Space elevator

A space elevator for Earth would consist of a cable anchored to the Earth's equator, reaching into space. By attaching a counterweight at the end (or by further extending the cable upward for the same purpose), the center of mass is kept well above the level of geostationary orbit. Inertia ensures that the cable remains stretched taut, countering the gravitational pull downward. Once above the geostationary level, climbers would have weight in the upward direction as the centrifugal force overpowers gravity. (The diagram is to scale. The height of the counterweight varies by design and a typical, workable height is shown.)

A space elevator is a proposed non-rocket spacelaunch structure (a structure designed to transport material from a celestial body's surface into space). Many elevator variants have been suggested, all of which involve travelling along a fixed structure instead of using rocket-powered space launch, most often a cable that reaches from the surface of the Earth on or near the equator to geostationary orbit (GSO) and a counterweight outside of the geostationary orbit.

Discussion of a space elevator dates back to 1895 when Konstantin Tsiolkovsky^[1] proposed a free-standing "Tsiolkovsky Tower" reaching from the surface of Earth to geostationary orbit 35,786 km (22,236 mi) up. Like all buildings, Tsiolkovsky's structure would be under compression, supporting its weight from below. Since 1959, most ideas for space elevators have focused on purely tensile structures, with the weight of the system held up from above. In the tensile concepts, a space tether reaches from a large mass (the counterweight) beyond geostationary orbit to the ground. This structure is held in tension between Earth and the counterweight 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.

While some variants of the space elevator concept are technologically feasible, current technology is not capable of manufacturing tether materials that are sufficiently strong and light to build an Earth-based space elevator of the geostationary orbital tether type. Recent concepts for a space elevator are notable for 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 carbon nanotubes appears great enough to make this possible.^[2] Technology as of 1978 could produce elevators for locations in the solar system with weaker gravitational fields, such as the Moon or Mars.^[3]

For human riders on an Earth-based elevator, adequate protection against radiation would likely need to be provided, depending on the transit time through the Van Allen belts. At the transit times expected for early systems, radiation due to the Van Allen belts would, if unshielded, give a dose well above permitted levels.^[4]

Geostationary orbital tethers

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 36,000 km (22,369 mi) 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. As with all leading-edge engineering projects, 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^{[citation needed]}.

History

Konstantin Tsiolkovsky

Early concepts

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 (22,238 mi) above sea level (geostationary orbit).^[5] 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).

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.

20th century

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.^[6] 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 cable constantly over the same spot on the surface of the Earth. Artsutanov's idea was introduced to the Russian-speaking public in an interview published in the Sunday supplement of Komsomolskaya Pravda in 1960,^[7] but was not available in English until much later. He also proposed tapering the cable thickness so that the stress in the cable was constant—this gives a thin cable at ground level, thickening up towards GSO.

Both the tower and cable ideas were proposed in the quasi-humorous Ariadne column in New Scientist, 24 December 1964.

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.^[8] 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^[9] 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 (90,000 miles, 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.

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,^[10] 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 and also for natural resources mined there to be able to leave for Earth. In David Gerrold's 2000 novel, Jumping Off The Planet, a family excursion up the Ecuador "beanstalk" is actually a child-custody kidnapping. Gerrold's book also examines some of the industrial applications of a mature elevator technology.

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 turn the concept into a reality.^[11] The publication he edited, compiling information from the workshop, "Space Elevators: An Advanced Earth-Space Infrastructure for the New Millennium",^[12] 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 (62,000 mi) 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, Edwards' work 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.^[13][14] 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 (19 million psi) (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 (7.5 million psi).^[15] Multi-walled carbon nanotubes have been measured with tensile strengths up to 63 GPa (9 million psi).^[16]

To speed space elevator development, proponents are planning several competitions, similar to the Ansari X Prize, for relevant technologies.^[17][18] Among them are Elevator:2010, which will organize annual competitions for climbers, ribbons and power-beaming systems, the Robogames Space Elevator Ribbon Climbing competition,^[19] 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.^[20][21] The first European Space Elevator Challenge (EuSEC) to establish a climber structure took place in August 2011.^[22]

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 mi) space elevator, this move will allow it to make money in the short term and conduct research and development into new production methods. The goal was a space elevator launch in 2010."^{[dated info][23]} 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 (2 in) wide and 1 mm (approx. 6 sheets of paper) thick, lifted with balloons.^[24]

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 (0.07 oz), 100% carbon nanotube entry into the competition.^[26] Japan held an international conference in November 2008 to draw up a timetable for building the elevator.^[27]

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.^[28] This has led to a Japanese announcement of intent to build a Space Elevator at a projected price tag of a trillion yen (£5 billion/ $8 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."^[27] In 2011, Google was revealed to be working on plans for a space elevator at its secretive Google X Lab location. ^[29]

Physics of space elevators

Apparent gravitational field

A space elevator cable rotates along with the rotation of the Earth. Objects fastened to the cable will experience upward centrifugal force that opposes some, all, or more than, the downward gravitational force at that point. The higher up the cable, the stronger is the upward centrifugal force and the more it opposes the downward gravity. Eventually it becomes stronger than gravity above the geosynchronous level. Along the length of the cable, this (downward) actual gravity minus the (upward) centrifugal force is called the apparent gravitational field.

The apparent gravitational field can be represented this way:

The downward force of actual gravity decreases with height: $g = -G \cdot M/r^2$

The upward centrifugal force due to the planet's rotation increases with height: $a = \omega^2 \cdot r$

Together, the apparent gravitational field is the sum of the two:

$g = -G \cdot M/r^2 + \omega^2 \cdot r$

where

g is the acceleration of actual gravity or apparent gravity down (negative) or up (positive) along the vertical cable (m s⁻²),

a is the centrifugal acceleration up (positive) along the vertical cable (m s⁻²),

G is the gravitational constant (m³ s⁻² kg⁻¹)

M is the mass of the Earth (kg)

r is the distance from that point to Earth's center (m),

ω is Earth's rotation speed (radian/s).

At some point up the cable, the two terms (downward gravity and upward centrifugal force) equal each other, objects fixed to the cable there have no weight on the cable. This occurs at the level of the stationary orbit. This level (r₁) depends on the mass of the planet and its rotation rate. Setting actual gravity and centrifugal acceleration equal to each other gives:

$r_1 = (G \cdot M/\omega^2)^{1/3}$

On Earth, this level is 35,786 km (22,236 mi) above the surface, the level of geostationary orbit.

Seen from a geosynchronous station, any object dropped off the tether from a point closer to Earth will initially accelerate downward. If dropped from any point above a geosynchronous station, the object would initially accelerate up toward space.

Cable section

Historically, the main technical problem has been considered the ability of the cable to hold up, with tension, the weight of itself below any particular point. The vertical point with the greatest tension on a space elevator cable is at the level of geostationary orbit, 35,786 km (22,236 mi) above the Earth's equator. This means that the cable material combined with its design must be strong enough to hold up the weight of its own mass from the surface up to 35,786 km. By making any cable larger in cross section at this level compared to at the surface, it can better hold up a longer length of itself. For a space elevator cable, an important design factor in addition to the material is how the cross section area tapers down from the maximum at 35,786 km to the minimum at the surface. To maximize strength of the cable compared to its weight, the cross section area will need to be designed in such a way that at any given point, it is proportional to the force it has to withstand. For such an idealized design without climbers attached, without thickening at high space-junk altitudes, etc., the cross-section will follow this differential equation:

$\sigma \cdot dS = g \cdot \rho \cdot S \cdot dr$,

where

g is the acceleration along the radius (m·s⁻²),

S is the cross-area of the cable at any given point r, (m²) and dS its variation (m² as well),

ρ is the density of the material used for the cable (kg·m⁻³).

σ is the stress the cross-section area can bear without yielding (N·m⁻²=kg·m⁻¹·s⁻²), its elastic limit.

The value of g is given by the first equation, which yields:

$\Delta\left[ \ln (S)\right]{}_{r_1}^{r_0} = \rho/\sigma \cdot \Delta\left[ G \cdot M/r + w^2 \cdot r^2/2 \right]{}_{r_1}^{r_0}$,

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: $\Delta\left[ \ln (S)\right] = \rho/\sigma \cdot g_0 \cdot r_0 \cdot ( 1 + x/2 - 3/2 \cdot x^{1/3} )$, or

$S_0 = S_1.e^{\rho/\sigma \cdot g_0 \cdot r_0 \cdot ( 1 + x/2 - 3/2 \cdot x^{1/3} )}$

where $x = \omega^2 \cdot r_0/g_0$ is the ratio between the centrifugal force on the equator and the gravitational force.

Cable material

The second technical problem is that the g₀ r₀ factor is quite large. Since its influence on the maximal cross-section is exponential, one needs to find materials where σ will be large enough to cancel our gravity. On Earth, we have:

$g_0 \cdot r_0 = 62.5 \cdot 10^6~m^2s^{-2}$ (or Joules per kg)

$\rho \approx 3 \cdot 10^3~kg~m^{-3}$ for most solid materials, so that σ needs to be:

$\sigma \approx 300 \cdot 10^9~kg~m^{-1}s^{-2}.$

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 un-tapered cylindrical cable at which it will break 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

$\Delta\left[ \ln (S)\right] = \rho/\sigma \cdot g_0 \cdot r_0 \cdot ( 1 + x/2 - 3/2 \cdot x^{1/3} )$, where $x = w^2 \cdot r_0/g_0.$

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:

$\sigma = \rho \cdot r_0 \cdot g_0.$

If the material can support a free breaking length of only one tenth this, the section needed at a geosynchronous orbit will be e¹⁰ times the ground section, which is more than a hundredfold in diameter.

Structure

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

There are a variety of space elevator designs. Almost every design includes a base station, a cable, climbers, and a counterweight. Earth's rotation creates upward centrifugal force on the counterweight. The counterweight is held down by the cable while the cable is held up and taut by the counterweight. The base station anchors the whole system to the surface of the Earth. Climbers climb up and down the cable with cargo.

Base station

The base station designs typically fall into two categories—mobile and stationary. Mobile stations are typically large oceangoing vessels.^[30] Stationary platforms would generally be located in high-altitude locations, such as on top of mountains, or even potentially on high towers.^[6]

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.

Cable

Carbon nanotubes are one of the candidates for a cable material

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,^[31] 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/density ratio. For example, the Edwards space elevator design assumes a cable material with a specific strength of at least 100,000 kN/(kg/m).^[32] This value takes into consideration the entire weight of the space elevator. A space elevator would need a material capable of sustaining a length of 4,960 kilometers (3,080 mi) of its own weight at sea level to reach a geostationary altitude of 35,786 km (22,236 mi) without tapering and without breaking.^[33] Therefore, a material with very high strength and lightness is needed.

For comparison, metals like titanium, steel or aluminium alloys have breaking lengths of only 20–30 km. Modern fibre materials such as kevlar, fibreglass and carbon/graphite fibre have breaking lengths of 100–400 km. Quartz fibers have an advantage that they can be drawn to a length of hundreds of kilometers^[34] even with the present-day technology. Nanoengineered materials such as carbon nanotubes and, more recently discovered, graphene ribbons (perfect two-dimensional sheets of carbon) are expected to have breaking lengths of 5000–6000 km at sea level, and also are able to conduct electrical power.

Carbon is such a good candidate material (for high specific strength) because, as only the 6th element in the periodic table, it has very few of the nucleons which contribute most of the dead weight of any material (whereas most of the interatomic bonding forces are contributed by only the outer few electrons); the challenge now remains to extend to macroscopic sizes the production of such material that are still perfect on the microscopic scale (as microscopic defects are most responsible for material weakness). The current (2009) carbon nanotube technology allows growing tubes up to a few tens of centimeters only.^[35]

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

Climbers

A conceptual drawing of a space elevator climbing through the clouds.

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.

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.^{[citation needed]}

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 force). 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 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^{[citation needed]}. Space elevators and their loads will be designed so that the center of mass is always well-enough above the level of geostationary orbit^[36] to hold up the whole system. 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.^[37]

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 design constraint will be the ascending speed of the climber. As geosynchronous orbit is at 35,786 km (22,236 mi), assuming the climber can reach the speed of a very fast car or train of 300 km/h (180 mph) it will take 5 days to climb to geosynchronous orbit.

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.

Various methods have been proposed to get that energy to the climber:

• Transfer the energy to the climber through wireless energy transfer while it is climbing.
• Transfer the energy to the climber through some material structure while it is climbing.
• Store the energy in the climber before it starts – requires an extremely high specific energy such as nuclear energy.
• Solar power – power compared to the weight of panels limits the speed of climb.^[38]

Wireless energy transfer such as laser power beaming is currently considered the most likely method. Using megawatt powered free electron or solid state lasers in combination with adaptive mirrors approximately 10 m (33 ft) wide and a photovoltaic array on the climber tuned to the laser frequency for efficiency.^[30] For climber designs powered by power beaming, this efficiency is an important design goal. Unused energy must be re-radiated away with heat-dissipation systems, which add to weight.

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.^[27]

Various mechanical means of applying power have also been proposed; such as moving, looped or vibrating cables.^{[citation needed]}

Counterweight

Several solutions have been proposed to act as a counterweight:

• a heavy, captured asteroid;^[5]
• a space dock, space station or spaceport positioned past geostationary orbit; or
• a further upward extension of the cable itself so that the net upward pull is the same as an equivalent counterweight;
• parked spent climbers that had been used to thicken the cable during construction, other junk, and material lifted up the cable for the purpose of increasing the counterweight.^[39]

Extending the cable has the advantage of some 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. Its disadvantage is the need to produce greater amounts of cable material as opposed to using anything that has mass.

Alternative concepts

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—62 mi), they are unlikely to reach geostationary orbit. The concept of a Tsiolkovsky tower combined with a classic space elevator cable has been suggested.^[6]

A mini version^[40] of the Space Elevator to access near-space altitudes of 20 km (12 mi) has been proposed by Canadian researchers. The structure would be pneumatically supported and free standing with control systems guiding the structure's center of mass. Proposed uses include tourism and commerce, communications, wind generation and low-cost space launch.^[41]

Other alternatives to a space elevator include an orbital ring, a pneumatic space tower,^[42] a space fountain, a launch loop, a Skyhook, a space tether, a space hoist and the SpaceShaft.^[43]

Launching into deep space

An object attached to a space elevator at a radius of approximately 53,100 km will be at escape velocity when released. Transfer orbits to the L1 and L2 Lagrangian points can be attained by release at 50,630 and 51,240 km, respectively, and transfer to lunar orbit from 50,960 km.^[44]

The velocities that might be attained at the end of Pearson's 144,000 km (89,000 mi) cable can be determined. The tangential velocity is 10.93 kilometers per second (6.79 mi/s), 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.^[45]

Extraterrestrial elevators

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.^[46] 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.^[47] However, building a Martian elevator would be complicated by the Martian moon Phobos, which is in a low orbit and intersects the Equator regularly (twice every orbital period of 11 h 6 min).^{[original research?]}

A lunar space elevator can possibly be built with currently available technology about 50,000 kilometers (31,000 mi) long extending through the Earth-Moon L1 point from an anchor point near the center of the visible part of Earth's moon.^[48] However, the lack of an atmosphere allows for other, perhaps better, alternatives to rockets, such as mass driver systems.

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.^[48]

Rapidly spinning asteroids or moons could use cables to eject materials to convenient points, such as Earth orbits;^{[citation needed]} or conversely, to eject materials 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^{[citation needed]} 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^[49] and described very succinctly on the Island One website as a "Tapered Sling".^[50]

A space elevator using presently available engineering materials could be constructed between mutually tidally locked worlds, such as Pluto and Charon or the components of binary asteroid Antiope, with no terminus disconnect, according to Francis Graham of Kent State University.^[51] However, spooled variable lengths of cable must be used due to ellipticity of the orbits.

Construction

Main article: Space elevator construction

The construction of a space elevator is considered to be a large project. Like other historical large projects it entails technical risk: some advances in engineering, manufacturing and physical technology are required. Once a first space elevator is built, the second one and all others would have the use of the previous ones to assist in construction, making their costs considerably cheaper. Such follow-on space elevators would also benefit from the great reduction in technical risk achieved by the construction of the first space elevator.

Construction is conceived as the deployment of a long cable from a large spool. The spool is initially parked in a geostationary orbit above the planned anchor point. When a long cable is dropped "down" (toward Earth), it must be balanced by balancing mass being dropped "up" (away from Earth) for the whole system to remain on the geosynchronous orbit. Some designs imagine the balancing mass being another cable (with counterweight) extending upward, other designs elevate the spool itself as the main cable is paid out. When the lower end of the cable is so long as to reach the Earth, it can be anchored at some place. Once anchored, the center of mass is elevated upward more (by adding mass at the upper end or by paying out more cable). This adds more tension to the whole cable, which can then be used as an elevator cable.

Safety issues and construction challenges

Main article: Space elevator safety

Depending on transit times through the Van Allen radiation belts passengers will need to be protected from radiation by shielding, which adds mass to the climber and decreases payload. For early systems, transit times are expected to be long enough where, if unshielded, total exposure would be above levels considered safe.^[4]

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.^[30]

Impacts by space objects such as meteoroids, micrometeorites and orbiting man-made debris, pose another design constraint on the cable. A cable would need to be designed to maneuver out of the way of debris, or absorb impacts of small debris without breaking.

Economics

Main article: Space elevator economics

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.^[52] Current proposals envision payload prices starting as low as $100 per pound ($220 per kilogram),^[53] similar to the $5–$300/kg estimates of the Launch loop, but higher than the $310/ton to 500 km orbit quoted^[54] 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 percent cost advantage and could potentially control all space activities."^[55]

See also

	Spaceflight portal
	Science portal

• Elevator:2010 – a space elevator prize competitions
• Lunar space elevator for the moon variant
• Space elevator construction discusses alternative construction methods of a space elevator.
• Space elevator economics discusses capital and maintenance costs of a space elevator.
• Space elevator safety discusses safety aspects of space elevator construction and operation.
• Space elevators in fiction
• Tether propulsion – for other transportation methods using long cables

• Non-rocket spacelaunch:
  • Launch loop – a hypervelocity belt system that forms a launch track at 80 km
  • Lightcraft – an alternative method for moving materials or people
  • Space gun or StarTram – among methods for launching materials
  • Space fountain – very tall structures using fast moving masses to hold it up
  • SpaceShaft – A atmospherically buoyant spar that could reach up to LEO and provide super-heavy lifting capacity.

References

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2. ^ Bradley C. Edwards IAC-04-IAA.3.8.2.01. THE SPACE ELEVATOR DEVELOPMENT PROGRAM
3. ^ Non-Synchronous Orbital Skyhooks for the Moon and Mars with Conventional Materials Hans Moravec 1978
4. ^ ^{a b} "Space elevators: 'First floor, deadly radiation!'". New Scientist. Reed Business Information Ltd.. 13 November 2006. http://www.newscientist.com/article/dn10520. Retrieved Jan 2, 2010. 
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15. ^ Yu, Min-Feng; Files, Bradley S.; Arepalli, Sivaram; Ruoff, Rodney S. (2000). "Tensile Loading of Ropes of Single Wall Carbon Nanotubes and their Mechanical Properties". Physical Review Letters 84 (24): 5552–5555. Bibcode 2000PhRvL..84.5552Y. doi:10.1103/PhysRevLett.84.5552. PMID 10990992. 
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22. ^ "What's the European Space Elevator Challenge?". European Space Elevator Challenge. http://eusec.warr.de/?eusec. Retrieved 2011-04-21. 
23. ^ "Space Elevator Group to Manufacture Nanotubes". Universe Today. 2005. http://www.universetoday.com/am/publish/liftport_manufacture_nanotubes.html?2742005. Retrieved 2006-03-05. 
24. ^ Groshong, Kimm (2006-02-15). "Space-elevator tether climbs a mile high". NewScientist.com (New Scientist). http://www.newscientistspace.com/article/dn8725.html. Retrieved 2006-03-05. 
25. ^ Elevator:2010 – The Space Elevator Challenge. spaceward.org
26. ^ Spaceward Games 2007. The Spaceward Foundation
27. ^ ^{a b c} Lewis, Leo (2008-09-22). "Japan hopes to turn sci-fi into reality with elevator to the stars". The Times (London). http://www.timesonline.co.uk/tol/news/uk/science/article4799369.ece. Retrieved 2010-05-23.  Lewis, Leo; News International Group; accessed 2008-09-22.
28. ^ "Leaving the Planet by Space Elevator". http://www.leavingtheplanet.com/.  Edwards, Bradley C. and Westling, Eric A. and Ragan, Philip; Leasown Pty Ltd.; accessed 2008-09-26.
29. ^ http://www.nytimes.com/2011/11/14/technology/at-google-x-a-top-secret-lab-dreaming-up-the-future.html
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32. ^ "The Space Elevator: Phase I Study" by Bradley Carl Edwards
33. ^ This 4,960 km "escape length" (calculated by Arthur C. Clarke in 1979) is much shorter than the actual distance spanned because centrifugal forces increase (and gravity decreases) dramatically with height: Clarke, A.C. (1979). "The space elevator: 'thought experiment', or key to the universe?". http://www.islandone.org/LEOBiblio/CLARK2.HTM. 
34. ^ World's Longest Laser – 270 Km Long – Created ScienceDaily, December 16, 2009
35. ^ Wang, X.; Li, Q.; Xie, J.; Jin, Z.; Wang, J.; Li, Y.; Jiang, K.; Fan, S. (2009). "Fabrication of Ultralong and Electrically Uniform Single-Walled Carbon Nanotubes on Clean Substrates". Nano Letters 9 (9): 3137–3141. Bibcode 2009NanoL...9.3137W. doi:10.1021/nl901260b. PMID 19650638. 
36. ^ "Why the Space Elevator's Center of Mass is not at GEO" by Blaise Gassend. Gassend.com. Retrieved on 2011-09-30.
37. ^ Cohen, Stephen S.; Misra, Arun K. (2009). "The effect of climber transit on the space elevator dynamics". Acta Astronautica 64 (5–6): 538–553. doi:10.1016/j.actaastro.2008.10.003. 
38. ^ Edwards. "NIAC Space Elevator Report – Chapter 4: Power Beaming". NASA. Archived from the original on 2007-10-13. http://web.archive.org/web/20071013160456/http://isr.us/Downloads/niac_pdf/chapter4.html. "Alternatives that have been suggested include running power up the cable, solar or nuclear power onboard and using the cable's movement in the environment's electromagnetic field. None of these methods are feasible on further examination due to efficiency or mass considerations. Another alternative is to run two cables, for carrying power (a high-voltage positive and a negative line) and each capable of holding the counterweight (system redundancy)." 
39. ^ Edwards BC, Westling EA. The Space Elevator: A Revolutionary Earth-to-Space Transportation System. San Francisco, USA: Spageo Inc.; 2002. ISBN 0-9726045-0-2.
40. ^ Boucher, Marc. (2009-09-01) Canadian Mini Space Elevator Paper Available – The Space Elevator Reference. Spaceelevator.com. Retrieved on 2011-09-30.
41. ^ Quine, B.M.; Seth, R.K.; Zhu, Z.H. (2009). "A free-standing space elevator structure: A practical alternative to the space tether". Acta Astronautica 65 (3–4): 365. Bibcode 2009AcAau..65..365Q. doi:10.1016/j.actaastro.2009.02.018. http://pi.library.yorku.ca/dspace/bitstream/handle/10315/2587/AA_3369_Quine_Space_Elevator_Final_2009.pdf. 
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44. ^ Kilian A. Engel. "IAC-04-IAA.3.8.3.04 Lunar transportation scenarios utilising the space elevator". www.spaceelevator.com. http://www.spaceelevator.com/docs/iac-2004/iac-04-iaa.3.8.3.04.engel.pdf. 
45. ^ P. K. Aravind (February 2007). "The physics of the space elevator". American Journal of Physics (American Association of Physics Teachers) 45 (2): 125. Bibcode 2007AmJPh..75..125A. doi:10.1119/1.2404957. 
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47. ^ SPACE ELEVATORS Robert L. Forward Hans P. Moravec March 22, 1980 Copyright 1980 Dr. Robert L. Forward and Hans P. Moravec "Interestingly enough, they are already more than strong enough for constructing skyhooks on the moon and Mars."
48. ^ ^{a b} Pearson, Jerome; Eugene Levin, John Oldson and Harry Wykes (2005). "Lunar Space Elevators for Cislunar Space Development Phase I Final Technical Report" (PDF). http://www.niac.usra.edu/files/studies/final_report/1032Pearson.pdf. 
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51. ^ Graham FG "Preliminary Design of a Cable Spacecraft Connecting Mutually Tidally Locked Planetary Bodies" AIAA 2009-4906, 45th Joint Propulsion Conference.
52. ^ "Delayed countdown". Fultron Corporation. The Information Company Pvt Ltd. 18 October 2002. http://www.domain-b.com/companies/companies_f/futron_corporation/20021018_countdown.html. Retrieved June 3, 2009. 
53. ^ The Spaceward Foundation. "The Space Elevator FAQ". Mountain View, CA. http://www.spaceward.org/elevator-faq. Retrieved June 3, 2009. 
54. ^ Pournelle, Jerry (23 April 2003). "Friday's VIEW post from the 2004 Space Access Conference". http://www.jerrypournelle.com/archives2/archives2view/view306.html#Friday. Retrieved Jan 1, 2010. 
55. ^ Ramadge, Andrew; Schneider, Kate (17 November 2008). "Race on to build world's first space elevator". http://www.news.com.au/technology/story/0,25642,24662622-5014239,00.html. Retrieved June 3, 2009. ^{[dead link]}

Further reading

• Edwards BC, Ragan P. "Leaving The Planet By Space Elevator" Seattle, USA: Lulu; 2006. ISBN 978-1-4303-0006-9 See Leaving The Planet
• Edwards BC, Westling EA. The Space Elevator: A Revolutionary Earth-to-Space Transportation System. San Francisco, USA: Spageo Inc.; 2002. ISBN 0-9726045-0-2.
• Space Elevators – An Advanced Earth-Space Infrastructure for the New Millennium [PDF]. A conference publication based on findings from the Advanced Space Infrastructure Workshop on Geostationary Orbiting Tether "Space Elevator" Concepts, held in 1999 at the NASA Marshall Space Flight Center, Huntsville, Alabama. Compiled by D.V. Smitherman, Jr., published August 2000.
• "The Political Economy of Very Large Space Projects" HTML PDF, John Hickman, Ph.D. Journal of Evolution and Technology Vol. 4 – November 1999.
• The Space Elevator NIAC report by Dr. Bradley C. Edwards
• A Hoist to the Heavens By Bradley Carl Edwards
• Ziemelis K. (2001) "Going up". In New Scientist 2289: 24–27. Republished in SpaceRef. Title page: "The great space elevator: the dream machine that will turn us all into astronauts."
• The Space Elevator Comes Closer to Reality. An overview by Leonard David of space.com, published 27 March 2002.
• Krishnaswamy, Sridhar. Stress Analysis — The Orbital Tower (PDF)
• LiftPort's Roadmap for Elevator To Space SE Roadmap (PDF)
• Space Elevators Face Wobble Problem: New Scientist

• Peter Swan & Cathy Swan, "Space Elevator Systems Architecture." Lulu.com 2007. isbn 978-1-4303-1405-9 See ref. 555344 at www.lulu.com

External links

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• The Space Elevator Reference
• Space Elevator Engineering-Development wiki
• Audacious & Outrageous: Space Elevators
• Ing-Math.Net (Germany) – Ing-Math.Net (German Max-Born Space Elevator Team 2006) (German)
• Project of the Scientific Workgroup for Rocketry and Spaceflight(WARR) (German)
• The Economist: Waiting For The Space Elevator (June 8, 2006 – subscription required)
• CBC Radio Quirks and Quarks November 3, 2001 Riding the Space Elevator
• Times of London Online: Going up ... and the next floor is outer space
• The Space Elevator: 'Thought Experiment', or Key to the Universe?. By Sir Arthur C. Clarke. Address to the XXXth International Astronautical Congress, Munich, 20 September 1979.