A space elevator is a proposed structure designed to transport material from a celestial body's surface into space. Many variants have been proposed, all of which involve traveling along a fixed structure instead of using rocket powered space launch. The concept most often refers to a structure that reaches from the surface of the Earth on or near the Equator to geostationary orbit (GSO) and a counter-mass beyond.
The concept of a space elevator dates back to 1895 when Konstantin Tsiolkovsky proposed a free-standing "Tsiolkovsky" tower reaching from the surface of Earth to geostationary orbit. Most recent discussions focus on tensile structures (specifically, tethers) reaching from geostationary orbit to the ground. This structure would be held in tension between Earth and the counterweight in space like a guitar string held taut. Space elevators have also sometimes been referred to as beanstalks, space bridges, space lifts, space ladders, skyhooks, orbital towers, or orbital elevators.
Current technology is not capable of manufacturing practical engineering materials that are sufficiently strong and light to build an Earth-based space elevator. The primary issue is that the total mass of conventional materials needed to construct such a structure would be far too great to be economical. Recent conceptualizations for a space elevator are notable in their plans to use carbon nanotube or boron nitride nanotube based materials as the tensile element in the tether design, since the measured strength of microscopic carbon nanotubes appears great enough to make this theoretically possible. Technology as of 1978 could produce elevators for locations in the solar system with weaker gravitational fields, such as the Moon or Mars.
A further issue is that for human riders on an Earth-based elevator, space radiation due to the Van Allen belts would give a dose well above permitted levels. This would not be an issue for most types of cargo however.
This concept, also called an orbital space elevator, geostationary 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).
Construction would be a large project: the minimum length of an Earth-based space elevator is well over 38,000km long. The 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. Materials currently available do 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, and there are problems regarding feasibility that have yet to be addressed. Nevertheless, the LiftPort Group stated in 2002 that by developing the technology, the first space elevator could be operational by 2014.
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 geostationary orbit (i.e. the castle would remain over the same spot on Earth's surface).
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 geostationary orbit. Unlike more recent concepts for space elevators, Tsiolkovsky's (conceptual) tower was a compression structure, rather than a tension (or "tether") structure.
Building a compression structure from the ground up proved an unrealistic task as there was no material in existence with enough compressive strength to support its own weight under such conditions. In 1959 another Russian scientist, Yuri N. Artsutanov, suggested a more feasible proposal. Artsutanov suggested using a geostationary satellite as the base from which to deploy the structure downward. By using a counterweight, a cable would be lowered from geostationary 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 in 1960, 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 GSO.
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. 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.
In 1975 an American scientist, Jerome Pearson, reinvented the concept yet again, publishing his analysis in the journal Acta Astronautica. He designed a tapered cross section that would be better suited to building the elevator. The completed cable would be thickest at the geostationary 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 centripetal 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.
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, 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.
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. In Kim Stanley Robinson's 1993 novel Red Mars, colonists build a space elevator on Mars that allows both for more colonists to arrive on Mars and also for natural resources mined on Mars to be able to leave Mars for Earth.
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. The publication he edited, compiling information from the workshop, "Space Elevators: An Advanced Earth-Space Infrastructure for the New Millennium", provides an introduction to the state of the technology at the time, and summarizes the findings.
Another American scientist, Bradley C. Edwards, suggested creating a 100,000 km long paper-thin ribbon using a carbon nanotube composite material. He chose a ribbon type structure rather than a cable because that structure might 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. The largest holdup to Edwards' proposed design is the technological limit 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. Multi-walled carbon nanotubes have been measured with tensile strengths up to 63 GPa.
In order to speed development of space elevators, proponents are planning several competitions, similar to the Ansari X Prize, for relevant technologies. Among them are Elevator:2010 which will organize annual competitions for climbers, ribbons and power-beaming systems, the Robolympics Space Elevator Ribbon Climbing competition, 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.
In 2005, "the LiftPort Group of space elevator companies 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. The space elevator is proposed to launch in 2010." 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.
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. No teams won the competition, but a team from MIT entered the first 2-gram, 100% carbon nanotube entry into the competition. Japan held an international conference in November of 2008 to draw up a timetable for building the elevator.
In 2008 the book "Leaving the Planet by Space Elevator", by Dr. Brad Edwards and Philip Ragan, was published in Japanese and entered the Japanese best seller list. This has led to a Japanese announcement of intent to build a Space Elevator at a projected price tag of £5 billion. In a report by Leo Lewis, Tokyo correspondent of The Times newspaper in England, plans by Shuichi Ono, chairman of the Japan Space Elevator Association, are unveiled. Lewis says: "Japan is increasingly confident that its sprawling academic and industrial base can solve those [construction] issues, and has even put the astonishingly low price tag of a trillion yen (£5 billion/ $8 billion) on building the elevator. Japan is renowned as a global leader in the precision engineering and high-quality material production without which the idea could never be possible."
In the rotating coordinate system whose origin is at Earth's center and turning with Earth's daily revolution, the acceleration of any static point in the equator's plane is:
The ground acceleration g0 at radius r0 is given by:
At some point r1 above the equator line, the two terms cancel out and provide a geosynchronous trajectory:
The same holds of course for any planet or satellite.
Seen from a geosynchronous station, any point closer from Earth will be accelerated downward, and any point above that would be accelerated toward space. If a long cable is dropped "down" (toward Earth), it must of course be properly balanced by a cable being dropped "up" (away from Earth), possibly with some mass at its remote end, for the whole system to remain on the geosynchronous orbit. When the downward one is so long as to reach the Earth, it can be anchored at some place. Once anchored, if more mass is added at the remote end, it will add a tension to the whole cable, which can then be used as an elevator cable.
The main technical problem is the long cable's own weight. The cable material combined with its design must be strong enough to hold up 35000 km of itself. The main design factor other than the material is the taper ratio, that is, the ratio and taper rate of the cross sectional area of the cable as it goes from GEO to ground level. The solution is to build it in such a way that at any given point, its cross section area is proportional to the force it has to withstand, that is, the section must follow the following differential equation:
The value of g is given by the first equation, which yields:
the variation being taken between r1 (geostationary) and r0 (ground).
It turns out that between these two points, this quantity can be expressed simply as: , or
where is the ratio between the centrifuge force on the equator and the gravitational force.
Thus, the factor which has the main influence is g0 r0, the combination of the planet's radius and its surface gravity. The rotational speed is slightly influential, but only as a corrective factor. For Earth, it reduces the strength needed by about one third.
The second technical problem is that the g0 r0 factor is quite large. Since its influence on the maximal cross-section is exponential, one need to find materials where σ will be large enough to cancel our gravity. On Earth, we have:
This corresponds to a cable capable of sustaining 30 tons with a cross-section of one square millimeter, under Earth's gravity.
The free breaking length can be used to compare materials: it is the length of a cylindrical cable at which it will split under its own weight (under constant gravity). For a given material, that length is σ/ρ/g0. The free breaking length needed is given by the equation
If one does not take into account the x factor (which reduces the strength needed by about 30%), this equation also says that the section ratio equals e (exponential one) when:
In other words, the free breaking length is approximately equal to the planet's radius under its own gravity. Since the section ratio varies exponentially, the free breaking length must be at least of that order of magnitude. If the material is only ten times less resilient, the section needed at a geosynchronous orbit will be e10 times the ground section, which is more than a hundredfold in diameter, which is practically impossible.
The centrifugal force of earth's rotation is the main principle behind the elevator. As the earth rotates, the centrifugal force tends to align the nanotube in a stretched manner. There are a variety of tether designs. Almost every design includes a base station, a cable, climbers, and a counterweight.
The base station designs typically fall into two categories—mobile and stationary. Mobile stations are typically large oceangoing vessels,. Stationary platforms would generally be located in high-altitude locations, such as on top of mountains, or even potentially on high towers.
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 (no more than a few kilometers), the cable thickness could be reduced over its entire length, significantly reducing the total weight.
A space elevator cable must 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 a 1998 report, NASA researchers noted that "maximum stress [on a space elevator cable] is at geosynchronous altitude so the cable must be thickest there and taper exponentially as it approaches Earth. Any potential material may be characterized by the taper factor – the ratio between the cable's radius at geosynchronous altitude and at the Earth's surface."
The cable must be made of a material with a large tensile strength/mass ratio. For example, the Edwards space elevator design assumes a cable material with a specific strength of at least 100,000 kN·m/kg. This value is consideration of the entire weight of the space elevator. A space elevator would need a material capable of sustaining 4,960 kilometers of its own weight at sea level to reach a geostationary altitude of 36,000 km without tapering. This is at least necessary value, and about 50,000 kN·m/kg if it shows by specific strength. Therefore, the material with very high strength and lightness is needed.
Carbon nanotubes' theoretical tensile strength has been estimated between 140 and 177 GPa depending on their geometry (chirality) and its measured tensile strength varies in the range 11–150 GPa, however only on a microscopic scale. The current technology does not allow growing tubes longer than a few tens of centimeters; this limit can be overcome by spinning nanotubes into a yarn, but at the price of significantly lowering the cable strength.
The density of carbon nanotubes depends greatly on their packing and can be estimated as 1.3 g/cm3. Therefore, necessary tensile strength is 65–130 GPa in the density. By comparison, most steel has a tensile strength of under 2 GPa, and the strongest steel resists no more than 5.5 GPa. The much lighter material Kevlar has a tensile strength of 2.6–4.1 GPa, while quartz fibers can reach 20 GPa. Quartz fibers have an advantage that they can be drawn to a length of hundreds kilometers (270 km) even with the present-day technology.
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.
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.
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.
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 geostationary 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. 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 force) and thus the climber "drags" on the cable.
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 geostationary orbit 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.
It has also been proposed to use a second cable attached to a platform to lift payload up the main cable, since the lifting device would not have to deal with its own weight against Earth's gravity. Out of the many proposed theories, powering any lifting device also continues to present a challenge.
Another problem will be the ascending speed of the climber. The climber has to drag itself along the cable, so there will always be a friction by design. The current speed of the climbers at the space elevator games is at 2 m/s  and the next goal is 5 m/s (= 18 km/h). As geosynchronous orbit is at 35,786 km it would take 83 days to reach that altitude. Assuming the climber can reach the speed of a very fast car or train of 300 km/h it still would take 5 days to climb to geosynchronous orbit.
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.
All proposals to get that energy to the climber fall into 3 categories:
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.
The proposed method 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. 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.
Yoshio Aoki, a professor of precision machinery engineering at Nihon University and director of the Japan Space Elevator Association, suggested including a second cable and using the conductivity of carbon nanotubes to provide power.
Various mechanical means of applying power have also been proposed; such as moving, looped or vibrating cables.
Several solutions have been proposed to act as a counterweight:
The third 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.
Additionally, Brad Edwards has proposed that initially elevators would be up-only, and that the elevator cars that are used to thicken the cable could simply be parked at the top of the cable and act as a counterweight.
Many different types of structures for accessing space have been suggested. As of 2004, concepts using geostationary tethers seem to be the only space elevator concept that is the subject of active research and commercial interest in space.
The original concept envisioned by Tsiolkovsky was a compression structure, a concept similar to an aerial mast. While such structures might reach the agreed altitude for space (100 km), they are unlikely to reach geostationary orbit (35,786 km). The concept of a Tsiolkovsky tower combined with a classic space elevator cable has been suggested. Other alternatives to a space elevator include an orbital ring, a pneumatic space tower  ,a space fountain, a launch loop, a Skyhook, a space tether, and a space hoist.
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 at least as far out as Jupiter. Once at Jupiter a gravitational assist maneuver permits solar escape velocity to be reached.
A space elevator could also be constructed on 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. Current materials are already sufficiently strong 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 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.
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. 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 and described very succinctly on the Island One website as a "Tapered Sling"
The construction of a space elevator would be a vast project requiring advances in engineering, manufacturing, and physical technology.
A yet-unsolved safety hazard is heavy radiation exposure to passengers that would give a total exposure well above permitted levels..
A space elevator would present a navigational hazard, both to aircraft and spacecraft. Aircraft could be diverted by air-traffic control restrictions. All objects in stable orbits that have perigee below the maximum altitude of the cable that are not synchronous with the cable will impact the cable eventually, unless avoiding action is taken. For spacecraft one potential solution proposed by Edwards is to use a movable anchor (a sea anchor) to allow the tether to "dodge" any space debris large enough to track.
Impacts by space objects such as meteoroids, micrometeorites and orbiting man-made debris, pose a more difficult problem, because the potential of a strand break to cause a failure cascade is, according to Tom Nugent, the Research Director of LiftPort Inc., "A potential show-stopper for construction of the space elevator [that] has not yet been adequately addressed." .
With a space elevator, materials might be sent into orbit at a fraction of the current cost. As of 2000, conventional rocket designs cost about $11,000 per pound ($25,000 per kilogram) for transfer to geostationary orbit. Current proposals envision payload prices starting as low as 100$ per pound ($220 per kilogram), similar to the $5-$300/kg estimates of the Launch loop, although nowhere near the $310/ton to 500km orbit quoted to Dr. Jerry Pournelle for an orbital airship system.
Philip Ragan, co-author of the book "Leaving the Planet by Space Elevator", states that "The first country to deploy a space elevator will have a 95 per cent cost advantage and could potentially control all space activities." 
[Isaa66] Isaacs, J. D., A. C. Vine, H. Bradner & G. E. Bachus (1966) ‘Satellite Elongation into a True “Sky-Hook”' Science 151: 682-683.