Momentum exchange tether

Momentum Exchange Tethers is one of many applications for space tethers. This sub-set represents an entire area of research using a spinning conductive and/or non-conductive tether to throw spacecraft up or down in orbit (like a sling), thereby transferring (or taking) its momentum.

Due to the centrifugal acceleration, the act of spinning a long tether will create a controlled force on the end-masses of the system. If the tether system is spun at a particular angular frequency then the objects on either end of the EDT system will experience continuous acceleration. This controlled gravity is manipulated by control of the angular frequency. From this, momentum exchange can occur if an endbody is released during the controlled rotation. The transfer in momentum to the released object will cause the system to lose orbital energy, and thus lose altitude. However, using electrodynamic tether thrusting it is possible to re-boost itself again without the expenditure of consumables.

Tether systems

Tidal stabilization

Main article: Gravity-gradient stabilization

A rotating tether and a tidally stabilised tether in orbit

Gravity-gradient stabilization, also called "gravity stabilization" and "tidal stabilization", is cheap and reliable. It uses no electronics, rockets or fuel.

An attitude control tether has a small mass on one end, and a satellite on the other. Tidal forces stretch the tether between the two masses. There are two ways of explaining tidal forces: In one, the upper part of an object goes faster than its natural orbital speed, so centrifugal force stretches the object upwards. The lower part moves slower than the orbital speed, so it pulls down. Another way to explain tidal force is that the top of a tall object weighs less than the bottom, so they are pulled by different amounts. The "extra" pull on the "bottom" of the object stretches it out. On Earth, these are small effects, but in space, nothing opposes them.

The resulting tidal forces stabilize the satellite so that its long dimension points towards the planet it is orbiting. Simple satellites have often been stabilized this way, with tethers or mass distribution. A small bottle of fluid may be mounted in the spacecraft to damp pendulum vibrations with viscous friction of the fluid motion.

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".)

Electrodynamic tethers

Main article: Electrodynamic tether

In a strong planetary magnetic field such as around the Earth or Saturn, a conducting rotovator can be configured as an electrodynamic tether. This can either be used as a dynamo, which slows the tether and changes the angular momentum whilst generating electrical power, or alternatively, its orbital speed and/or angular momentum can be increased electrically from solar or nuclear power by running current through a wire that goes the length of the tether. Thus the tether can be used either to accelerate or brake an orbiting spacecraft.^[1]

In both cases the tether pushes against the planet, and thus the momentum gained or lost ultimately comes from the planet.

One complication to these techniques is that if the tether rotates, the direction of current must reverse (such as is the case in alternating currents).

Bolo

A rotating tether, or "bolo," is a high speed rotating tether, spinning so that the tips have a significant speed (~1–3 km/s).

The maximum speed is limited by stress tolerance and safety factor of the tether but the speed can be greatly increased if it is of thicker cross-section in the middle and tapers and is lighter, thinner at the tips.

A spacecraft could rendezvous with one end of the tether, latch to it, and be accelerated by the tether's rotation. The tether and spacecraft would then separate at a later point when the spacecraft's velocity has been changed by the rotovator.

The momentum imparted to the spacecraft is not free. The tether's momentum and angular momentum is changed, and this costs energy that must be recouped. The idea is that the recharge could be done with some form of energy (for instance solar panels generating current for electromagnetic propulsion) that is far cheaper than multi-stage-rocket fuel.

Rotating tethers can also be used to slow down incoming spacecraft, thus increasing the rotational momentum. If the average momentum gained from inward traffic equals that imparted to outward traffic, there is no net energy cost, and thus nothing to recoup.

Rotovators

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. (Image from the cycloid article)

The word rotovator is a portmanteau derived from the words rotor and elevator. Rotovators would be momentum exchange tethers, with a retrograde motion of the tip closest to their parent body relative to the center of the tether.

Because the tips have a significant speed (typically 1–3 km/s), it can be possible in some cases to cancel the orbital speed such that the tips are stationary at their lowest point with respect to a planetary surface or lunar body. As described by Moravec,^[2][3] this is "a satellite that rotates like a wheel." 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. (As with the bolo, discussed above, the momentum and energy given to the payload must be made up, either with a high-performance rocket engine, or with momentum gathered from payload moving the other direction.)

On bodies with an atmosphere, such as the Earth, the tether tip must stay above the dense atmosphere. On bodies with reasonably low orbital speed (such as the Moon and possibly Mars), a rotovator in low orbit can potentially touch the ground, thereby providing cheap surface transport as well as launching materials into cislunar space.

Earth launch assist bolo

Unfortunately an Earth-to-orbit rotovator cannot be built from currently available materials since the thickness and tether mass to handle the loads on the rotovator would be uneconomically large. A "watered down" rotovator with two-thirds the rotational speed, however, would halve the centripetal acceleration stresses.

Therefore another trick to achieve lower stresses is that rather than picking up a cargo from the ground at zero velocity, a rotovator could pick up a moving vehicle and sling it into orbit. For example, a rotovator could pick up a Mach-12 aircraft from the upper atmosphere of the Earth and move it into orbit without using rockets, and could likewise catch such a vehicle and lower it into atmospheric flight. It is easier for a rocket to achieve the lower tip speed, so "Single Stage To Tether" has been proposed.^[4] One such is called the Hypersonic Airplane Space Tether Orbital Launch (HASTOL).^[5] 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.

Skyhooks

Main article: Skyhook (structure)

Orbital tether lengths compared.

A tidal stabilized tether is called a "skyhook" since it appears to be "hooked onto the sky".^{[citation needed]} This term was introduced relating to satellites and orbital mechanics by the Italian scientist Giuseppe Colombo. Skyhooks rotate precisely once per orbit and hence are always oriented the same way to the parent body.

Some are called "hypersonic skyhooks" because the tip nearest the earth travels about Mach-12 to 16 in typical designs. Longer tethers would travel more slowly. At the limit of zero ground speed, it would be re-classified as a space elevator or beanstalk.

An aircraft or sub-orbital vehicle transports cargo to one end of the skyhook.

Skyhook designs typically require climbers to transport the cargo to the other end (like a beanstalk).

Robert Raymond Boyd and Dimitri David Thomas (with Lockheed Martin Corporation) patented the Skyhook idea in 2000 in a patent titled "Space elevator"[1].

The company Tethers Unlimited Inc (founded by Dr. Robert Forward and Dr. Robert P. Hoyt)^[6] has called this approach "Tether Launch Assist".^[7]

Space elevator (beanstalk)

Main article: space elevator

A beanstalk (a type of space elevator) is a skyhook that is attached to planetary body. For example, on Earth, a beanstalk would go from the equator to geosynchronous orbit.

A beanstalk does not need to be powered as a rotovator does, because it gets any required angular momentum from the planetary body. The disadvantage is that it is much longer, and for many planets a beanstalk cannot be constructed from known materials. A beanstalk on Earth would require material strengths outside current technological limits (2007). Martian and Lunar beanstalks could be built with modern-day materials however.^[8] A space elevator on Phobos has also been proposed.^[9]

Beanstalks also have much larger amounts of potential energy than a rotovator, and if heavy parts should fail they might cause multiple impact events as objects hit the earth at near orbital speeds. Most anticipated cable designs would burn up before hitting the ground.

Cislunar transportation system

Although it might be thought that this requires constant energy input, it can in fact be shown to be energetically favourable 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.^[10][11]

Potential energy in the Earth Moon system. Because the moon has higher potential energy, tethers can work together to pick objects 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.

Rotovators can thus be charged by momentum exchange. Momentum charging uses the rotovator to move mass from a place that is "higher" in a gravity field to a place that is "lower". 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. For example, it is possible to use a system of two or three rotovators to implement trade between the Moon and Earth. The rotovators are charged by lunar mass (dirt, if exports are not available) dumped on or near the Earth, and can use the momentum so gained to boost Earth goods to the Moon. The momentum and energy exchange can be balanced with equal flows in either direction, or can increase over time.

Similar systems of rotovators could theoretically open up inexpensive transportation throughout the solar system.

Tether cable catapult system

A tether cable catapult system is a system where two or more long conducting tethers are held rigidly in a straight line, attached to a heavy mass. 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. Near the end of the cable the vehicle releases a payload and slows and stops itself and the payload carries on at very high velocity. The calculated maximum speed for this system is extremely high, more than 30 times the speed of sound in the cable; and velocities of more than 30 km/s seem to be possible.^[12]

References

1. ^ NASA, Tethers In Space Handbook, edited by M.L. Cosmo and E.C. Lorenzini, Third Edition December 1997 (accessed 20 October 2010); see also version at NASA MSFC; available on scribd
2. ^ Hans Moravec "Orbital Bridges," (1986) (accessed Oct. 10, 2010)
3. ^ Hans Moravec, "Non-Synchronous Orbital Skyhooks for the Moon and Mars with Conventional Materials" (Hans Moravec's thoughts on skyhooks, tethers, rotovators, etc., as of 1987) (accessed 10 October 2010)
4. ^ AIAA95-2895 "Potential launch cost savings of a tether transport facility"
5. ^ Hypersonic Airplane Space Tether Orbital Launch (HASTOL) System
6. ^ Space Tethers: Slinging Objects in Orbit? by Nell Boyce - National Public Radio - 16 April 2007
7. ^ Tethers Unlimited Inc, "Tether Launch Assist"
8. ^ Space Elevator - Chapter 7: Destinations
9. ^ Space Colonization Using Space-Elevators from Phobos Leonard M. Weinstein
10. ^ "Tether Transport from LEO to the Lunar Surface", R.L. Forward, AIAA Paper 91-2322, 27th Joint Propulsion Conference, 1991
11. ^ THE CISLUNAR TETHER TRANSPORT SYSTEM ARCHITECTURE Robert P. Hoyt Tethers Unlimited, Inc.
12. ^ US Patent 6290186