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Momentum Exchange Space Tethers

textA momentum exchange tether is a long thin cable used to couple two objects in space together so that one transfers momentum and energy to the other. A tether is deployed by pushing one object up or down from the other. Once the two objects are separated by enough distance, the difference in the gravitational force at the two locations will cause the objects to be "pulled" apart. This is called the "gravity gradient force". The tether can then be let out at a controlled rate, pulled by the tension caused by the gravity gradient force. Once the tether is deployed, if there are no other forces on the tether it will have an equilibrium orientation that is aligned vertically. There are a number of different concepts for momentum exchange using tethers. Some general categories are:

A stationary tether is one that connects two masses together and remains at constant length, except, of course, for deployment and retrieval. A stationary tether could drag a payload through the upper atmosphere of a planet and lower payloads to the surface of an asteroid. If the tether is conducting and is moving through electric or magnetic fields, then it can be used as a generator to provide electrical power, or as a motor to provide propulsion. If the tether and its masses are orbiting a massive body, then typically the system will be gravity gradient stabilized, with the tether pointed along the radius vector to the massive body. Thus, although the tether is stationary in the orbital reference frame, it is really rotating once per orbit in inertial space, and so is a slowly rotating bolo.

A bolo is a long rotating cable anywhere in space that is used as a "momentum-energy bank". It could be used to "catch" a payload coming from any given direction (in its plane of rotation) at any given speed (less than its maximum tip speed), and then some time later, "launch" the payload off in some other direction at some other speed. A gravity gradient stabilized bolo orbiting some planet has the property that if the tether is cut, then one-half an orbit later, the separation distance between the two masses is seven times larger than the initial separation. This can be used to deorbit the lower mass, or throw the upper mass to a rendezvous or to escape.

A "rotovator" is a long bolo in low orbit around a planet (or moon) that is used as a giant elevator to reach down from space to lift payloads from a planet or to deposit payloads onto a planet. To reach the surface of the planet, the orbital altitude should be equal to half the length of the rotating cable. By proper adjustment of the cable rotation period to the orbital period of the center of mass of the cable (plus or minus the planetary rotation period), the relative velocity of the planetary surface and the tip of the cable can be made zero at the time of touchdown, allowing for easy payload transfer. A half-rotation later, the payload is at the top of the trajectory with a cable tip velocity that is twice the orbital velocity. Although present day material strengths do not allow the construction of rotovators around Earth or the major planets, they can be built for Mars, Mercury, and most moons, especially including Earth's Moon.

Tip Velocity and Material Strength
The maximum tip speed of all these systems is a function of the "launcher to payload mass ratio" of the tether system and the "characteristic velocity" of the material used. The characteristic velocity of the material in a tether is given by the square root of the ratio of the design tensile strength T of the tether to the density D of the tether material. u = (T_d/D)^1/2. In practice, the design tensile strength is usually chosen to be 50% of the measured strength for metals and 25% of the measured short-term individual fiber strength for other materials. Thus, using imperfect materials with reasonable safety margins, the characteristic velocity of most metals and fibers is around 1 km/s, with optimistic predictions for graphite and improved polymers reaching 3 km/s. With the development of a design for a high strength-to-weight tapered Hoytether, the design tensile strength can be safely chosen to be 60% of the measured strength of the individual fibers, allowing commercially available fibers to have characteristic velocities up to 4 km/s.

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