The space elevator concept has been in the public eye since the publication of Arthur C. Clarke’s The Fountains of Paradise in 1979. Its pedigree among scientists is older still. With obvious benefits in terms of moving people and materials into space, elevators seize the imagination because of their scale and the engineering they would require. But we needn’t confine space elevators to Earth. As Alex Tolley explains in today’s essay, a new idea being discussed in the literature explores anchoring one end of the elevator to the Moon. Balanced by Earth’s gravity (and extending all the way into the domain of geosynchronous satellites), such an elevator opens the possibility of moving water and materials between Earth and a lunar colony, though the engineering proves as tricky as that needed for a system anchored on Earth. Is it even possible given the orbital characteristics of the Moon? Read on.

by Alex Tolley

Image: Space elevator connecting the moon to a space habitat. Credit: coolboy.

It is 2101, and the 22nd century has proven the skeptics wrong about space. Sitting comfortably in an Aries-1B moon shuttle on its way to Amundsen City in the Aitken basin at the lunar south pole, I am enjoying a bulb of hot Earl Grey tea. Sadly, without artificial gravity, no one has worked out how to dunk a digestive biscuit in hot drinks. The viewscreen shows the second movie of our almost 24-hour trip. Having been transferred from a spaceplane (far better than those giant VTOL rockets that reduced the cost of space access and paved the way for our multi-planetary advances), the moon-bound shuttle has crossed the Clarke orbit, past the remaining telecomm birds that haven’t been obsoleted by the swarms of comsats in low earth orbit (LEO).

A strange string of bright glints catches my eye. They are arrayed in an arrow-straight line, looking like dew on an invisible spiderweb seeking infinity. Nothing seems to move, the objects just apparently hanging in space. The flight attendant notices my apparent confusion. “What are they?” I ask as she crouches down beside me. “That is the newly operational Spaceline, a geosynchronous orbit to lunar surface space elevator. Those lights are the elevator cars carrying supplies to and from the moon. “But they are not moving,” I say. “They are moving, but too slowly to notice at this distance”, she replies, smiling, as this was probably a common observational mistake by passengers on the Moon run. “We should be seeing the expanding set of facilities at the Earth-Moon Lagrange Point 1 (EML1) nearer the Moon. The captain usually puts a magnified image on the viewscreens as we pass.”

This post is about space elevators, but not the Earth to Geosynchronous orbit that is most known, but rather a lesser known lunar space elevator {LSE), and in particular the one that rises from the lunar surface and terminates somewhere between the Earth’s surface and the Earth-Moon Lagrange Point 1 (EML1).

Because the Moon is tidally locked to Earth, an LSE from its surface can hang over the Earth, with the cable tension maintained by the gravitational pull of the Earth. Deployment of the cable is similar to the Earth space elevator (SE) which uses the Clarke orbit as a stable position that keeps the same point on the Earth below it, but in the case of the Moon, that deployment position is at the gravitationally neutral EML1. The cable is then simultaneously unrolled towards the Moon’s surface, and balanced by cable unrolled towards Earth and pulled towards Earth by gravity.

The idea of an LSE is not new and may even predate that of the Earth space elevator with a 1910 note by Friedrich Zander. Unlike the Earth space elevator that cannot be built as no material available can support its own mass, existing high-strength plastics like Zylon® can in principle be used today to build an LSE. Prior work by Pearson in 1979 on the LSE, and in 2005, with collaborators Levin, Oldson and Wykes published a NASA report on the LSE for two LSE cases, one passing through EML1 and the other anchored on the lunar farside passing through EML2 (using centrifugal force to tension the cable). These works and others demonstrated that an LSE could be built that would reduce the cost of transporting water and regolith to and from the Moon.

Prior work assumed that the cable would terminate in the Earth direction with a mass to provide the tension. The shorter the EML1 to terminus length, the greater the mass, and also the total mass of the LSE. A design tradeoff.

Image: The Lunar Space Elevator concept. A tapered cable from the Moon’s surface, through EML1 and terminating inside the geosynchronous orbit.

A 2019 arXiv preprint by Penoyre and Sandford adds their calculations for an LSE that they call the “Spaceline”. The authors show that a cable can be created without any counterweight between the Earth and the Moon, with the end of the cable dipping inside the geosynchronous orbital height. The total length of their optimal design is about 340,000 km, with a total mass of 40,000 kg (40 MT). The deployment facility and payload carriers are extra mass. The total mass of the system would therefore be lower than a design with a shorter cable and terminus mass. The authors also indicated that with the cable terminating inside the geosynchronous orbit, it would be easier to reach the cable from Earth and therefore reduce the transport costs further.

As with prior work, this all-cable design ensures that maximum tension in the cable is at the EML1 point, and declines towards both ends. The design ensures that the cable cannot collapse onto the Moon, nor break under load and fall towards Earth.

Table 1. Materials with values for density (ρ), breaking stress (B), specific strength (S), and relative strength (α). Materials with relative strength greater than 1.0 can be used in an LSE. Zylon have the highest relative strength that can be mass-manufactured. Carbon nanotubes can only be made in very short lengths at present. Source – Penoyre & Sandford.

This paper is primarily an exercise in designing an all-cable system using fixed area cross-sections, tapered cross-sections, and a hybrid of these two designs to simplify manufacture, deployment, and operation. Figure 2 shows that a Zylon cable of uniform cross-section suffices as an LSE that neither collapses nor breaks. Their calculations show that the tapered design is the most efficient with total mass, but the hybrid design using mostly uniform cross-section cable is a good compromise that simplifies manufacture and operation that reaches geosynchronous orbit.

Image: The white area is a feasible space for a cable of a uniform cross-section. With a relative strength above a critical value, a cable length can be constructed that neither collapses back to the Moon nor breaks under its own mass. Zylon can achieve this, albeit not to the desired geosynchronous orbit height. Not shown are the cases for a tapered and hybrid cable that can reach geosynchronous orbit. Source modified from Penoyre & Sandford

No attempt is made to determine other masses to support, such as the crawlers to carry payloads, how many could be supported, and the deployment hardware that must be transported to EML1. The assumption is that scaling up the area or number of cables will allow for the payload masses to be carried.

The authors do not justify the construction of the cable beyond showing that the cost of delivering payloads to the Moon, as well as returning material to space or Earth, is significantly reduced using a cable compared to spacecraft requiring propellant to transport the payloads.

The cost savings are not new, and no doubt a cable would be built if there were no other issues. But as with the SE, some issues complicate the construction of an LSE. Other authors have analyzed the LSE in more detail including survivability to space hazards [Eubanks], payload capability, speed of crawlers, ROI, and even transport of materials to and from the lunar South Pole to the LSE base on the lunar surface [Pearson et al, 2005].

So far so good. Penoyre and Sandford have shown that an unweighted cable can be used as an LSE which can stretch from the lunar surface to geosynchronous orbit, a mere 36,000 km from the Earth’s surface. Not quite as complete as the web between Earth and Moon in Aldiss’ Hothouse, but close. To reach the start of the cable, a spaceplane needn’t have to maintain geosynchronous orbit, but rather make a ballistic trajectory with the apogee reaching the terminus of the cable, and be captured by it similar to that of a skyhook, but with less difficulty.

But wait. Isn’t the paper skipping some important issues that could make this LSE impractical?

With the SE the geosynchronous orbit is circular. Once the orbital station is constructed and the cables reeled out to Earth and the counterweight, the system is very stable. This is not the case for the LSE.

The Moon’s orbit, with an eccentricity of 0.055, varies in distance from the Earth over its period from 362,600 km at perigee to 405,400 km at apogee, a difference of 42,800 km. This will result in the EML1 point moving back and forth towards the lunar surface about 36,300 km over the orbit, or about 18,000 km back and forth over the average EML1 distance. As the semi-major axis distance of EML1 to the lunar surface is about 57,000km, this is about a 2/3rd change in distance. Therefore the extra mass of the cable from EML1 to the lunar surface at apogee must be balanced by an extra length of the cable from EML1 to geosynchronous orbit, and vice versa at perigee. The base station at EML1 must therefore reel in or out cable continuously over the Moon’s orbital period. This is a dynamic situation that cannot fail or the LSE will be destabilized and potentially break or collapse.

Eubanks [2016] calculated that the micrometeoroid impacts would break a cable of uniform circular cross-section within hours, effectively breaking the cable before it could be deployed. The longer the cable, especially the long section between EML1 and geosynchronous orbit, the more quickly the break. A break in the cable would result in the section attached to the lunar surface falling back onto the Moon, wrapping itself around the Moon as it continued its orbit.

The other section would fall towards Earth, crossing the lower orbits and probably having a perigee that would enter the Earth’s atmosphere and likely burn up on entry over some time. Eubanks calculated that making the cable with a flat cross-section would ensure a lifetime between possible breaks of 5 years. Penoyre and Sandford acknowledged the danger of such breaks and also suggested a flat cross-section, although this would be less effective where the cable tapered.

While the LSE is relatively free of satellites and other artifacts, the question arises why the Earth’s terminus of the cable is inside the geosynchronous orbit. Geosynchronous satellites have a relative velocity of about 3 km/s relative to the end of the cable, posing a hazard to both satellites and cable. This is made worse if the cable length is not adjusted fast enough as it would dip deeper into the orbits of satellites with corresponding higher impact velocities and increased numbers of possible impacts. All this for the advantage of easier access to the end of the cable.

While accepting that cables with moving payloads are a cheaper way to transport material to and from the lunar surface, the speed at which these payloads can be moved is also relevant. An analogy might be that while walking across a country might be the cheapest form of travel, it is far slower than taking powered transport and time is important for commercial transport.

Various authors have used different assumptions of travel speed on the cable, up to 3600 kph (1.0 kps) [Radley 2017]. A more realistic speed might be 100 kph. At this speed, a payload from geosynchronous orbit to the lunar surface would take about 20 weeks. This is the same order of time to reach Mars on a Hohman orbit and similar to transoceanic voyages in the age of square-rigged sailing ships, This is entirely unsuited for transportation of humans or goods that can perish or be damaged by radiation from the solar wind or galactic cosmic rays. It would be suited for carrying bulk materials and equipment.

If the cable were a constant area flat ribbon, probably woven into a Hoytether [Eubanks 2016, Radley 2017], the payloads may not need to be self-powered but simply attached to the cable and moved like a cable car. Transport from the lunar surface to a station at EML1 would take about 3-4 weeks. Therefore people and some food supplies would still need to be ferried by rocket to and from the Moon.

While we think of the Moon as tightly locked facing the Earth, in practice it has a libration that would move the relative position of the lunar surface sideways back and forth over the month. This would send waves up the cable with a velocity dependent on the design of the cable. The dynamics of this oscillation would need to be investigated. Similarly, while Coriolis forces do not affect a static LSE, they will be a factor with the carriers moving on a cable from a low velocity at geosynchronous orbit to the Moon’s orbital velocity of about 1 kps. This is an order of magnitude higher than at the Earth terminus of the cable, and these forces will need to be determined for their effect on cable dynamics.

The authors also state that a base station of potentially immense size could be positioned at EML1 where the cable would be deployed. EML1 would be a convenient place to expand facilities making use of the zero gravity at that point. While Arthur Clarke had a manned telescope at EML1 in his novel A Fall of Moondust, EML1 is not a stable point or attractor, but rather unstable. This is made even worse by the orbit of the Moon which changes the position of this point and the surface over its orbit, as well as its position in orbit. As a result, the proposed Lunar Gateway space station is not placed at EML1 but rather in a Near Rectilinear Halo Orbit (NRHO) that requires far less fuel for station keeping. While the idea of a station at EML1 sounds attractive, it might be a costly facility to maintain, even with the advantage of having a cable to adjust its position.

Despite these caveats, there are good scientific and potential commercial reasons for reducing the cost of transporting mass to and from the Moon, as well as maintaining a facility close to the EML1. These have been explained in more detail by [Pearson 2005, Eubanks 2016]. I would add, as a fan of solar and beamed sails, that this could be a good place to deploy and launch these sails. There are no satellite hazards to navigate, and the low to zero gravity would allow these sails to reach escape velocity without needing the slow spiral out from Earth if started at LEO.

I propose that rather than having a cable reach geosynchronous orbit, it might be better to have a shorter weighted cable as proposed by Pearson even at the cost of a greater total mass of the LSE. Used in combination with a rotating tether in LEO (skyhook), transport to the tether could be achieved with an aircraft or suborbital rocket, attaching the payload to the skyhook, and having it launched into a high orbit to reach the end of the LSE. This would have to be a well-coordinated maneuver, reducing the costs even further albeit with the potential problems of skyhook and satellite impacts, especially with satellite swarms in LEO.

Our journey to the Moon has nearly ended. On the surface, I can see the long tracks of what looks like monorail lines. They were designed to launch packages of regolith or basic metal components into space, as originally envisaged by Gerard O’Neill in the late 20th century, to construct space solar power satellites and habitats. China’s AE Corp’s Spaceline (太空线) proved more economic, obsoleting the mass driver’s original purpose. They were repurposed to accelerate probes brought up from the Earth to the Moon, into deep space. One day their larger descendants will launch crewed spaceships on their journeys to the planets.

References

Penoyre, Z, Sandford E, (2019) The Spaceline: A Practical Space Elevator Alternative Achievable With Current Technology https://arxiv.org/abs/1908.09339

Pearson J, et al (2005) Lunar Space Elevators For Cislunar Space Development. Phase I Final Technical Report.

Eubanks, T. M. (2013). A space elevator for the far side of the moon. Annual Meeting of the Lunar Exploration Analysis Group, 1748, 7047. http://ui.adsabs.harvard.edu/abs/2013LPICo1748.7047E/abstract

Eubanks, T. M., & Radley, C. F. (2017). Extra-Terrestrial space elevators and the NASA 2050 Strategic Vision. Planetary Science Vision 2050 Workshop, 1989, 8172. https://ui.adsabs.harvard.edu/abs/2017LPICo1989.8172E/abstract

Eubanks, T. M., & Radley, C. F. (2016). Scientific return of a lunar elevator. Space Policy, 37, 97–102. https://doi.org/10.1016/j.spacepol.2016.08.005

Radley, C. F. (2017). The Lunar Space Elevator, a near term means to reduce cost of lunar access. 2018 AIAA SPACE and Astronautics Forum and Exposition. https://doi.org/10.2514/6.2017-5372