This is the space elevator idea. Steel is not strong enough for Earth. Though it could work to lower a space elevator to the Moon. The thing is, steel, titanium etc can support 20 to 30 of kilometers of its own weight in an untapered cable (can go up higher if the cable starts very wide and tapers), but not the thousands of kilometers.
For that you need carbon nanofibres, which are just strong enough - but with no safety margin, and in any case can only be used to make tiny, microscopic even, sections - certainly can't yet be made into a long cable.
See the wikipedia entry: Space elevator -cable
You can reduce the required strength of the material with a tapered space elevator - but that also increases its total mass.
For details, looking at various materials that have been made so far, and to see how close or far we are from having the materials needed, at various tapers, see
The Spaceward Foundation - When
The details are pretty well worked out, if we had a strong enough material which we may have in a few decades. You'd need a counterweight to keep the cable stretched and the cable would go beyond geostationary orbit.
It would then be very easy to go into space. The gravity goes down slowly as you go up the cable, is zero at geostationary - and then you get the centrifugal effect pushing you away from the Earth after that.
Indeed without even doing that, just releasing them at various points beyond geostationary, they have the delta v needed to go to various places - either the moon, or elsewhere in the solar system - just release a spaceship from the end of the tether and it has enough delta v to go to Jupiter without need to use any rocket fuel at all to do it Space elevator - launching into deep space
That's for the future as we don't have the materials to do it.
But you can do a space tether from the Moon with existing materials. Best way is to do it from the center of the near side of the Moon going up through the L1 position towards the Earth. You could build that out of kevlar for instance, though the authors take as their reference material a similar stronger material called M5 fiber
Here is the paper about the lunar elevator design Lunar space elevators for cis-lunar space development.
It is something you could, at least according to the author of the paper, do within the budget of a return of humans to the Moon, and could launch tens of thousands of tons of material from the lunar surface which you could then use e.g. to build settlements in space or whatever, Might be a better way of doing that than the rail guns of the Stanford Torus design.
The LiftPort Group have plans to actually create this lunar elevator. They did a successful Kickstarter project as an early phase of their project. Space Elevator Science - Climb to the Sky - A Tethered Tower. Here is their page about it Lunar Elevator | LiftPort Group
LiftPort plans to build space elevator on the Moon by 2020
You can also use elevators for launching materials from rapidly spinning asteroid. So if your asteroid was rotating quickly enough, you could attach a tether to it, and use that to launch the materials to the Earth. So rather than move the asteroid, and rather than have rockets shuttling back and forth, just use a tether to launch the materials you mine to Earth or anywhere else in the solar system you need it.
You can also use a similar system for diverting asteroids - if we have an asteroid that's projected to hit the Earth, and it's spinning, as most do, then apart from all the other ways of diverting its course, you could attach a tether to it, and by mining the asteroid and sending the material away from it in calculated trajectories (hopefully do something useful with the material at the same time) you could divert its course pretty easily.
Another idea involves a permanently attached counter weight to change the orbit of an asteroid, a minor effect in this case, but someone looked into it and found it could make a difference for light weight comets and such like if likely to hit the Earth Asteroid Diversion Using Long Tether and Ballast
Tethers can also be used as a way for spacecraft to do a slingshot type change of course - but instead of using gravity as you do for huge planets - instead it just throws out a grappling hook, as it were, on the end of a long tether as it approaches. This then diverts its course around the asteroid, and then when it reaches its desired course change, it releases the tether.
This is an old 1986 paper describing the idea: Tethers and asteroids for artificial gravity assist in the solar system
You also have the idea of a Rotovator, - this is a tether that's not permanently connected to the ground, but instead - e.g. for the Moon - you have it spinning around a center of gravity in orbit - and once every orbit it touches ground - and you arrange it so that it is spinning against the orbital velocity in such a way as to exactly balance out, so that it's stationary relative to the ground when it touches the ground. So then you can put materials into it at that point and is an easy way to transfer those materials into orbit.
You can have similar ones like that in Earth orbit, but of course not touching the ground, and you can have shorter ones - so the lower tip is simply rotating at a rather slower orbital delta v so easier to get to from the ground, gets rid of the need to accelerate once you get into orbit, or not so much.
And one idea takes that a bit further, and has the tip actually extend down into the atmosphere. Although with existing materials it couldn't be stationary at the Earth surface, it would be able to snatch a rocket or extremely fast aircraft in a suborbital trajectory --, and fling it into high orbits.
Normally, you need about Mach 20-25 to go into low Earth orbit (depending on how high), by comparison, Virgin Galactic would go at about Mach 3, and the unmanned HTV2 Falcon Hypersonic Technology Vehicle 2 at Mach 17, and the North American X-15 at Mach 5.4 approx. (using Miles Per Hour to Mach Number converter) - those two are Rocket-powered aircraft.
The launch assist tether reduces that to Mach 12 or less
See Launch Assist Tethers
This requires constant input of energy as the tether would slowly de-orbit - loses delta v every time it does one of these gravitational assists. But it can get the energy back again by using solar power and then sending electric current along the tether to accelerate it back into orbit using the Earth's magnetic field for a motor.
This was fully worked out in a plan called the Hypersonic Airplane Space Tether Orbital Launch (HASTOL) System
Then finally, remarkably, you can have a complete transportation system combining a rotovator in lunar orbit, and a gravity assist tether bolo in LEO - and then because the Moon is higher in the gravity well, if you arrange things carefully, then simply by dumping lots of lunar dirt into the tether system continually at the lunar end - that can power up the whole system, giving all the energy you need to send materials from Earth to the Moon - and simultaneously transferring lunar materials to LEO or to the Earth itself. See the cislunar tether transport system architecture
There are many other ways of using space tethers. I got most of this from Wikipedia, then following up the links, see for instance Space elevator
and Momentum exchange tether, also Non-rocket spacelaunch
Wikipedia content can be a bit mixed in quality sometimes, depending on the subject matter, but those are good.
For that you need carbon nanofibres, which are just strong enough - but with no safety margin, and in any case can only be used to make tiny, microscopic even, sections - certainly can't yet be made into a long cable.
You can reduce the required strength of the material with a tapered space elevator - but that also increases its total mass.
For details, looking at various materials that have been made so far, and to see how close or far we are from having the materials needed, at various tapers, see
The Spaceward Foundation - When
The details are pretty well worked out, if we had a strong enough material which we may have in a few decades. You'd need a counterweight to keep the cable stretched and the cable would go beyond geostationary orbit.
It would then be very easy to go into space. The gravity goes down slowly as you go up the cable, is zero at geostationary - and then you get the centrifugal effect pushing you away from the Earth after that.
Indeed without even doing that, just releasing them at various points beyond geostationary, they have the delta v needed to go to various places - either the moon, or elsewhere in the solar system - just release a spaceship from the end of the tether and it has enough delta v to go to Jupiter without need to use any rocket fuel at all to do it Space elevator - launching into deep space
That's for the future as we don't have the materials to do it.
But you can do a space tether from the Moon with existing materials. Best way is to do it from the center of the near side of the Moon going up through the L1 position towards the Earth. You could build that out of kevlar for instance, though the authors take as their reference material a similar stronger material called M5 fiber
Here is the paper about the lunar elevator design Lunar space elevators for cis-lunar space development.
It is something you could, at least according to the author of the paper, do within the budget of a return of humans to the Moon, and could launch tens of thousands of tons of material from the lunar surface which you could then use e.g. to build settlements in space or whatever, Might be a better way of doing that than the rail guns of the Stanford Torus design.
The LiftPort Group have plans to actually create this lunar elevator. They did a successful Kickstarter project as an early phase of their project. Space Elevator Science - Climb to the Sky - A Tethered Tower. Here is their page about it Lunar Elevator | LiftPort Group
You can also use elevators for launching materials from rapidly spinning asteroid. So if your asteroid was rotating quickly enough, you could attach a tether to it, and use that to launch the materials to the Earth. So rather than move the asteroid, and rather than have rockets shuttling back and forth, just use a tether to launch the materials you mine to Earth or anywhere else in the solar system you need it.
You can also use a similar system for diverting asteroids - if we have an asteroid that's projected to hit the Earth, and it's spinning, as most do, then apart from all the other ways of diverting its course, you could attach a tether to it, and by mining the asteroid and sending the material away from it in calculated trajectories (hopefully do something useful with the material at the same time) you could divert its course pretty easily.
Another idea involves a permanently attached counter weight to change the orbit of an asteroid, a minor effect in this case, but someone looked into it and found it could make a difference for light weight comets and such like if likely to hit the Earth Asteroid Diversion Using Long Tether and Ballast
Tethers can also be used as a way for spacecraft to do a slingshot type change of course - but instead of using gravity as you do for huge planets - instead it just throws out a grappling hook, as it were, on the end of a long tether as it approaches. This then diverts its course around the asteroid, and then when it reaches its desired course change, it releases the tether.
This is an old 1986 paper describing the idea: Tethers and asteroids for artificial gravity assist in the solar system
You also have the idea of a Rotovator, - this is a tether that's not permanently connected to the ground, but instead - e.g. for the Moon - you have it spinning around a center of gravity in orbit - and once every orbit it touches ground - and you arrange it so that it is spinning against the orbital velocity in such a way as to exactly balance out, so that it's stationary relative to the ground when it touches the ground. So then you can put materials into it at that point and is an easy way to transfer those materials into orbit.
And one idea takes that a bit further, and has the tip actually extend down into the atmosphere. Although with existing materials it couldn't be stationary at the Earth surface, it would be able to snatch a rocket or extremely fast aircraft in a suborbital trajectory --, and fling it into high orbits.
Normally, you need about Mach 20-25 to go into low Earth orbit (depending on how high), by comparison, Virgin Galactic would go at about Mach 3, and the unmanned HTV2 Falcon Hypersonic Technology Vehicle 2 at Mach 17, and the North American X-15 at Mach 5.4 approx. (using Miles Per Hour to Mach Number converter) - those two are Rocket-powered aircraft.
The launch assist tether reduces that to Mach 12 or less
See Launch Assist Tethers
This requires constant input of energy as the tether would slowly de-orbit - loses delta v every time it does one of these gravitational assists. But it can get the energy back again by using solar power and then sending electric current along the tether to accelerate it back into orbit using the Earth's magnetic field for a motor.
This was fully worked out in a plan called the Hypersonic Airplane Space Tether Orbital Launch (HASTOL) System
Then finally, remarkably, you can have a complete transportation system combining a rotovator in lunar orbit, and a gravity assist tether bolo in LEO - and then because the Moon is higher in the gravity well, if you arrange things carefully, then simply by dumping lots of lunar dirt into the tether system continually at the lunar end - that can power up the whole system, giving all the energy you need to send materials from Earth to the Moon - and simultaneously transferring lunar materials to LEO or to the Earth itself. See the cislunar tether transport system architecture
There are many other ways of using space tethers. I got most of this from Wikipedia, then following up the links, see for instance Space elevator
and Momentum exchange tether, also Non-rocket spacelaunch
Wikipedia content can be a bit mixed in quality sometimes, depending on the subject matter, but those are good.
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