Tether problem

Leovinus · Jan 26, 2005

Assume two spacecraft of the same mass are orbiting in the same plane, but at different altitudes. Let's assume 100 miles and 120 miles. At some point in their orbits, they would be one right over the other. Let's say that at this time, an non-stretching rope was instantaneously connected to both ships. What will happen? My guess is that the lower craft, moving faster, will tend to move forward in the united system whereas the higher craft will tend to move backward in the united system. Thus, I predict a rotating system with a center of rotation midpoint in the rope at 110 miles. At the bottom of the loop, you're moving faster around the orbit and at the top of the loop you're moving slower. I hope I explained that correctly. What do you think? Will the rope stay straight? Will the two craft crash into each other? Will the whole thing come tumbling down to Earth? <div class="Discussion_UserSignature"> </div>

bobw · Jan 26, 2005

Is it a massless teather? <img src="/images/icons/smile.gif" /> I don't have a clue but I think that if the teather was stationary when it got attatched then pulling on the ends would not accelerate the center intstantaneously. This would cause the teather to curve hence shortening the distance between the satellites. Also, I think that accelerating the teather would use a larger fraction of the momentum of the lower satellite. It would get chaotic, radiate energy as heat and crash (edit: into the planet) eventually. Don't use this answer on your homework! <div class="Discussion_UserSignature"> </div>

Saiph · Jan 26, 2005

they'd start spinning together, around a point halfway between them. It's exactly analogous to running past a person, and grabbing them,and holding them at arms length. <div class="Discussion_UserSignature"> --------------------SaiphMOD@gmail.com -------------------"This is my Timey Wimey Detector. Goes "bing" when there's stuff. It also fries eggs at 30 paces, wether you want it to or not actually. I've learned to stay away from hens: It's not pretty when they blow" -- The Tenth Doctor, "Blink" </div>

Leovinus · Jan 27, 2005

Let's assume a tether that has mass, is flexible, but doesn't stretch. If it instantaneously was attached to both ships, then the weight of the tether would probably outweigh the ships. As such,I think it would tend to fall straight to the ground and pull the ships down with it. So let's simplify the problem a bit: Assume a Star Trek tractor beam type set up. When the ships line up, the beam is turned on. The effect of the beam is to maintain a constant distance between the two ships. The beam has no mass and therefore serves as the instananeous masseless tether. Then I think we're back to the problem as I initially imagined it and we would end up with some kind of rotating system. <div class="Discussion_UserSignature"> </div>

igorsboss · Jan 27, 2005

they'd start spinning together, around a point halfway between them. It's exactly analogous to running past a person, and grabbing them,and holding them at arms length. Too simple... Although this is a reasonable first-cut guess at the solution, it is extremely significant that these objects are not in an inertial frame of reference. Space is warped significantly more for the object at 100 miles high than it is for the object 120 miles high. That is, the acceleration due to gravity is significantly more for the lower object than it is for the upper object. Since F=ma, the masses are the same, but the acceleration is different, the lower object contributes more force to the tension on the tether than the upper object does. This force imbalance accelerates the upper object, and slows the lower object. Although they may spin about each other, I think the center of the spin will always be at an altitude which is LOWER THAN the midpoint of the two objects. (Except when they are at exactly the same altitude.) As a reference experiment, suppose you connected two weights of different weights by a string, and started them spinning on a low-friction table here on Earth's surface. The center of the spin would be their mtual center of mass, which would be closer to the heavier ball. But in the tether case, the warpage of space makes the lower-altitude object behave as if it were always heavier than the other one. For each half-revolution, the light vs. heavy roles reverse, so that the lower object always seems heavier. I haven't checked these results. I'm quite willing to be wrong about this. If you disagree, I invite you to please back up your claim.

bobw · Jan 28, 2005

I cheated. I'm surprised. I'm no rocket scientist (not surprised that I'm no rocket scientist) <img src="/images/icons/smile.gif" /> http://cfa-www.harvard.edu/spgroup/TetherHBK_file3.pdf <blockquote>In reply to:<hr /> When it is oriented such that there is a vertical separation between the two masses, the upper mass experiences a larger centrifugal than gravitational force, and the lower mass experiences a larger gravitational than centrifugal force. (The reason for this is described later in the discussion.) The result of this is a force couple applied to the system, forcing it into a vertical orientation. This orientation is stable with equal masses, and with unequal masses either above or below the center of gravity. Displacing the system from the local vertical produces restoring forces at each mass, which act to return the system to a vertical orientation. The restoring forces acting on the system are shown in Figure 4.2 If the two end masses were in Keplerian circular orbits at their respective altitudes and were not connected by a tether, their orbital speeds would be different from the tethered configuration. For the upper mass, applying equations (1) and (2), bunch of math stuff here It can be seen that without the tether, the upper mass would move at a slower speed and the lower mass would move at a higher speed. The tether, therefore, speeds up the upper mass and slows down the lower mass. This is why the upper mass experiences a larger centrifugal than gravitational acceleration, and why the lower mass experiences a larger gravitational than centrifugal acceleration. The resulting upward acceleration of the upper mass and downward acceleration of the lower mass give rise to the balancing tether tension. They also produce the restoring forces when the system is deflec</blockquote> <div class="Discussion_UserSignature"> </div>

Leovinus · Jan 28, 2005

Artificial gravity was not quite what I expected. Thanks for digging that up. <div class="Discussion_UserSignature"> </div>

siarad · Jan 28, 2005

That seems a great form of artificial gravity, no dizzyness. <img src="/images/icons/wink.gif" />

Saiph · Jan 28, 2005

igor: Just a note, relativistic affects of space time are quite neglibible for the earth. It really doesn't enter into it. anywho, good approach, as this section: <blockquote>In reply to:<hr />Since F=ma, the masses are the same, but the acceleration is different, the lower object contributes more force to the tension on the tether than the upper object does. This force imbalance accelerates the upper object, and slows the lower object. <hr /></blockquote> was in the exerpt bobvanx posted. We both however, failed to fully think through the situation. That's what I get for "shooting from the hip" as my advisor says. <div class="Discussion_UserSignature"> --------------------SaiphMOD@gmail.com -------------------"This is my Timey Wimey Detector. Goes "bing" when there's stuff. It also fries eggs at 30 paces, wether you want it to or not actually. I've learned to stay away from hens: It's not pretty when they blow" -- The Tenth Doctor, "Blink" </div>

igorsboss · Jan 28, 2005

Stability, huh? Well I'll be darned. I haven't read the excerpt yet. I think I'll go work it out for myself on paper, when I have a moment. Very interesting.

remcook · Jan 29, 2005

the whole thing will be gravity gradient stabilised. This means that there will always be a force acting in such a way that the tether will tend to point towards the centre of the Earth (if it's a rigid tether). Some satellites, and especially small ones, are stabilised in this way, because it requires no fuel! Because the two spacecraft will have different (angular) velocities at the start, they will start oscillating around the c.g., around the line c.g. - centre of the Earth.

nexium · Mar 30, 2005

Vertical with respect to Earth's surface seems correct in light of some space elevator theory. Real tethers are elastic and do stretch which is good otherwise the tether would break when the system took up the slack. A few rotations and long term oscillations would occur unless they were surpressed. 120 miles is not high enough to avoid a decaying orbit, so you should think perhaps 150 miles and 300 miles. You can likely start with both about 225 miles, give either a tiny push and they would move gently to the vertical position in a week or so. Even with the much longer tether the artifical gravity would be (I think) less than 1/10 that on Earth's surface, so the artifical gravity would be worse than useless. Neil

nexium · Mar 31, 2005

Artificial gravity can be produced by tethering two craft (somewhat different mass is ok) A lot of energy is needed to get them to rapidly rotate about their center of mass. There will be a small amount of precession and wobble as the pair orbit Earth, which can be partially corrected for at a small cost of energy. The craft with the least mass will have the most gravity. Present tethers are marginally strong enough to produce one g at a length that minimizes the dizzy effect when one is walking and moving = corriellus effect. A sudden breaking of the tether would cause a very bad jerk, throw everything across the room (including people, not strapped in) and possibly cause one of the craft to be thrown into Earth's atmosphere where it would burn up. A carefully planned cutting of the tether could send the smaller craft to the Moon, possibly to Mars! Neil

Saiph · Mar 31, 2005

Mass wouldn't affect the artificial gravity in that situation, only rotation speed. Disconnecting wouldn't produce a jerk at all (well, technically it would, as all acceleration would cease, and a change in acceleration is a "jerk"). However, the contents of the craft would only notice a weightlessness had returned (they've entered free fall conditions again). The precession may not be a big deal, depending on the size, orientation and rotation speed of the craft. I certainly wouldn't want to counter it with any active system. I'd just adjust everything so it isn't there, or isn't fast enough to matter. 1g is not required, as even a low g environment does wonders for human phsiology. It's still detrimental, but not nearly as bad. <div class="Discussion_UserSignature"> --------------------SaiphMOD@gmail.com -------------------"This is my Timey Wimey Detector. Goes "bing" when there's stuff. It also fries eggs at 30 paces, wether you want it to or not actually. I've learned to stay away from hens: It's not pretty when they blow" -- The Tenth Doctor, "Blink" </div>

Saiph · Apr 1, 2005

actually the answer to them being connected in orbit was for them to become verticle with respect to the earth's surface due to torque effects. <div class="Discussion_UserSignature"> --------------------SaiphMOD@gmail.com -------------------"This is my Timey Wimey Detector. Goes "bing" when there's stuff. It also fries eggs at 30 paces, wether you want it to or not actually. I've learned to stay away from hens: It's not pretty when they blow" -- The Tenth Doctor, "Blink" </div>

najab · Apr 1, 2005

<blockquote>In reply to:<hr />If they become connected then the orbit of the higher will fall and the lower will rise, to a orbit between the 2 proportional to an average energy of their masses and and altitudes.<hr /></blockquote>Not so. Each object is in a stable orbit before they are joined. The two satellites will continue to orbit at their original altitudes, but the lower one will be going too slow for it's orbit, and the higher one will be going too fast, hence the tether will be in tension.

nexium · Apr 6, 2005

Hi naja: You have expressed the majority opinion, which is correct, I think. Neil

Saiph · Apr 6, 2005

steve, did you read bob's post: <blockquote>In reply to:<hr />I cheated. I'm surprised. I'm no rocket scientist (not surprised that I'm no rocket scientist) http://cfa-www.harvard.edu/spgroup/TetherHBK_file3.pdf <blockquote>In reply to:<hr /> When it is oriented such that there is a vertical separation between the two masses, the upper mass experiences a larger centrifugal than gravitational force, and the lower mass experiences a larger gravitational than centrifugal force. (The reason for this is described later in the discussion.) The result of this is a force couple applied to the system, forcing it into a vertical orientation. This orientation is stable with equal masses, and with unequal masses either above or below the center of gravity. Displacing the system from the local vertical produces restoring forces at each mass, which act to return the system to a vertical orientation. The restoring forces acting on the system are shown in Figure 4.2 If the two end masses were in Keplerian circular orbits at their respective altitudes and were not connected by a tether, their orbital speeds would be different from the tethered configuration. For the upper mass, applying equations (1) and (2), bunch of math stuff here It can be seen that without the tether, the upper mass would move at a slower speed and the lower mass would move at a higher speed. The tether, therefore, speeds up the upper mass and slows down the lower mass. This is why the upper mass experiences a larger centrifugal than gravitational acceleration, and why the lower mass experiences a larger gravitational than centrifugal acceleration. The resulting upward acceleration of the upper mass and downward acceleration of the lower mass give rise to the balancing tether tension. They also produce</blockquote></blockquote> <div class="Discussion_UserSignature"> --------------------SaiphMOD@gmail.com -------------------"This is my Timey Wimey Detector. Goes "bing" when there's stuff. It also fries eggs at 30 paces, wether you want it to or not actually. I've learned to stay away from hens: It's not pretty when they blow" -- The Tenth Doctor, "Blink" </div>

heyscottie · Apr 6, 2005

It really does seem like a surprising result at first, but think of it this way: Instead of having two distinct masses connected by a long tether, imagine what really comes down to being an equivalent situation. Imagine a very long rigid bar in space, pointed toward the body it orbits. Now, the top of the bar is going too fast for its orbit, while the bottom is going too slow, just like in the tether example. This does NOT, however, cause the bar to start rotating, or to move to a "horizontal" configuration to balance it out. A gravity gradient will keep it pointed vertically, and the bar will experience internal tensioning stresses. Remember also that this is the whole priniciple that the space elevator concept works on -- the system will stay vertical. No, it isn't a democracy, but that doesn't mean that the majority is wrong!

najab · Apr 6, 2005

>The facts and science are NOT democratic. The universe is not the way we vote it to be, it is the way it is.It isn't autocratic either - it is the way it is , not the way you decree it to be.The tether 'problem' posed initially is easily solved using basic Newtonian dynamics, and the result is that the two bodies continue to orbit at their original altitudes - the additional gravitational force acting on the lower body is exactly balanced by the additional "centrifugal force" on the higher body.

nacnud · Apr 6, 2005

Seems like an easy way to achieve gravity stabilised space stations/satellites, just tether a mass under/over it, that would save a lot of structure/propellant/gyros etc. I wonder if any plans are being drawn up to use this effect. (I've not read the rest of the thread so sorry if this has already been mentioned.)

Saiph · Apr 6, 2005

1) Doing the physics at this level is more than enough, it's what the designers of spacecraft do. They work it out, build it, and send it up. There is no vague cutting edge stuff here. It's newtonian mechanics. Enough experimental evidence has been acrued through the last 300 years we don't need to check on what a stick does if we let it sit there. 2) Have you looked? plug things into google, it's what I'd have to do. I'm pretty sure it works, as satellites themselves are rigid extended objects, and they don't spin just because they are in orbit. Here, try these three words: satellite boom stabilize. Tell me what you see. <div class="Discussion_UserSignature"> --------------------SaiphMOD@gmail.com -------------------"This is my Timey Wimey Detector. Goes "bing" when there's stuff. It also fries eggs at 30 paces, wether you want it to or not actually. I've learned to stay away from hens: It's not pretty when they blow" -- The Tenth Doctor, "Blink" </div>

najab · Apr 7, 2005

>I simply stated that the problem must be experimentally verified.Steve, this isn't a problem that has to be experimentally verified at all. It is a relatively trivial result of Newton's laws of Gravitation.>Where are the references?For one, you could start reading up on STS-75, where they did deploy a tethered satellite from the Space Shuttle.

najab · Apr 7, 2005

>I did not do any decreeing.Does this sound familiar:<blockquote>If the higher moving satellite continued moving at the slower speed, the distance between it and the lower would increase steadily increase and the tether would break. If the tether were strong enough then the lower would slow down & the higher speed up, falling to an average orbit. There is no other possibility than that.</blockquote>That sounds like a decree to me, it certainly doesn't sound like you are proposing an experiment.

siarad · Apr 7, 2005

The centre of gravity is between the two in the tether. Both rotate about it throwing objects on the lower one apparently down-wards & the upper apparently up-wards but in truth rotating about each other. The rotation produces the effect of gravity. So it seems if this was a complete wheel we'd have an artificial gravity space station driven around by earth gravity. If a generator was fixed at the centre this would give free electricity but alas how to fix it <img src="/images/icons/smile.gif" />

Tether problem

Leovinus

Guest

bobw

Guest

Saiph

Guest

Leovinus

Guest

igorsboss

Guest

bobw

Guest

Leovinus

Guest

siarad

Guest

Saiph

Guest

igorsboss

Guest

remcook

Guest

nexium

Guest

nexium

Guest

Saiph

Guest

Saiph

Guest

najab

Guest

nexium

Guest

Saiph

Guest

heyscottie

Guest

najab

Guest

nacnud

Guest

Saiph

Guest

najab

Guest

najab

Guest

siarad

Guest

Similar threads

TRENDING THREADS

Latest posts

Moderators online

Share this page