A space elevator would consist of a cable [4] anchored to the Earth's surface [6], reaching into space. By attaching a counterweight [3] at the end (or by further extending the cable for the same purpose), inertia ensures that the cable remains stretched taut, countering the gravitational pull on the lower sections, thus allowing the elevator to remain in geostationary orbit [1]. Once beyond the gravitational midpoint [2], carriage [5] would be accelerated further by the planet's rotation. (Diagram not to scale.)

A space elevator is a proposed megastructure designed to transport material from a celestial body's surface into space as a way of non-rocket spacelaunch. The term most often refers to a structure that reaches from the surface of the Earth to geosynchronous orbit (GSO) and a counter-mass beyond. The concept of a structure reaching to geosynchronous orbit was first conceived by Konstantin Tsiolkovsky,^[1] who proposed a compression structure, or "Tsiolkovsky tower." Most recent discussions focus on tensile structures (tethers) reaching from geosynchronous orbit to the ground. Space elevators have also sometimes been referred to as beanstalks, space bridges, space ladders, skyhooks, orbital towers, or orbital elevators. Download high resolution version (381x657, 30 KB)Structural diagram of a space elevator. ... Download high resolution version (381x657, 30 KB)Structural diagram of a space elevator. ... This article is about Earth as a planet. ... Layers of Atmosphere - not to scale (NOAA)[1] Outer space, sometimes simply called space, refers to the relatively empty regions of the universe outside the atmospheres of celestial bodies. ... A geostationary orbit (abbreviated GEO) is a circular orbit in the Earths equatorial plane, any point on which revolves about the Earth in the same direction and with the same period as the Earths rotation. ... A megastructure, in science fiction and speculative (or exploratory) engineering, is an enormous self-supporting artificial construct. ... Look up material in Wiktionary, the free dictionary. ... Astronomical objects are significant physical entities, associations or structures which current science has confirmed to exist in space. ... An open surface with X-, Y-, and Z-contours shown. ... Layers of Atmosphere - not to scale (NOAA)[1] Outer space, sometimes simply called space, refers to the relatively empty regions of the universe outside the atmospheres of celestial bodies. ... It has been suggested that this article or section be merged with geostationary orbit. ... Konstantin Eduardovich Tsiolkovsky Konstantin Eduardovich Tsiolkovsky (Константин Эдуардович Циолковский, Konstanty CioÅ‚kowski) (September 5, 1857 new style – September 19, 1935) was a Russian and Soviet rocket scientist and pioneer of cosmonautics who spent most of his life in a log house on the outskirts of the Russian town of Kaluga. ... Tension is a reaction force applied by a stretched string (rope or a similar object) on the objects which stretch it. ... The Space Tether idea started as just a thought during the late 1800’s then progressed to lofty ideas in the 60’s that forced NASA to step in and put control on the field in the 70’s. ... This article is about the transportation device. ...

The most common proposal is a tether, usually in the form of a cable or ribbon, spanning from the surface near the equator to a point beyond geosynchronous orbit. As the planet rotates, the inertia at the end of the tether counteracts gravity, and also keeps the cable taut. Vehicles can then climb the tether and reach orbit without the use of rocket propulsion. Such a structure could hypothetically permit delivery of cargo and people to orbit at a fraction of the cost of launching payloads by rocket. A tether is a cord that anchors something, such as an animal, to something else, such as a pole. ... For other uses, see Cable (disambiguation). ... For a monthly Japanese shōjo manga magazine, see Ribon. ... It has been suggested that this article or section be merged with geostationary orbit. ... This article is about transported goods. ...

Current technology is not capable of manufacturing materials that are sufficiently strong and light enough to build an Earth based space elevator as the total mass of conventional materials needed to construct such a structure would be far too great. Recent proposals for a space elevator are notable in their plans to use carbon nanotube-based materials as the tensile element in the tether design, since the theoretical strength of carbon nanotubes appears great enough to make this practical. Current technology may be able to support elevators in other locations in the solar system however, and other designs for space elevators exist that use current materials. // 3D model of three types of single-walled carbon nanotubes. ...

Geostationary orbital tethers

This concept, also called an orbital space elevator, geosynchronous orbital tether, or a beanstalk, is a subset of the skyhook concept, and is what people normally think of when the phrase 'Space elevator' is used (although there are variants). Artists conception of satellite with a tether Tether propulsion uses long, strong strings (known as tethers) to change the orbits of spacecraft. ... For other uses, see Skyhook (disambiguation). ...

Construction would be a vast project: a tether would have to be built of a material that could endure tremendous stress while also being light-weight, cost-effective, and manufacturable in great quantities. Today's materials technology does not meet these requirements, although carbon nanotube technology shows great promise. A considerable number of other novel engineering problems would also have to be solved to make a space elevator practical. Not all problems regarding feasibility have yet been addressed. Nevertheless, the LiftPort Group believes that the necessary technology might be developed as early as 2008^[2] and that by developing the technology, the first space elevator could be operational by 2014.^[3][4] Look up material in Wiktionary, the free dictionary. ... Stress is a measure of force per unit area within a body. ... By the mid 20th century humans had achieved a mastery of technology sufficient to leave the surface of the Earth for the first time and explore space. ... // 3D model of three types of single-walled carbon nanotubes. ... LiftPort Group is a privately-held Washington State corporation with headquarters in Bremerton, Washington. ...

History

Early concepts

Konstantin Tsiolkovsky

The key concept of the space elevator appeared in 1895 when Russian scientist Konstantin Tsiolkovsky was inspired by the Eiffel Tower in Paris to consider a tower that reached all the way into space, built from the ground up to an altitude of 35,790 kilometers above sea level (geostationary orbit). He noted that a "celestial castle" at the top of such a spindle-shaped cable would have the "castle" orbiting Earth in a geosynchronous orbit (i.e. the castle would remain over the same spot on Earth's surface). Image File history File links Please see the file description page for further information. ... Image File history File links Please see the file description page for further information. ... Konstantin Eduardovich Tsiolkovsky Konstantin Eduardovich Tsiolkovsky (Константин Эдуардович Циолковский, Konstanty Ciołkowski) (September 5, 1857 new style – September 19, 1935) was a Russian and Soviet rocket scientist and pioneer of cosmonautics who spent most of his life in a log house on the outskirts of the Russian town of Kaluga. ... Konstantin Eduardovich Tsiolkovsky Konstantin Eduardovich Tsiolkovsky (Константин Эдуардович Циолковский, Konstanty Ciołkowski) (September 5, 1857 new style – September 19, 1935) was a Russian and Soviet rocket scientist and pioneer of cosmonautics who spent most of his life in a log house on the outskirts of the Russian town of Kaluga. ... The Eiffel Tower (French: , ) is an iron tower built on the Champ de Mars beside the Seine River in Paris. ... This article is about the capital of France. ... To help compare different orders of magnitude, this page lists lengths starting at 107 m (10,000 km). ... Geostationary orbit A geostationary orbit (GEO) is a geosynchronous orbit directly above the Earths equator (0° latitude), with orbital eccentricity of zero. ... This article is about Earth as a planet. ...

Tsiolkovsky's tower would be able to launch objects into orbit without a rocket. Since the elevator would attain orbital velocity as it rode up the cable, an object released at the tower's top would also have the orbital velocity necessary to remain in geosynchronous orbit. Unlike more recent concepts for space elevators, Tsiolkovsky's (conceptual) tower was a compression structure, rather than a tension (or "tether") structure.

Twentieth century

Building a compression structure from the ground up proved an unrealistic task; there was no material in existence with enough compressive strength to support its own weight under such conditions.^[5] In 1959 another Russian scientist, Yuri N. Artsutanov, suggested a more feasible proposal. Artsutanov suggested using a geosynchronous satellite as the base from which to deploy the structure downward. By using a counterweight, a cable would be lowered from geosynchronous orbit to the surface of Earth, while the counterweight was extended from the satellite away from Earth, keeping the center of gravity of the cable motionless relative to Earth. Artsutanov's idea was introduced to the Russian-speaking public in an interview published in the Sunday supplement of Komsomolskaya Pravda (usually named in English, "Young Person's Pravda") in 1960,^[6] but was not available in English until much later. He also proposed tapering the cable thickness so that the tension in the cable was constant—this gives a thin cable at ground level, thickening up towards GEO. Yuri N. Artsutanov (1929-) is an Russian engineer born in Leningrad. ... This article is about artificial satellites. ... This article or section does not cite its references or sources. ... Komsomolskaya Pravda (in Russian Комсомольская правда, meaning Komsomols Truth) is an all-Russian newspaper and is the product of the long-lived but now extinct Komsomol organization. ... Geostationary orbit A geostationary orbit (GEO) is a geosynchronous orbit directly above the Earths equator (0° latitude), with orbital eccentricity of zero. ...

Making a cable over 35,000 kilometers long is a difficult task. In 1966, Isaacs, Vine, Bradner and Bachus, four American engineers, reinvented the concept, naming it a "Sky-Hook," and published their analysis in the Journal Science.^[7] They decided to determine what type of material would be required to build a space elevator, assuming it would be a straight cable with no variations in its cross section, and found that the strength required would be twice that of any existing material including graphite, quartz, and diamond. A kilometer (Commonwealth spelling: kilometre), symbol: km is a unit of length in the metric system equal to 1,000 metres (from the Greek words χίλια (khilia) = thousand and μέτρο (metro) = count/measure). ... Science is the academic journal of the American Association for the Advancement of Science and is considered one of the worlds most prestigious scientific journals. ... For other uses, see Graphite (disambiguation). ... -1... This article is about the mineral. ...

In 1975 an American scientist, Jerome Pearson, reinvented the concept yet again, publishing his analysis in the journal Acta Astronautica. He designed^[8] a tapered cross section that would be better suited to building the elevator. The completed cable would be thickest at the geosynchronous orbit, where the tension was greatest, and would be narrowest at the tips to reduce the amount of weight per unit area of cross section that any point on the cable would have to bear. He suggested using a counterweight that would be slowly extended out to 144,000 kilometers (almost half the distance to the Moon) as the lower section of the elevator was built. Without a large counterweight, the upper portion of the cable would have to be longer than the lower due to the way gravitational and centrifugal forces change with distance from Earth. His analysis included disturbances such as the gravitation of the Moon, wind and moving payloads up and down the cable. The weight of the material needed to build the elevator would have required thousands of Space Shuttle trips, although part of the material could be transported up the elevator when a minimum strength strand reached the ground or be manufactured in space from asteroidal or lunar ore. Jerome Pearson is an American space scientist best known for his work on Space elevators and Lunar space elevators. ... This article is about Earths moon. ... Gravity is a force of attraction that acts between bodies that have mass. ... This article is about the space vehicle. ... For other uses, see Asteroid (disambiguation). ...

In 1977, Hans Moravec published an article called "A Non-Synchronous Orbital Skyhook", in which he proposed an alternative space elevator concept, using a rotating cable,^[9] in which the rotation speed exactly matches the orbital speed in such a way that the instantaneous velocity at the point where the cable was at the closest point to the Earth was zero. This concept is an early version of a space tether transportation system. Hans Moravec (born November 30, 1948 in Austria) is a research professor at the Robotics Institute (Carnegie Mellon) of Carnegie Mellon University. ... Artists conception of satellite with a tether Tether propulsion uses long, strong strings (known as tethers) to change the orbits of spacecraft. ...

In 1979, space elevators were introduced to a broader audience with the simultaneous publication of Arthur C. Clarke's novel, The Fountains of Paradise, in which engineers construct a space elevator on top of a mountain peak in the fictional island country of Taprobane (loosely based on Sri Lanka, albeit moved south to the equator), and Charles Sheffield's first novel, The Web Between the Worlds, also featuring the building of a space elevator. Three years later, in Robert A. Heinlein's 1982 novel Friday the principal character makes use of the "Nairobi Beanstalk" in the course of her travels. Sri Lankabhimanya Sir Arthur Charles Clarke, CBE (16 December 1917–19 March 2008), was a British science fiction author, inventor, and futurist, most famous for the novel 2001: A Space Odyssey, written in collaboration with director Stanley Kubrick, a collaboration which led also to the film of the same name... The Fountains of Paradise is a 1979 novel by Arthur C. Clarke. ... Charles Sheffield (June 25, 1935 – November 2, 2002), was an English-born mathematician, physicist and science fiction author. ... Robert Anson Heinlein (July 7, 1907 – May 8, 1988) was one of the most popular, influential, and controversial authors of hard science fiction. ... Friday is a 1982 science fiction novel by Robert A. Heinlein. ...

Kim Stanley Robinson's Mars trilogy chronicles the fictional settlement and terraforming of Mars and a space elevator is a focus point for one of the plotlines. In 1999, Larry Niven authored the book Rainbow Mars which contained a "Hanging Tree" - an organic 'Skyhook' which was capable of interstellar travel. The book skillfully discussed several merits/demerits of such an approach to the Beanstalk - the primary demerit being that the water necessary to sustain such an enormous 'tree' would require the drying up of all of its host planet's water bodies - which is used as a plot device to explain the drying up of Mars. The Mars trilogy is a series of award-winning science fiction novels by Kim Stanley Robinson, chronicling the settlement and terraforming of the planet Mars. ... This article does not cite any references or sources. ... Rainbow Mars is a science fiction novel by Larry Niven, in which humans from Earth visit the Mars and find it populated by the creations of Edgar Rice Burroughs, Ray Bradbury, C.S. Lewis, H.G. Wells, and Stanley Weinbaum - in short, all the great acience fiction writers who have...

21st century

After the development of carbon nanotubes in the 1990s, engineer David Smitherman of NASA/Marshall's Advanced Projects Office realized that the high strength of these materials might make the concept of an orbital skyhook feasible, and put together a workshop at the Marshall Space Flight Center, inviting many scientists and engineers to discuss concepts and compile plans for an elevator to turning the concept into a reality.^[10] The publication he edited compiling information from the workshop, "Space Elevators: An Advanced Earth-Space Infrastructure for the New Millennium",^[11] provides an introduction to the state of the technology at the time, and summarizes the findings. For other uses, see NASA (disambiguation). ... Aerial view of the test area at Marshall Space Flight Center The George C. Marshall Space Flight Center (MSFC) is a lead NASA center for propulsion, Space Shuttle propulsion, external fuel tank, crew training and payloads, International Space Station (ISS) design and construction, for computers, networks, and information management. ...

Another American scientist, Bradley C. Edwards, suggested creating a 100,000 km long paper-thin ribbon using nanotube fibers, suggesting that this structure would stand a greater chance of surviving impacts by meteoroids. Supported by the NASA Institute for Advanced Concepts, the work of Edwards was expanded to cover the deployment scenario, climber design, power delivery system, orbital debris avoidance, anchor system, surviving atomic oxygen, avoiding lightning and hurricanes by locating the anchor in the western equatorial Pacific, construction costs, construction schedule, and environmental hazards.^[12][13] The largest holdup to Edwards' proposed design is the technological limits of the tether material. His calculations call for a fiber composed of epoxy-bonded carbon nanotubes with a minimal tensile strength of 130 GPa (including a safety factor of 2); however, tests in 2000 of individual single-walled carbon nanotubes (SWCNTs), which should be notably stronger than an epoxy-bonded rope, indicated the strongest measured as 52 GPa.^[14] Multi-walled carbon nanotubes have been measured with tensile strengths up to 63 GPa.^[15] NASA Institute for Advanced Concepts is apparently an organisation within NASA that funds research on advanced concepts, that is, not some boring present day concepts, but exciting future technologies. ... Space debris or orbital debris, also called space junk and space waste, are the objects in orbit around Earth created by man that no longer serve any useful purpose. ... // 3D model of three types of single-walled carbon nanotubes. ... For other uses, see Pascal. ... Factor of safety (FoS), also known as Safety Factor, is a multiplier applied to the calculated maximum load (force, torque, bending moment or a combination) to which a component or assembly will be subjected. ...

In order to speed development of space elevators, proponents are planning several competitions, similar to the Ansari X Prize, for relevant technologies.^[16][17] Among them are Elevator:2010 which will organize annual competitions for climbers, ribbons and power-beaming systems, the Robolympics Space Elevator Ribbon Climbing competition,^[18] as well as NASA's Centennial Challenges program which, in March 2005, announced a partnership with the Spaceward Foundation (the operator of Elevator:2010), raising the total value of prizes to US$400,000.^[19][20] For other uses, see X Prize (disambiguation). ... The Centennial Challenges are NASA inducement prize contests for non-government-funded technological achievements by American teams. ...

In 2005, "the LiftPort Group of space elevator companies has announced that it will be building a carbon nanotube manufacturing plant in Millville, New Jersey, to supply various glass, plastic and metal companies with these strong materials. Although LiftPort hopes to eventually use carbon nanotubes in the construction of a 100,000 km (62,000 mile) space elevator, this move will allow it to make money in the short term and conduct research and development into new production methods."^[21] The group also announced that they had obtained permission from the Federal Aviation Administration to use airspace to conduct preliminary tests of its high altitude robotic lifters.^[22] The experiment was successful. Year 2005 (MMV) was a common year starting on Saturday (link displays full calendar) of the Gregorian calendar. ... LiftPort Group is a privately-held Washington State corporation with headquarters in Bremerton, Washington. ... The Maurice River in Millville in 2006 Millville is a city in Cumberland County, New Jersey, United States. ... FAA redirects here. ...

On February 13, 2006 the LiftPort Group announced that, earlier the same month, they had tested a mile of "space-elevator tether" made of carbon-fiber composite strings and fiberglass tape measuring 5 cm wide and 1 mm (approx. 6 sheets of paper) thick, lifted with balloons.^[23] is the 44th day of the year in the Gregorian calendar. ... Year 2006 (MMVI) was a common year starting on Sunday of the Gregorian calendar. ...

On August 24, 2006 the Japanese National Museum of Emerging Science and Technology in Tokyo has started to show the animation movie 'Space Elevator', based on ATA Space Elevator Project, also directed and edited by project leader, Dr. Serkan Anilir. This movie shows a possible image about the cities of future, placing the space elevator tower as a new infrastructure into the city planning, and aims to contribute children education. Currently, the movie is shown in all science museums in Japan.^[24] is the 236th day of the year (237th in leap years) in the Gregorian calendar. ... Year 2006 (MMVI) was a common year starting on Sunday of the Gregorian calendar. ...

The x-Tech Projects company has also been founded to pursue the prospect of a commercial Space Elevator.

In 2007, Elevator:2010 held the 2007 Space Elevator games which featured US$500,000 awards for each of the two competitions, (US$1,000,000 total) as well as an additional US$4,000,000 to be awarded over the next five years for space elevator related technologies.^[25] No teams won the competition, but a team from MIT entered the first 2-gram, 100% carbon nanotube entry into the competition.^[26] Year 2007 (MMVII) was a common year starting on Monday of the Gregorian calendar in the 21st century. ... Mapúa Institute of Technology (MIT, MapúaTech or simply Mapúa) is a private, non-sectarian, Filipino tertiary institute located in Intramuros, Manila. ...

Physics and structure

One concept for the space elevator has it tethered to a mobile seagoing platform.

There are a variety of tether designs. Almost every design includes a base station, a cable, climbers, and a counterweight. Download high resolution version (2048x1536, 71 KB)A conceptual drawing of a space elevator lifting off. ... Download high resolution version (2048x1536, 71 KB)A conceptual drawing of a space elevator lifting off. ...

Base station

The base station designs typically fall into two categories—mobile and stationary. Mobile stations are typically large oceangoing vessels,^[27] though airborne stations have been proposed as well.^{[citation needed]} Stationary platforms would generally be located in high-altitude locations, such as on top of mountains, or even potentially on high towers.^[5]

Mobile platforms have the advantage of being able to maneuver to avoid high winds, storms, and space debris. While stationary platforms don't have these advantages, they typically would have access to cheaper and more reliable power sources, and require a shorter cable. While the decrease in cable length may seem minimal (typically no more than a few kilometers), that can significantly reduce the minimal width of the cable at the center, and reduce the minimal length of cable reaching beyond geostationary orbit significantly. Space debris or orbital debris, also called space junk and space waste, are the objects in orbit around Earth created by man that no longer serve any useful purpose. ...

Cable

The cable must be made of a material with a large tensile strength/density ratio. A space elevator can be made relatively economically feasible if a cable with a density similar to graphite and a tensile strength of ~65–120 GPa can be mass-produced at a reasonable price. Tensile strength isthe measures the force required to pull something such as rope, wire, or a structural beam to the point where it breaks. ... For other uses, see Graphite (disambiguation). ... The gigapascal, symbol GPa is an SI unit of pressure. ...

Carbon nanotubes would be a highly useful material for creating a space elevator

By comparison, most steel has a tensile strength of under 2 GPa, and the strongest steel resists no more than 5.5 GPa, but steel is dense. The much lighter material Kevlar has a tensile strength of 2.6–4.1 GPa, while quartz fiber^{[citation needed]} and carbon nanotubes^[28] can reach upwards of 20 GPa; the tensile strength of diamond filaments would theoretically be minimally higher. Image File history File links Kohlenstoffnanoroehre_Animation. ... Image File history File links Kohlenstoffnanoroehre_Animation. ... // 3D model of three types of single-walled carbon nanotubes. ... Kevlars molecular structure; BOLD: monomer unit; DASHED: hydrogen bonds. ... -1... This article is about the mineral. ...

Carbon nanotubes' theoretical tensile strength has been estimated between 140 and 177 GPa (depending on plane shape),^[28] and its observed tensile strength has been variously measured from 63 to 150 GPa, close to the requirements for space elevator structures.^[28][29] Even the strongest fiber made of nanotubes is likely to have notably less strength than its components. // 3D model of three types of single-walled carbon nanotubes. ...

Improving tensile strength depends on further research on purity and different types of nanotubes.

Designs call for single-walled carbon nanotubes. While multi-walled nanotubes are easier to produce and have similar tensile strengths, there is a concern that the interior tubes would not be sufficiently coupled to the outer tubes to help hold the tension. However, if the nanotubes are long enough, even weak Van der Waals forces will be sufficient to keep them from slipping, and the full strength of individual nanotubes (single or multiwalled) could be realized macroscopically by spinning them into a yarn. It has also been proposed to chemically interlink the nanotubes in some way, but it is likely that this would greatly compromise their strength. One such proposal is to take advantage of the high pressure interlinking properties of carbon nanotubes of a single variety.^[30] While this would cause the tubes to lose some tensile strength by the trading of sp² bond (graphite, nanotubes) for sp³ (diamond), it will enable them to be held together in a single fiber by more than the usual, weak Van der Waals force (VdW), and allow manufacturing of a fiber of any length. The title given to this article is incorrect due to technical limitations. ... Notice: For a full understanding of this article, it is important to read and understand the article on orbital hybridization. ... four sp³ orbitals three sp² orbitals In chemistry, hybridisation or hybridization (see also spelling differences) is the concept of mixing atomic orbitals to form new hybrid orbitals suitable for the qualitative description of atomic bonding properties. ... In chemistry, the term van der Waals force originally referred to all forms of intermolecular forces; however, in modern usage it tends to refer to intermolecular forces that deal with forces due to the polarization of molecules. ...

A seagoing anchor station would incidentally act as a deep-water seaport.

The technology to spin regular VdW-bonded yarn from carbon nanotubes is just in its infancy: the first success in spinning a long yarn, as opposed to pieces of only a few centimeters, was reported in March 2004; but the strength/weight ratio was not as good as Kevlar due to the inconsistent quality and short length of the tubes being held together by VdW. Download high resolution version (800x1100, 39 KB)A conceptual drawing of a space elevators anchor platform. ... Download high resolution version (800x1100, 39 KB)A conceptual drawing of a space elevators anchor platform. ... It has been suggested that this article or section be merged with Port. ...

As of 2006, carbon nanotubes cost $25/gram, and even a space elevator that did not reach GEO would have a mass of 20,000 kg. However, this price is declining, and large-scale production could result in strong economies of scale.^[31] 2006 is a common year starting on Sunday of the Gregorian calendar. ... The increase in output from Q to Q2 causes a decrease in the average cost of each unit from C to C1. ...

Carbon nanotube fiber is an area of energetic worldwide research because the applications go much further than space elevators. Other suggested application areas include suspension bridges, new composite materials, lighter aircraft and rockets, armor technologies, and computer processor interconnects. This is good news for space elevator proponents because it is likely to push down the price of the cable material further.

Cable taper

Due to its enormous length a space elevator cable must be carefully designed to carry its own weight as well as the smaller weight of climbers. The required strength of the cable will vary along its length, since at various points it has to carry the weight of the cable below, or provide a centripetal force to retain the cable and counterweight above. In an ideal cable, the actual strength of the cable at any given point would equal to the required strength at that point (plus a safety margin). This implies a tapered design. The centripetal force is the external force required to make a body follow a circular path at constant speed. ...

Using a model that takes into account the Earth's gravitational and "centrifugal" forces (and neglecting the smaller solar and lunar effects), it is possible to show^[8] that the optimal cross-sectional area of the cable as a function of height is given by:

Cable Taper Plot

where A(r) is the cross-sectional area as a function of distance r from the Earth's center. Image File history File links Metadata Size of this preview: 633 × 599 pixelsFull resolution (699 × 662 pixel, file size: 365 KB, MIME type: image/jpeg) I made this for a project for university. ... Image File history File links Metadata Size of this preview: 633 × 599 pixelsFull resolution (699 × 662 pixel, file size: 365 KB, MIME type: image/jpeg) I made this for a project for university. ...

The constants in the equation are:

• A₀ is the cross-sectional area of the cable on the earth's surface.
• ρ is the density of the material the cable is made out of.
• s is the tensile strength of the material.
• ω is the angular velocity of the Earth about its axis, 7.292 × 10⁻⁵ rad·s⁻¹.
• r₀ is the distance between the Earth's center and the base of the cable. It is approximately the Earth's equatorial radius, 6378 km.
• g₀ is the acceleration due to gravity at the cable's base, 9.780 m·s⁻².

This equation gives a shape where the cable thickness initially increases rapidly in an exponential fashion, but slows at an altitude a few times the Earth's radius, and then gradually becomes parallel when it finally reaches maximum thickness at geostationary orbit. The cable thickness then decreases again out from geosynchronous orbit. The relative thickness at all points is determined by the strength density ratio. This is shown in the figure to the right. The radian per second (symbol: rad/s) is the SI unit of angular velocity. ... World map showing the equator in red For other uses, see Equator (disambiguation). ... Gravity is a force of attraction that acts between bodies that have mass. ... Geostationary orbit A geostationary orbit (GEO) is a geosynchronous orbit directly above the Earths equator (0° latitude), with orbital eccentricity of zero. ...

Thus the taper of the cable from base to GEO (r = 42,164 km),

Using the density and tensile strength of steel, and assuming a diameter of 1 cm at ground level, yields a diameter of several hundred kilometers at geostationary orbit height, showing that steel, and indeed all materials used in present day mechanical engineering, are unsuitable for building a space elevator.

The equation shows us that there are four ways of achieving a more reasonable thickness at geostationary orbit:

• Using a lower density material. Not much scope for improvement as the range of densities of most solids that come into question is rather narrow, somewhere between 1000 kg·m⁻³ and 5000 kg·m⁻³.
• Using a higher strength material. This is the area where most of the research is focused. Carbon nanotubes are tens of times stronger than the strongest types of steel, hugely reducing the cable's cross-sectional area at geostationary orbit.
• Increasing the height of a tip of the base station, where the base of cable is attached. If the cable is properly tapered, however (see next point) this will not make much difference unless a tower of the order of 1000 km is built.
• Making the cable as thin as possible at its base. It still has to be thick enough to carry a payload however, so the minimum thickness at base level also depends on tensile strength. A cable made of carbon nanotubes (a type of fullerene), would typically be just a millimeter wide at the base^{[citation needed]}.

The Icosahedral Fullerene C540 C60 and C-60 redirect here. ...

Climbers

Most space elevator designs call for a climber to move autonomously along a stationary cable.

A space elevator cannot be an elevator in the typical sense (with moving cables) due to the need for the cable to be significantly wider at the center than the tips. While various designs employing moving cables have been proposed, most cable designs call for the "elevator" to climb up a stationary cable. Download high resolution version (2336x3208, 128 KB)A conceptual drawing of a space elevator climbing through the clouds. ... Download high resolution version (2336x3208, 128 KB)A conceptual drawing of a space elevator climbing through the clouds. ...

Climbers cover a wide range of designs. On elevator designs whose cables are planar ribbons, most propose to use pairs of rollers to hold the cable with friction. Usually, elevators are designed for climbers to move only upwards, because that is where most of the payload goes. For returning payloads, atmospheric reentry on a heat shield is a very competitive option, which also avoids the problem of docking to the elevator in space.

Climbers must be paced at optimal timings so as to minimize cable stress and oscillations and to maximize throughput. Lighter climbers can be sent up more often, with several going up at the same time. This increases throughput somewhat, but lowers the mass of each individual payload.

Powering climbers

Both power and energy are significant issues for climbers- the climbers need to gain a large amount of potential energy as quickly as possible to clear the cable for the next payload.

Nuclear energy and solar power have been proposed, but generating enough energy to reach the top of the elevator in any reasonable time without weighing too much is not feasible.^[32]

The current method of favor is laser power beaming, using megawatt powered free electron or solid state lasers in combination with adaptive mirrors approximately 10 m wide and a photovoltaic array on the climber tuned to the laser frequency for efficiency.^[27] A major obstacle for any climber design is the dissipation of the substantial amount of waste heat generated due to the less than perfect efficiency of any of the power methods.

Counterweight

There have been several methods proposed for dealing with the counterweight need: a heavy object, such as a captured asteroid or a space station, positioned past geosynchronous orbit, or extending the cable itself well past geosynchronous orbit. The latter idea has gained more support in recent years due to the relative simplicity of the task and the fact that a payload that went to the end of the counterweight-cable would acquire considerable velocity relative to the Earth, allowing it to be launched into interplanetary space. The International Space Station in 2007 A space station is an artificial structure designed for humans to live in outer space. ...

Additionally, Brad Edwards has proposed that initially elevators would be up-only, and that the elevator cars that are used to thicken up the cable could simply be parked at the top of the cable and act as a counterweight.

Angular momentum, speed and cable lean

As the car climbs, the elevator takes on a 1 degree lean, due to the top of the elevator traveling faster than the bottom around the Earth (Coriolis effect). This diagram is not to scale.

The horizontal speed of each part of the cable increases with altitude, proportional to distance from the center of the Earth, reaching orbital velocity at geosynchronous orbit. Therefore as a payload is lifted up a space elevator, it needs to gain not only altitude but angular momentum (horizontal speed) as well. Image File history File links Download high-resolution version (700x650, 48 KB) File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Space elevator ... Image File history File links Download high-resolution version (700x650, 48 KB) File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Space elevator ... The orbital speed of a body, generally a planet, a natural satellite, an artificial satellite, or a multiple star, is the speed at which it orbits around the barycenter of a system, usually around a more massive body. ... This box:      This gyroscope remains upright while spinning due to its angular momentum. ...

This angular momentum is taken from the Earth's own rotation. As the climber ascends it is initially moving slightly more slowly than the cable that it moves onto (Coriolis effect) and thus the climber "drags" on the cable, carrying the cable with it very slightly to the west (and necessarily pulling the counterweight slightly to the west, shown as an offset of the counterweight in the diagram to right, slightly changing the motion of the counterweight). At a 200 km/h climb speed this generates a 1 degree lean on the lower portion of the cable. The horizontal component of the tension in the non-vertical cable applies a sideways pull on the payload, accelerating it eastward (see diagram) and this is the source of the speed that the climber needs. Conversely, the cable pulls westward on Earth's surface, insignificantly slowing the Earth, from Newton's 3rd law. In the inertial frame of reference (upper part of the picture), the black object moves in a straight line. ... Newtons First and Second laws, in Latin, from the original 1687 edition of the Principia Mathematica. ...

Meanwhile, the overall effect of the centrifugal force acting on the cable causes it to constantly try to return to the energetically favourable vertical orientation, so after an object has been lifted on the cable the counterweight will swing back towards the vertical like an inverted pendulum. Provided that the Space Elevator is designed so that the center of weight always stays above geosynchronous orbit^[33] for the maximum climb speed of the climbers, the elevator cannot fall over. Lift and descent operations must be carefully planned so as to keep the pendulum-like motion of the counterweight around the tether point under control.

By the time the payload has reached GEO the angular momentum (horizontal speed) is enough that the payload is in orbit.

The opposite process would occur for payloads descending the elevator, tilting the cable eastwards and insignificantly increasing Earth's rotation speed.

Launching into outer space

The velocities that might be attained at the end of Pearson's 144,000 km cable can be determined. The tangential velocity is 10.93 kilometers per second which is more than enough to escape Earth's gravitational field and send probes as far out as Saturn. If an object were allowed to slide freely along the upper part of the tower, a velocity high enough to escape the solar system entirely would be attained. This is accomplished by trading off overall angular momentum of the tower for velocity of the launched object, in much the same way one snaps a towel or throws a lacrosse ball. After such an operation a cable would be left with less angular momentum than required to keep its geostationary position. The rotation of the Earth would then pull on the cable increasing its angular velocity, leaving the cable swinging backwards and forwards about its starting point. Space Shuttle Atlantis launches on mission STS-71. ... Atmospheric characteristics Atmospheric pressure 140 kPa Hydrogen >93% Helium >5% Methane 0. ... This article is about the Solar System. ... For other uses, see Lacrosse (disambiguation). ...

For higher velocities, the cargo can be electromagnetically accelerated, or the cable could be extended, although that would require additional strength in the cable.

Extraterrestrial elevators

A space elevator could also be constructed on some of the other planets, asteroids and moons.

A Martian tether could be much shorter than one on Earth. Mars' surface gravity is 38% of Earth's, while it rotates around its axis in about the same time as Earth. Because of this, Martian areostationary orbit is much closer to the surface, and hence the elevator would be much shorter. Exotic materials might not be required to construct such an elevator. However, building a Martian elevator would be a unique challenge because the Martian moon Phobos is in a low orbit, and intersects the equator regularly (twice every orbital period of 11 h 6 min). A collision between the elevator and the 22.2 km diameter moon would have to be avoided through active steering of the elevator. One simpler way to resolve the problem of Phobos (1.1 degree orbital inclination) or Deimos (1.8 degree orbital inclination) interaction is to position the tether anchor perhaps five (5) degrees off the Martian equator. There would be a small payload penalty, but the tether would pass outside the orbital inclination of the two moons. Also, the tether would depart the Martian anchor at 5–10 degrees from vertical. This article is about the planet. ... Gravity is a force of attraction that acts between bodies that have mass. ... An areostationary orbit (abbreviated ASO) is a circular areo­synchronous orbit in the Martian equatorial plane 11,000 km above the surface, any point on which revolves about Mars in the same direction and with the same period as the Martian surface. ... Phobos (IPA: or [ˈfoÊŠ.bÉ™s]) (systematic designation: ) is the larger and closer of Mars two moons (the other being Deimos). ... Deimos (IPA or ; Greek Δείμος: Dread), is the smaller and outermost of Mars’ two moons, named after Deimos from Greek Mythology. ...

Conversely, a Venusian space elevator would need to be much longer. Although a tether placed at the stationary orbit of the slowly rotating Venus would intersect the Sun, one could be constructed that rotated with the fast-moving cloud decks of the planet which take only four Earth days to make a complete cycle. The cable would need to exceed 100,000 kilometers long but, counter-intuitively, would experience less stress due to the slightly smaller gravity exerted on the cable. Such an elevator could service aerostats or floating cities in the benign regions of the atmosphere. For other uses, see Venus (disambiguation). ... Uncrewed aerostats can carry instruments and sensors for long durations that are impractical for humans and other aircraft. ... In science fiction, floating cities are settlements that use buoyancy to remain in the atmosphere of a planet. ... Venus, the second planet from the Sun, has an atmosphere very different from that of Earth. ...

Another Venusian design would require the anchor to be a mobile ground level platform that would circle Venus at the same rate that it rotates, 6.52 km/h. The counterweight on the other end would be hung toward the sun at all times, past the point where the Sun's and Venus's gravity cancel each other out, thereby keeping the tether balanced by the Sun's pull of gravity. This point is called a Lagrangian point, specifically L1. This is 1,000,000 km from Venus. A contour plot of the effective potential (the Hills Surfaces) of a two-body system (the Sun and Earth here), showing the five Lagrange points. ...

A lunar space elevator can possibly be built with currently available technology about 50,000 kilometers long extending though the Earth-moon L1 point from an anchor point near the center of the visible part of Earth's moon.

On the far side of the moon, a lunar space elevator would need to be very long (more than twice the length of an Earth elevator) but due to the low gravity of the Moon, can be made of existing engineering materials. Alternatively, due to the lack of atmosphere on the Moon, a rotating tether could be used with its center of weight in orbit around the Moon with a counterweight (e.g. a space station) at the short end and a payload at the long end. The path of the payload would be an epicycloid around the Moon, touching down at some integer number of times per orbit. Thus, payloads are lifted off the surface of the Moon, and flung away at the high point of the orbit. A lunar space elevator (also called a moonstalk) is a proposed cable running from the surface of the Moon into space. ... A tether is a cord that anchors something, such as an animal, to something else, such as a pole. ... This article or section does not cite its references or sources. ... The International Space Station in 2007 A space station is an artificial structure designed for humans to live in outer space. ... In military aircraft or space exploration, the payload is the carrying capacity of an aircraft or space ship, including as cargo, munitions, scientific instruments or experiments, or external fuel, although internal fuel is usually not included. ... In geometry, an epicycloid is a plane curve produced by tracing the path of a chosen point of a circle — called epicycle — which rolls around without slipping around a fixed circle. ...

Rapidly spinning asteroids or moons could use cables to eject materials in order to move the materials to convenient points, such as Earth orbits; or conversely, to eject materials in order to send the bulk of the mass of the asteroid or moon to Earth orbit or a Lagrangian point. This was suggested by Russell Johnston in the 1980s. Freeman Dyson, a physicist and mathematician, has suggested using such smaller systems as power generators at points distant from the Sun where solar power is uneconomical. For the purpose of mass ejection, it is not necessary to rely on the asteroid or moon to be rapidly spinning. Instead of attaching the tether to the equator of a rotating body, it can be attached to a rotating hub on the surface. This was suggested in 1980 as a "Rotary Rocket" by Pearson^[34] and described very succinctly on the Island One website as a "Tapered Sling"^[35] A contour plot of the effective potential (the Hills Surfaces) of a two-body system (the Sun and Earth here), showing the five Lagrange points. ... The Right Honourable David Russell Johnston, Baron Russell-Johnston, PC (born July 28, 1932) is a leading Scottish Liberal Democrat politician. ... Freeman John Dyson FRS (born December 15, 1923) is an English-born American theoretical physicist and mathematician, famous for his work in quantum mechanics, solid-state physics, nuclear weapons design and policy, and for his serious theorizing in futurism and science fiction concepts, including the search for extraterrestrial intelligence. ...

It may also be possible to construct space elevators at the three smaller gas giants, Saturn, Uranus and Neptune. These would all involve tapering several times greater than those of the inner solar system^{[citation needed]}. These outer space elevators could facilitate the exchange of supplies and helium-3 between floating mining colonies in the atmospheres and local moon settlements. However, difficulties such as the equatorially orbiting lower rings and moons of these giant planets would first need to be overcome. This article does not cite any references or sources. ... This article is about the planet. ... For other uses, see Uranus (disambiguation). ... For other uses, see Neptune (disambiguation). ... Helium-3 is a non-radioactive and light isotope of helium. ... A planetary ring is a ring of dust and other small particles orbiting around a planet in a flat disc-shaped region. ...

Pluto could also have an elevator and tether. In recent years physicists have suggested that due to the Pluto and Charon dynamics, it could be possible to link the two planets by a single tether.^{[citation needed]} For other uses, see Pluto (disambiguation). ...

Construction

The construction of a space elevator would be a vast project, requiring advances in engineering, manufacture and physical technology. David Smitherman of NASA has published a paper that identifies "Five Key Technologies for Future Space Elevator Development":^[36] For other uses, see NASA (disambiguation). ...

1. Material for cable (e.g. carbon nanotube and nanotechnology) and tower
2. Tether deployment and control
3. Tall tower construction
4. Electromagnetic propulsion (e.g. magnetic levitation)
5. Space infrastructure and the development of space-based industry and economy

Two different ways to deploy a space elevator have been proposed. The Materials Science Tetrahedron, which often also includes Characterization at the center Materials science or Materials Engineering is an interdisciplinary field involving the properties of matter and its applications to various areas of science and engineering. ... // 3D model of three types of single-walled carbon nanotubes. ... Nanotechnology refers to a field of applied science and technology whose theme is the control of matter on the atomic and molecular scale, generally 100 nanometers or smaller, and the fabrication of devices that lie within that size range. ... Artists conception of satellite with a tether Tether propulsion uses long, strong strings (known as tethers) to change the orbits of spacecraft. ... For many millennia the record holder for worlds tallest structure was clearly defined (see table below. ... Electromagnetic Propulsion using the concepts and applications of electromagnets. ... This article is about magnetic levitation. ... Space-based industry is a blanket term sometimes used to cover a variety of future forms of human activity in outer space, including space mining, space manufacturing, space trade, construction performed in space such as the building of space stations, space burial, and space advertising. ...

Traditional way

One early plan involved lifting the entire mass of the elevator into geosynchronous orbit, and simultaneously lowering one cable downwards towards the Earth's surface while another cable is deployed upwards directly away from the Earth's surface. It has been suggested that this article or section be merged with geostationary orbit. ...

Tidal forces (gravity and centrifugal force) would naturally pull the cables directly towards and directly away from the Earth and keep the elevator balanced around geosynchronous orbit. As the cable is deployed, coriolis forces would pull the upper portion of the cable somewhat to the West and the lower portion of the cable somewhat to the East; this effect can be controlled by varying the deployment speed. Comet Shoemaker-Levy 9 after breaking up under the influence of Jupiters tidal forces. ... This article covers the physics of gravitation. ... In physics, the Coriolis effect is an inertial force first described by Gaspard-Gustave Coriolis, a French scientist, in 1835. ...

However, this approach requires lifting hundreds or even thousands of tons on conventional rockets, an expensive proposition. Hypothetically, such a plan could make extensive use of materials available in space to reduce costs, but this would require considerable space mining and space-based processing of materials, neither of which is currently practical using existing technology. This article is about vehicles powered by rocket engines. ... In astronautics, In-Situ Resource Utilization (ISRU) is the way to describe the use the resources of the planetary body which is explored (Moon, Mars,...) to provide propellant, energy or consumables to the science payload or to the crew which has been deployed there. ... Space mining refers to the future practise of mining asteroids, meteorites, the moon and planets - any natural body beyond the orbit of the Earth. ...

Brad Edwards' proposal

Bradley C. Edwards, former Director of Research for the Institute for Scientific Research (ISR), based in Fairmont, West Virginia proposed that, if nanotubes with sufficient strength could be made in bulk, a space elevator could be built in little more than a decade, rather than the far future. He proposed that a single hair-like 18-metric ton (20 short ton) 'seed' cable be deployed in the traditional way, giving a very lightweight elevator with very little lifting capacity. Then, progressively heavier cables would be pulled up from the ground along it, repeatedly strengthening it until the elevator reaches the required mass and strength. This is much the same technique used to build suspension bridges. Downtown Fairmont and the Monongahela River in 2006 The Marion County Courthouse in Fairmont Fairmont is a city in Marion County, West Virginia, USA. The population was 19,097 at the 2000 census. ... This article is about the metric tonne. ... Look up ton in Wiktionary, the free dictionary. ... For other uses, see Cable (disambiguation). ... For other uses, see Mass (disambiguation). ... Strength of materials is materials science applied to the study of engineering materials and their mechanical behavior in general (such as stress, deformation, strain and stress-strain relations). ... A suspension bridge is a type of bridge where the main load-bearing elements are hung from suspension cables. ...

Although 18 tonnes for a seed cable may sound like a lot, it would actually be very lightweight — the proposed average mass is about 200 grams per kilometer. In comparison, conventional copper telephone wires running to consumer homes weigh about 4 kg/km. For other uses, see Copper (disambiguation). ...

Loop elevator design

This is a less well developed design, but offers some other possibilities.

If the cable provides a useful tensile strength of about 62.5 GPa or above, then it turns out that a constant width cable can reach beyond geosynchronous orbit without breaking under its own weight. The far end can then be turned around and passed back down to the Earth forming a constant width loop, which would be kept spinning to avoid tangling. The two sides of the loop are naturally kept apart by coriolis forces due to the rotation of the Earth and the loop. By increasing the thickness of the cable from the ground a very quick (exponential) build-up of a new elevator may be performed (it helps that no active climbers are needed, and power is applied mechanically.) However, because the loop runs at constant speed, joining and leaving the loop may be somewhat challenging, and the carrying capacity of such a loop is lower than a conventional tapered design.^[37] In physics, the Coriolis effect is an inertial force first described by Gaspard-Gustave Coriolis, a French scientist, in 1835. ...

Failure modes, safety issues and construction difficulties

As with any structure, there are a number of ways in which things could go wrong. A space elevator would present a considerable navigational hazard, both to aircraft and spacecraft. Aircraft could be dealt with by means of simple air-traffic control restrictions, but impacts by space objects (in particular, by meteoroids and micrometeorites) pose a more difficult problem.

Cable strength

The current strength/mass ratio of cables of any construction is inadequate to build a space elevator at the present time. Although carbon nanotubes embedded in the tether would give it enough strength to be practical, nanotubes of sufficient length have not yet been made. 2008 (MMVIII) will be a leap year starting on Tuesday of the Gregorian calendar. ... An electronic device known as a diode can be formed by joining two nanoscale carbon tubes with different electronic properties. ...

Theoretical objections have been raised to manufacturing bulk carbon nanotube structures with strengths approaching that which simple models and microscopic strengths suggest. H. K. D. H. Bhadeshia argues that the presence of defects would significantly reduce the strength actually attainable.^[38]

Satellites

If nothing were done, essentially all satellites with perigees below the top of the elevator would eventually collide with the elevator cable. Twice per day, each orbital plane intersects the elevator, as the rotation of the Earth swings the cable around the equator. Usually the satellite and the cable will not line up. However, except for synchronized orbits, the elevator and satellite will eventually occupy the same place at the same time, almost certainly leading to structural failure of the space elevator and destruction of the satellite. Perigee is the point at which an object in orbit around the Earth makes its closest approach to the Earth. ...

Most active satellites are capable of some degree of orbital maneuvering and could avoid these predictable collisions, but inactive satellites and other orbiting debris would need to be either preemptively removed from orbit by "garbage collectors" or would need to be closely watched and nudged whenever their orbit approaches the elevator. The impulses required would be small, and need be applied only very infrequently; a laser broom system may be sufficient to this task. In addition, Brad Edward's design actually allows the elevator to move out of the way, because the fixing point is at sea and mobile. However, such movements would excite transverse oscillations of the cable. Edwards claims that these oscillations could be controlled so as to ensure that the cable avoids satellites on known paths. A laser broom is a proposed ground-based laser beam-powered propulsion system whose purpose is to sweep space debris out of the path of the International Space Station. ...

Meteoroids and micrometeorites

Meteoroids present a more difficult problem, since they would not be predictable and much less time would be available to detect and track them as they approach Earth. It is likely that a space elevator would still suffer impacts of some kind, no matter how carefully it is guarded. However, most space elevator designs call for the use of multiple parallel cables separated from each other by struts, with sufficient margin of safety that severing just one or two strands still allows the surviving strands to hold the elevator's entire weight while repairs are performed. If the strands are properly arranged, no single impact would be able to sever enough of them to overwhelm the surviving strands. Worlds second largest Meteorite in Culiacan, Mexico A meteorite is a relatively small extra-terrestrial body that reaches the Earths surface. ... A strut is a structural component designed to resist longitudinal compression. ...

Far worse than meteoroids are micrometeorites; tiny high-speed particles found in high concentrations at certain altitudes. Avoiding micrometeorites is essentially impossible, and they will ensure that strands of the elevator are continuously being cut. Most methods designed to deal with this involve a design similar to a hoytether or to a network of strands in a cylindrical or planar arrangement with two or more helical strands. Constructing the cable as a mesh instead of a ribbon helps prevent collateral damage from each micrometeorite impact. A Micrometeoroid (also micrometeorite, micrometeor) is a tiny meteoroid; a small particle of rock from space, usually weighing less than a gram, that poses a threat to space exploration. ... The Hoytether is a trademarked name from the Tethers Unlimited Incorporated [1] for a novel topology for a space elevator cable, consisting of a lattice of strands, arranged in a circular cross-section, and having redundancy to handle potential damage from space debris or micro meteroids. ...

Failure cascade

It is not enough that other fibers be able to take over the load of a failed strand — the system must also survive the immediate, dynamical effects of fiber failure, which generates projectiles aimed at the cable itself. For example, if the cable has a working stress of 50 GPa and a Young's modulus of 1000 GPa, its strain will be 0.05 and its stored elastic energy will be 1/2 × 0.05 × 50 GPa = 1.25×10⁹ joules per cubic meter. Breaking a fiber will result in a pair of de-tensioning waves moving apart at the speed of sound in the fiber, with the fiber segments behind each wave moving at over 1,000 m/s (more than the muzzle velocity of a standard .223 caliber (5.56 mm) r