Explain the orbital physics of the JAXA Tether experiment?

[sophiecentaur]

Interestingly, that does seem to be the preferred deployment.

How can that be a stable situation when the natural orbit periods at the two levels are different? But I see you use the word "deployment" so perhaps you are referring just to the initial condition. If that's the case, I still see the possibility of a long term 'pendulum' swinging of the (undamped) tether. But I suppose that an electrical tether could dissipate that energy due to resistance.
It's good that you have been in contact with the JAXA KITE team.

 

[SteveO33]

How can that be a stable situation

I had wondered the same... and that orbital observation is correct... It appears that the lower end is dominated by centripetal forces of gravity - it's pulling forward... the upper end is in a lower gravitational gradient and not as dominant so it drags... End forces are tangential and along the radii, but the one along the tether isn't?
And as we had discussed, if you un-tether the two objects, the one in lower orbit, will have a faster orbital period (having to circumscribe less distance per orbit) than the upper one which is in a slightly higher orbit (will have a slightly slower orbital period having to circumscribe slightly more distance per orbit).

But some how the EMF (electromotive force) does help stabilize...
Consider: in one of the Non-Conducting Tether experiment of old, they did observe a "librating" (oscillating) condition... but later experiments with Conductive Tether's do not mention this... The one thing they do mention is voltages and currents far in excess (3x) of what was predicted by calculations - just getting into this area. That aside, agree, the EMF resistance along the entire tether length could be providing the necessary damping of the two body (ends) system - probably doesn't need much to dampen any oscillatory forces caused by the deployment which would allow it to settle nicely into a stable state. Still suspect that over a really long time, the two body system would settle into a single orbit around the center of mass of the two, but EMF would prevail before this and cause it to deorbit.

 

[mfb]

If you un-tether the objects in the stable vertical configuration, both will follow an eccentric orbit. The upper one will have its perigee at the point of disconnection (because it is moving faster than the speed of a circular orbit there), the lower one will have its apogee there (because it is moving slower than the speed of a circular orbit there).

But some how the EMF (electromotive force) does help stabilize...

A vertical tether is stable without any electromagnetic forces.

 

[sophiecentaur]

If you un-tether the objects in the stable vertical configuration, both will follow an eccentric orbit. The upper one will have its perigee at the point of disconnection (because it is moving faster than the speed of a circular orbit there), the lower one will have its apogee there (because it is moving slower than the speed of a circular orbit there).A vertical tether is stable without any electromagnetic forces.

I can appreciate that the two ends will leave a circular orbit of the tether breaks because there will be a change in force imparted to each end as the tension is removed.
having thought about it further, it now seems reasonable that a radial tether can be stable - in fact the only way for the orbit to be circular is if there is a constant radial resultant force from gravity plus the tension. For that to happen, and gravity always acts radially, so the tension should also be radial. I now have a problem with the idea of a 'trailing' tether. Any electromagnetic braking force would then cause the tether to trail and produce a change in orbit, with the resultant being no longer radial.

 

[mfb]

A non-radial tether needs a position-dependent force to keep its orientation. Unless it is exactly aligned with the flight direction, then it is in an unstable equilibrium.

 

[sophiecentaur]

So we are still left with the question about what is going wrong with the experiments. I guess no one wants to spend more or less the whole cost of a launch on this sort of project, on the grounds that not everyone is convinced that it's worth doing in the first place. They don't do "nice if" experiments in Space.
I guess the Moon Elevator could turn out to make tethers more popular. (So lucky that the Moon happens to be locked to Earth).

 

[SteveO33]

Ah, not exactly buying that whole Moon Elevator thing... it still makes good sci-fi...
But, I did find a gem of a real video on YouTube...
This shows the Tether deployment that was part of STS-75 way back in 1996...! Confirmed a bunch of things for me...
Check out that curve (they call it a bow) in the tether... yeah...
Thrusters on the Tether-end satellite to move to a higher orbit and to 'pull' the tether from the Tether-source.. yeah...
Perpendicular / orbitally-rearward deployment.. yeah...
Clearly NASA put a lot of money and effort put into this experiment...
Very, very long tether deployed - 19-20 KM...
Lots of power (their term) generated... couple of KW's...
Tether broke - actually looks more like it was electrically fried (melted)... at the near end...
And last, but not least - much more power (3x) than was expected/predicted and ultimately, too unpredictable in behavior..
Now I see why NASA is not doing tethers anymore...
I'm probably going to put Space Tethers into my Unsolved Mysteries folder along with "how do clouds hold up tons of rain moisture"...

 

[sophiecentaur]

"how do clouds hold up tons of rain moisture"...

An H₂O molecule has much less mass than an O₂ or N₂ molecule so water vapour is 'lighter than air'. The condensed water droplets are held up by convection until they have accumulated sufficient weight to drop out as rain.
Air is 'not a sponge, holding water'.