Can a Rope Stay in Orbit After Rocket Launched?

[crop]

Interesting Question...

If I were to tie one end of a rope (a very very long rope) to the ground and the other end to a rocket, and fired the rocket into space, would the rope stay in orbit without falling back down to earth?

Assume once the rope was fully vertical that the rocket was detached and was not pulling the rope any longer.

 

[theperthvan]

Try it and see if it works!

 

[tim_lou]

I think it probably will, the center of mass of that rope might stay in orbit in the right condition. If you want to describe the motion of the rope:

hmmm, firstly, it is probably best to describe the motion of the center of mass of the rope...motion of points other than the center of mass should be quite complicated. Secondly, you will have to consider the length of the rope, when r and the angle is a certain value, it cannot increase any further.. this constraint really complicates the problem. Thirdly, one must take the rotation of the Earth into account, since one end is anchored on the ground. So, it is best to treat the system in the rotating frame of reference.

 

[crop]

So you're saying if the centre of the rope is in orbit then the entire rope will stay in orbit but if the centre of the rope is in the Earth's atmosphere then gravity will pull the rest of the rope down?

What about momentum in space? Since there are no forces (friction) acting on the rope, won't it's momentum be stopped by the other end which is on earth, and therefore tugging the entire ropes momentum back to earth, unless you somehow manage to stop that from happening.

 

[tim_lou]

hmmm, after giving it some thought, a stable orbit might not be achievable. Either way, gravity does not necessary have to pull the rope down if the rope is given a significant velocity. My worry is that a circular orbit is impossible, since the force required for circle orbit goes like v^2/r or $\omega^2 r$ and the force for Newtonian gravity goes like 1/r^2 gravity. The furthest end of the rope will be sort of dragged behind and the whole rope will eventually be wrapped by the earth.

the system is indeed very complicated, the contraints are non-holonomic so Lagrangian seems useless...

 

[theperthvan]

It would need to be geostationary

 

[Fletcher]

Wouldn't the rope fall (or be pulled) back on the Earth in a spiral somewhat like a yo-yo string due to the rotation?

 

[tim_lou]

yeah, that's what I think should happen. but can it be rigorously proved?

 

[russ_watters]

This is the principle behind the space elevator. If the rope is long enough (or is shorter and just has a counterweight attached to it), the far end is moving faster than orbital velocity, which provides enough force to hold the rope up.

 

[crop]

This may seem like a useless thing to do, but the idea I had in mind is somewhat interesting. If instead of the rope we could make a conductor orbit in space, the potential difference between the one end of the conductor on Earth and the other end in orbit would be significantly different producing voltage and power. Could this somehow be made into a generator?

 

[ranger]

This may seem like a useless thing to do, but the idea I had in mind is somewhat interesting. If instead of the rope we could make a conductor orbit in space, the potential difference between the one end of the rope on Earth and the other end in orbit would be significantly different producing voltage and power. Could this somehow be made into a generator?

I don't know what kind of [electrical] potential difference you are taking about.Besides the resistance would cause the venture to be inefficient. But there is an easier way.
NASA did something similar to that. They took a conductor, which was not Earth bound, and moved it through the Earth's magnetic field and induced current.

http://www-istp.gsfc.nasa.gov/Education/wtether.html

 

[tim_lou]

This is the principle behind the space elevator. If the rope is long enough (or is shorter and just has a counterweight attached to it), the far end is moving faster than orbital velocity, which provides enough force to hold the rope up.

let's say one has an extremely long and uniform rope attached to the ground of the earth. is it possible that the rope will result in a circular motion like a rigid rod? viewing things in the rotating frame requires that the tension of the in each segment of the rope be a certain function:
$$T_\text{net}=\omega^2r-\frac{GmM}{r^2}$$

but how can one guarantee that it is possible for T to behave like that as a function of r? Does one simply assume that T behaves according to the constraint and the given force? The thing that bothers me is that how can one be sure that the rope is always taut and that at every segment of the rope, the net force is equal to the centripetal force?

 

[linux kid]

This is such a great question. Thanks for asking crop.

If the answer to this is true it would prove the scientific community wrong and give them the humiliation they deserve for insisting that perpetual energy is impossible. I have always believed in perpetual energy and I still do.

 

[Dbjergaard]

Wouldn't the rope fall (or be pulled) back on the Earth in a spiral somewhat like a yo-yo string due to the rotation?

if this holds then why can't I get in helicopter and hover above a point while Earth turns below me?

Is the rope attached to the pad or just really really long?

 

[crop]

I think it's Faradays law that states if you move a piece of conductor through a magnetic field, voltage will be induced in the conductor (this is the principle on how most, if not all electric motors work), so NASA's experiment probably worked, but it didn't really do any good for us down here on earth, so I guess you can say it was just a really really expensive experiment to prove something we already knew.

I've been questioning how we can use the Earth's magetic field and orbit to generate power, and this is one of the first thoughts that came to me, but there are a few factors that need to be met;

1. Will the conductor even stay in orbit?

2. Will there be any electric activity on the conductor (ie. induced voltage, current)?

 

[crop]

if this holds then why can't I get in helicopter and hover above a point while Earth turns below me?

Is the rope attached to the pad or just really really long?

You probably could, but since you'd be so high, you'd be lacking oxygen, which is why astronauts have the outfits they have.

Other than that, airlines use the Earth's rotation to there advantage. If you have a two way flight from Los Angeles to New York, your flight back (New York to Los Angeles) will be shorter (not a lot shorter, but shorter)

 

[LURCH]

The NASA experiment actually had a very practical purpose; a tether of this type can be used to generate electricity to power. Scientific equipment and other onboard systems within the shuttle.

As for using a wire tethered to the ground to generate electricity: the tether wire would move at the same rate as the ground. Therefore, it would have no motion will a two to the magnetic field of year, and would generate no electricity.

 

[russ_watters]

if this holds then why can't I get in helicopter and hover above a point while Earth turns below me?

The atmosphere rotates with the earth.

If the answer to this is true it would prove the scientific community wrong and give them the humiliation they deserve for insisting that perpetual energy is impossible. I have always believed in perpetual energy and I still do.

This has nothing to do with perpetual motion/energy and talk like that is not scientific. Learn why.

 

[russ_watters]

let's say one has an extremely long and uniform rope attached to the ground of the earth. is it possible that the rope will result in a circular motion like a rigid rod? viewing things in the rotating frame requires that the tension of the in each segment of the rope be a certain function:
$$T_\text{net}=\omega^2r-\frac{GmM}{r^2}$$

but how can one guarantee that it is possible for T to behave like that as a function of r? Does one simply assume that T behaves according to the constraint and the given force? The thing that bothers me is that how can one be sure that the rope is always taut and that at every segment of the rope, the net force is equal to the centripetal force?

You can calculate the forces on it and figure out that it is always taught. Heck, how could it not? If you suspend a string from a helicopter, is it slack anywhere along the string? If you do an around-the-world with a yoyo, is the string slack anywhere? This is just a combination of the two.

 

[ranger]

I think it's Faradays law that states if you move a piece of conductor through a magnetic field, voltage will be induced in the conductor (this is the principle on how most, if not all electric motors work), so NASA's experiment probably worked, but it didn't really do any good for us down here on earth, so I guess you can say it was just a really really expensive experiment to prove something we already knew.

I've been questioning how we can use the Earth's magetic field and orbit to generate power, and this is one of the first thoughts that came to me, but there are a few factors that need to be met;

1. Will the conductor even stay in orbit?

2. Will there be any electric activity on the conductor (ie. induced voltage, current)?

This seems to be the common notion among the public with their views on the tether experiment. The experiment wasnt a failure nor was it a waste of time. Of course there are practical applications for the experiment that NASA did. And I've already stated that if you drag a conductor through the Earth magnetic field, you will have induced current, which was firmly established by the tether experiment. And as LURCH already stated, if its connected to the ground (earth), it will be moving at the same rate and nothing will happen. So merely "shooting" a conductor into space [having one end on earth] would not be practical for the situations we have discussed.

This is such a great question. Thanks for asking crop.

If the answer to this is true it would prove the scientific community wrong and give them the humiliation they deserve for insisting that perpetual energy is impossible. I have always believed in perpetual energy and I still do.

What

 

[Shundra]

I think it probably will, the center of mass of that rope might stay in orbit in the right condition. If you want to describe the motion of the rope:

hmmm, firstly, it is probably best to describe the motion of the center of mass of the rope...motion of points other than the center of mass should be quite complicated. Secondly, you will have to consider the length of the rope, when r and the angle is a certain value, it cannot increase any further.. this constraint really complicates the problem. Thirdly, one must take the rotation of the Earth into account, since one end is anchored on the ground. So, it is best to treat the system in the rotating frame of reference.

can you help me with a problen on equations

 

[Shundra]

The atmosphere rotates with the earth.
This has nothing to do with perpetual motion/energy and talk like that is not scientific. Learn why.

could you help me with a problem with equations

 

[tim_lou]

You can calculate the forces on it and figure out that it is always taught. Heck, how could it not? If you suspend a string from a helicopter, is it slack anywhere along the string? If you do an around-the-world with a yoyo, is the string slack anywhere? This is just a combination of the two.

I can see how it is possible to have a rope be taut going tangent to the equator. but what about a rope going straight up perpendicular to the equator?

 

[gabee]

I can see how it is possible to have a rope be taut going tangent to the equator. but what about a rope going straight up perpendicular to the equator?

I...can't see how it is possible to have a rope be taut going tangent to the equator.

 

[russ_watters]

I guess if the rope was long enough, it would be taut for the same reason one perpendicular would be, but it would still sag due to gravity. And since the centripedal acceleration isn't aligned with the gravitational force, it would pull itself vertical.

You're probably thinking that the Earth has to drag the cable around, but why? What force is it opposing? Does a weed-whacker do that?

 

[ranger]

I...can't see how it is possible to have a rope be taut going tangent to the equator.

You can't have it.

EDIT: Damn I had to blow my nose :)

 

[planish]

If one end was fixed to the surface, and the center of gravity was slightly farther than a geosynchronous orbit (a la "Fountains of Paradise" by Arthur C. Clarke), then it should be quite stable.

Also see http://www.tethers.com/index.html - Tethers Unlimited Inc. - particularly http://www.tethers.com/EDTethers.html for "electrodynamic tethers".

One of it's founders (Robert L. Forward) also wrote science fiction, and often mentioned speculative devices like "rotovators" which went in non-geosynchronous orbits, and sort of stepped down periodically, like a tossed caber that keeps flipping end over end.

 

[LURCH]

It should be pointed out that there is currently no "rope" capable of supporting its own weight at such great lengths.

 

[FredGarvin]

It should be pointed out that there is currently no "rope" capable of supporting its own weight at such great lengths.

It should also be pointed out that the winds aloft at high altitudes are extremely high. The magic rope would buckle in the center and fall back to Earth in no time.