Momentum exchange tether

However, using electrodynamic tether thrusting, or ion propulsion the system can then re-boost itself with little or no expenditure of consumable reaction mass.

A sky-hook is a theoretical class of orbiting tether propulsion intended to lift payloads to high altitudes and speeds.

The maximum speed of the endpoints is limited by the strength of the cable material, the taper, and the safety factor it is designed for.

The idea is that the replacement energy would come from a more efficient and lower cost source than a chemical rocket motor.

The tip of the tether moves in approximately a cycloid, in which it is momentarily stationary with respect to the ground.

In this case, a payload that is "grabbed" by a capture mechanism on the rotating tether during the moment when it is stationary would be picked up and lifted into orbit; and potentially could be released at the top of the rotation, at which point it is moving with a speed significantly greater than the escape velocity and thus could be released onto an interplanetary trajectory.

A "watered down" rotovator with two-thirds the rotational speed, however, would halve the centripetal acceleration stresses.

It is easier for a rocket to achieve the lower tip speed, so "single stage to tether" has been proposed.

[7] Either air breathing or rocket to tether could save a great deal of fuel per flight, and would permit for both a simpler vehicle and more cargo.

[17] An Earth-to-Earth Skyhook, similar to the Earth launch assist bolo, would still require an aircraft to reach the upper atmosphere.

In this scenario, the aircraft is transported to a different location while the skyhook remains in a similar energy state as before.

A space elevator does not need to be powered as a rotovator does, because it gets any required angular momentum from the planetary body.

[23] Space elevators also have larger amounts of potential energy than a rotovator, and if heavy parts (like a "dropped wrench") should fall they would reenter at a steep angle and impact the surface at near orbital speeds.

Although it might be thought that this requires constant energy input, it can in fact be shown to be energetically favorable to lift cargo off the surface of the Moon and drop it into a lower Earth orbit, and thus it can be achieved without any significant use of propellant, since the Moon's surface is in a comparatively higher potential energy state.

The technique to do this uses the Oberth effect, where releasing the payload when the tether is moving with higher linear speed, lower in a gravitational potential gives more specific energy, and ultimately more speed than the energy lost picking up the payload at a higher gravitational potential, even if the rotation rate is the same.

The momentum and energy exchange can be balanced with equal flows in either direction, or can increase over time.

Power is applied to the tethers and is picked up by a vehicle that has linear magnet motors on it, which it uses to push itself along the length of the cable.

A rotating tether and a tidally stabilized tether in orbit
Electrons flow through the conductive structure of the tether to the power system interface, where it supplies power to an associated load, not shown. (Source: U.S. patent 6,116,544, "Electrodynamic Tether And Method of Use".)
If the orbital velocity and the tether rotation rate are synchronized, in the rotovator concept the tether tip moves in a cycloid, and at the lowest point is momentarily stationary with respect to the ground, where it can "hook" a payload and swing it into orbit.)
Rotating skyhook used for Earth to Earth travel
Rotating Skyhook used for Earth-to-Earth travel
Non-rotating Sky-hook first proposed by E. Sarmont in 1990
Potential energy in the Earth–Moon system. Because the Moon has higher potential energy, tethers can work together to pick an object off the Moon (the tiny dimple on the right), and place it closer to the Earth in LEO, taking essentially no propellant and even generating energy while doing so.