One of the most restrictive barriers to space travel is cost. It costs a huge amount of money to send a relatively small payload into orbit or beyond(Falcon 9, as of now the lowest cost option, costs approximately $2,700/kg sent into Low Earth Orbit(LEO)). This could be solved by the construction of a space elevator. If properly built, the space elevator could vastly reduce both launch costs, and the emissions produced by space travel.
Even though the tether will still be subject to almost all of the gravitational force that we experience on the surface, if built properly, it will not fall back down due to gravity. This is because centrifugal force (an apparent force actually the result of the change in direction of a moving object) acts outwards, in opposition to gravity. The tether would have a geostationary orbit at the equator, with the tether being perpendicular to the Earth's surface.
The tether would need to be slowly lowered from a satellite already in geostationary orbit, while a counterweight with a tether was also released from the other side of the satellite. To stay in geostationary orbit, the satellite would need to be at the height and speed where gravity and centrifugal force cancel each other out. Therefore, as the cable is lowered, the equilibrium would be disrupted, so another cable with counterweight would need to be released in the opposite direction.
This cable would be placed under extreme tension due to the non-uniform forces acting on it (the force downwards increases as you go down, while the force upwards increases as you go up). This could be minimised by varying the width of the cable along its length, in a tapered fashion, such that the cable is thickest when closest to the satellite, and thinnest when furthest away. This is because the tension in the cable is weaker the further away from the satellite you get, so a less strong cable is required. This would reduce the tension in the cable, as well as the material needed to make it
Unfortunately, the tether would need to be composed of an impossibly strong material so that it did not snap under the extreme tension which it was placed. High-strength high-density materials such as steel would not be suitable, and while high-strength low-density materials such as kevlar would be better, as due to the lower mass, the gravitational and centrifugal forces would be weaker. Nevertheless, the cost of manufacturing the tether out of kevlar would be extremely prohibitive, while the ultimate tensile strength/kg of the material may suffer if it was fashioned into a very thick wire. As a result, this kind of tether wouldn't reduce the cost of spaceflight, even if it was used very many times over a long period of time.
While building this tether isn't feasible currently, it might be possible in the future using carbon nanotubes. The ultimate tensile strength estimates for perfect, defectless carbon nanotubes are in the range of 100-200GPa, which would be enough for a space elevator. Sadly, there are several challenges in the way. Firstly, real carbon nanotubes have a much lower tensile strength, due to defects, and so a cable constructed out of carbon nanotubes wouldn't have as high a tensile strength as suggested by the calculations. In addition, carbon nanotubes are far more expensive than kevlar, so therefore a cable made out of carbon nanotubes wouldn't reduce the cost of space flight either.
Another problem is that the tether would be very vulnerable to space debris. Currently, there are roughly 900,000 pieces of debris with a size of between 1 and 10cm, and 128 million pieces of debris with a size of between 0.1 and 1cm (ESA 2020). The smaller pieces of debris wouldn't significantly damage the tether, but might slightly weaken it over time. The larger pieces of debris would pose a bigger problem, and repeated impacts in the same place (unlikely but still possible) could greatly damage the integrity of the cable, causing it to break. If a break occurred, the section below the break would be pulled down back to Earth by gravity, while the section above would be flung into space by centrifugal force. This scenario would be worst if the cable snapped at the top, as the cable falling back to Earth could cause significant damage. Luckily, this probably wouldn't happen, as the cable increases in width the higher it gets, so even a cable made out of a very strong material like kevlar would be 80m in diameter at the top.
Potentially a greater hazard is the likelihood of a terrorist attack on the base of the tether. As the tether would be very thin at the bottom, a single missile would be capable of snapping it and causing it to leave for space. As a result, the tether would likely be the single most heavily guarded structure in the world, with good reason.
While a space elevator currently couldn't be built on Earth, building a prototype on the Moon is a much more enticing prospect. The Moon rotates more slowly and has lower gravity, so the tension felt by the cable will be much less. In addition, the cable itself will be much smaller. The Moon has abundant fuel reserves, in the form of water which can be split by electrolysis to produce hydrogen and oxygen, which can then be cooled to produce rocket fuel (liquid hydrogen and liquid oxygen). In addition, helium-3 can be mined from the Moon's surface, and then used as fuel for nuclear fusion reactions, to power the electrolysis. The Moon is also abundant in other metals, such as titanium and iron in ilmenite, which can be used to make rockets. The Moon could be our staging post for exploration of the solar system, and costs could be significantly reduced by the creation of a tether using currently available materials (kevlar would be suitable). Furthermore, space debris is very rare near the Moon, so this wouldn't be a problem for our space elevator either.
Overall, building a space elevator on Earth is an enticing prospect that could significantly reduce the cost of spaceflight and of putting satellites in orbit. However, it is not feasible with current technology, and would take advances in the field of materials science to be a serious proposal. Building a tether on the Moon, however, would be a very useful and currently feasible tool for space exploration, and therefore this project should be built soon, even though it would not assist with placing satellites in Earth's orbit.
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