of the possible control methods for accomplishing this are:

• vectoring and varying the thrust of the ion propulsion system
• pausing for a period of time in a specific orbit that has an orbital period or nodal precession rate that allows the skyhook to end up in the desired orbit at the desired time
• timing the release of refuse from the lower end of the skyhook into a re-entry orbit such that the resulting change in orbit to the skyhook assists in the navigation to the desired orbit at the desired time.

Tip speed, tether mass, and launch vehicle mass ratio

The speed for orbit at the lower endpoint altitude of 185 km for a skyhook in orbit around the Earth is 7.8 km/s. The tip speed of the lower end of the 200 km long non-rotating skyhook in orbit around the Earth is 7.5 km/s. The tip speed of the lower end of the 1,550 km long non-rotating skyhook in orbit around the Earth is 6.6 km/s. The tip speed of the lower end of a 3,800 km long non-rotating skyhook in orbit around the Earth is 5.5 km/s.

A slightly longer non-rotating skyhook with a lower tip speed of 5.0 km/s and a design safety factor of 2, has a tether mass of 25 times the payload mass. Further lengthening this skyhook until its lower tip speed drops to 4.0 km/s will result in a tether mass greater than 200 times the payload mass.

When the "mass of the tether alone started to exceed 200 times the mass of the payload, then that was an indication the particular scenario being considered was not engineeringly feasible using presently available materials."

This means that a non-rotating Earth orbiting skyhook with a lower endpoint velocity of 4.0 km/s is most likely the lowest speed that we can design for with currently available materials.

Payload capture, non-rotating skyhooks

The rendezvous and docking of a spacecraft such as the Soyuz, Progress, Dragon, or Cygnus with the International Space Station, is usually divided into multiple phases. The first two phases, called drift orbit A and drift orbit B, extend from half a world away to 1 km from the space station. Closing this gap can take days. The next phase, called proximity operations A, extends from 1 km (1,000 meters) to 100 meters. Time for this phase can take anywhere from 1 to 8 hours. From 100 meters to 10 meters is called proximity operations B and that usually takes from 45 to 90 minutes. The final docking phase extends from 10 meters to contact, and that takes approximately 2.5 minutes using a closing speed of .2 feet per second. It is the final docking phase that is most relevant to the docking of an arriving sub-orbital spacecraft with the lower end of a non-rotating skyhook.

On page 174 of the "Tethers in Space Handbook" it states:

"Rendezvous of a spacecraft with the end of a tether may appear ambitious, but with precise relative-navigation data from GPS (the Global Positioning System) it may not be difficult. The relative trajectories required are simply a time-reversal of relative trajectories that occur after tether release. Approach to a hanging-tether rendezvous is shown at right. Prompt capture is needed with this technique: if capture is not achieved within a few minutes, one should shift to normal free-fall techniques."

The key words here are "hanging-tether rendezvous", which refers to docking with a non-rotating skyhook, and "if capture is not achieved within a few minutes . . . ", which says that the amount of time available for the docking phase is measured in minutes. While a few minutes to perform the docking maneuver might not sound like much, when viewed in light of current practice, it "may not be difficult."

Additional information on the Earth orbiting non-rotating skyhook concept can be found in the following non-internet available articles.