: Cool reference, thanks. Formal title "Space Elevators: An Assessment of the Technological Feasibility and the Way Forward". I would suggest to other editors that when citing from this report, please use section numbers, since the page numbers are probably going to change as formatting errors in the document are fixed (e.g., equation 6.82 on page 172 is almost unreadable, so needs a fix - and that will probably change the length of that page moving text around). [[User:Tarlneustaedter|Tarl.Neustaedter]] ([[User talk:Tarlneustaedter|talk]]) 18:18, 26 February 2014 (UTC)
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It seems to me that "skyhook" being an alias for a "Space Elevator" might be a bit of a misnomer, as sky-hook is often used to refer to the apparatus seen in the most recent Batman movie - do we have a reference for "skyhook" in terms of a space elevator? 192.35.35.35 (talk) 19:44, 17 February 2010 (UTC)[reply]
Actually, a 'skyhook' is a fictional device that literally hooks onto the sky itself. Often used in humorous folk stories and jokes initiating apprentices at workplaces. In recent years the name has been used for real devices. Ashmoo (talk) 11:50, 24 February 2011 (UTC)[reply]
The name “Skyhook” to describe the structure of an object in orbit or near-orbit with a cable (of some sort) to the planet below is the proper name; Giuseppe COLOMBO, an Italian Mathematician and engineer, coined the term. A “space elevator” (the thing that goes up and down) is not requisite to the operation of a skyhook.Wikipedia- Best Source Of Information Since The Weekly World News. (talk) 01:56, 3 July 2011 (UTC)Andering J REDDSON[reply]
The section that begins as follows has OK analysis but wrong language:
"Physical analysis
[edit] Apparent gravitational field
In the rotating coordinate system whose origin is at Earth's center and turning with Earth's daily revolution, the acceleration of any static point in the equator's plane is:"
problem 1: if the point is "static" then the acceleration is zero and not the given formula.
problem 2: this formula is really referring to the unit force per mass (gravitational force plus centrifugal force). If the unit force is zero then there is no acceleration, so setting this term equal to zero and solving yields the orbital radius at which a free-falling mass is static (in the rotational coordinate frame.) —Preceding unsigned comment added by Burressd (talk • contribs) 21:35, 2 July 2010 (UTC)[reply]
Spindle extraction system
Why use a permanent system of transportation? Apply the mechanics of a reel on a fishing rod, on a bigger scale, and combine that with whatever cable would be used or invented for almost any other space elevator and use these simple too;s to extract things from Earth. The Basic principles of a stationary elevator without the commitment, or dangers of being stationary, are applied, the only change is in the propulsion. —Preceding unsigned comment added by JDMONTY (talk • contribs) 23:18, 25 September 2010 (UTC)[reply]
While the physics section is reasonable, it also appears to be WP:OR. This is an encyclopedia, not a physics class tutorial, so the article should just summarise the findings of physicists on its feasibility. There is no need to walk the reader through the equations, step by step. Ashmoo (talk) 11:52, 24 February 2011 (UTC)[reply]
I agree. Even calling it "Physics" is a distraction. "Mechanics" is what people need to understand. While is IS satisfying for one to write that stuff down for one's own understanding, it's more like pedanticism to cram anything more than the basic basics of equations down lay people's throats. All that stuff is really not encyclopedic. Skyway (talk) 03:37, 2 April 2011 (UTC)[reply]
The purpose of an encyclopedia is to be a reference work. You're supposed to be able to find a complete summary of the topic here. Those equations and the physics is really fundamental; not everything in the Wikipedia is easy; if you don't believe me, check out some of the maths articles ;-).Rememberway (talk) 15:05, 2 April 2011 (UTC)[reply]
Yeah. I hear ya. And, I think your point of view is valid. I just disagree for all but the most basic of basic equations (like E=MC^2 or F=ma for example). It's a matter of where the line is drawn probably. On WP, so much of the "complete summary", when it includes equations, is done in a way that disengages the reader's otherwise rapt attention and "drinking in" of the material. So much of it really is a pedantic spewing by some 20-something male grad student. Okay, maybe the "spewing" isn't intentionally pedantic, rather it is an "admirable enthusiasm for the material" by the guy, but the style of the material often reads as pedantic and makes eyes glaze over. Expanding on what Ashmoo said, most equations in WP come off looking like a physics tutorial. It can usually be done better. It's often uncited "original research" too.
The "Apparent gravitational field" equations may fall into the category of basic of basic, but they need to be presented better. What better illustrates my point however, is the "Cable section" differential (differential!!) equations. These are not fundamental for a "complete summary". The fact that taper vastly increases the performance of the cable is fundamental, but the arcane details are not. (Actually, I think a small increase in the taper ratio of a simple linear taper has a much bigger effect than the same ratio turned into one of those "optimized" profiles. But I need to confirm that.) It is of greater importance that the cable will need to be fatter in the high micrometeor/spacejunk region than given for that uber-idealized arcane "perfect taper profile". That thicker section isn't mentioned, and it would drastically change the rest of the shape to be quite unlike the ideal form given. In fact, I think those equations and conclusions are indeed dubious for other reasons as well...
-- No mention is made of taper ratio (except for the changes I had made in the first paragraph of the section),
-- "reduces required strength by a third" is ambiguous.
-- No mention is made for the fact that the lower sections will need to be fatter to support climbers with the same safety margin. (With the focus on making perfect little equations, it got the design criteria all wrong.)
-- Actual cross-section design work will be done numerically anyway.
-- It is uncited and likely to be original research of the kind I've described above.
In other words, dubious.
So, now that you've gotten me thinking more deeply about it, I agree the "Apparent gravitational field" equations are good (with some fixes), but those "Cable section" equations really do need to go. Would you be okay with that? I am confident I can come up with something better about cross section that is well cited with reliable references. :-)
We need equations about the cable area more than we need equations on the apparent gravity. If I find that there are no equations on this in the article I will revert to a version that has them again. But other than that if you can improve the article in any other way.Rememberway (talk) 19:38, 2 April 2011 (UTC)[reply]
That's pretty tough talk, man. I've given thorough, hopefully tone-free, argument as to why the "Cable section" equations are dubious. They are obviously uncited. The same WP:OR complaint has also been issued by at least one other. And you respond with a threat to summarily revert? Without justification? I don't think that's the way you work (I've checked). When I asked if you would be okay with it, I wasn't suggesting that you had go-no-go approval privileges. I was trying to be civil and cooperative, hoping to elicit some reasoned argument. You aren't the owner of this article, don't be trying to force your way by throwing weight around. Justify, dude!
There are two arguments here: 1) The applicability of equations in general, and 2) the validity and inclusion of the equations currently in "Cable section". We can disagree on question 1). Although I generally disfavor equations, I'm not hard-over on it, and I'm not on an anti-equation spree. So, don't worry about that. But, on question 2) I have made good arguments for the non-inclusion of those particular equations. I haven't seen any actual backed-up argument for inclusion. I seem to be supported as well by Ashmoo.
Instead of changing them right away, I'll just tag them "Citation needed" or "Dubious" or some such label if you prefer. Then we can let things settle a bit while others hopefully pipe in. Another alternative is to mention the equations as depicting the "idealized" taper form (like an ideal gas), but that a number of factors will require the design to deviate from this, then go on to talk about those factors and their influence on cross section form. If that were done, the equations would still need to satisfy the other criteria for inclusion (reliable references, etc.).
With all respect, "tone-free" after "pedantic spewing by some 20-something male" (!?!), and I think the points made at WP:NOTOR need emphasising here (individual equations should not necessarily be citable nor transparent to lay-readers). I do agree the article is a bit of a mess yet, and appreciate your effort, but I also agree with Rememberway that it could never be an improvement to have no equations here. (Personally I think one problem is that certain equations are given excessive explanation in the text; it would be better to rely instead on better linking to other wiki articles for those readers who need the background foundations explained in detail.) If I recall correctly, Arthur C Clark's article (from the external links section) should suffice to demonstrate that the physics isn't original. Cesiumfrog (talk) 02:51, 6 April 2011 (UTC)[reply]
Okay, I take back the "... by 20-something males" comment. I was referring (only in my own mind apparently) to some studies I had heard about the demographics of WP editors, and to jokes about the aspergery-like proclivities of that population.
I don't actually advocate "no equations", it's just that equations without (good) explanation are very little communication at all. We technical people understand them (sometimes), but we must put ourselves in the minds of people who aren't inside our own minds. When we don't care about actually communicating, than what results looks a lot like mere showing off. Even E=Mc2 can't sit by itself. If equations must be included (ugh! :-) ), then really good explanation must surround them.
There could be a section dedicated to the deeper understand (the physics at a physicist’s level), with the rest of the article dedicated to layman understanding. Equally, this section itself can be summarized, then linked to a full article (as is usually done in these cases). Wikipedia- Best Source Of Information Since The Weekly World News. (talk) 02:01, 3 July 2011 (UTC)Andering J REDDSON[reply]
Image error
The image says that the elevator should be in a geosynchronous orbit. Actually it should be in a geostationary orbit, which is different. Could somebody fix this please? 67.173.108.82 (talk) 04:30, 8 March 2011 (UTC)[reply]
3 options: You can edit it yourself. You can show us some documentation for why it should be this way. You can explain it. Both terms are all over this article and I'm no expert on the stuff. The picture says "geosynchronous" so if someone thinks that's wrong we need to know why and find a better picture. I could easily edit the picture and re-upload it if I had a reasonable expectation not to mess up the science behind this page. Pär Larsson (talk) 11:50, 10 March 2011 (UTC)[reply]
Once it's anchored, I'm not so sure it can be said to be in any type of orbit. It's just an upsidedown pendulum at that point. Only during initial deployment will it need to be in Geostationary orbit. Actually, when you think about it, that's true only during the last 80 miles or so when the bottom dips into the atmosphere. If we have the ability to adroitly maneuver the whole thing when it's fully extended (~100,000 km), then there isn't even a need to be geostationary/geosynchronous at all during deployment. Indeed, we will need at least some kind of maneuverability during deployment, that means some of the time the system won't be exactly geostationary. Skyway (talk) 00:59, 2 April 2011 (UTC)[reply]
1) The scale isn't right. It is easy to get the ratio between the GEO level height above the surface and the Earth radius correct. That ratio is about 5.62 by the way. It should be a simple matter to make the Earth a little smaller.
2) The center of mass of the system at all times must be at least somewhat above the GEO level. The diagram shows the center of mass to be at GEO level. The arrow pointing to GEO needs to be scooted up a bit.
3) Modern (post Edwards-Westling) concepts don't use an asteroid as a counterweight. The diagram shows something that looks like an asteroid.
If no one makes the fixes in the next week or so, I will have a go at it. It is pretty important I think. The association of space elevators with GEO isn't as significant as most think. We tend to frequently invoke the idea of "dropping a massless line from a satellite at GEO" to explain, but that misleads people to give undue significance to GEO in the idea of space elevators. It also leaves the idea of "pulling a space elevator down" nagging in the minds of novices, as if that really could happen in a properly managed system. It would happen immediately however, in the system illustrated in that diagram. The CM being above GEO, even when under load, and providing a margin of "excess tension" is an essential element of the concept. That's why it should be correctly illustrated in that diagram.
I couldn't wait a few days. I went ahead and made the above changes along with the relabeling of "Geosynchronous orbit" to "Geostationary orbit" as was also suggested. I still need to correct an error I made with regard to the Name header. I had incorporated it into the picture then saw that it was a part of the infobox and taking up space even if I nulled it out. I will edit the diagram to remove the name, then restore the Name as part of the infobox as it was before.
While the length of the cable may be to scale, the size of the chamber and counterweight most certainly aren't. The figure caption should be updated to reflect this. — Preceding unsigned comment added by 203.206.172.171 (talk) 01:54, 14 July 2012 (UTC)[reply]
This space elevator article (and the carbon nanotube article it is partially based on) may be misleading on just comparing the strength of individual carbon nanotubes, atoms wide and defect free, to the aggregate strength of macro scale materials like commercial steel, kelvar, etc. See, for instance, monocrystalline whisker:
Typical whisker materials are graphite, alumina, iron, or silicon. Single-crystal whiskers of these (and some other) materials are noted for having very high tensile strength (on the order of 10–20 GPa). Whiskers are used in some composites, but large-scale fabrication of defect-free whiskers is very difficult.
Prior to the discovery of carbon nanotubes, single-crystal whiskers had the highest tensile strength of any materials known, and were featured regularly in science fiction as materials for fabrication of space elevators, arcologies, and other large structures.
Many materials (iron, carbon graphite, silicon, etc.) can have around an order of magnitude higher strength in submicroscopic test samples than those materials do in practice on large scale for the macro-scale aggregate of quintillions of atoms, defects and all (where, in contrast, strengths drop to a fraction of a GPa to low single-digit GPa instead of the 10-20 GPa for the single-crystal whiskers).
Likewise, google any carbon nanotube composite or even carbon nanotube rope (of fraction of a millimeter or greater diameter) made in the decades since their discovery, and measured strengths range from a fraction of a GPa to single-digit GPa. The up to 50-150 GPa mentioned in the articles for test results is only for individual nanotubes, but very few people will learn the magnitude of the difference. Indirectly encouraging a space policy of waiting for CNT materials to
hopefully later in our lifetimes get nearly the same strength on the aggregate macro scale that the best atoms-wide samples do (which has not happened with other materials) may be disadvantageous if the validity of the implicit assumptions behind such is in question.
This isn't such a ridiculous statement as you make it out to be. If we were to assume that the current, nascent, state of CNT production and technology were to be the technical limit, it would be akin to declaring that pearlite and martensite were the best you could possibly do with steel, and deciding you might as well not bother. The article does say that this is new technology, and that these are expected but not extant material candidates. siafu (talk) 23:31, 12 August 2011 (UTC)[reply]
Has the effect of ultraviolet radiation and exposure to ionized forms of oxygen, nitrogen and NO on ribbon material been adequately examined?184.66.110.161 (talk) 03:20, 15 March 2012 (UTC)[reply]
That's the wrong question. We don't have the material yet, so technically of course that hasn't been conclusively examined. But if it were going to be a problem, we could simply increase the cross section sufficiently to support just adding an arbitrarily thick layer of shielding to eliminate it. Producing a material of very high strength on a macroscopic scale really is the one and only issue of importance here, everything else is ammenable to trivial work arounds. Cesiumfrog (talk) 03:39, 15 March 2012 (UTC)[reply]
I agree that getting the material strength-to-density in the first place is the primary concern, but I wouldn't say it's the wrong question. The answer to the question is "Yes". I would say it's been "adequately examined" for the current state of development. That is, practitioners know it is necessary to design for the environment and that that is one aspect of the environment that's been looked at (see Edwards Westing Phase Two). It's not expected to be too much of a problem. Like Cesiumfrog said, it looks amenable to "trivial work arounds" or as I would put it "routine design to given constraints" (or something like that). Skyway (talk) 17:37, 26 March 2012 (UTC)[reply]
Center of mass vs center of weight
My change was reverted. The article currently states:
"Once anchored, if the center of mass is moved upward to be above the level of geosynchronous orbit (by adding mass at the upper end or by paying out more cable), it will add a tension to the whole cable, which can then be used as an elevator cable."
This makes no sense. The center of mass is always above GEO once the cable is played out because centrifugal forces will require more mass above GEO to balance the gravitational forces below GEO. The correct term should be "center of weight" — Preceding unsigned comment added by Nydoc001 (talk • contribs) 23:39, 12 August 2011 (UTC)[reply]
I don't think it's the correct term in this instance. A much larger percentage of the cable mass will be above GEO, but if you look at the weight pulling down versus the weight pulling up it will be very close to 50/50. Should the article use "center of weight" if it's the correct term but also more confusing? — Preceding unsigned comment added by Nydoc001 (talk • contribs) 00:13, 13 August 2011 (UTC)[reply]
I think "center of gravity" would make sense here. If you think the mass below GEO providing "downward gravity" and the mass above GEO providing "upward gravity" then the gravitating sections of cable will be opposed with the center of gravity being slightly above GEO. — Preceding unsigned comment added by Nydoc001 (talk • contribs) 00:57, 13 August 2011 (UTC)[reply]
By the way, the image at the top should say "Center of gravity for cable (above geostationary level)" instead of "Center of mass for system (above geostationary level)." I could edit the image to fix this, but I don't know how to upload it. Nydoc001 (talk) 01:17, 13 August 2011 (UTC)Nydoc001[reply]
No. This isn't a matter of the same term for different things, center of gravity and center of mass are different points. Unless you have a reference, I don't think it should be changed.- Sheer Incompetence (talk) Now with added dubiosity!01:50, 13 August 2011 (UTC)[reply]
Well I'll try to find a reference for you. I'm sure I remember seeing it in either Bradley Edward's or Jerome Pearson's papers, but I know for a fact that we can't be talking about either the center of mass of the cable or the center of mass of the earth-cable system. Those are at different locations than GEO. Nydoc001 (talk) 01:59, 13 August 2011 (UTC)Nydoc001[reply]
I found some references:
Space Elevators - An Advanced Earth-Space Infrastructure for the New Millennium
Compiled by D.V. Smitherman, Jr.
Marshall Space Flight Center, Huntsville, Alabama, August 2000.
In this paper, Smitherman does say the GEO station is the center of gravity of the system:
"At the GEO transfer station (fig. 2(d)), passengers and cargo are transferred into the station or to outbound space transfer vehicles. This station is the center of gravity for the total system; consequently, large reels are illustrated to adjust the location of the station, tension of the structure, and the counterbalance mass."
However, Smitherman seems to use the terms "center of gravity" and "center of mass" interchangeably:
"A space elevator is a physical connection from the surface of the Earth to a geostationary Earth orbit (GEO) above the Earth ≈35,786 km in altitude. Its center of mass is at the geostationary point such that it has a 24-hr orbit and stays over the same point above the equator as the Earth rotates on its axis."
Dr. Bradley Edwards comments on the complications of gravity when altering the center of mass:
"A second fact that complicates our calculations is that as the cable is deployed different parts of it experience different gravitational acceleration. This changes our apparent mass distribution and if we want to maintain a geosynchronous orbit during deployment we must dramatically increase our orbital angular momentum. In our specific situation the geosynchronous orbit altitude for our center of mass depends on how much cable we have deployed."
If you take a look at the wikipedia article for Center of gravity, there is a section about weighted average which states "Asimov (1988) writes that a body in the earth's gravitational field has a center of gravity that is lower than its center of mass, because its lower portion is more strongly influenced by the earth's gravity." This is exactly what's going on with the space elevator. The center of mass is closer to the counterweight, but the center of gravity is nearly at GEO because of earth's gravity.
As the article currently stands, it contains the terms "center of mass," "center of gravity," and "center of weight." I don't think it should use "center of weight" because it isn't a physics term. The only term that should be used when describing the point slightly above GEO is "center of gravity" because it is most accurate. Nydoc001 (talk) 04:15, 13 August 2011 (UTC)Nydoc001[reply]
No, it's actually, categorically, wrong. The centre of gravity is a long way below geo, since most of the gravity is quite near the earth, so the centre of gravity is near there (I've never done the maths on it, but it must be a few thousand kilometres up). The centre of mass is slightly above geo, as Bradley notes.- Sheer Incompetence (talk) Now with added dubiosity!05:17, 13 August 2011 (UTC)[reply]
If you're thinking of the center of gravity of the earth-cable system, it would be almost exactly at the center of the earth. The final mass of Edward's ribbon, including the counterweight is 1500 tons and the mass of the earth is 6.585x10^21 tons so the cable and counterweight masses hardly make a difference. What makes sense to talk about are the centers of mass and gravity of just the cable. Only a quarter of the cable's length is below GEO. The other three quarters are above GEO. This puts the center of mass of the cable far, far above GEO, but because a body that is in a gravitational field has a center of gravity that is lower than it's center of mass, the center of gravity of the cable will be just above GEO. This is the balance point of forces pulling down and forces pulling up, so it's the center of gravity. Nydoc001 (talk) 05:46, 13 August 2011 (UTC)Nydoc001[reply]
If the "centre of mass" and "centre of weight" of the cable are at different locations then the article needs to say so. Particularly if the difference has to be allowed for during construction and for safe operation of the space elevator. Include definitions. Andrew Swallow (talk) 20:34, 15 August 2011 (UTC)[reply]
They would be at different locations. The balance point of upward forces and downward forces (you said "center of weight" but you could say "the elevator's center of gravity") by necessity needs to be slightly above GEO. The altitude of the center of mass will vary depending on how big the counterweight is. For example:
Assuming a ribbon taper ratio from base to GEO of 1.5 and the ribbon having sufficient length above GEO that it doesn't require a counterweight:
143,800 km - total length of ribbon
35,786 km - height at GEO
250.7 cm - final ribbon thickness at GEO
167.1 cm - final ribbon thickness at base and terminal point
0.002089 * 35786 = 74.756954 km^2 - surface area of ribbon below GEO
0.002089 * 108014 = 225.641246 km^2 - surface area of ribbon above GEO
This means that a cable with maximum possible length would have approximately 25% of it's mass below GEO and 75% of it's mass above GEO. Therefore the maximum possible altitude for the center of mass should be somewhere around 70,000 km.
I like that this subject has come up and I applaud Nydoc001 for having the courage to see that we get it right. I myself ponder over the correctness of CG vs. CM (or some other kind of "center") for space elevators. I'm airplane guy, and I'm used to CG and CM being interchangeable. Clearly, for space elevators, they are not. I've adopted the probably-correct convention of using "CM" as the place where, if all the mass of the free-flying very tall satellite (such as during deployment) were concentrated, the relevant orbital parameters (such as period) would be unchanged. But, I am unsure of this because I haven't yet sat down and worked it out for myself. The community of serious practitioners do use CM to describe that point and I have reason to trust them, but I won't have absolute trust in it until I get around to figuring it out myself!
CG vs. CM is important to get right. An actual explanation of the meanings and differences might be off-topic for this article, but the example of a space elevator might be right-on for the CG and CM articles.
The gravity of Earth is about 100 times stronger at sea level than at altitude 54,000 kilometers (60,000 km from the center of the earth), so it would take more mass beyond GEO altitude to counter balance the mass below GEO altitude.
There is a balancing point. The balancing point is the point for which the total force on the mass above that point (mass times (centripetal acceleration - gravitational acceleration)) is balanced by (equal to) the total force on the mass below that point (mass times (gravitational acceleration - centripetal acceleration)). The balancing point should be slightly above GEO so you could have a natural 20 ton upward force and not pull it out of the sky when you put a 15 ton climber on it. Could you call this point "the cable's center of gravity" or is there really no common physics term for this point?
Neato. I've come across Blaise Gassend's site before and found him to be very reliable. Yes, when anchored and operational, the "balance point" (whether it is a "CG", "CM", or other "center" -- "CM" for now) will need to be above GEO to provide "excess tension", or "ultimate lifting capacity", or "pull-down margin" - that 20 ton upward force you mention. So, things are different pre-anchored vs. post-anchored. During deployment, the system is in orbit. While anchored and operational, it is not in orbit, not one bit of it. During deployment, the "balance point" (presumably "CM") will need to be exactly at GEO level and over the equator if the deploying system is to remain over the anchor point. Personally, I'm not sure it needs to be perfectly stationary over the anchor point during deployment. Technically, such positioning is only really necessary during the last 100 km of the lowering of the lower "transponder" end. During deployment, we may want to let it precess East or West or let it increase or decrease it's period for whatever reasons we have at the time.
If you're going for accuracy, you could say "center of gravity adjusted for centripetal acceleration" (that's a mouthful! CGACA?). I don't think "center of mass" is accurate, but would "center of balance" cause less confusion?Nydoc001 (talk) 21:21, 19 August 2011 (UTC)Nydoc001[reply]
This might be a better explanation of why the balance point is not the center of mass:
The "center of balance" is the point at which the net force acting on the elevator mass below that point is equaled by the net force acting on the elevator mass above that point.
Since we want the whole elevator to have a 20 ton pull-down margin, we put the center of balance slightly above GEO (an elevator having a net downward force would have it's center of balance below GEO).
But the center of mass isn't anywhere near GEO! This is because gravity increases faster exponentially as you go downward than does centripetal acceleration as you go upward. A given elevator mass below GEO will have a stronger net downward force than the net upward force acting on an equivalent elevator mass above GEO. You'll have to compensate for gravity by placing a much larger cable mass above GEO, in order to provide yourself with more centripetal acceleration. This is why you end up with your center of mass being perhaps 10,000 km above the center of balance.Nydoc001 (talk) 03:12, 20 August 2011 (UTC)Nydoc001[reply]
I'm starting to suspect you are right. THE reliable reference ("The Space Elevator" by Edwards and Westling) refers to the CM being at GEO during deployment for the system to remain stationary over a spot above the equator. But, I "did the math" last night and it looks like the point that needs to be at GEO is somewhere below CM and above CG. I did this analysis very quickly and I'm still in the process of verifying it, so definitely don't hold me to it! I suggest we keep the article saying "CM" for the time being. Even if you are right, I think the difference is probably small, and the correct idea still gets across. If we took our study and published it here it would clearly amount to original research, which is verboten in WP. It's definitely a cool thing to think about though.
I just re-read that reference you mentioned (http://gassend.net/spaceelevator/center-of-mass/index.html) with new eyes. He confirms that the CM is above GEO even for an un-anchored (deploying, synchronous) SE. Now we can carefully review the text with this reference in our back pocket for misuse of "CM" where it implies that CM is at GEO during deploy. We don't need to go on to actually name that point though (unless there is a source for it). As an article about SEs and not a textbook about them, we don't actually have to go into that detail.
Eureka! I've found the missing link! The trouble we-all have been having is with the common use of "center of mass" in describing what's at geosynchronous orbit level. The modern-day bible (Edwards-Westling, "The Space Elevator") consistently uses this term, but we know that the CM must be above GEO if the period of a deploying system is to be one (sidereal) day. "How could the man get it wrong?" we all wonder. Well, check out the top half of page 72 of that reference:
"In our specific situation the geosynchronous
orbit altitude for our center of mass depends
on how much ribbon we have deployed."
So, Edwards redefines GEO level in some contexts to depend on the vertical mass distribution of very tall satellites. He is right, and we are technically correct to use "CM", but only if we make it clear that we are also using a variable definition of GEO.
The big problem is that this subtlety is lost on most readers and editors, even non-lay readers/editors! So, too frequently, in fact almost always, people end up just describing the center of mass to be at the "normal" GEO level and not thinking about it too much - until someone (like Nydoc001) comes along and says "Hey! the emperor has no clothes!".
I suggest that this article picks only one method of describing the situation and keeps it consistent, lest we continue to confuse readers (and ourselves!).
Method A) Define "GEO" as non-varying and never state or imply that CM is at GEO, but is in fact above GEO for a deploying (yet un-anchored) system. Maybe we should put some hidden notes in the text warning future editors to not misinterpret Edwards' use of "CM at GEO".
Method B) Allow CM to be described as being at GEO for a deploying system as long as it is always clear that the "GEO" referred to in that context is not at the same level as "normal GEO".
I strongly favor Method A because "GEO" not being at the "normal" altitude is only applicable during deployment. In almost all other situations, such as normal use of a SE, GEO is right back at the normal level (where it belongs!). It would be confusing to let GEO move sometimes and not move other times.
I read Nydoc001's short-term edit with the short-lived new section (2 edits ago?) and it made me realize that there can be confusion as to exactly what objects are included in whatever we are considering the center of mass of. Here is the answer (I do declare! :-) ) :
During deployment the system includes:
1) The concentrated mass at the top, i.e. the spool including the portion of undeployed tether on it. When fully deployed, this mass along with additional mass added to it, is called the counterweight.
2) The thus-far deployed tether.
3) The concentrated mass at the bottom of the tether. I call this the "lower counterweight". It is the smaller spacecraft containing transponder for location, and rocketry for initial deployment (which is necessary until tidal forces can keep the tether taut). The mass of the transponder & rocketry will slightly pre-tension the tether. Additional "dead weight" might be added to further pretension the tether.
At the exact moment the "lower counterweight" is grabbed and affixed to the Earth, it becomes not part of the "system", and instantly the CM moves upward. This is somewhat mere re-definition (!), but not fully because the lower counterweight does transition from being free-flying as a part of a "tall satellite" to not being part of it and being fixed to the ground and constrained in it's movements. At this moment, the rest of the "tall satellite" (upper CW and tether) is no longer "in orbit" either (!), so it is also no longer a satellite because it is also constrained in it's movements (at the bottom) - an important point. At the moment the lower counterweight is grabbed, the tension that was on the tether just above the lower counterweight becomes the "excess tension"/"pull-down margin" of the system. This initial "excess tension" equals the weight of what was the "lower counterweight". After anchoring, as the spool continues with its remaining deployment upward, that initial "excess tension" at the bottom increases until the spool is fully deployed. With this now-greater "excess tension", the lower part of the tether can hold the first climbers.
While anchored to the ground the system includes:
1) The counterweight.
2) The tether.
3) All mass attached to the tether such as climbers, stations, etc.
When anchored, the system doesn't include that "lower counterweight" that was so important during deployment.
There you go everybody. Just wanted to clarify that point of confusion.
When anchored, the system has to include either the Earth (which it is anchored to) or the force being provided by the Earth extending out of the control volume both as a body force (gravity) and as a point force (tension), otherwise it doesn't really gain much in terms of it's usefulness as an arbitrarily defined system. siafu (talk) 01:14, 19 August 2011 (UTC)[reply]
You should consider Earth's gravitational force when locating the elevator's center of gravity, but you wouldn't need to include the Earth's mass into the system when locating the center of mass. Typical skyscrapers have a center of mass (very important when planning for earthquakes) but the Earth's mass isn't included to find a skyscraper's center of mass. The CG and CM of a skyscraper are very close together, but a space elevator is so tall that these points would be very far apart. For an elevator having the longest possible tether and smallest possible counterweight they could be as far apart as 36,000 km. Even for shorter tethers they will still be thousands of kilometers apart.Nydoc001 (talk) 01:27, 19 August 2011 (UTC)Nydoc001[reply]
By "the system" I meant the collection of things that we are talking about the center of (gravity, mass, or whatever) of. I should have been more clear about that. Which kind of "center" wasn't my purpose. What "the system" should mean in this context was also not my purpose. I wanted to provide the practical information to you all that, when active modern practitioners say "CM", the control volume (CV) they are referring to is the CV I describe above.
Any spacecraft that attached itself to the elevator would become part of the system, but if they attach at GEO altitude they will be in free fall with zero weight and so not add any additional force or tension to the tether. You could theoretically add infinite mass at GEO altitude without altering the tether's profile.Nydoc001 (talk) 20:07, 19 August 2011 (UTC)Nydoc001[reply]
Were I not an astrodynamicist, I would not feel compelled to object, but alas I must point out that a large mass at GEO would be problematic due to its gravitational effects, as well as the more serious effects on the structure's overall oscillatory behavior. siafu (talk) 20:51, 19 August 2011 (UTC)[reply]
You have a very valid point. Infinite point mass would be a problem for the universe as a whole. But I'm sure you could get away with attaching something with mass equal to a few dozen times the ISS at a space elevator's GEO without causing too adverse an effect. I think the change in oscillatory behavior would be the most noticeable effect. — Preceding unsigned comment added by Nydoc001 (talk • contribs) 21:05, 19 August 2011 (UTC)Nydoc001[reply]
Hi guys, I composed this while you were "talking", then had an edit conflict. I was responding to Nydoc001's 20:07 comment, but it applies to siafu.20:51 and Nydoc001.21:05 too...
Nydoc001, (your 20:07 comment) is true for the static situation, and true for the situation we are/were talking about with regard to the "balance point" being above GEO and all that. (For the dynamic situation, as in the contemplation of oscillations, any mass attached at GEO will definitely be material. But, dynamics is outside the topic for now. :-) ) Hmmm... let me think about that static (vertical) situation some more... I'm thinking you make a very good mind-expanding point. Now that I think about it, if a very very large mass (order of the whole SE) was just parked next to and not touching a cable at GEO, it is no different statically than if it was attached to the cable at GEO. The "excess tension"/"pull-down margin" will not change (just like you suggested). The CM will still be above GEO, but less so. Hmmm... Dang, you're making me think...
Okay, I have an answer for what it's worth. Here it is:
The distance from GEO upward to the center of mass is not a direct measure of resistance to being pulled down. That distance must be compensated somehow for mass (and maybe other factors) for it to be a measure of pull-down margin.
SO, what we are saying in the article is still true with regard to the CM being above GEO. The (above) descriptions of CV also still hold true. That large mass attached at GEO is in the CV when it is attached and is not in the CV when not attached, just like the CV definitions I described above. The pull-down margin is not changed even though the center of mass is changed (!). It's just that the amount that CM is above GEO is not a direct measure of pull-down margin. In the non-attached case, the distance from GEO to CM is compensated for by a lesser mass. In the attached case, the distance from GEO to CM is compensated for by a greater mass. In both cases, when compensated for mass, the pull-down margin will be the same. This makes sense because, at GEO, attaching adds no vertical force.
I think you've moved the bar, man. Space elevator engineering is a little further advanced today. (Seriously! :-) )
Should the phrase "transit times are expected to be long enough where, if unshielded, total exposure would be above levels considered safe." be rather "transit times are expected to be long enough where, if unshielded, total exposure would be above levels considered unsafe."? — Preceding unsigned comment added by 175.39.42.46 (talk) 10:18, 29 March 2012 (UTC)[reply]
Some phrases in the "21st century" section are in a different font and without spaces. For example "which featured US500,000awardsforeachofthetwocompetitions,(US1,000,000 total)". I can't see what it's caused by and do not find manual editing reliable enough to re-type the text without typos. What is the problem here, exactly? --Gryllida02:07, 22 May 2012 (UTC)[reply]
What exactly would the effect be of the space elevator on the orbit of the earth itself (earth's orbit around the sun) ? Could it pull the earth of it's trajectory (similar to a rocket near an asteroid effecting the path of an asteroid, ie see article on impact event)
91.182.27.70 (talk) 08:17, 12 July 2012 (UTC)[reply]
It would be good to have a section explaining why the orbit (or path) of the counterweight remains stable despite the extra forces acting on it when the climber moves up. This is a central question because otherwise the entire concept of a space elevator wouldn't be feasable.
And indeed from a naive perspective one would expect that the horizontal speed the payload gets for "free" when moving up is not only taken from the earth's roational energy but also from the counterweight's kinetic energy which would in turn cause its orbit to decay every time a payload is moved up. — Preceding unsigned comment added by 92.20.87.48 (talk) 10:11, 28 August 2012 (UTC)[reply]
Land and Sea, but what about Air?
There is discussion of the advantages of Sea and Land bases, but why is Air not considered?
An air base would have all the advantages a sea base as it could be manoeuvred, could be in international air space, it could also be high enough to avoid atmospheric storms and has the advantage of altitude and hence less stress.
A flying air base needs enormous amounts of fuel to stay in the sky - which is why the air force does not build them. Also the bottom of the space elevator has to be heavy enough to hold it down, a flying item would not be. Andrew Swallow (talk) 11:18, 22 September 2012 (UTC)[reply]
Also, the transfer of the Earth's angular momentum to rising cargo is a key aspect and advantage of the idea of a (ISEC-type) space elevator. This diagram in the article (under "Climbers") illustrates that momentum transfer (see thumbnail left).
Without an anchor, that momentum transfer could only be achieved via air drag through the atmosphere resulting in migration of the base over all the countries on the equator. Logistically pretty difficult to chase down. Actually, a base suspended in the air without a way of fixing the altitude and position means the system is exactly balanced (and in orbit!) for the mass currently hanging on it at the base. Adding more mass at the base would immediately start to pull the system downward and it would then precess eastward in its orbit. Not only would this not give air drag any chance to add momentum to the flying system, but the opposite would happen and the westward air drag would take orbital momentum from the flying system. That would cause more eastward precession, more descent, and so on. The system would be unstable with that lower end dipped into the atmosphere. Any new weight added would cause continued descent to touchdown/crash, and any weight taken off would cause continued ascent until the base was in space (i.e. high enough that the boosting air drag becomes vanishingly small).
Now then, when the base hits the ground (assuming it held together up to that point), the base would now be "anchored" to the earth and the rest of the system would either continue to crash to earth or would remain standing with its former "base plus cargo" as it's anchor (depending on the distribution of mass on the system before and after the landing/crash of the base and other factors). Andrew Swallow's comment about fuel usage is right on. Keeping the base in position is essential. And it would be necessary to use big propellers with fuel consumption to do that. Even then, if the base was at high altitude as suggested, the ability to hold the system down is less in the high thin air and decreases more with altitude. There would be a risk of overpowering the base thrusters and losing the whole thing to space (particularly when a mass was released/dropped below GEO for whatever reason).
Yup, that'd be difficult controlability-wise, and it defeats defining advantages of an ISEC-type space elevator: momentum transfer with Earth and simplicity of a static system without the need for constant power and control. Skyway (talk) 05:57, 6 October 2012 (UTC)[reply]
Could someone please add to this article the total mass of space elevator?
Preferably both the initial "seed cable" mass and the much larger "finished cable" mass?
Would it be relevant to compare that mass to the total mass of all the stuff people have already installed in geostationary orbit, including the stuff that has since been moved to a graveyard orbit?
Would it be relevant to compare that mass to the total mass of a recent year's production of natural gas?
(Natural gas is the raw feedstock for most recent nanotube production, right?)
--DavidCary (talk) 08:42, 6 January 2013 (UTC)[reply]
I went ahead and added the masses of a few space elevator designs to this article, with references.
Later I see that siafu seems to be warning me that "this" (?) is against policy. Oops. Am I misunderstanding the policy, or misunderstanding siafu, or (most likely) both? --DavidCary (talk) 18:52, 7 January 2013 (UTC)[reply]
I think finding out what confusions or misconceptions people have about space elevators then adjusting the article accordingly is a good thing. This article is the "go to" place where most people get all of what they know about Space Elevators. If there is a prevalent idea out there that SEs would be impossibly massive, we should make sure it's addressed in the article. We should probably cite something showing that reasonably anticipated designs require only a small number of large rocket launches (as DavidCary made a start on). Skyway (talk) 03:21, 8 January 2013 (UTC)[reply]
Original research equations
The ribbon thickness and material strength equations are labelled as original research. I have seen them on a website. I wish to remove the label. Have the equations occurred in a formal paper or textbook? Andrew Swallow (talk) 04:42, 9 January 2013 (UTC)[reply]
Personally, I wish the equations would go away (I see them as pedantic). But, I know there are other opinions out there. The other trouble with them (besides "pedantic") is they really aren't up to date. Before Edwards-Westling (Phase II) (~2002), the level of detail in people's thinking regarding taper was only at the level of "Gosh, how do we taper it to most efficiently hold itself up?" Those idealized equations did apply before 2002. Since then, with the work of Edwards (~2002) and more recently the publications of ISEC (~2012), the bar has been moved. Nowadays we consider thickening at space-junk altitudes, load concentrations as they vary with the distribution of climbers, distribution of non-structural mass, etc. That equal stress idea is an important principle yes, and it should be mentioned, but it's not so important these days to go into its excruciating details IMHO.
I haven't done a complete search, but my expectation is that those equations (similar to as they appear now) would be found in pre-2002 sources (which are outdated), or "unreliable" post-2002 sources (because they regurgitate pre-2002 sources), or just somebody's intellectual exercise they published on WP as OR. What we're really trying to do is describe taper and constraints on the taper design (right?). I would trust descriptions of taper from Edwards Phase II, or the ISEC stuff. Both refs are already in the reflist. It would be a matter of reviewing them to find the good stuff in them. Skyway (talk) 09:25, 10 January 2013 (UTC)[reply]
The cable is thickest at GSO (Geo Stationary Orbit) since it has to carry the weight of the cable below it. A tapered cable gets narrower as it approaches the ground and the counter weight. This ignores any protective layers that may be added to say prevent oxidation. With some designs only the width changes.
Andrew Swallow (talk) 17:52, 10 March 2013 (UTC)[reply]
Although this article is fascinating I was intrigued that there was no mention of Earth weather conditions that would be experienced by the tether - say the effects of a lightning strike on the line (yes it may be an opportunity to charge massive capacitors and power the operation of the elevator ... but is there any chance it would survive? ... would the geostationary component need thrusters as a back-up? would multiple separate tethers help?) - or the impact of a tether going through a twister?
My read is that terrestrial weather would be effectively irrelevant - forces are orders of magnitude smaller than the ones needed to simply support itself, and passing through the Van Allen belts means higher electrical charges than you'd get from terrestrial storm clouds. As for thrusters, moving cargo up and down the elevator will cause changes in angular momentum, moving the geosync point forwards and back. This would presumably be adjusted by simply pulling in or letting out some of the counterweight to shift the center of gravity. Tarl.Neustaedter (talk) 19:13, 7 September 2013 (UTC)[reply]
Climbers section
The changes which have been whip-sawing back and forth in the Climbers section are getting tiresome. The 66% is simply wrong (it's unreferenced, and my back-of-the-envelope calculations come up with a different height, which isn't a magic number), but the other changes which keep being put in are even worse. If nobody comes up with references for that section, I'm going to delete the entire chunk of text. Tarl.Neustaedter (talk) 02:27, 15 December 2013 (UTC)[reply]
I should add - it's absurd to talk about achieving low-earth orbit from a geocentric space elevator. Any object released from a beanstalk (to use the other common name) will be co-planar with the cable and eventually (probably in less than two orbits) impact the structure, destroying it. This is one reason we need references, so we don't have arguments like this - someone writing for a reliable source will have either addressed this issue or responses to it will have been made and we can quote those too. This is very much a case where we should avoid original research. Tarl.Neustaedter (talk) 02:33, 15 December 2013 (UTC)[reply]
I already reverted the edits of IP68. We're back where we started, I think were safe now from those efforts by IP68 (I think they really were "good faith", just muddled, digressive, etc.). It's not necessary to delete entire chunks of text IMHO. I think a simple "citation needed" tag would be a less drastic solution for the time being. In the process of mass-reverting IP68's stuff, that recently-added tag got wiped out too. I let it stay removed because I was lazy and I honestly would have preferred it without the tag. But, if it has to be there that's better than wholesale removal :-).
Check your calculation again on the release from 66%. If something is released from that height, it's perigee will be just above the atmosphere. As far as a ref goes, there's one here (http://www.endlessskyway.com/2010/05/space-elevator-to-low-orbit.html). I'd cite it, but I'm not allowed because I wrote it. If you think it's reliable or if others do, it might be okay to cite it I suppose. I'm definitely not looking for links to my essay there, it's been there for three years and I haven't mentioned here until now. I only mention it now because I'm hoping to ease your urge to delete for want of a citation :-). There's also a crude Javascript simulator there to play with real time orbital mechanics and releases from any level of an Earth or Lunar Space Elevator. Again, I only mention it because it might be useful or fun for you to play with, not to promote it.
Also, as far as getting to LEO from a SE, that link discusses how to do it. Basically drop from a height slightly less than 66% so that the perigee dips slightly into the atmosphere for aerobraking. It might take a number of orbits with draggy perigees to gradually knock the apogee from "66%" down to about 350 km. Then at the 350 km apogee a very small delta-V is needed to bring the perigee up so it doesn't dip into the atmosphere anymore. No one is saying it can be done without any delta-V. It's just that the delta-V needed is extremely small compared to the 35,000 fps needed to get to LEO from the surface with a rocket. The delta-V needed to lift the perigee out of the atmosphere is somewhat smaller than a normal de-orbit retro burn from LEO (which is only about 300 fps). In fact, it's the very same thing in concept except it's backwards, the "negative" of a de-orbit burn.
The maximum altitude shown in the graph shows the altitude at which the dropped object does not intersect the Earth. From what I can see, this ref considers intersection with the surface, ignoring the atmosphere. That would put it at a lower end of "about 66%, but it still supports "about 66%" for a perigee just at the top of the atmosphere.
Gassend's work on this site is considered to be very reliable.
Regarding hitting the cable. Yes, this subject is undiscussed (as I recall) in the article and it's probably a good (notable) candidate for inclusion. To summarize it, in a two dimensional world, most free-flying satellites would hit the cable in very short order. In a three dimensional operational world, factors conspire to cause them to miss:
1) "Big sky theory" -- The cable is thin, satellites are small, space is big.
2) Active management -- Collision avoidance is a major factor in SE design and operation. Most designs are able to maneuver out of the way of approaching satellites. Satellites themselves are able to maneuver.
3) Inclination -- Most satellites would have a thrusting phase after release to put them at the desired inclination. This puts them in the 3D world where the frequency of close approach is drastically reduced.
4) The cable itself oscillates like an upside down plumb bob and like a guitar string, meaning that even w/o post release thrusting the satellite would have a small inclination. The cable would also oscillate to somewhere else the next time around. This gives a statistical "fuzz" to how close the encounter would be each time.
Please curb your enthusiasm deleting section about equilibrium at geostatioanry orbit. Everything there is correct, factual, and true. This is Physics 101. — Preceding unsigned comment added by 68.228.67.228 (talk) 21:23, 17 December 2013 (UTC)[reply]
Two things. First, it's unreferenced. For inclusion into Wikipedia, being accurate isn't sufficient - you have to cite a Reliable Source saying so. This article has a real problem of Original Research, don't make it worse. Second, it's not relevant. That the geostationary point on a beanstalk is an equilibrium point is (as you point out) obvious, and thus unnecessary. It's simply not relevant, it's an unimportant description. Tarl.Neustaedter (talk) 21:41, 17 December 2013 (UTC)[reply]
It's not as obvious as it seems; the scenario described in the text being inserted by the IP relies on a number of unrealistic assumptions, e.g. unrestricted or frictionless vertical motion, in order to be a valid conclusion. Given a small push in either vertical direction, the climber's natural inclination would be to follow a similar (to GEO) orbit per Hill's Equations, and only its constraint to the cable would prevent that. The harder the push, the more elliptic the natural resulting orbit. This is again why OR is so dangerous. siafu (talk) 19:59, 18 December 2013 (UTC)[reply]
IP68,
Some of it may be factual and true, but it was and still is so unclearly expressed that we (well, I) couldn't figure out at all what you meant. The words appeared as gibberish regardless of what actual correct Physics 101 ideas you may have in your mind. The adversarial relationship established early on signaled that hand-holding you to figure out what you were trying to say would be a lot of work and would very likely be unfruitful. Skyway (talk) 07:04, 18 December 2013 (UTC)[reply]
When converting 2/3 to decimal allow for the error bounds. Mathematically 2/3 may equal 66.6667 but the figures may only be accurate to 3 significant figures, giving 66.7 . The references actually gave the height, which someone removed. Andrew Swallow (talk) 12:57, 18 December 2013 (UTC)[reply]
Andrew, Tarl, I think we've got a bigger problem on our hands than refining the way we express that level. Now blocked, it looks like the former IP68 is now IP hopping and making the same changes. I don't recommend semi-protection quite yet unless it has a hard and fast expiration. (Too many other permanently semi-protected articles are now moribund without the efforts of IPs, all with the only very thinly supported justification of "persistent vandalism") This guy is offended and it looks like he's determined. Does anyone know a next step other than semi-protection? Skyway (talk) 17:02, 18 December 2013 (UTC)[reply]
Yeah, it could be more than one person. I checked the locations too. Still, it's not too hard to proxy around the country by a number of means, such as using friends' computers with remote desktop software. It's hard to say. Skyway (talk) 18:55, 18 December 2013 (UTC)[reply]
Possible GEO stability problem
There may be a stability problem with objects on the space elevator. If the horizontal velocity is reduced they will fall to a lower orbit. To get back to LEO from GEO a free flying object needs a delta-V of 3.9 km/s to slow them down. Objects going above GEO need a gain of delta-v. However if an object is attached to the ribbon then an exchange of velocity can occur. Consequently objects can move with only a small motor providing they follow gravity. Such movement can be unintentional and may enter a feed back loop. The climbers need to be equipped with brakes.
I was reading the article and something popped into my mind. Probably other people already thought of it, but i would like to know if it's a good idea or not.
If you place the elevator on the pole, and let it rotate 1 revolution per day, in the same direction as the earth rotation, you already need a considerable lower elevator. You need an additional 6000 km since you are connected to the pole instead of the equator, but you save 27000 km because the new stationary orbit is 4 times lower due to the rotating and thus increased centrifugal force. (86.93.56.137 (talk) 10:55, 16 February 2014 (UTC))[reply]
Where is the pole? If the pole is at the North or South Pole something like that may work but will require enormous amounts of energy to move the entire elevator. Outside of about the Arctic and Antarctic Circles the elevator will crash into the Earth. Andrew Swallow (talk) 13:02, 16 February 2014 (UTC)[reply]
Yes, it must be the north or South Pole. The amount of energy needed is not that much. Only overcoming friction. The rotational kinetic energy is always there, just like the international space station. It has the kinetic energy but is not lessening it. 77.168.45.146 (talk) 13:20, 16 February 2014 (UTC)
Sorry I see my ip 77.168.45.146 (talk) 14:25, 16 February 2014 (UTC) is changed since I'm now on my smartphone.[reply]
F=rw^2 if w is halved then r quadruples. therefor radius goes from 36 Mm to 9 Mm. Thats how i got to the 27 Mm. Anyways it is a lot easier to just build a 100km tower since then you're already in space (according to definition) 194.105.120.70 (talk) 15:22, 18 February 2014 (UTC)[reply]
There would be no way to transfer angular momentum back and forth between Earth and the climbers. That's the key thing that separates a space elevator from all those other cutesy little space tethers (rotorvators, skyhooks, whatever). Off-equator anchor points would conceptually work, but only in a small range about the equator (+/-10 degrees or so). The vibration dynamics are much more complicated too. The other issue with a polar anchor point is that the cable would run horizontal to the ground for many hundreds of miles, it might not even be lifted off the ground for many degrees away from the pole.
Off-equator anchor points have been discussed in the literature, but more as a novelty. I don't think it's important enough to include except for a small mention of the possibility of moderate off-equator anchor points. An anchor point at the pole should not be mentioned IMHO. It would be a distraction.
The moon could handle larger latitudes for the anchor point because the elevator is held up not by centrifugal (pseudo)force as for an Earth elevator, but with the center of mass being well on the other side of L1. This could potentially be a notable mention.
Placed over the pole, either north or south, the payload will gain absolutely NOTHING from the earth rotation, because the effective radius of rotation there is ZERO....so how can it be advantageous over equatorial placement where radis of rotation is 4000 miles just standing on the ground? — Preceding unsigned comment added by 68.228.67.228 (talk) 04:58, 26 February 2014 (UTC)[reply]
The pole is a rival to the equator. All the rotation has to be provided by an engine. Countries may have access to one of the poles but not the equator. Andrew Swallow (talk) 05:58, 26 February 2014 (UTC)[reply]
