# Interesting Question

1. Jan 12, 2007

### 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.

2. Jan 12, 2007

### theperthvan

Try it and see if it works!

3. Jan 12, 2007

### 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.

Last edited: Jan 12, 2007
4. Jan 12, 2007

### 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.

5. Jan 12, 2007

### 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....

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6. Jan 12, 2007

### theperthvan

It would need to be geostationary

7. Jan 12, 2007

### 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?

8. Jan 12, 2007

### tim_lou

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

9. Jan 12, 2007

### Staff: Mentor

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.

10. Jan 12, 2007

### 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?

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11. Jan 12, 2007

### ranger

I dont 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

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12. Jan 12, 2007

### tim_lou

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?

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13. Jan 13, 2007

### 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.

14. Jan 13, 2007

### Dbjergaard

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?

15. Jan 13, 2007

### 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)?

16. Jan 13, 2007

### crop

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)

17. Jan 13, 2007

### 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.

18. Jan 13, 2007

### Staff: Mentor

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

19. Jan 13, 2007

### Staff: Mentor

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.

20. Jan 13, 2007

### ranger

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.

What

Last edited: Jan 13, 2007