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There are examinations of lunar tethers going through the EML1 point, and rotating tethers in various orbits of the Moon. But I haven't seen an examination of a tether in orbit that doesn't rotate. Wouldn't that have advantages?

A tether with its center of gravity at 3000 km altitude would orbit at a speed of 1.02 km/s. If the foot of the tether extends to as near the surface as it safely can - say 10 km away - then the foot would travel over the surface at a speed of 370 m/s.

That is less than a quarter of the speed needed to attain orbit from the surface. Sure, you still need a rocket to get to the foot, but it doesn't need to get very high or go very fast. The same approach using a tether at 10 000 km gives a speed at the foot of 95 m/s.That is still a sixth of the distance needed to go through the L1 Lagrange point, and avoids the issue that that point moves around. The best length would seem to mostly depend on getting the needed Zylon into place, construction and maintenance issues, and issues of climbing and descending the tether.

We were considering this as especially attractive as a way to move material from the lunar poles to the lunar equator, as the craft wouldn't need to climb the tether, it just grabs hold of it until it has reached its destination, and then lets go. It only needs enough propulsion to catch up to the foot and then land softly.

What would be the issues with such a system?

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  • $\begingroup$ This tend to generate large electrostatic potentials due to the ionizing radiation from the sun and the object moving through magnetic fields. $\endgroup$ – honeste_vivere Aug 29 '16 at 12:44
  • $\begingroup$ @honeste_vivere The Moon doesn't have much of a magnetic field. That really applies to tethers orbiting Earth, doesn't it? $\endgroup$ – kim holder Aug 29 '16 at 13:40
  • $\begingroup$ True, the resultant electric field would be smaller as there are only anomaly fields at the moon but there is the solar wind as well and that moves much faster than spacecraft orbit. It would be an interesting problem to work out though... $\endgroup$ – honeste_vivere Aug 29 '16 at 13:56
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Employing Wolfe's spreadsheet I'm getting numbers similar to Hohmann fan's. That's reassuring.

With tether center balance point at 3000 km altitude and tether foot at 10 km altitude I get:

Foot speed: .375 km/s

Acceleration at foot 1.52 m/s^2

Zylon taper ratio 1.43

Tether mass/payload mass ratio: 1.63

With tether center balance point at 10000 km altitude and tether foot at 10 km altitude I get:

Foot speed: .096 km/s

Acceleration at foot 1.6 m/s^2

Zylon taper ratio 1.8

Tether mass/payload mass ratio: 7.11

CONCERNS

Momentum change

Unless the tether and anchor mass is substantially more massive than the payload, catching or dropping payloads would substantially change the tether's orbit. Which is why a big anchor mass is desirable.

The anchor mass I'd like to see is a small asteroid retrieved with a Keck style vehicle. Not only would the Keck vehicle retrieve a massive rock, it also has Hall thrusters and robust solar arrays. Hall thrusters can have 30 km/s exhaust velocity. Yes, thrust is minute but it can build up over time if catches and throws aren't too frequent.

But in your scenario, the net momentum change the ion engines have to compensate for is zero. In the act of catching a payload as it passes over the equator, the tether drops a little. In the act of releasing the same payload over the poles, the tether rises a little.

Making the Catch

The payload would have to be fired at the right time and speed so that it matches position and velocity with tether foot at it's apolune. But even when it matches position and velocity, the approximately 1/6 g is pulling the payload away. The catch must be done quickly.

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  • $\begingroup$ Wolfe's spreadsheet - right, i'd forgotten i even had that. I'll set it up in the morning... And i'll check out the Keck set up as a reference point. There are other things being considered too, and i'm trying to shape it into a series of sensible questions, hopefully. For instance, if a large tug from Earth docked with the asteroid counterweight, it could add its mass and engine power to the tether while the heavy stuff was being sent down it, making the balancing act easier just when most needed. $\endgroup$ – kim holder Jul 1 '16 at 3:00
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Concern 1: as the ship crawls up the tether, the tether is pushed downward. You can have a counterweight crawling the other way to balance it, but you ultimately need as many kilogram-trips from top to bottom as bottom to top, or spend stationkeeping thrust, or something.

Concern 2: all the spacecraft rendezvous we've done thus far have been in free fall with the two craft in very similar orbits. This can done in a very leisurely way with little fuel expenditure. In your case, though, the bottom of the tether is moving much slower than orbital speed, so from the frame of reference of the arriving spacecraft, it's accelerating constantly at 1/6g. The ship has to match that acceleration on the approach, and every second counts. If the grabber doesn't work, the ship is not left on a safe trajectory.

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  • $\begingroup$ Concern 2 says to me the craft needs to be able to soft land under its own power rather than taking advantage of any fixed launch or landing mechanism (which we'd considered). So if it doesn't make the grabber, it is an abort situation, using the fuel it had for landing anyhow. That seems fine for a cargo vessel, and SpaceX's precision with their first stage landings seems a hopeful sign. $\endgroup$ – kim holder Jun 30 '16 at 21:07
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    $\begingroup$ Fair enough. It roughly doubles the needed delta-v; for fungible cargo it might make more sense to just write the ship off if it can't grab. $\endgroup$ – Russell Borogove Jun 30 '16 at 21:19
  • $\begingroup$ Note that for what i'm planning right now, a lot of the cargo stays on the Moon, so for that the delta-v was needed anyhow. It also occurs to me that it might be possible to raise the altitude of the COG enough to slow the horizontal speed, and shave the height of the foot enough to lower the vertical speed, that maybe an emergency system of airbags would make sense. Maybe. $\endgroup$ – kim holder Jun 30 '16 at 21:31
  • $\begingroup$ Alas, Selenosynch orbit altitude is outside of the moon's Hill sphere, so you can't just jump up and grab. $\endgroup$ – Russell Borogove Jun 30 '16 at 22:31
  • $\begingroup$ Yep. Ran into that already :) $\endgroup$ – kim holder Jun 30 '16 at 22:53
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If you are going specifically for the issues, here are some:

Orbital stability

  1. Your tether is in reality orbiting in a two-body system, as the Earth's gravity have a significant influence when getting far enough from the Moon. The altitudes you are talking about is well within the Hill sphere of the Moon though, so this disturbance is pretty minor.
  2. Mass-cons in the lunar crust causes irregularities in lower orbits, affecting the foot of the tether.

Any of the above factors are possible to correct for, but that requires some station keeping propellant budget.

Changing distribution of mass

  1. A craft climbing the tether, either up from the foot, or down for landing changes how the mass is distributed along the tether.
  2. Even a craft only grabbing the foot and hanging there would change the centre of mass.

This can have some consequences. Firstly, this applies a torque on the tether system, causing things like pendulum movement, stress, and in some cases a slightly changed orbit. It would be a bad thing if the foot collides with the lunar surface. Secondly, momentum change over time has to be balanced, otherwise the change in momentum necessarily alters the orbit of the tether.

To reduce the short term problems, having a grater tether mass is a good idea, as all types of oscillations and momentum change would have smaller consequences. To preserve momentum over time, you could either have a strict management of up-mass versus down-mass, or use things like ion-engines to provide momentum at high efficiency.

Force on the tether

Is this a problem? Let me see..

from 10 km above the surface to orbital velocity at an altitude of 3000 km, the "stress" (acceleration over length) should be $1.32 \cdot 10^6 \frac{m^2}{s^2}$. Considering the density and tension strength of Zylon, the taper ratio is only 1.4, meaning there should be plenty of margin left for movable counterweights, power cables for an elevator and other things.

Docking

At $1.52 \frac{m}{s^2}$, the acceleration is significant at the tether foot. That means docking a craft is very different from docking in weightlessness. As a minute of hoover time costs you $90 \frac{m}{s}$ of $\Delta v$, landing and docking may as well be as costly as actually getting up to $370 \frac{m}{s}$. The acceleration requires a more powerful RCS system as well. In short, time is expensive, and cutting time may come at the cost of a less gentle and more risky docking. The connection would also have to support the weight of the spacecraft.

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  • $\begingroup$ The 3000 km orbital altitude was rather arbitrarily selected... I'll see if it might be worth a follow up question that considers what altitude might be best for a specific system (using Zylon and SEP engines on the counterweight, and whatever other specifics can be defined). $\endgroup$ – kim holder Jun 30 '16 at 21:13
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    $\begingroup$ I'm inclined to say you ride the main engine at low throttle to match acceleration and use small RCS to make the docking maneuvers, rather than make the RCS bigger. $\endgroup$ – Russell Borogove Jul 1 '16 at 2:48

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