Space Elevator From the Moon to Geostationary Earth Orbit

The new lunar space elevator study differs from previous proposal would be anchored on the moon and stretch 200,000 miles toward Earth until hitting the geostationary orbit height (about 22,236 miles above sea level). We do not have materials for a space elevator from the Earth to Geostationary orbit. The moon spaceline would be longer but would only have to overcome the moon’s gravity.

The biggest hurdle to mankind’s expansion throughout the Solar System is the prohibitive cost of escaping Earth’s gravitational pull. In its many forms the space elevator provides a way to circumvent this cost, allowing payloads to traverse along a cable extending from Earth to orbit. However, modern materials are not strong enough to build a cable capable of supporting its own weight.

The Spaceline is a new analysis of lunar space elevators. By extending a line, anchored on the moon, to deep within Earth’s gravity well, we can construct a stable, traversable cable allowing free movement from the vicinity of Earth to the Moon’s surface. With current materials, it is feasible to build a cable extending to close to the height of geostationary orbit, allowing easy traversal and construction between the Earth and the Moon.

The most efficient solution is one in which we start at the Earth-end of the Spaceline with a constant area cable, as thin as is practical, which extends until the point at which it reaches its breaking stress, then tapers outwards from that point to avoid breaking. Past the Lagrange point, close to the Moon, where the tension (and therefore the allowable area) reduces again, there may be another section of uniform cable reaching down to the anchor point on the Moon’s surface, though whether this second uniform-area section is possible depends on the value of h.

For sufficiently high α, or large h, the cable may never reach its breaking stress, and the most efficient solution is just that of a uniform-area cable. This hybrid cable, by construction, cannot break but can collapse. In fact the same constraints (and solutions) apply here as did for the uniform-area cable. As long as h is less than ∼ 0.24, the cable will not collapse; for larger h, other solutions such as an anchor weight can similarly be implemented.

A line was made of a cable with a0 = 10^−7m2 : its total mass would then be around 40,000 kg. This is about twice the mass of the original lunar lander, and would make transporting and constructing such a cable completely plausible. The raw cost of the materials and transport could be numbered in the hundreds of millions of dollars.

40,000 kg could be transported to the moon with about four launches of a SpaceX Falcon Heavy. However, a lunar lander would need to be developed. A single mission with a SpaceX Super Heavy Starship could also transport the spaceline. There would need to be work done on the deployment.

Many technological and sociological challenges stand between the idea and it’s execution. However, this is a doable project. It would provide benefits for industrializing the Earth-Moon system.

Building a base-camp at the Lagrange3 point is one of the most immediately useful and exciting utilities of the spaceline. A small habitat there could house many scientists and engineers, much like the Antarctic base camp. This would allow experimentation and construction in a near-pristine, gravity-free environment.

There are two huge advantages of fabricating and assembling structures at the Lagrange point rather than any other stable orbit:

• No debris – The region of space between Earth and geostationary orbit is filled with the remnants of past missions and abandoned satellites. Also, stable (and thus long-lived) fast moving orbits can exist here, raising the fear of bombardment with naturally occurring meteoroids. The Lagrange point has been mostly untouched by previous missions, and orbits passing through here are chaotic, greatly reducing the amount of meteoroids.

• Non-dispersive – If you drop a tool from the ISS it will seem to rapidly accelerate away from you. This is because of the slight difference in the gravitational force felt at different distances from the Earth, leading to orbits that quickly diverge. This makes it a difficult and dangerous place for construction. The Lagrange point has an almost negligible gradient in gravitational force, the dropped tool will stay close at hand for a much longer period. With small corrective thrusters or a minimal system of tethers, many objects (habitats, science equipment or spacecraft) can be held in a stable configuration indefinitely. Space now has a ”next-door”.

Manned large-scale construction projects would become much easier to build and maintain. These could include a new generation of significantly larger space telescopes, a network of isolated gravitational wave detectors and particle accelerators on scales much surpassing what can feasibly be built upon Earth’s surface.

Similarly, the base camp itself can be extended, with prefabricated panels added to allow increased space for habitation and experimentation. Scientific and industrial testing in vacuum or zero-gravity environments can be undertaken over longer periods and bigger scales than previously imaginable.

There is one caveat though, the nature of the Lagrange point between the Earth is unstable. The effective potential (in the corotating frame) is a saddle point. If an object undergoes small displacements in the tangential direction (constant radius) the will feel a restoring force back to the Lagrange point. However, if the object wanders in the radial direction (towards the Moon or Earth) it will be pulled more and more strongly in that direction. Thus to keep an object at the Lagrange point indefinitely there needs to be a corrective force in the radial direction.

The spaceline naturally provides this force, and this is one of the two major reasons why constructing a spaceline makes a Lagrange point base camp significantly easier to use and maintain. The other being that it allows material transport easily to and from the base camp (via a spaceship carrying material from Earth, or directly from the surface of the moon), without the need for coordinating rocket flight through a region of space that may quickly fill with delicate habitats and scientific equipment.

In the simplest version of the safeline there can be a force of up to 100N either towards Earth or the Moon before there is any danger of the cable breaking or collapsing.

Arxiv – The Spaceline: A Practical Space Elevator Alternative Achievable With Current Technology.

SOURCES – Arxiv The Spaceline: A Practical Space Elevator Alternative Achievable With Current Technology
Written By Brian Wang, Nextbigfuture.com