orbital tethers

[SkiCarver]

For some years now i have had this frustration with the concept of orbital tethers. Basically, it has been oft repeated that you could have a lump of stuff tied to the ground by a fixed 'rope'. this lump would be in geostationary orbit around the earth.

I cannot see how this is even remotely feasible, as tidal forces (from the moon) would cause the orbit of the 'lump' to vary in altitude significantly.

People way smarter than me keep repeating the same idea, so I must be missing something. If someone could explain to me how the issue of tidal forces is not a problem, I would greatly appreciate it!

Many thanks in advance,

Ski.

[Peter B]

I admit I don't know the ins and outs of this technology, but why would there be lunar tidal effects? How much does the altitude of geostationary satellites change at the moment?

In other words, if you have a geostationary satellite, and it stays where you put it, how are things altered by attaching a hypothetical tether between the satellite and the Earth?

By the way, welcome to the BAUT Forum!

[SkiCarver]

Hi Peter, and thanks for the welcome!

I am assuming that satelites are affected by the gravity of the moon as they orbit, but as they are free to move, and the effect has been allowed for in the orbital calculations, i assume it isn't a problem. The tethered 'lump' will have much the same motion as the oceans in that it will rise and fall twice per revolution of the earth (approx).

I may be completely wrong on this, but i would need a good explaination as to why!

[Krowser]

I'm not an expert either but since we have used geostationary satelites for quite some time now, I'd say its ok to assume that the moon's pull is not strong enough to disturb them.

As for a cable, you just need a strong enough material.

I can just imagine:
-Hey! Look, it's a full moon tonight!
--Oh S***!!! The cable!

*SNAP*

[NEOWatcher]

I can just imagine:
-Hey! Look, it's a full moon tonight!
--Oh S***!!! The cable!

*SNAP*

I see an imbedded joke phased into that.

[Gandalf223]

Seems to me this idea, as intriguing as it is, can't work.

A satellite in geostationary orbit is ca. 25,000 miles above the earth. While the satellite itself is moving at the correct speed to stay in orbit, the 'rope' that connects it to the ground will not be. The 24-hour orbital period of the satellite will not be the correct orbital period for any portion of the 'rope', which in fact will NOT be kept in place by orbital forces. Rather, the rope will simply feel the pull of gravity (to a greater or lesser degree, depending on the altitude of a given point on the rope.)

Because the rope is not in orbit, the weight of the rope will add a downward pull to the satellite; this will be in addition to the gravitational force on the satellite. The centrifugal force due to the satellite's 24-hour orbital period is only be sufficient to keep the mass of the satellite up there, not the rope. Therefore, the rope will pull the satellite down, and out of the geostationary orbital sphere.

[NEOWatcher]

Seems to me this idea, as intriguing as it is, can't work.

It's the center of gravity of the system that is in geostationary orbit, not the satellite that holds the rope. That satellite is somewhere above Geostationary. The tension keeps the unit moving together.

[SkiCarver]

Seems to me this idea, as intriguing as it is, can't work.

A satellite in geostationary orbit is ca. 25,000 miles above the earth. While the satellite itself is moving at the correct speed to stay in orbit, the 'rope' that connects it to the ground will not be. The 24-hour orbital period of the satellite will not be the correct orbital period for any portion of the 'rope', which in fact will NOT be kept in place by orbital forces. Rather, the rope will simply feel the pull of gravity (to a greater or lesser degree, depending on the altitude of a given point on the rope.)

Because the rope is not in orbit, the weight of the rope will add a downward pull to the satellite; this will be in addition to the gravitational force on the satellite. The centrifugal force due to the satellite's 24-hour orbital period is only be sufficient to keep the mass of the satellite up there, not the rope. Therefore, the rope will pull the satellite down, and out of the geostationary orbital sphere.

You are correct in that the 'lump' will need to hold the up the weight of the rope. The geostationary position of the 'lump' would be at a higher altitude than a normal geostationary satellite. The additional force required to maintain the orbital period would come from the tension in the rope.

oops, beaten to it!

[Krowser]

What is the point of having a cable? Unless you're thinking of building a space elevator.

[nauthiz]

What is the point of having a cable? Unless you're thinking of building a space elevator.

I think the whole point is to build a space elevator.

[NEOWatcher]

What is the point of having a cable? Unless you're thinking of building a space elevator.

The thread did say "tether" instead of "cable" which implies that special case of a cable that controls another object.

[Krowser]

Well in my main language, a tether is a cable is a rope.

In any case, I guess the tether is the way to go until we find a feasible way of building the mass driver tower. (wiki, space elevator)

[Gandalf223]

It's the center of gravity of the system that is in geostationary orbit, not the satellite that holds the rope. That satellite is somewhere above Geostationary. The tension keeps the unit moving together.

Before we go much farther, we need to agree on at least one thing: any imaginable tether (i.e., one constructed by humans) will be completely flexible. IOW, anything we build, no matter the material or method, will be as limp as a piece of thread by the time we make it 25,000+ miles long. Thus we must postulate that our tether can work ONLY in direct tension; a tether that goes straight up from the surface of the earth, can ONLY pull straight down.

Now that our satellite has been forced to be above the geostationary orbit, its natural orbital period will be slower than 24 hours. In order to keep up with the ground beneath it, the satellite will require an outside force to (a) speed it up, and (b) prevent it from rising into an even higher orbit.

Our tether must therefore reach the satellite at an angle, such that it is pulling the satellite forward, in addition to downward.

Because our tether is as limp as wet spaghetti, it must therefore assume a spiral pattern, all the way down to the surface of the earth. Something like the yellow line in the image below.

Unfortunately, any part of the now-spiral tether which is below the geostationary orbit, will now be orbiting TOO SLOWLY to retain its own altitude. Any part of the tether that is below geostationary altitude, will now require an UPWARD force to prevent it from falling into a lower orbit.

Meanwhile, as some portion of the tether falls to a lower orbit, it must assume a shorter orbital period, lest it fall all the way to the ground. Unfortunately, the satellite above, with its 24-hour period, will prevent the tether from orbiting faster than 24 hours. Therefore, any portion of the tether that is below geostationary altitude will fall to earth unless held up from below.

But our tether has no compressive strength. So the tether cannot maintain the required spiral path (from ground to satellite) to maintain the satellite in the required orbit. Instead, the tether will pull itself downward, and the angle of force it imparts to the satellite will never stabilize at the angle required.

Worse, for any additional increase in energy (i.e., moving the satellite to an even higher orbit) the increased mass of the tether will outweigh (sorry) the advantage of the higher orbit. Nor will the center of mass of the system stabilize at the geostationary orbit, since it lacks the rigidity to function as a unit. The tether will inexorably pull the satellite downward, until the satellite falls to earth, or the tether breaks.



[Note to admins: the linked image is on my own webspace.]

[NEOWatcher]

Before we go much farther, we need to agree on at least one thing: any imaginable tether (i.e., one constructed by humans) will be completely flexible.

Yes; but listening to your explanation gave me a headache, and the example explains to me why.
Yes; the rope is tight, but let's say the satellite is at 26000 miles. How far around the earth do you think that upper portion of the tether will reach?
What happens is that the lower and lower portion of the tether is going faster and faster. Because of the higher speed, it is continually being held very tight as the upper portions try to speed up the lower portions.

As a rope get's tight, it gets straight. So, it won't wrap around, it will just slant around the center of gravity.

So, with the center of gravity at GEO, the satellite at 26000 miles will be pulled along, and that extra angular momentum will cause the satellite to impart a pull upward. It would be the same force that the 25000 speed at the 26000 altitude would elongate the orbit.

Added.
It's the same thing spinning a bucket tied to a rope around your head.
As you speed it up, how come that rope doesn't wrap around your body because the bucket is going slower than you are pulling on the rope.
Same thing, the bucket is the satellite, and your grip on the rope is the weight of the lower part of the tether.

[Grey]

You can also solve the problem of the downward pull by having the satellite at normal geostationary altitude, but have the tether extend well beyond that. The tether below pulls downward on the satellite, but the tether above pulls upward on the satellite. You can get those to balance out, and that actually works out nicely for an elevator. You can send things you want to launch all the way to the far end, and then let them go, and they've already got a very large velocity boost.

Of course, the real problem is that to actually build one of these, you need a material with a tensile strength to mass ratio a few orders of magnitude higher than anything we know how to make. Carbon nanotubes show promise, and have a theoretical tensile strength high enough, but currently, we can only manufacture them a few millimeters long (and the tensile strength of a bundle of separate fibers is significantly lower than the strength of each fiber individually).

[Gandalf223]

... but the tether above pulls upward on the satellite.

I'm having a hard time understanding what the other end of the "tether above" is going to be attached to. The moon?

[NEOWatcher]

I'm having a hard time understanding what the other end of the "tether above" is going to be attached to. The moon?

Nothing.
Since that portion of the tether wants to move slower than the sat at geo, it will also get pulled tight.
The tether doesn't even require a satellite. The effects come from its own mass.

[Krowser]

Added.
It's the same thing spinning a bucket tied to a rope around your head.

What exactly made you want to try this?

It's a good example though.

[NEOWatcher]

What exactly made you want to try this?

It's a variation of a very common example that demonstrates centripital force usually done vertically.

Or "see? the water doesn't come out even when it's upside-down"

I thought of other examples, but didn't think they would be as universal.
For example, a toy plane on a string.

[Delvo]

To account for little things that might tend speed up or slow down the thing's orbit or cause it to fall forward or backward, including the mass and weight of things being moved up or down, the basic engineering of any such device would have to include some "extra" length of cable and a mechanism to reel the cable in or out (on the orbiting mass's end), and maybe some little rockets pointing forward, back, right, and left. Then whenever something seems to disturb your path in the thing, you just disturb it back the opposite way yourself by letting some cable out or pulling some in (or maybe using a rocket).

[neilzero]

Skicarver is correct, the space elevator won't work if the the lump = counter weight is at GEO orbit. It needs to be higher than GEO = perhaps 84,000 kilometers = twice GEO radius. The counter weight travels twice as fast as the GEO point on the tether, so it pulls the tether taught by centripetal force (centrifugal if you prefer)
If the lump = counter weight is low mass and the tether is tapered = more mass near GEO, the total radius can be as much as 336,000 kilometers = 8 times GEO radius = just barely clears the Moon. This means the counterweight is traveling 8 times faster than GEO orbital speed = ideal for getting to Mars and other planets fast with no propellant except to slow down at the destination, and for mid course correction.
Earth's gravity is reduced by about 21 squared = 441 times at an altitude of 84,000 kilometers, so the gravity only opposes the centripetal force slightly. The moon and sun gravity are almost as significant, so they do need to be considered. The elevator is unstable, if it only pulls on the Earth anchor a few hundred kilograms. One design is thinking 20 tons average pull for a space elevator with a 20 ton climber gross weight. Even so it may occasionally be prudent not to launch another climber when the the sun and moon will be at max and minimum counter weight effect while there are climbers somewhere on the tether other than near GEO altitude. The climber is weightless at GEO altitude. The climbers can manage the transients at least a little by accellerating or decellerating at the apropriate instant.
There are more complications. The tether behaves like an extremely long period bungee cord = It starts to stretch as soon as the 20 ton climber is attached, but the stretch transient does not travel at the speed of light; perhaps only a few hundred miles per hour, so a fast ascending climber can out run it's stretch transient producing some effects something like supersonic aircraft. Perhaps this is one reason they are thinking not much faster than 200 kilometers per hour for assent speed of the climbers. Faster would be nice as it takes 420 hours to reach the far end at an average of 200 ilometers per hour , a distance of 84,000 kilometers.
Besides the stretch transients which may persist for weeks, there will be horizontal transients, such that the tether is not a straight line. These will be used to dodge the tether around satellites and space junk which will occasionally be on a collision course. Some have supposed a large space station at GEO altitude: But my guess is all kinds of transients will shake the GEO altitude station if it is attached to the tether, possibly over stressing the tether. As I see it the payload is released from the tether at about GEO altitude and needs to travel several miles in free fall to land safely on the GEO station. Typically the tether is called a ribbon. www.liftport.com has a great forum on the space elevator and related topics. Neil

[mugaliens]

I cannot see how this is even remotely feasible, as tidal forces (from the moon) would cause the orbit of the 'lump' to vary in altitude significantly.

The lump's not in orbit. It's higher in altitude than a geosynchronous orbit, so it's pulling on the tether full time.

[tony873004]

... as tidal forces (from the moon) would cause the orbit of the 'lump' to vary in altitude significantly.

An object placed in a circular orbit at geostationary altitude will experience an oscillating eccentricity due to the moon and sun. In a period of approximately 10 years, its orbit will go from circular to a maximum eccentricity of about 0.0007, and back to circular. At maximum eccentricity, there will be a difference of about 60 kilometers between the object's apogee and perigee. During this cycle, its semi-major axis, and hence its period will remain steady.

[korjik]

Seems like everyone missed that the moon is up to 23 +/- 5 degrees off of the plane the skyhook would be on. Sun would be 23 degrees off.

The sat at the top of the tether would need to be able to flex enough to handle those perterbations.

[SkiCarver]

An object placed in a circular orbit at geostationary altitude will experience an oscillating eccentricity due to the moon and sun. In a period of approximately 10 years, its orbit will go from circular to a maximum eccentricity of about 0.0007, and back to circular. At maximum eccentricity, there will be a difference of about 60 kilometers between the object's apogee and perigee. During this cycle, its semi-major axis, and hence its period will remain steady.

interesting answer. what would be the variation in altitude of the 'lump' on a normal orbit in the short term? There will be some thanks to the moon and sun, and i find it hard to think that stretch in the cable or lifting/lowering the cable twice an orbit is feasible!

[Van Rijn]

interesting answer. what would be the variation in altitude of the 'lump' on a normal orbit in the short term? There will be some thanks to the moon and sun, and i find it hard to think that stretch in the cable or lifting/lowering the cable twice an orbit is feasible!

Remember, with the synchronous cable concept, there is a "counterweight" somewhat beyond geostationary orbit holding a cable under significant tension. It is not a spacecraft in free orbit. The main effect of the moon and sun would be as a source of cable oscillations. If you google around you can find articles on the subject.

[Jeff Root]

My uninformed thoughts:

If the cable were magically unstretchable, the altitude of any weights
along it would not need to change as the forces from the Moon and
Sun change. The cable is always under tension. That's a key to
understanding its behavior. It will curve in different directions along
its length, dynamically, and forces will need to be applied to it to limit
the speed and extent of the deviations from straightness.

But with a non-magical cable, the biggest problem may be unwanted
stretching and resulting longitudinal vibrations.

-- Jeff, in Minneapolis

[Gandalf223]

What happens is that the lower and lower portion of the tether is going faster and faster. Because of the higher speed, it is continually being held very tight as the upper portions try to speed up the lower portions.

That's not possible. The top end of the tether is attached to a satellite with a 24 hour orbital period. The bottom end of the tether is attached to the ground, which not coincidentally also has a 24 hour rotation. All parts of the tether will therefore have a 24 hour orbital period, and any part of the tether below geosynchronous altitude will lack the orbital speed (= energy) to maintain its orbit.

Obviously, I remain unconvinced that this pipe dream is even remotely possible outside the Science Fiction Book Club. Even if it were (which it ain't) it's gonna get cut into pieces by bits and pieces of Iridium 33...

[cjameshuff]

That's not possible. The top end of the tether is attached to a satellite with a 24 hour orbital period. The bottom end of the tether is attached to the ground, which not coincidentally also has a 24 hour rotation. All parts of the tether will therefore have a 24 hour orbital period, and any part of the tether below geosynchronous altitude will lack the orbital speed (= energy) to maintain its orbit.

Pick up a string...does it swing out to one side because it is moving some 7906 km/s too slowly to remain in orbit? No, it stretches out along a line between your hand and the center of the Earth, and takes up a rotational period of 24 hours.

Viewing the tether as a series of elements, the only element in orbit is the one exactly at geosynchronous altitude. The elements below that, moving at velocities that would otherwise leave them at apogee of elliptical orbits, are hanging from the tether above them, and the elements above it (including a possible counterweight), which would be at perigee of elliptical orbits if not attached to each other, are hanging from the tether below them.

Your problem seems to be that you're failing to account for forces other than gravity. At every point along the elevator, the tension of the tether to either side and the gravitational acceleration add up to force that portion of the elevator along a circular path with a 24 hour period, despite it moving at the wrong velocity for a circular ballistic orbit of either that altitude or that period. This isn't a contradiction, those portions of the tether aren't ballistic.

An Earth space elevator is currently science fiction, but only because the needed materials currently exist only in theory. They do exist in theory, and there's plenty of motivation to develop them aside from the potential for a space elevator. Elevators on Mars, asteroids, and several other bodies are possible with current materials. There is no fundamental instability, the elevator will not wrap around in a spiral. It will sway from side to side as payloads go up and down, but will experience restoring forces from its ground anchor that return it to its original position.

[mugaliens]

But with a non-magical cable, the biggest problem may be unwanted stretching and resulting longitudinal vibrations.

So long as they're not harmonically edditive every half orbit...