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Background

The normal space elevator (that reaches from the Earth's surface to a counterweight beyond geostationary) needs a material that's strength/weight ratio is better than any material we have available.

I've another idea, that I assume isn't possible either, but I'd like to know what makes it impossible?...

The idea

What if, rather than starting the tether from the Earth's surface, it starts from 2000km above the Earth? This will massively reduce the necessary strength/weight ratio of the material. Not only is the part closest to Earth experiencing the greatest gravitational force (per unit mass) but there's a sort of vicious circle: To add a metre to the length of the tether we need to strengthen the whole tether (above this new segment), which means making it heavier, which means making it stronger, and heavier, etc.

I found, using the numbers for Zylon, it works.

"How's it stay up?"

This elevator, unlike a real space elevator is in 'proper orbit', or at least it is, on average. The part that hangs towards the Earth will be suborbital (indeed will be going quite slowly relative to low-earth orbit), while the part that extends beyond geostationary will be at superorbital speed. It is in orbit.

"But how do we get to the start of the tether if it’s 2000km up?"

Going up into space is easy, getting into orbit is the expensive bit. A rockoon might be a neat way to get to the 2000km mark with a very modest rocket (the rocket equation means that we can use a very small rocket to get to 2000km, compared to the rocket required to get to 2000km orbit) - about 3kg of propellant per kg of payload, I think.

"But won’t you pull the whole thing down as you climb it?"

Yes. To correct for this, ion-engines will be arranged on the tether for station-keeping. Some of the payload can be used for refuelling these (they have a specific impulse 10 times better than a rocket launcher, and the rocket equation helps here, so hopefully we’ll need far less fuel!)

Numbers

I wrote a python script with a few assumptions (that it's 'suspended' from something geostationary, so it has a length of 27415km), it ends 2000km above the Earth's surface. It has a tensile strength of 5.8GPa and density of 1.54 g/cm^3 (Zylon). It can hold a 400kg payload at the bottom of the tether. I found it needed to have a total weight of 2100 tonnes and a maximum diameter of 10.4mm.

Questions

enter image description here caption: simulated space elevator - plotted every two minutes. Not sufficiently high to be geostationary, and I suspect either the initial conditions or modelling errors mean that it failed to remain orbital!

Does this work? I've modelled a simple 7-segment tether, but I need to tweak the initial conditions a little to get it into a good orbit. I worry that something weird happens with orbital mechanics that means this isn't going to be a stable object? Can a tether stay 'vertical' without too much station keeping?

If it does work, it's neat, as it'll take less than 100 flights of the falcon heavy to get it up there, and after than geostationary orbit will be cheap :)

Code for the model and mass calculations.

Edit #1

To look at @kamran's point that "The system is...doomed to...pull the higher eleveation parts into lower/ heavier orbits and crash eventually." It does seem it's inherently overly sensitive to initial conditions, if it is slightly too low, then the gravitational force on it scales much quicker than it would if the object were a point mass. I wonder if this can be mitigated by shortening the tether: The centre of such a contraction would be the centre-of-mass, thus it would 'pull up' the centre-of-gravity out of the gravity well a little. Maybe this would be the mechanism to control this effect? But it does feel like it's not in a stable state and will require active control. See 'fall-to-earth' scenario below!

enter image description here

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    $\begingroup$ Basically a duplicate : engineering.stackexchange.com/questions/3467/… $\endgroup$
    – Solar Mike
    Commented Jan 21, 2018 at 21:07
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    $\begingroup$ More answers on the Space Exploration site such as : space.stackexchange.com/questions/260/… $\endgroup$
    – Solar Mike
    Commented Jan 21, 2018 at 21:15
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    $\begingroup$ This is intriguing stuff, thanks for making the code public. Might have a little play with it if I get chance. $\endgroup$
    – Petrichor
    Commented Jan 22, 2018 at 16:07
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    $\begingroup$ Yes it's easier to fly "part-way" up rather than all the way, but one of the selling points of a space elevator is that no airborne operation is required at all. The energy -to-payload ratio for even an ultralight propellor airplane is way worse than that for the cable/wormgear carriage going up the ground-based tether. $\endgroup$
    – Carl Witthoft
    Commented Jan 22, 2018 at 17:58
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    $\begingroup$ @Petrichor thanks! Feel free - I'm sure there must be a better modelling system somewhere though. Two warnings: 1. The tether force equations include both compressive and tensile components (maybe alter to make it tensile only?). 2. you'll probably want a smaller step size - the energy of the system doesn't quite remain constant (I might add a fiddle factor to enforce this). I've not really seen why this isn't possible yet - it might be unstable - but I think that can be managed. Maybe it's just not worth the benefit. Also I'm not sure what happens when something 'latches on'. $\endgroup$
    – lionfish
    Commented Jan 22, 2018 at 21:09

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I can see the image: A long thin cable arced in a sharp slant backwards, strained by the huge forces of orbital velocity trying to tear it apart and cut it to free orbiting segments.

Also what is there to balance a possible whiplash effect which could possibly run up and down the length of cable and wind the whole system into a violant dance like a wounded snake?

What is the balancing force keeping the end at approximately 2000 kilometers?

What about tidal effects? This is a classical case of effects of moon's gravity working with different intensity on higher and lower parts of the cable twice daily!

The system is inherently imbalances and doomed to coil down and pull the higher eleveation parts into lower/ heavier orbits and crash eventually.

Yes it is coceivebale to have counter balance boosters and rockets to try to maintain the geometry of the system, but most likely whith anacceptable expenses and logistics!

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  • $\begingroup$ Great imagery - but it doesn't answer the engineering question: Is it possible? I don't quite get what you mean about the balancing force? Re last point: All satellites require station-keeping. It's almost certainly not practical today, but I'm just wondering if it's possible/or why it's not. My intuition also is that it'll be unstable, but how and why? What could be done to mitigate such instability? I'll see what other answers appear - I'm surprised this particular design hasn't already been looked at somewhere. I'll run the model at a higher fidelity and see what happens! $\endgroup$
    – lionfish
    Commented Jan 22, 2018 at 9:38
  • $\begingroup$ Your point "doomed to...pull the higher elevation parts into lower/heavier orbits and crash eventually." is interesting - the modelling suggests that yes, the outcome is very sensitive to whether the initial conditions are slightly too low (the tether ends up a little closer to Earth, which increases its weight quicker than for a normal point-mass in orbit, which makes it fall closer, etc). From a practical point, a quick mitigation might be to "shorten" the tether to control this effect - the centre of such contraction would be the centre of mass, therefore moving the centre-of-gravity up? $\endgroup$
    – lionfish
    Commented Jan 22, 2018 at 9:57

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