Reverse Lunar Space Elevator

Question

The possibility of a space elevator from the lunar surface is discussed in this question. A lunar elevator for the purpose of return to Earth could be achieved at the L1 Lagrange Point between Earth and the moon. I'm wondering if we could acheive a lift from Low Earth Orbit up to the moon by extending such a space elevator far beyond L1 from the Moon toward Earth.

As I imagine it, when the elevator extends past L1, Earth gravity would take over, drawing the extension always toward Earth. The closer we get to Earth, the heavier the pull toward Earth and away from the Lunar surface. So by the time the structure is completed, the tension at the lunar surface pulling away from the surface toward the Earth would be very high. So the anchors to the Lunar surface would have to be strong.

If we can extend such a structure close to LEO in this fashion, would I be wrong to think that we could then launch to the moon merely by achieving that relatively low orbit, docking to the reverse elevator (delevator?) and then climbing the rest of the way toward the moon? Perhaps getting all the way to LEO would be too much for the strength of currently known materials like carbon nanotubes. But even bridging half the gap would cut down the energy required for a lunar commute dramatically, wouldn't it?

Answer 1

Here's a pic of the tether proposed by Liftport.

Go 160,000 km beyond EML1 and drop a payload from that point. It will follow an elliptical path whose perigee grazes low earth orbit. A 3 km/s burn at perigee would circularize the orbit at LEO.

Doing a 3 km/s burn from LEO and you will get the same ellipse. At the apogee of this ellipse, the rocket is moving very nearly the same velocity as the tether, so little delta V is needed for rendezvous.

Go farther towards the earth from that point and the tether will be moving slower than apogees of transfer orbits from LEO. So extending the tether further and boost delta V for rendezvous with the foot.

The pictured elevator has low enough stress that Kevlar or some other existing material might be used. If extended all the way to LEO, we're back to needing Bucky tubes.

Answer 2

I'm going to elaborate on the limitations of a Lunar elevator - things which can be done, but probably shouldn't, particulary in the context of bringing the elevator close to LEO.

Given sufficiently strong materials, there is no reason why a lunar elevator can't be dangled arbitrarily close to Earth's atmosphere - however there are very good reasons why you might not want to do this. The foot of the elevator will always 'orbit' the Earth in the same time as the Moon takes to orbit the earth, that is around 27 days. The Earth rotates in 24 hours, so in affect the foot of the elevator hangs in space, and the Earth rotates under it. Nevertheless, the delta-v required to reach the foot of the elevator would be very low - just enough to get above the atmosphere, and counteract the velocity from the rotation of Earth.

However, while this would make it convenient for travel between the the Moon and Earth or vice-verca (at least for freight - crawlers would take a long time to make the journey), it does not make it even slightly easier to get materials from the Moon to LEO for orbital manufacturing. The reason is that orbital velocity in LEO is around 7.7km/s. The foot of the elevator, hanging in LEO, orbiting every 27 days, would be travelling at a stately 18m/s. This means the delta-v from the elevator's foot hanging in LEO, to orbiting in LEO, would be around 7.7km/s. Compare this with the numbers in HopDavid's answer, where dropping the payload from higher up requires only 3km/s delta-v to circularize the orbit (this is because the payload builds up the required velocity as it freefalls towards Earth). The foot of the elevator would also not be a microgravity environment as it is not in orbit, it would instead suffer nearly full earth gravity (and incidentally, the cable has to bear that weight).

Besides being impractical for inserting resources into LEO, the elevator has another huge disadvantage - it would sweep through the orbits of satellites from LEO to GEO. Actually the elevator darn near stays still, while the satellites zip past it (or into it!) at orbital velocities. It would also menace any Earth space elevator if one is ever built. Space is pretty roomy so these aren't necessarily insurmountable things, but every additional object up there complicates orbital traffic control, and a lunar elevator would be much worse than an Earth one, as the Earth one at least travels at orbital velocity in GEO.

So while lowering the cable to near LEO, would make it possible to travel cheaply from Earth to the Moon due to a low delta-v from Earth's surface to the elevator foot, the same low velocities would make it a very impractical thing to build, a menace to satellites and requiring much stronger materials due to the gravity it is subjected to.

Most of the advantages of a luna elevator are accomplished with a shorter one, with none of these hazards.

Answer 3

As you have figured out, space elevators are bidirectional. They're useful for landing as well as taking off. It's just that taking off is the bigger deal for the places that elevators are usually proposed--you can aerobrake down on any body with an atmosphere.

Answer 4

The ideal Lunar Space Elevator and the ideal Earth Space Elevator actually have the ends of their elevators amazingly close, near-Earth astronomically speaking. The centrifugal force at the end of an Earth Elevator and the gravitational force at the end of a Lunar elevator actually makes the transition between the two points have an effective near-zero energy cost. So although we might be able to put the Lunar Elevator under the additional strain necessary to get it to LEO, it makes more sense to just, after there's a Lunar elevator, to take advantage of pico-gravity station at L1 and precision-create nanotubes for the Earth elevator.