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On one hand, the Moon has lower gravity, and the gravity from Earth also reduces the distance the it has to span. This is particularly true for EML-1, and a little less so for EML-2. I don't know if there are any other coherent ideas of a lunar space elevator, so restricting the discussion to EML-1 would be best.

On the other hand, Mars has a rotation similar to Earth. Its day length is nearly 30 times the moon, so it seems like this would very heavily favor Mars.

Which one would have the lower requirement for material specific strength?

A similar question has been asked on Quora, but lacked any genuine empiricism.

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  • $\begingroup$ Wikipedia suggests that a lunar elevator could be built today with commercially available materials, The plan there uses a Lagrange point, and does not require a connection at the equator. But it also does not mention anything about tidal forces which I imagine could be significant. $\endgroup$
    – James Jenkins
    Sep 25, 2013 at 15:05
  • $\begingroup$ @JamesJenkins Interesting, they seem to have usable numbers in that article. FWIW, you can't exactly not have a lunar space elevator at a Lagrange point. Because it's tidally locked, those points are Lunar-stationary. I think they include the south lunar pole because it's an interesting location. I don't think anything will beat Lunar equator to EML-1 in terms of strength requirement. $\endgroup$
    – AlanSE
    Sep 25, 2013 at 15:15

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This Wikipedia article says that The Lagrange points L1 and L2 are the only places where you could place a lunar elevator. L1 is 56,000 km away from the Earth-facing side of the Moon, (at the lunar equator) and L2 is 67,000 km from the center of the Moon's far side. Moon gravity is 1.6 $m/s^2$.
A stationary orbit around Mars is 17,000 km. Mars gravity is 3.7 $m/s^2$.
Getting from this data to a tensile strength requirement requires more complex math than I can handle right now.

A study done for NASA's Institute of Advanced Concepts states "Current composites have characteristic heights of a few hundred kilometers, which would require taper ratios of about 6 for Mars, 4 for the Moon, and about 6000 for the Earth. This suggests that the Moon elevator is has lower tensile strength requirements.

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recent paper I wrote on the lunar space elevator

For a Mars elevator, the Moon Phobos gets in the way ..... a more practical solution on Mars is to use Phobos as an attach point for a partial elevator, called PAMSE "Phobos And Mars Space Elevator". If you drop a tether down from Phobos it will drag across the atmosphere of Mars a few hundred km / hour, such that an aircraft could rendezvous with it.

See this paper.

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    $\begingroup$ While these are valuable insights, you should make sure to also address the central question. $\endgroup$
    – called2voyage ♦
    Oct 5, 2017 at 11:29
  • $\begingroup$ which is what ? $\endgroup$
    – Charles F Radley
    Oct 10, 2017 at 16:03
  • $\begingroup$ "which [Moon or Mars] would have lower material strength requirement?" $\endgroup$
    – called2voyage ♦
    Oct 10, 2017 at 16:03
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The Moon is considerably less. A Lunar Elevator tether would require the strength of Kevlar. From what I've been able to tell, Kevlar would just barely work for a Mars elevator, but wouldn't be practical as it would be at the safety margin, any small defect could cause it to stop working. The thought is that a Mars elevator would be easier than Earth, as it could work with either M5 or Zylon, both of which are much easier to manufacture then carbon nanotubes, which is the only substance that is known to work for Earth.

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