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118-416: Tether satellites might be used for various purposes, including research into tether propulsion , tidal stabilization and orbital plasma dynamics. Five main techniques for employing space tethers are in development: Electrodynamic tethers are primarily used for propulsion. These are conducting tethers that carry a current that can generate either thrust or drag from a planetary magnetic field , in much

236-400: A n o d e {\displaystyle V_{\mathrm {anode} }} and V c a t h o d e {\displaystyle V_{\mathrm {cathode} }} represent the potential difference from their respective tether ends to the plasma, and V − V p {\displaystyle V-V_{p}} is the potential anywhere along

354-448: A t h o d e {\displaystyle V_{\mathrm {cathode} }} ). The KVL voltage loop is then closed in the ionosphere where the potential difference is effectively zero. Due to the nature of the bare EDTs, it is often not optional to have the entire tether bare. In order to maximize the thrusting capability of the system a significant portion of the bare tether should be insulated. This insulation amount depends on

472-438: A space bolas . The company's goals have drifted to deorbit assist modules and marine tethers as in 2020 though. Investigation of "Tether Launch Assist" concepts in 2013 have indicated the concept may become marginally economical in near future as soon as rotovators with high enough (~10 W/kg) power-to-mass ratio are developed. A space elevator is a space tether that is attached to a planetary body. For example, on Earth ,

590-569: A thermionic cathode , plasma cathode, plasma contactor, or field electron emission device. Since both ends of the tether are "open" to the surrounding plasma, electrons can flow out of one end of the tether while a corresponding flow of electrons enters the other end. In this fashion, the voltage that is electromagnetically induced within the tether can cause current to flow through the surrounding space environment , completing an electrical circuit through what appears to be, at first glance, an open circuit . The amount of current ( I ) flowing through

708-461: A "characteristic length", L c , which is also known as its "self-support length" and is the length of untapered cable it can support in a constant 1 g gravity field. where σ is the stress limit (in pressure units) and ρ is the density of the material. Hypersonic skyhook equations use the material's "specific velocity" which is equal to the maximum tangential velocity a spinning hoop can attain without breaking: For rotating tethers (rotovators)

826-413: A 500-meter conducting tether. In 1996, NASA conducted an experiment with a 20,000-meter conducting tether. When the tether was fully deployed during this test, the orbiting tether generated a potential of 3,500 volts. This conducting single-line tether was severed after five hours of deployment. It is believed that the failure was caused by an electric arc generated by the conductive tether's movement through

944-709: A Skyhook, while spacecraft bound for higher orbit, or returning from higher orbit, would use the upper end. In 2000, NASA and Boeing considered a HASTOL concept, where a rotating tether would take payloads from a hypersonic aircraft (at half of orbital velocity) to orbit . A tether satellite is a satellite connected to another by a space tether. A number of satellites have been launched to test tether technologies, with varying degrees of success. There are many different (and overlapping) types of tether. Momentum exchange tethers are one of many applications for space tethers. Momentum exchange tethers come in two types; rotating and non-rotating. A rotating tether will create

1062-431: A base-station orbit and allowing orbital insertion by lifting the cargo. Most proposals spin the tether so that its angular momentum also provides energy to the cargo, speeding it up to orbital velocity or beyond while slowing the tether. Some form of propulsion is then applied to the tether to regain the angular momentum. A Bolo, or rotating tether, is a tether that rotates more than once per orbit and whose endpoints have

1180-426: A controlled force on the end-masses of the system due to centrifugal acceleration. While the tether system rotates, the objects on either end of the tether will experience continuous acceleration; the magnitude of the acceleration depends on the length of the tether and the rotation rate. Momentum exchange occurs when an end body is released during the rotation. The transfer of momentum to the released object will cause

1298-522: A magnetic field. The force is given by Faraday's Law of Induction : Without loss of generality, it is assumed the tether system is in Earth orbit and it moves relative to Earth's magnetic field. Similarly, if current flows in the tether element, a force can be generated in accordance with the Lorentz force equation In self-powered mode ( deorbit mode), this EMF can be used by the tether system to drive

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1416-401: A modular staged tether system maybe used to achieve the same goal. Multiple tethers would be used between stages. The number of tethers would determine the strength of any given cross-section. For rotating tethers not significantly affected by gravity, the thickness also varies, and it can be shown that the area, A, is given as a function of r (the distance from the centre) as follows: where R

1534-583: A more efficient and lower cost source than a chemical rocket motor. Two possible lower cost sources for this replacement energy are an ion propulsion system, or an electrodynamic tether propulsion system that would be part of the Bolo. An essentially free source of replacement energy is momentum gathered from payloads to be accelerated in the other direction, suggesting that the need for adding energy from propulsion systems will be quite minimal with balanced, two-way, space commerce. Rotovators are rotating tethers with

1652-555: A more realistic model for current collection is to include the magnetic field effects and plasma flow effects. Assuming a collisionless plasma, electrons and ions gyrate around magnetic field lines as they travel between the poles around the Earth due to magnetic mirroring forces and gradient-curvature drift. They gyrate at a particular radius and frequency dependence upon their mass, the magnetic field strength, and energy. These factors must be considered in current collection models. When

1770-448: A non-flowing plasma), current collection in space occurs in a flowing plasma, which introduces another collection effect. These issues are explored in greater detail below. The electron Debye length is defined as the characteristic shielding distance in a plasma, and is described by the equation This distance, where all electric fields in the plasma resulting from the conductive body have fallen off by 1/e, can be calculated. OML theory

1888-406: A number of effects, some of which are plasma density, the tether length and width, the orbiting velocity, and the Earth's magnetic flux density. An electrodynamic tether is attached to an object, the tether being oriented at an angle to the local vertical between the object and a planet with a magnetic field. The tether's far end can be left bare, making electrical contact with the ionosphere . When

2006-454: 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

2124-531: A protective coating is needed, including relative to UV and atomic oxygen . For applications that exert high tensile forces on the tether, the materials need to be strong and light. Some current tether designs use crystalline plastics such as ultra-high-molecular-weight polyethylene , aramid or carbon fiber . A possible future material would be carbon nanotubes , which have an estimated tensile strength between 140 and 177  GPa (20.3 and 25.7 million psi; 1.38 and 1.75 million atm), and

2242-544: A proven tensile strength in the range 50–60 GPa (7.3–8.7 million psi; 490,000–590,000 atm) for some individual nanotubes. (A number of other materials obtain 10 to 20 GPa (1.5 to 2.9 million psi; 99,000 to 197,000 atm) in some samples on the nano scale, but translating such strengths to the macro scale has been challenging so far, with, as of 2011, CNT-based ropes being an order of magnitude less strong, not yet stronger than more conventional carbon fiber on that scale). For some applications,

2360-480: A result, there are a number of theories for the varying collection techniques. The primary passive processes that control the electron and ion collection on an EDT system are thermal current collection, ion ram collection effects, electron photoemission, and possibly secondary electron and ion emission. In addition, the collection along a thin bare tether is described using orbital motion limited (OML) theory as well as theoretical derivations from this model depending on

2478-410: A rotational direction such that the lower endpoint of the tether is moving slower than the orbital velocity of the tether and the upper endpoint is moving faster. The word is a portmanteau derived from the words rotor and elevator . If the tether is long enough and the rotation rate high enough, it is possible for the lower endpoint to completely cancel the orbital speed of the tether such that

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2596-406: 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. On most anticipated designs, if the cable component itself fell, it would burn up before hitting the ground. 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

2714-450: A significant tip speed (~ 1–3 km/s or 2,200–6,700 mph or 3,600–10,800 km/h). 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 purpose of the Bolo is to either speed up, or slow down, a spacecraft that docks with it without using any of the spacecraft's on-board propellant and to change the spacecraft's orbital flight path. Effectively,

2832-427: A similar voltage. Fortunately, the Earth's magnetosphere is not "empty", and, in near-Earth regions (especially near the Earth's atmosphere) there exist highly electrically conductive plasmas which are kept partially ionized by solar radiation or other radiant energy . The electron and ion density varies according to various factors, such as the location, altitude, season, sunspot cycle, and contamination levels. It

2950-400: 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 end mass of the system is moving faster than orbital velocity for its altitude, so centrifugal force makes it want to move further away from the planet it is orbiting. At the same time, the lower end mass of the system

3068-661: A space elevator would go from the equator to well above geosynchronous orbit. A space elevator 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 space elevator cannot be constructed from known materials. A space elevator on Earth would require material strengths outside current technological limits (2014). Martian and lunar space elevators could be built with modern-day materials however. A space elevator on Phobos has also been proposed. Space elevators also have larger amounts of potential energy than

3186-399: A specific height above the surface of the celestial body, but lower than (A). Instead of rotating end for end, tethers can also be kept straight by the slight difference in the strength of gravity over their length. A non-rotating tether system has a stable orientation that is aligned along the local vertical (of the earth or other body). This can be understood by inspection of the figure on

3304-485: A study of tether launch systems including two-stage tethers that had been commissioned by the NASA Institute for Advanced Concepts . 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

3422-416: A tether depends on various factors. One of these is the circuit's total resistance ( R ). The circuit's resistance consist of three components: In addition, a parasitic load is needed. The load on the current may take the form of a charging device which, in turn, charges reserve power sources such as batteries. The batteries in return will be used to control power and communication circuits, as well as drive

3540-410: A tether satellite, which can operate on electromagnetic principles as generators , by converting their kinetic energy to electrical energy , or as motors , converting electrical energy to kinetic energy. Electric potential is generated across a conductive tether by its motion through the Earth's magnetic field. The choice of the metal conductor to be used in an electrodynamic tether is determined by

3658-400: A tower so tall that it reached into space, so that it would be held there by the rotation of Earth . However, at the time, there was no realistic way to build it. In 1960, another Russian, Yuri Artsutanov , wrote in greater detail about the idea of a tensile cable to be deployed from a geosynchronous satellite , downwards towards the ground, and upwards away, keeping the cable balanced. This

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3776-480: A unique phenomenon whereby the orbiting body 'rams' through the surrounding ions in the plasma creating a beam like effect in the reference frame of the orbiting body. Porous endbodies have been proposed as a way to reduce the drag of a collecting endbody while ideally maintaining a similar current collection. They are often modeled as solid endbodies, except they are a small percentage of the solid spheres surface area. This is, however, an extreme oversimplification of

3894-577: A variety of factors. Primary factors usually include high electrical conductivity and low density . Secondary factors, depending on the application, include cost, strength, and melting point. An electrodynamic tether was profiled in the documentary film Orphans of Apollo as technology that was to be used to keep the Russian space station Mir in orbit. This is the use of a (typically) non-conductive tether to connect multiple spacecraft. Tethered Experiment for Mars inter-Planetary Operations (TEMPO³)

4012-664: 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. One such is called the Hyper-sonic Airplane Space Tether Orbital Launch (HASTOL). 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. The company Tethers Unlimited, Inc. (founded by Robert Forward and Robert P. Hoyt ) has called this approach "Tether Launch Assist". It has also been referred to as

4130-411: Is a kind of space tether that could theoretically be used as a launch system, or to change spacecraft orbits. Momentum exchange tethers create a controlled force on the end-masses of the system due to the pseudo-force known as centrifugal force . While the tether system rotates, the objects on either end of the tether will experience continuous acceleration; the magnitude of the acceleration depends on

4248-400: Is a proposed 2011 experiment to study the technique. A theoretical type of non-rotating tethered satellite system, it is a concept for providing space-based support to things suspended above an astronomical object. The orbital system is a coupled mass system wherein the upper supporting mass (A) is placed in an orbit around a given celestial body such that it can support a suspended mass (B) at

4366-518: Is a rotating tether that rotates exactly once per orbit so that it always has a vertical orientation relative to the parent body. A spacecraft arriving at the lower end of this tether, or departing from the upper end, will take momentum from the tether, while a spacecraft departing from the lower end of the tether, or arriving at the upper end, will add momentum to the tether. In some cases momentum exchange systems are intended to run as balanced transportation schemes where an arriving spacecraft or payload

4484-501: Is attained when the cylinder radius is small enough such that all incoming particle trajectories that are collected are terminated on the cylinder's surface are connected to the background plasma, regardless of their initial angular momentum (i.e., none are connected to another location on the probe's surface). Since, in a quasi-neutral collisionless plasma, the distribution function is conserved along particle orbits, having all “directions of arrival” populated corresponds to an upper limit on

4602-408: Is defined with the assumption that the electron Debye length is equal to or larger than the size of the object and the plasma is not flowing. The OML regime occurs when the sheath becomes sufficiently thick such that orbital effects become important in particle collection. This theory accounts for and conserves particle energy and angular momentum. As a result, not all particles that are incident onto

4720-557: Is derived for charged particles of zero initial energy, and is termed the Child-Langmuir Law. This limit depends on the emission surface area, the potential difference across the plasma gap and the distance of that gap. Further discussion of this topic can be found. There are three active electron emission technologies usually considered for EDT applications: hollow cathode plasma contactors (HCPCs), thermionic cathodes (TCs), and field emission cathodes (FEC), often in

4838-414: Is exchanged with one leaving with the same speed and mass, and then no net change in momentum or angular momentum occurs. Gravity-gradient stabilization, also called "gravity stabilization" and "tidal stabilization", is a simple and reliable method for controlling the attitude of a satellite that requires no electronic control systems, rocket motors or propellant. This type of attitude control tether has

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4956-469: Is generated across a conductive tether by its motion through a planet's magnetic field. A number of missions have demonstrated electrodynamic tethers in space, most notably the TSS-1 , TSS-1R , and Plasma Motor Generator (PMG) experiments. As part of a tether propulsion system, craft can use long, strong conductors (though not all tethers are conductive) to change the orbits of spacecraft . It has

5074-449: Is known that a positively charged bare conductor can readily remove free electrons out of the plasma. Thus, to complete the electrical circuit, a sufficiently large area of uninsulated conductor is needed at the upper, positively charged end of the tether, thereby permitting current to flow through the tether. However, it is more difficult for the opposite (negative) end of the tether to eject free electrons or to collect positive ions from

5192-456: Is less than one Debye length in radius, it will collect according to the OML theory. However, once the width exceeds this distance, then the collection increasingly deviates from this theory. If the tether geometry is a flat tape, then an approximation can be used to convert the normalized tape width to an equivalent cylinder radius. This was first done by Sanmartin and Estes and more recently using

5310-426: Is moving at less than orbital speed for its altitude, so it wants to move closer to the planet. The end result is that the tether is under constant tension and wants to hang in a vertical orientation. Simple satellites have often been stabilized this way; either with tethers, or with how the mass is distributed within the satellite. As with any freely hanging object, it can be disturbed and start to swing. Since there

5428-404: Is no atmospheric drag in space to slow the swing, a small bottle of fluid with baffles may be mounted in the spacecraft to damp the pendulum vibrations via the viscous friction of the fluid. In a strong planetary magnetic field such as around the Earth, a conducting tether can be configured as an electrodynamic tether . This can either be used as a dynamo to generate power for the satellite at

5546-408: Is presently being investigated through recent work, and is not fully understood. This section discusses the plasma physics theory that explains passive current collection to a large conductive body which will be applied at the end of an ED tether. When the size of the sheath is much smaller than the radius of the collecting body then depending on the polarity of the difference between the potential of

5664-458: Is similar to the de-orbit mode, except for the fact that a High Voltage Power Supply (HVPS) is also inserted in series with the tether system between the tether and the higher positive potential end. The power supply voltage must be greater than the EMF and the polar opposite. This drives the current in the opposite direction, which in turn causes the higher altitude end to be negatively charged, while

5782-456: 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-efficiency rocket engine, or with momentum gathered from payload moving

5900-462: Is the space elevator idea, a type of synchronous tether that would rotate with the Earth. However, given the materials technology of the time, this too was impractical on Earth. In the 1970s, Jerome Pearson independently conceived the idea of a space elevator, sometimes referred to as a synchronous tether, and, in particular, analyzed a lunar elevator that can go through the L1 and L2 points , and this

6018-583: Is the radius of tether, v is the velocity with respect to the centre, M is the tip mass, δ {\displaystyle \delta } is the material density, and T is the design tensile strength. Integrating the area to give the volume and multiplying by the density and dividing by the payload mass gives a payload mass / tether mass ratio of: where erf is the normal probability error function . Let V r = V / V c {\displaystyle V_{r}=V/V_{c}\,} , then: This equation can be compared with

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6136-623: 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

6254-485: Is therefore within the OML regime. Tether geometries outside this dimension have been addressed. OML collection will be used as a baseline when comparing the current collection results for various sample tether geometries and sizes. In 1962 Gerald H. Rosen derived the equation that is now known as the OML theory of dust charging. According to Robert Merlino of the University of Iowa, Rosen seems to have arrived at

6372-596: Is typically a non-conductive tether that accurately maintains a set distance between multiple space vehicles flying in formation. A form of solar wind sail with electrically charged tethers that will be pushed by the momentum of solar wind ions . A concept for suspending an object from a tether orbiting in space. Many uses for space tethers have been proposed, including deployment as space elevators , as skyhooks , and for doing propellant-free orbital transfers. Konstantin Tsiolkovsky (1857–1935) once proposed

6490-435: Is used towards developing a current collection model to account for all conditions encountered during an EDT mission. In a non-flowing quasi-neutral plasma with no magnetic field, it can be assumed that a spherical conducting object will collect equally in all directions. The electron and ion collection at the end-body is governed by the thermal collection process, which is given by Ithe and Ithi. The next step in developing

6608-411: Is very unlikely that multiple redundant cables would be damaged near the same point on the cable, and hence a very large amount of total damage can occur over different parts of the cable before failure occurs. Beanstalks and rotovators are currently limited by the strengths of available materials. Although ultra-high strength plastic fibers ( Kevlar and Spectra ) permit rotovators to pluck masses from

6726-476: The Solar 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

6844-603: The Van Allen belts can have markedly lower life than those that stay in low earth orbit or are kept outside Earth's magnetosphere. Tether properties and materials are dependent on the application. However, there are some common properties. To achieve maximum performance and low cost, tethers would need to be made of materials with the combination of high strength or electrical conductivity and low density. All space tethers are susceptible to space debris or micrometeoroids. Therefore, system designers will need to decide whether or not

6962-399: The lunar surface. It would also be able to hold 100 cargo vehicles, each with a mass of 580 kg (1,280 lb), evenly spaced along the length of the elevator. Other materials that could be used are T1000G carbon fiber, Spectra 2000, or Zylon. For gravity stabilized tethers, to exceed the self-support length the tether material can be tapered so that the cross-sectional area varies with

7080-465: The rocket equation , which is proportional to a simple exponent on a velocity, rather than a velocity squared. This difference effectively limits the delta-v that can be obtained from a single tether. In addition the cable shape must be constructed to withstand micrometeorites and space junk . This can be achieved with the use of redundant cables, such as the Hoytether ; redundancy can ensure that it

7198-418: The "control resistor". The charging battery load is not treated as a "base resistance" though, as the charging circuit can be turned off at any time. When off, the operations can be continued without interruption using the power stored in the batteries. Understanding electron and ion current collection to and from the surrounding ambient plasma is critical for most EDT systems. Any exposed conducting section of

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7316-454: The 2-Dimensional Kinetic Plasma Solver (KiPS 2-D) by Choiniere et al. There is at present, no closed-form solution to account for the effects of plasma flow relative to the bare tether. However, numerical simulation has been recently developed by Choiniere et al. using KiPS-2D which can simulate flowing cases for simple geometries at high bias potentials. This flowing plasma analysis as it applies to EDTs have been discussed. This phenomenon

7434-410: The Bolo acts as a reusable upper stage for any spacecraft that docks with it. The momentum imparted to the spacecraft by the Bolo is not free. In the same way that the Bolo changes the spacecraft's momentum and direction of travel, the Bolo's orbital momentum and rotational momentum is also changed, and this costs energy that must be replaced. The idea is that the replacement energy would come from

7552-463: The EDT system can passively ('passive' and 'active' emission refers to the use of pre-stored energy in order to achieve the desired effect) collect electron or ion current, depending on the electric potential of the spacecraft body with respect to the ambient plasma. In addition, the geometry of the conducting body plays an important role in the size of the sheath and thus the total collection capability. As

7670-433: The Earth's magnetic field, in the north-south direction, is approximately 0.18–0.32  gauss up to ~40° inclination, and the orbital velocity with respect to the local plasma is about 7500 m/s. This results in a V emf range of 35–250 V/km along the 5 km length of tether. This EMF dictates the potential difference across the bare tether which controls where electrons are collected and / or repelled. Here,

7788-403: The Earth's magnetic field. When a tether is moved at a velocity ( v ) at right angles to the Earth's magnetic field ( B ), an electric field is observed in the tether's frame of reference. This can be stated as: The direction of the electric field ( E ) is at right angles to both the tether's velocity ( v ) and magnetic field ( B ). If the tether is a conductor, then the electric field leads to

7906-486: The ProSEDS de-boost tether system is configured to enable electron collection to the positively biased higher altitude section of the bare tether, and returned to the ionosphere at the lower altitude end. This flow of electrons through the length of the tether in the presence of the Earth's magnetic field creates a force that produces a drag thrust that helps de-orbit the system, as given by the above equation. The boost mode

8024-465: The angle τ is between the length vector ( L ) of the tether and the electric field vector ( E ), assumed to be in the vertical direction at right angles to the velocity vector ( v ) in plane and the magnetic field vector ( B ) is out of the plane. An electrodynamic tether can be described as a type of thermodynamically "open system" . Electrodynamic tether circuits cannot be completed by simply using another wire, since another tether will develop

8142-407: 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

8260-419: The collected current per unit area (not total current). In an EDT system, the best performance for a given tether mass is for a tether diameter chosen to be smaller than an electron Debye length for typical ionospheric ambient conditions (Typical ionospheric conditions in the from 200 to 2000 km altitude range, have a T_e ranging from 0.1 eV to 0.35 eV, and n_e ranging from 10^10 m^-3 to 10^12 m^-3 ), so it

8378-528: The concept. Much has to be learned about the interactions between the sheath structure, the geometry of the mesh, the size of the endbody, and its relation to current collection. This technology also has the potential to resolve a number of issues concerning EDTs. Diminishing returns with collection current and drag area have set a limit that porous tethers might be able to overcome. Work has been accomplished on current collection using porous spheres, by Stone et al. and Khazanov et al. It has been shown that

8496-485: The conducting body is negatively biased with respect to the plasma and traveling above the ion thermal velocity, there are additional collection mechanisms at work. For typical Low Earth Orbits (LEOs), between 200 km and 2000 km, the velocities in an inertial reference frame range from 7.8 km/s to 6.9 km/s for a circular orbit and the atmospheric molecular weights range from 25.0 amu (O+, O2+, & NO+) to 1.2 amu (mostly H+), respectively. Assuming that

8614-412: The cost of slowing its orbital velocity, or it can be used to increase the orbital velocity of the satellite by putting power into the tether from the satellite's power system. Thus the tether can be used to either accelerate or to slow an orbiting spacecraft without using any rocket propellant. When using this technique with a rotating tether, the current through the tether must alternate in phase with

8732-423: The current collection in an EDT system are photoemission, secondary electron emission, and secondary ion emission. These effects pertain to all conducting surfaces on an EDT system, not just the end-body. In any application where electrons are emitted across a vacuum gap, there is a maximum allowable current for a given bias due to the self repulsion of the electron beam. This classical 1-D space charge limit (SCL)

8850-490: The current gain from point A to B , the current lost from point B to C , and the current lost at point C , respectively. Since the current is continuously changing along the bare length of the tether, the potential loss due to the resistive nature of the wire is represented as ∫ A C I ( y ) d R t {\displaystyle \textstyle \int _{A}^{C}I(y)\,dR_{t}} . Along an infinitesimal section of tether,

8968-633: The current through the tether and other electrical loads (e.g. resistors, batteries), emit electrons at the emitting end, or collect electrons at the opposite. In boost mode, on-board power supplies must overcome this motional EMF to drive current in the opposite direction, thus creating a force in the opposite direction, as seen in below figure, and boosting the system. Take, for example, the NASA Propulsive Small Expendable Deployer System (ProSEDS) mission as seen in above figure. At 300 km altitude,

9086-441: The displacement of charges along the tether. Note that the velocity used in this equation is the orbital velocity of the tether. The rate of rotation of the Earth, or of its core, is not relevant. In this regard, see also homopolar generator . With a long conducting wire of length L , an electric field E is generated in the wire. It produces a voltage V between the opposite ends of the wire. This can be expressed as: where

9204-408: The electron and ion temperatures range from ~0.1 eV to 0.35 eV, the resulting ion velocity ranges from 875 m/s to 4.0 km/s from 200 km to 2000 km altitude, respectively. The electrons are traveling at approximately 188 km/s throughout LEO. This means that the orbiting body is traveling faster than the ions and slower than the electrons, or at a mesosonic speed. This results in

9322-405: The electron emitting devices at the negative end of the tether. As such the tether can be completely self-powered, besides the initial charge in the batteries to provide electrical power for the deployment and startup procedure. The charging battery load can be viewed as a resistor which absorbs power, but stores this for later use (instead of immediately dissipating heat). It is included as part of

9440-414: The equation 30 years before anyone else. For a variety of practical reasons, current collection to a bare EDT does not always satisfy the assumption of OML collection theory. Understanding how the predicted performance deviates from theory is important for these conditions. Two commonly proposed geometries for an EDT involve the use of a cylindrical wire and a flat tape. As long as the cylindrical tether

9558-401: The feasibility of the idea and gave direction to the study of tethered systems, especially tethered satellites. In 1990, Eagle Sarmont proposed a non-rotating Orbiting Skyhook for an Earth-to-orbit / orbit-to-escape-velocity Space Transportation System in a paper titled "An Orbiting Skyhook: Affordable Access to Space". In this concept a suborbital launch vehicle would fly to the bottom end of

9676-485: The form of field emitter arrays (FEAs). System level configurations will be presented for each device, as well as the relative costs, benefits, and validation. Thermionic emission is the flow of electrons from a heated charged metal or metal oxide surface, caused by thermal vibrational energy overcoming the work function (electrostatic forces holding electrons to the surface). The thermionic emission current density, J, rises rapidly with increasing temperature, releasing

9794-408: The improved versions listed here, but these are currently tracked on radar and have predictable orbits. Although thrusters could be used to change the orbit of the system, a tether could also be temporally wiggled in the right place, using less energy, to dodge known pieces of junk. Radiation, including UV radiation tend to degrade tether materials, and reduce lifespan. Tethers that repeatedly traverse

9912-446: The length of the tether and the rotation rate. Momentum exchange occurs when an end body is released during the rotation. The transfer of momentum to the released object will cause the rotating tether to lose energy, and thus lose velocity and altitude. 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 non-rotating tether

10030-423: The lower altitude end is positively charged(Assuming a standard east to west orbit around Earth). To further emphasize the de-boosting phenomenon, a schematic sketch of a bare tether system with no insulation (all bare) can be seen in below figure. The top of the diagram, point A , represents the electron collection end. The bottom of the tether, point C , is the electron emission end. Similarly, V

10148-414: The lower endpoint is stationary with respect to the planetary surface that the tether is orbiting. As described by Moravec, 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

10266-413: The lower mass. The system must move at a single speed, so the tether must therefore slow down the lower mass and speed up the upper one. The centrifugal force of the tethered upper body is increased, while that of the lower-altitude body is reduced. This results in the centrifugal force of the upper body and the gravitational force of the lower body being dominant. This difference in forces naturally aligns

10384-458: The maximum current collected by a grid sphere compared to the mass and drag reduction can be estimated. The drag per unit of collected current for a grid sphere with a transparency of 80 to 90% is approximately 1.2 – 1.4 times smaller than that of a solid sphere of the same radius. The reduction in mass per unit volume, for this same comparison, is 2.4 – 2.8 times. In addition to the electron thermal collection, other processes that could influence

10502-644: The more efficient and lighter the tether can be in relation to the payloads that they can carry. Eventually however, the mass of the tether propulsion system will be limited at the low end by other factors such as momentum storage. Proposed materials include Kevlar , ultra-high-molecular-weight polyethylene , carbon nanotubes and M5 fiber . M5 is a synthetic fiber that is lighter than Kevlar or Spectra. According to Pearson, Levin, Oldson, and Wykes in their article "The Lunar Space Elevator", an M5 ribbon 30 mm (1.2 in) wide and 0.023 mm (0.91 mils) thick, would be able to support 2,000 kg (4,400 lb) on

10620-553: The most appropriate heading for the purposes of this table. All of the applications mentioned in the table are elaborated upon in the Tethers Handbook. Three fundamental concepts that tethers possess, are gravity gradients, momentum exchange, and electrodynamics. Potential tether applications can be seen below: EDT has been proposed to maintain the ISS orbit and save the expense of chemical propellant reboosts. It could improve

10738-414: 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 . In January 2000, The Boeing Company completed

10856-616: 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 (67,000 mph; 110,000 km/h) seem to be possible. Electrodynamic tether Electrodynamic tethers ( EDTs ) are long conducting wires , such as one deployed from a tether satellite, which can operate on electromagnetic principles as generators , by converting their kinetic energy to electrical energy , or as motors , converting electrical energy to kinetic energy. Electric potential

10974-406: The physical size with respect to the plasma Debye length. These processes take place all along the exposed conducting material of the entire system. Environmental and orbital parameters can significantly influence the amount collected current. Some important parameters include plasma density, electron and ion temperature, ion molecular weight, magnetic field strength and orbital velocity relative to

11092-462: The plasma. It is plausible that, by using a very large collection area at one end of the tether, enough ions can be collected to permit significant current through the plasma. This was demonstrated during the Shuttle orbiter's TSS-1R mission, when the shuttle itself was used as a large plasma contactor to provide over an ampere of current. Improved methods include creating an electron emitter, such as

11210-431: The potential to make space travel significantly cheaper. When direct current is applied to the tether, it exerts a Lorentz force against the magnetic field, and the tether exerts a force on the vehicle. It can be used either to accelerate or brake an orbiting spacecraft. In 2012 Star Technology and Research was awarded a $ 1.9 million contract to qualify a tether propulsion system for orbital debris removal. Over

11328-436: The quality and duration of microgravity conditions. The choice of the metal conductor to be used in an electrodynamic tether is determined by a variety of factors. Primary factors usually include high electrical conductivity , and low density . Secondary factors, depending on the application, include cost, strength, and melting point. An electromotive force (EMF) is generated across a tether element as it moves relative to

11446-427: The resistance d R t {\displaystyle dR_{t}} multiplied by the current I ( y ) {\displaystyle I(y)} traveling across that section is the resistive potential loss. After evaluating KVL & KCL for the system, the results will yield a current and potential profile along the tether, as seen in above figure. This diagram shows that, from point A of

11564-408: The right where two spacecraft at two different altitudes have been connected by a tether. Normally, each spacecraft would have a balance of gravitational (e.g. F g1 ) and centrifugal (e.g. F c1 ) forces, but when tied together by a tether, these values begin to change with respect to one another. This phenomenon occurs because, without the tether, the higher-altitude mass would travel slower than

11682-615: The rotating tether to lose energy, and thus lose velocity and altitude. 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 skyhook is a theoretical class of orbiting tether propulsion intended to lift payloads to high altitudes and speeds. Proposals for skyhooks include designs that employ tethers spinning at hypersonic speed for catching high speed payloads or high altitude aircraft and placing them in orbit. Electrodynamic tethers are long conducting wires, such as one deployed from

11800-522: The rotation rate of the tether in order to produce either a consistent slowing force or a consistent accelerating force. Whether slowing or accelerating the satellite, the electrodynamic tether pushes against the planet's magnetic field, and thus the momentum gained or lost ultimately comes from the planet. A sky-hook is a theoretical class of orbiting tether propulsion intended to lift payloads to high altitudes and speeds. Simple sky-hooks are essentially partial elevators, extending some distance below

11918-402: The same way as an electric motor does. These can be either rotating tethers, or non-rotating tethers , that capture an arriving spacecraft and then release it at a later time into a different orbit with a different velocity. Momentum exchange tethers can be used for orbital maneuvering , or as part of a planetary-surface-to-orbit / orbit-to-escape-velocity space transportation system. This

12036-425: 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. Also, this system could be built with a total mass of less than 28 times the mass of the payloads. Rotovators can thus be charged by momentum exchange. Momentum charging uses the rotovator to move mass from

12154-520: The surface of the Moon and Mars, a rotovator from these materials cannot lift from the surface of the Earth. In theory, high flying, supersonic (or hypersonic ) aircraft could deliver a payload to a rotovator that dipped into Earth's upper atmosphere briefly at predictable locations throughout the tropic (and temperate) zone of Earth. As of May 2013, all mechanical tethers (orbital and elevators) are on hold until stronger materials are available. Momentum exchange tether A momentum exchange tether

12272-425: The surface of the thick sheath are collected. The voltage of the collecting structure with respect to the ambient plasma, as well as the ambient plasma density and temperature, determines the size of the sheath. This accelerating (or decelerating) voltage combined with the energy and momentum of the incoming particles determines the amount of current collected across the plasma sheath. The orbital-motion-limit regime

12390-413: The surrounding plasma. Then there are active collection and emission techniques involved in an EDT system. This occurs through devices such as hollow cathode plasma contactors, thermionic cathodes , and field emitter arrays. The physical design of each of these structures as well as the current emission capabilities are thoroughly discussed. The concept of current collection to a bare conducting tether

12508-507: The system along the local vertical, as seen in the figure. Objects in low Earth orbit are subjected to noticeable erosion from atomic oxygen due to the high orbital speed with which the molecules strike as well as their high reactivity. This could quickly erode a tether. Simple single-strand tethers are susceptible to micrometeoroids and space junk . Several systems have since been proposed and tested to improve debris resistance: Large pieces of junk would still cut most tethers, including

12626-491: The tensile force on the tether is projected to be less than 65 newtons (15 lbf). Material selection in this case depends on the purpose of the mission and design constraints. Electrodynamic tethers, such as the one used on TSS-1R, may use thin copper wires for high conductivity (see EDT ). There are design equations for certain applications that may be used to aid designers in identifying typical quantities that drive material selection. Space elevator equations typically use

12744-611: The tether and attached object, slowing their orbital motion. In a loose sense, the process can be likened to a conventional windmill- the drag force of a resistive medium (air or, in this case, the magnetosphere) is used to convert the kinetic energy of relative motion (wind, or the satellite's momentum) into electricity. In principle, compact high-current tether power generators are possible and, with basic hardware, tens, hundreds, and thousands of kilowatts appears to be attainable. NASA has conducted several experiments with Plasma Motor Generator (PMG) tethers in space. An early experiment used

12862-414: The tether and that of the ambient plasma, (V – Vp), it is assumed that all of the incoming electrons or ions that enter the plasma sheath are collected by the conductive body. This 'thin sheath' theory involving non-flowing plasmas is discussed, and then the modifications to this theory for flowing plasma is presented. Other current collection mechanisms will then be discussed. All of the theory presented

12980-409: The tether down to point B , there is a positive potential bias, which increases the collected current. Below that point, the V − V p {\displaystyle V-V_{p}} becomes negative and the collection of ion current begins. Since it takes a much greater potential difference to collect an equivalent amount of ion current (for a given area), the total current in

13098-437: The tether intersects the planet's magnetic field , it generates a current, and thereby converts some of the orbiting body's kinetic energy to electrical energy. Functionally, electrons flow from the space plasma into the conductive tether, are passed through a resistive load in a control unit and are emitted into the space plasma by an electron emitter as free electrons. As a result of this process, an electrodynamic force acts on

13216-440: The tether is reduced by a smaller amount. Then, at point C , the remaining current in the system is drawn through the resistive load ( R l o a d {\displaystyle R_{\mathrm {load} }} ), and emitted from an electron emissive device ( V e m i t {\displaystyle V_{\mathrm {emit} }} ), and finally across the plasma sheath ( V c

13334-569: The tether with respect to the plasma. Finally, point B is the point at which the potential of the tether is equal to the plasma. The location of point B will vary depending on the equilibrium state of the tether, which is determined by the solution of Kirchhoff's voltage law (KVL) and Kirchhoff's current law (KCL) along the tether. Here I A B {\displaystyle I_{AB}} , I B C {\displaystyle I_{BC}} , and I C {\displaystyle I_{C}} describe

13452-415: The total load at each point along the length of the cable. In practice this means that the central tether structure needs to be thicker than the tips. Correct tapering ensures that the tensile stress at every point in the cable is exactly the same. For very demanding applications, such as an Earth space elevator, the tapering can reduce the excessive ratios of cable weight to payload weight. In lieu of tapering

13570-403: The value used is the material's 'characteristic velocity' which is the maximum tip velocity a rotating untapered cable can attain without breaking, The characteristic velocity equals the specific velocity multiplied by the square root of two. These values are used in equations similar to the rocket equation and are analogous to specific impulse or exhaust velocity. The higher these values are,

13688-412: The years, numerous applications for electrodynamic tethers have been identified for potential use in industry, government, and scientific exploration. The table below is a summary of some of the potential applications proposed thus far. Some of these applications are general concepts, while others are well-defined systems. Many of these concepts overlap into other areas; however, they are simply placed under

13806-523: Was first formalized by Sanmartin and Martinez-Sanchez. They note that the most area efficient current collecting cylindrical surface is one that has an effective radius less than ~1 Debye length where current collection physics is known as orbital motion limited (OML) in a collisionless plasma. As the effective radius of the bare conductive tether increases past this point then there are predictable reductions in collection efficiency compared to OML theory. In addition to this theory (which has been derived for

13924-430: Was found to be possible with materials then existing. In 1977, Hans Moravec and later Robert L. Forward investigated the physics of non-synchronous skyhooks , also known as rotating skyhooks, and performed detailed simulations of tapered rotating tethers that could pick objects off, and place objects onto, the Moon , Mars and other planets , with little loss, or even a net gain of energy. In 1979, NASA examined

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