Lunar Space Elevator Design

Posted on April 23, 2026 by Kirk Sorensen

The previous posts in this series described what the lunar space elevator can do. This one works through the structural mechanics that determine how much ribbon material you actually need to build it.

The central engineering question for any space elevator is: how thick does the ribbon need to be? Too thin and it snaps under the loads imposed by the gravitational and centrifugal forces acting along its length. Too thick and the ribbon’s own weight dominates the design, driving up the total mass until the system becomes impractical. The answer is a tapered ribbon — thicker at the balance point (EML2) where tensions are highest, thinner at the surface where they are lowest — and the governing equations tell you exactly how that taper must vary with position.

What makes the lunar elevator tractable, as discussed previously, is that the Moon’s weak gravity keeps the required taper ratio to a modest value of around 4 using materials available today. The derivation below shows exactly where that number comes from.

Setting Up the Problem

Consider a small element of the ribbon at position $x$ along its length, measured from the center of the Earth-Moon system. The element has cross-sectional area $A$, length $dx$, and material density $\rho$. Its mass is:

(1)   \begin{equation*} dm = \rho A \, dx \end{equation*}

This element experiences a net acceleration $a(x)$ from three sources: the Moon’s gravity pulling it toward the Moon, the Earth’s gravity pulling it toward Earth, and the centrifugal acceleration from the rotation of the Earth-Moon system pushing it outward from the system’s center of mass. The net force on the element is:

(2)   \begin{equation*} dF = a(x) \, dm \end{equation*}

In the rotating reference frame of the Earth-Moon system, the net acceleration at position $x$ is:

(3)   \begin{equation*} a(x) = \frac{\mu_L}{(x - \mu^*)^2} + \frac{\mu_E}{(x + \mu)^2} - \omega^2 x \end{equation*}

where $\mu_L$ and $\mu_E$ are the gravitational parameters of the Moon and Earth respectively, $\mu^*$ is the distance from the system barycenter to the Moon, $\mu$ is the distance from the barycenter to the Earth, and $\omega$ is the angular velocity of the Earth-Moon system. The first two terms are gravitational (attractive toward their respective bodies), and the third is centrifugal (repulsive from the barycenter). At EML2, these three terms sum to zero by definition — it is the balance point, the location where a free particle experiences no net force in the rotating frame.

Note that the sign convention here is important. Below EML2 (between the Moon and L2), the Moon’s gravity dominates and the net force pulls the ribbon toward the surface. Above EML2, the centrifugal term dominates and pulls the ribbon away from the Moon. The ribbon is therefore in tension everywhere, with maximum tension at EML2. This is exactly the condition that allows a tethered structure to be self-supporting.

Integrating Along the Ribbon

To find the total change in tension $\Delta F$ between two points $x_0$ and $x_1$ along the ribbon, we integrate the differential force over the ribbon element masses:

(4)   \begin{equation*} \int dF = \rho A \int \left(\frac{\mu_L}{(x - \mu^*)^2} + \frac{\mu_E}{(x + \mu)^2} - \omega^2 x\right)dx \end{equation*}

Separating the integrals:

(5)   \begin{equation*} \Delta F = \rho A \left(\mu_L\int\frac{dx}{(x - \mu^*)^2} + \mu_E\int\frac{dx}{(x + \mu)^2} - \omega^2 \int x \, dx \right) \end{equation*}

Each of these is a standard integral. The gravitational terms integrate to $-1/(x - \mu^*)$ and $-1/(x+\mu)$ respectively, and the centrifugal term integrates to $x^2/2$. Evaluating the antiderivative:

(6)   \begin{equation*} \Delta F = \rho A \left(-\frac{\mu_L}{x - \mu^*} - \frac{\mu_E}{x + \mu} - \frac{\omega^2 x^2}{2}\right) \end{equation*}

Evaluating between the limits $x_0$ (lower point) and $x_1$ (upper point):

(7)   \begin{equation*} \Delta F = \rho A \left(\frac{\mu_L}{x_0 - \mu^*} - \frac{\mu_L}{x_1 - \mu^*} + \frac{\mu_E}{x_0 + \mu} - \frac{\mu_E}{x_1 + \mu} + \frac{\omega^2}{2}(x_0^2 - x_1^2)\right) \end{equation*}

This expression gives the net tension change along any segment of the ribbon as a function of the positions of its endpoints, the material density and cross-sectional area, and the gravitational and rotational parameters of the Earth-Moon system. It is the core structural equation for the lunar space elevator.

The Taper Relationship

The ribbon must not break. At any point along its length, the cross-sectional area $A$ must be large enough to support the tension $F$ acting on it. If the ribbon material has a tensile strength $\tau$ and we apply a safety factor $f$, the required area at a point where tension is $F + \Delta F$ is:

(8)   \begin{equation*} A = \frac{(F + \Delta F) f}{\tau} \end{equation*}

Combining this with the integrated force expression, we can write the ratio of the tension change to the total tension at any point:

(9)   \begin{equation*} \frac{\Delta F}{F + \Delta F} = \frac{\rho f}{\tau} \left(\frac{\mu_L}{x_0 - \mu^*} - \frac{\mu_L}{x_1 - \mu^*} + \frac{\mu_E}{x_0 + \mu} - \frac{\mu_E}{x_1 + \mu} + \frac{\omega^2}{2}(x_0^2 - x_1^2)\right) \end{equation*}

Rearranging to isolate the material properties on the left:

(10)   \begin{equation*} \frac{\tau}{\rho f \left(\dfrac{F}{\Delta F} + 1\right)} = \left(\frac{\mu_L}{x_0 - \mu^*} - \frac{\mu_L}{x_1 - \mu^*}\right) + \left(\frac{\mu_E}{x_0 + \mu} - \frac{\mu_E}{x_1 + \mu}\right) + \frac{\omega^2}{2}(x_0^2 - x_1^2) \end{equation*}

The left-hand side is determined entirely by the ribbon material — its tensile strength $\tau$, density $\rho$, safety factor $f$, and the local tension ratio. The right-hand side is determined entirely by the geometry and the gravitational/rotational parameters of the Earth-Moon system. This clean separation between material properties and orbital mechanics is what makes the equation so useful for design: given a material, you can immediately calculate what taper profile is required, and given a desired taper, you can determine what material performance is needed.

The Lunar-Gravity Approximation

For a first-pass design, if the elevator spans only the region close to the Moon (well inside the Earth-Moon distance), we can simplify by assuming lunar gravity alone. In this case, the Earth’s gravitational term and the centrifugal term are small compared to the Moon’s gravity near the surface, and the acceleration reduces to:

    \begin{displaymath} a(x) \approx \frac{\mu_L}{(x - \mu^*)^2} \end{displaymath}

Under this approximation, we define a characteristic length $L$ related to the material’s breaking length:

    \begin{displaymath} L \equiv \frac{\tau}{\rho g_L f} \end{displaymath}

where $g_L$ is the lunar surface gravitational acceleration. This is essentially the breaking height — the maximum length of a uniform cable of the material that could support its own weight in a uniform $g_L$ field. One important check: $L$ must always be greater than $r_0$, the lunar radius, for the material to be capable of supporting even the lower portion of the elevator. Materials that fail this check — those with breaking heights shorter than the Moon’s radius of 1,737 km — cannot be used for a lunar elevator under any circumstances. Fortunately, all the candidate materials in the table from the previous post satisfy this condition comfortably.

For M5 fiber with its breaking height of 342–570 km (depending on whether you use the current or planned stress limit), $L$ is well above the lunar radius, and the taper ratio across the full elevator length works out to approximately 2.7–4.0. For T1000G carbon fiber with a breaking height of 361 km, the result is similar. These are the modest taper ratios that make the lunar elevator buildable with today’s materials — in stark contrast to the Earth elevator’s requirement for a taper ratio of roughly 6,000.

What the Equations Tell Us

A few insights emerge directly from the structure of these equations that are worth making explicit.

First, the taper is exponential. The ribbon cross-section doesn’t decrease linearly from EML2 to the surface — it decreases as an exponential function of the integrated gravitational potential difference. This means that the ribbon is relatively thick for a long stretch near EML2, and thins rapidly near the surface. The “waist” of the ribbon is at the lunar surface, where tension is lowest. If the elevator is going to fail, it will fail there first.

Second, the full three-body force field matters for accurate design. The simplified lunar-gravity approximation gives you the right order of magnitude, but the Earth’s gravity and the centrifugal term are not entirely negligible, especially in the upper portion of the elevator near EML2. A real design will integrate the full expression in the equation above, numerically if necessary.

Third, and most importantly, the right-hand side of the taper equation depends only on positions and physical constants. The material choice scales the left-hand side. This means that for any candidate material, you can immediately calculate whether it produces an acceptable taper ratio for a given elevator configuration — no iteration required. The design space is well-defined and directly computable.

The ribbon designed by these equations is not a speculative structure awaiting a materials breakthrough. The numbers close today, with materials you can order from a catalog. That is not true of any proposed Earth space elevator. It is true of the lunar version — and it has been true since Pearson first worked through this analysis in the 1970s.

In the next post, we’ll examine these equations implemented in actual computer code.

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Kirk Sorensen

MS, nuclear engineering, University of Tennessee, 2014, Flibe Energy, president, 2011-present, Teledyne Brown Engineering, chief nuclear technologist, 2010-2011, NASA Marshall Space Flight Center, aerospace engineer, 2000-2010, MS, aerospace engineering, Georgia Tech, 1999

About Kirk Sorensen

MS, nuclear engineering, University of Tennessee, 2014, Flibe Energy, president, 2011-present, Teledyne Brown Engineering, chief nuclear technologist, 2010-2011, NASA Marshall Space Flight Center, aerospace engineer, 2000-2010, MS, aerospace engineering, Georgia Tech, 1999
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3 Responses to Lunar Space Elevator Design

  1. gbaikie says:
    April 27, 2026 at 8:04 pm

    I would make a lunar elevator to be a hydropower dam. Or have a pipe drop water towards the lunar surface, and water turbine to slow the water down and one gets electrical power from it.
    The power gained is mostly from gravity loss.
    Or it takes a lot energy to slowly land or leave the lunar surface. Or if you land or leave the Moon at a constant speed of 100 mph, it requires a lot of rocket propellant. And if slow water down, to less than 100 mph, while falling to towards the moon, one would gain a lot of energy from the water.

    Though generally speaking a “problem” with space elevators is gravity loss.

  2. Hop David says:
    May 15, 2026 at 4:55 pm

    The distance from the moon’s surface to EML2 is about 63,000 km. How fast could an elevator car ascend the tether?

    How would the elevator cars travel up the elevator?

  3. Archibald says:
    May 28, 2026 at 7:01 am

    Now there is a pretty logical mission for an EML-1 space elevator.
    Lifting lunar dust to create a shield against global warming.

    https://en.wikipedia.org/wiki/Space_sunshade

    It makes so much sense.

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