Space Elevator problem:

sonhouse
Posers and Puzzles 29 Mar '06 17:59
1. sonhouse
Fast and Curious
29 Mar '06 17:59
I was looking at the formula for circular orbits, its
P(orbital period in seconds)=SQRT (4 (PI^2)* R^3)/GM
R = distance of orbit from center of earth, and the 4PI^2/GM for the planet earth is just a constant, 9.904 E-14 (to 4 places) so its really easy, R is in meters, which is the radius of the earth in meters added to the altitude of the orbit in meters, so at the geosync orbital height, in miles is 22,414 miles high or 35862400 meters plus 6,378,140 meters so R in this case is 42,240,540 meters.
R^3= 7.536E22, so the whole thing boils down to
P=(9.904E-14 * 7.535E22)^1/2 Which in this case = 86397 seconds, rounding errors take it from exact solution here but my problem is the dudes designing the space elevator, assuming of course it can ever work, want to add an extension of some 100,000 Km as a stabalizing element.
My problem with that is the orbital velocity at geosync is about 3 Km/sec but the velocity at 100,000 Km works out to about 2 ish Km/s.
How can two masses connected by a line ever be stable in such an arrangement?
2. 29 Mar '06 21:24
Originally posted by sonhouse
[...]but my problem is the dudes designing the space elevator, assuming of course it can ever work, want to add an extension of some 100,000 Km as a stabalizing element.
My problem with that is the orbital velocity at geosync is about 3 Km/sec but the velocity at 100,000 Km works out to about 2 ish Km/s.
How can two masses connected by a line ever be stable in such an arrangement?
i understood everything except the above (which is actually your question ðŸ˜‰)
where do they add the stabilazing element? is it really 100,000 km long? is it made from metal? how do they get so much metal into space?

and well, the other part...if i got your right, then you just have 2 different velocities but also two different circumferences. so (in theory) it should all be stable as long as the ratio of these two variables stays constant. if not, you will have a problem with the t variable ðŸ˜‰
other question: is there acceleration? (your formula for P was independent of all a, v or s). if yes, then it might be more tricky.
3. sonhouse
Fast and Curious
29 Mar '06 21:54
Originally posted by crazyblue
i understood everything except the above (which is actually your question ðŸ˜‰)
where do they add the stabilazing element? is it really 100,000 km long? is it made from metal? how do they get so much metal into space?

and well, the other part...if i got your right, then you just have 2 different velocities but also two different circumferences. so (in th ...[text shortened]... on? (your formula for P was independent of all a, v or s). if yes, then it might be more tricky.
The formula is for the time of a single orbit. So it assumes you are already there and the formula just says how many seconds it takes. If you want velocity, you have to massage it a bit further by the D*PI for the circumferance and then dividing the time into it. The original formula is P=(4PI^2*R^3)/G*M but the 4PI^2/GM is always a constant for any given planet so its silly to have to include all that crap when it just boils down to 9.904E-14 for the earth.
But the 'stabalizer element'is just a string, albeit a strong one, that connects the geosync section with another mass 100,000 Km further up. If you google in 'space elevator' you will come to the article that describes the need for such a string but I just don't see how it could be stable, I can see the theory for the bottom section, if you get a string that is about 100 times stronger than steel for the same mass, and you can run it down (or up) from the satellite to someplace on the equator (the thing has to be in an equatorial orbit) then you climb up the rope and basically walk your way into space. Note however, you are not able to just step off and go to the moon, you still have to add 3 1/2 Km/second of velocity away from earth to achive escape velocity,
but at least you are halfway there speedwise when you arrive at the top of the elevator. So far so good. What I am having trouble with is how do they expect to make the extension stable? It seems to me it would whip around, the rope maybe even dipping into the atmosphere or something. Draw it out, make the earth 2 cm in diameter, then the first station out about 22 cm then the stabalizer a meter away from all that, then imagine the whole thing flying around in orbit, the 22 cm line tugging on the mass a meter away. Don't see much in the way of stablizing going on here.
4. 30 Mar '06 12:58
thats some cool stuff. wonder why ive never heard about that at all. to me the stability of the masses dont seem to be so much the problem. im not sure if i understood the english correct, but wouldnt this be an answer for you: "As the planet rotates, the inertia at the end of the tether counteracts gravity and keeps the tether taut." (from wikipedia).

what i see as the bigger problem (as far as realization of the elevator is concerned) is the lenght of the "cablestring". remember the puzzle with the string lowered into the bottomless pit? it will break under its own weight at some point. so they gotta find some really good material to do that. these carbon nanotubes they talk about dont seem to be enough yet.

i think all rhp readers should test all kind of materials on stability. imagine your fame if you discover the material that makes this project possible ðŸ™„
5. Alcra
Lazy Sod
30 Mar '06 13:28
There was a book written along these lines. I seem to recall it was called "Fountains of Paradise", where an elevator / train was built to geosynchronous orbit.

6. sonhouse
Fast and Curious
30 Mar '06 15:012 edits
Originally posted by Alcra
There was a book written along these lines. I seem to recall it was called "Fountains of Paradise", where an elevator / train was built to geosynchronous orbit.

Arthur C Clarke, he was the first to realize the value of geosynchronous orbits for communications. He published his findings but got no money out of it, later wrote an article called
"How I lost a billion dollars in my spare time"! Wrote "fountains..".
Carbon nanotubes so far seem our only hope of such a device as it is
over 200 times stronger than steel pound for pound with the minor hitch that we have no idea how to make a million miles of it!, couple of inches, yes, but miles? Come back in ten years, maybe we will have figured it out by then.
On the stability problem, I wonder if you somehow have to have the upper portion going at the velocity of a 24 hour orbit but higher up?
obviously it would not be stable by itself but suppose it was going a bit faster, then centrifugal force might keep the line taut. Don't know if that would be stable either.
7. leisurelysloth
Man of Steel
30 Mar '06 18:21

http://en.wikipedia.org/wiki/Space_elevator
8. Bowmann
Non-Subscriber
30 Mar '06 20:20
Originally posted by sonhouse
I was looking at the formula for circular orbits...
Get a life.
9. 30 Mar '06 23:20
Originally posted by Bowmann
Get a life.
Some are interested in astronomy (like sonhouse), some study it (like me), and some are just interested in pissing off others (like bowmann). Now the question is, who of them should get a life. ðŸ™‚

A) sonhouse
B) crazyblue
C) bowmann

This is a tricky new puzzle.
10. leisurelysloth
Man of Steel
31 Mar '06 01:051 edit
I think you forgot

D) leisurelysloth

and most importantly

E) all of the above

EDIT: The original question is still open. Who's going to do the math to work out whether or not this contraption can be stabilized? Or does it matter, since it seems that it isn't physically realizable due to the lack of strong enough tethers and natural hazards like micrometeorites?
11. 31 Mar '06 02:46
Originally posted by crazyblue
Some are interested in astronomy (like sonhouse), some study it (like me), and some are just interested in pissing off others (like bowmann). Now the question is, who of them should get a life. ðŸ™‚

A) sonhouse
B) crazyblue
C) bowmann

This is a tricky new puzzle.
i am going to go with E. all of the above.
12. sonhouse
Fast and Curious
31 Mar '06 04:23
Originally posted by leisurelysloth
I think you forgot

D) leisurelysloth

and most importantly

E) all of the above

EDIT: The original question is still open. Who's going to do the math to work out whether or not this contraption can be stabilized? Or does it matter, since it seems that it isn't physically realizable due to the lack of strong enough tethers and natural hazards like micrometeorites?
I think it can be stabalized but not by something that long, maybe more like 1000 Km where the velocity change wouldn't be so great and the length would not allow it to dip down to the surface.
Actually there is a company that is starting the engineering work on the beast now, working out how to make miles of nanotube line, etc.
13. sonhouse
Fast and Curious
31 Mar '06 04:29
Originally posted by Zelinda
i am going to go with E. all of the above.
Thank you Z!
14. sonhouse
Fast and Curious
31 Mar '06 04:33
Here is something else to consider:
What is the best way to actually do this, assuming you have a million miles of cable and spacecraft to do it.
Would it be easier/better to lift the cable up with a rocket from a big drum doing about 15,000 RPM and the rocket pulls the cable all the way into sync orbit. OR,
You take the nanotube manufacturing machinery into sync orbit, manufacture the nanotube line there and peel it down from orbit.
OR,
Have one humungus launcher lift all one million miles of cable directly into orbit and peel it down from there.
That part has me bolluxed too.
15. Alcra
Lazy Sod
31 Mar '06 06:53
Originally posted by sonhouse
Here is something else to consider:
What is the best way to actually do this, assuming you have a million miles of cable and spacecraft to do it.
Would it be easier/better to lift the cable up with a rocket from a big drum doing about 15,000 RPM and the rocket pulls the cable all the way into sync orbit. OR,
You take the nanotube manufacturing machinery ...[text shortened]... miles of cable directly into orbit and peel it down from there.
That part has me bolluxed too.
Lifting it by rocket might not be possible. We need to consider the weight of the cable, the higher up you go, the more cable you have below you and the more weight (mass?) you are lifting. I would think the second option is the only easy(haha!) one.