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Moon Space

A Lunar Space Elevator Is Actually Feasible and Inexpensive, Scientists Find (observer.com) 161

An anonymous reader shares a report: In a paper [PDF] published on the online research archive arXiv, Columbia astronomy students Zephyr Penoyre and Emily Sandford proposed the idea of a "lunar space elevator," which is exactly what it sounds like -- a very long elevator connecting the moon and our planet. The concept of a moon elevator isn't new. In the 1970s, similar ideas were floated in science fiction (Arthur C. Clarke's The Fountains of Paradise, for example) and by academics like Jerome Pearson and Yuri Artsutanov. But the Columbia study differs from previous proposal in an important way: instead of building the elevator from the Earth's surface (which is impossible with today's technology), it would be anchored on the moon and stretch some 200,000 miles toward Earth until hitting the geostationary orbit height (about 22,236 miles above sea level), at which objects move around Earth in lockstep with the planet's own rotation.

Dangling the space elevator at this height would eliminate the need to place a large counterweight near Earth's orbit to balance out the planet's massive gravitational pull if the elevator were to be built from ground up. This method would also prevent any relative motion between Earth's surface and space below the geostationary orbit area from bending or twisting the elevator. These won't be problems for the moon because the lunar gravitational pull is significantly smaller and the moon's orbit is tidally locked, meaning that the moon keeps the same face turned toward Earth during its orbit, therefore no relative motion of the anchor point.

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A Lunar Space Elevator Is Actually Feasible and Inexpensive, Scientists Find

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  • Watch out Satellites!

    How much energy is saved launching something to 22k miles above sea level, as compared to total escape velocity? Is it worth the technological hurdle of then somehow linking up with the elevator (and using energy to slow yourself down again as you approach it)?

    • Since you can get there with helium, theoretically a whole fuck load of energy could be saved this way.

    • by Geoffrey.landis ( 926948 ) on Wednesday September 18, 2019 @02:50PM (#59209962) Homepage

      Watch out, geosynchronous orbit satellites!

      You can extend a cable from the moon down to the distance of geosynchronous orbit. But they are proposing a cable that would be locked to the moon's orbital period. Objects at the end of the cable would not be in geosynchronous orbit (it would be in the location of geosynchronous orbit, but not in geosynchronous orbit.

      The satellites in geosynchronous orbit-- and there's a lot of them--are moving at an orbital velocity of 3.07 km/s, something like ten times faster than a rifle bullet. You do not want to be in this position moving at 0.11 km/sec (the velocity the end of the cable would be moving at).

      Frankly, I can't think of any reason you'd want to do that.

      • by apoc.famine ( 621563 ) <apoc.famine@gm[ ].com ['ail' in gap]> on Wednesday September 18, 2019 @03:05PM (#59210032) Journal

        Landing on anything is hard. Landing on anything without an atmosphere is very hard. If you can just transfer to a space station and ride the elevator down, it takes a lot of the complexity out of getting on and off the surface.

        One major concern that doesn't get nearly enough press is that the lack of an atmosphere on the moon means that rocket exhaust kicks dust and pebbles up on the moon's surface which can move at a thousand miles an hour and circle half or more of the moon. There's no atmosphere to slow them down, so they just fly off on a ballistic trajectory until they intersect with the moon once more.

        Landing a rocket on the same side of the moon as any established base would put anything above the surface in real danger. If we ever go back to the Apollo landing sites and look at the rovers and equipment left there, there's a significant chance that they'll look like someone shot them with a shotgun. And that was a relatively small rocket, nothing like the Starhopper in terms of thrust.

        • by dryeo ( 100693 )

          200,000 miles makes a long elevator ride.
          Never heard of rocket exhaust kicking rocks off at a thousand miles an hour, be pretty scary when Spacex lands a rocket, Besides the lunar module used the first stage as a launch pad, so didn't launch from the ground. I guess according to you, there was a good chance of knocking out the command module in orbit when the lunar module landed.

      • >You do not want to be in this position moving at 0.11 km/sec (the velocity the end of the cable would be moving at).
        Hear, hear.

        That is no doubt why they choose geostationary orbit as the cuttoff point. Geostationary orbits are incredibly useful, we don't want to impede them, and virtually all other useful orbits are lower than that. End your tether many miles above geostationary you don't interfere at all. Even falling debris from the tether will fall straight down into the atmosphere and not become

      • You can extend a cable from the moon down to the distance of geosynchronous orbit. But they are proposing a cable that would be locked to the moon's orbital period. Objects at the end of the cable would not be in geosynchronous orbit (it would be in the location of geosynchronous orbit, but not in geosynchronous orbit.

        This was going to be my objection too. You would want to terminate the elevator at a safe distance above geosynchronous, to avoid walloping a host of large expensive satellites.

      • an orbital velocity of 3.07 km/s, something like ten times faster than a rifle bullet.

        Minor quibble - 3.07 km/s is about 10000 ft/sec. Which is ten (to 15, depending on the pistol) times as fast as a pistol bullet, but only 3-4 times as fast as a rifle bullet.

    • The velocity needed to orbit at that altitude is pretty close to the velocity needed to escape from the same altitude.

      Think about what would happen if you attempted a geosynchronous orbit, but you were going a little too fast. You'd end up drifting away from earth. As your altitude increased, the velocity needed for a stable orbit would decrease, meaning your "extra" velocity increases - you start going away from earth faster and faster, being less affected by gravity. At some altitude Earth's gravity wou

      • by suutar ( 1860506 )

        That's interesting; I hadn't realized "escape velocity" dropped so fast with altitude. I just remembered that at the surface it's about 11km/s and assumed that 35Mm wouldn't make that much difference. But yeah, at that altitude orbital velocity is 3.11 km/s and escape velocity works out to 4.35 km/s

        But I'm confused about your scenario - as you gain altitude you lose kinetic energy (it becomes "potential" energy), so you lose velocity... if you're above escape velocity you won't lose enough to stop, but if y

        • by Immerman ( 2627577 ) on Wednesday September 18, 2019 @04:26PM (#59210448)

          Yeah, they're scenario is... a bit off.

          The rule is escape velocity = 1.414 * circular orbital velocity. With circular orbital velocity falling rapidly as the radius increases, as v=1/sqrt(r).

          In their scenario, if you overshot geostationary orbit, but with less than escape velocity, what would actually happen is that you'd just slow down until the you started falling back, gained your speed back, and started climbing again, in an elliptical orbit that passes through geostationary orbit altitude. Elliptical orbits are considerably more complicated than circular ones, and the highest point you reach will be above the point where you match circular orbital speed, but you will most assuredly start falling down and picking up speed once again, not just drift away

          Here's some quick reference points for the amount of energy associated with various orbits:
          by convention, orbital energies are always negative, measured from the common zero-point of a non-orbit at infinite distance. The larger the negative number, the more deeply trapped you are in a gravity well.
          https://en.wikipedia.org/wiki/... [wikipedia.org]

        • Yes, I wasn't clear about that. That's why the two velocities are "about" the same, rather than being the same by definition.

          On the hand, once you exceed orbit velocity you're "stably" moving further and further from Earth. The further you go, the less velocity you need, so your net speed away from Earth would keep increasing.

          On the other hand, you're only far from Earth's surface, not outside of its gravity well, so gravity will tend to slow you down.

          At velocities above orbit velocity, it's a contest betw

      • Byt you don't want to reach geostationary orbital velocity, because then you'd whizz past the cable at great speed. You want a highly elliptical orbit that touches the cable at its own speed during apogee. This requires a lot less energy. Calculations for two transfer orbits are at the very end of the paper.
      • by ceoyoyo ( 59147 )

        Except you're not going into orbit. A lunar tether hanging down to the *altitude* of geosynchronous orbit would be close to stationary. You'd have to kill your lateral velocity at the surface, not add to it.

        Ignoring that last factor, you'd be comparing the energy needed for a suborbital flight to 22 k miles and one to the moon, plus slowing down at the other end.

    • by lazarus ( 2879 )

      How much energy is saved launching something to 22k miles above sea level, as compared to total escape velocity?

      30% or less (probably a lot less). Any circular orbital velocity is about 70% escape velocity. When you consider that most of your energy expenditure is on the ground just getting lift on all the fuel you need to consume, there is very little to be gained from doing this, and you are adding a lot of complexity.

      This isn't going to happen, but it is a fun exercise.

      • Once this is up there, then it becomes dirt cheap to bring cargo to the lunar surface as well as bring minerals, elements, and esp. water up to space.
    • by White Yeti ( 927387 ) on Wednesday September 18, 2019 @03:11PM (#59210066) Homepage Journal
      In Appendix B of the paper (see conclusions in B.5) they show up to 25% fuel savings to reach the Moon, and guesstimate up to 66% savings if you include lunar soft landing.
    • https://en.wikipedia.org/wiki/... [wikipedia.org]

      Specific energy at Earth's equator: 62.6 MJ/kg
      Specific energy at Geostationary: 4.6 MJ/kg
      difference = 58MJ/kg (assuming 100% efficiency)
      Specific kinetic energy at Geostat: 1/2*(3.07 km/s)^2 = 9.42MJ/kg

      So orbital speed at geostationary accounts for roughly 1/6th of the total energy difference with the Earth's surface. I'd say that probably, no, it's not worth it for getting to orbit from Earth unless it could be done *very* cheaply. It would however be an elegant way t

    • by ceoyoyo ( 59147 )

      It's a pretty substantial saving. Note that you're not going to geosynchronous *orbit*, you're just flying up to that height. You'd work it out so you're in a suborbital trajectory that at it's apogee just touches the elevator, then you can hook on.

      The real saving is the convenience of not having to worry about landing and taking off from the moon. Being able to ride to/from within 22 k miles of the Earth's surface is just a bonus you get by building the elevator the cheapest way possible.

      Also, obviously yo

  • Libration (Score:5, Informative)

    by Mononymous ( 6156676 ) on Wednesday September 18, 2019 @02:29PM (#59209860)

    moon's orbit is tidally locked, meaning that the moon keeps the same face turned toward Earth during its orbit, therefore no relative motion of the anchor point.

    Well, not exactly the same face. Due to libration [wikipedia.org] we can see about 59% of the moon's surface from Earth. I don't know what solutions the paper proposes, but the elevator will be swinging around from our point of view.

    • Well, not exactly the same face.

      Right? I thought the same thing, like the moon keeps *roughly* the same face towards us, but it ISN'T stationary relative to the Earth, which would be required to place the end point in "geostationary orbit" (even says "stationary" in the word!)

      • by AmiMoJo ( 196126 )

        It says "geostationary orbit height", as in just that distance above the Earth but not actually in a geostationary orbit. In fact if you check the paper they have the cable dangling down and moving relative to the surface of the Earth.

        • Re: (Score:2, Insightful)

          by JoeDuncan ( 874519 )

          It says "geostationary orbit height", as in just that distance above the Earth but not actually in a geostationary orbit. In fact if you check the paper they have the cable dangling down and moving relative to the surface of the Earth.

          Which is meaningless bullshitting. The only reason to even mention "geostationary" in this context is to imply to the reader that the endpoint will be stable, when they know full well it wouldn't be, which means the whole thing is just fuckery all the way down on their part...

          • by Megol ( 3135005 )

            You being pissed because you didn't understand something isn't due to "fuckery" by the authors. Be an adult.

            • Well, since you're being a child, I'll respond in kind:

              "Wow. You really are an ass aren't you? Don't be such a pointless dick and maybe you'll make some friends one day"

              Now, for the record, and any adults reading:

              --------------------

              Things that ARE childish:

              • -being pointlessly pedantic and literal
              • -assuming others emotional state without reason
              • -assuming others understanding without reason
              • -being unable to tolerate mild expletives
              • -personal attacks

              --------------------

              Things that are NOT childish:

              • -pointing
          • It is pretty rudimentary scientific knowledge that stuff in a geostationary orbit orbits the earth once a day. It is also similarly rudimentary knowledge that the moon orbits the earth in a period much longer than that. With the information given in the summary (elevator "would be anchored on the moon and stretch some 200,000 miles toward Earth until hitting the geostationary orbit height"), it's not that hard for someone with a *very* basic understanding of orbital mechanics who is also familiar with the b

            • BTW, I don't really think this elevator would be practial and useful enough to actually make sense to produce. It's a huge engineering project in order to make it just a bit easier to get stuff to the Moon, and there might be better and more ways to accomplish that. Let's build a Lofstrom loop instead :)

              Still, I find the idea nifty enough that it is worth pondering. Besides, a lot of scientific- and engineering breakthroughs startet with either "That's strange..." or "What if..".

              • by ceoyoyo ( 59147 )

                The point is to get things *off* the moon, and also down to the surface, gently. It's a lunar space elevator. The fact that it saves you a bit getting *to* the moon is just a bonus.

        • But the Moon is not in a circular orbit. It's distance from the Earth varies from 363,396 km to 405,504 km

          The difference (42,000 km) is much greater than the distance to geostationary orbit (36,000 km). So unless the plan has a method of shortening the cable by that amount and then reeling it back out every 28 days, it won't even be at a fixed height: geostationary or anything else.

          • by ceoyoyo ( 59147 )

            That's probably not a big issue. You'd just have to adjust your trajectory (or timing) to intercept the end. It would be easy to predict its altitude.

      • The endpoint is specifically NOT in geostationary orbit, it's at geostationary orbit *altitude*, but moving much too slow and only staying up because it's tied to the moon. Geostationary orbit requires moving at is ~3km/s, while the end of a tether tied to the moon would only be moving at about ~0.1km/s.

        • The endpoint is specifically NOT in geostationary orbit.

          Congratulations on actually getting the point, seems rare around here LOL

      • But how slow is the wobble? And what is the resonant frequency of the cable? Is the moon is going to pull the end around like a skipping rope? Or swing the whole thing like a hammer throw?
    • by fsh ( 751959 )
      The paper does not take libration into account, but the good news is that the math here also doesn't require a huge anchor point on the moon like the earth-based space elevator as all of the tension is accounted for by gravitation. But you're right, roughly seven degrees of bend due to libration (both latitude and longitude) would present a big "last mile" problem. Do I hear another paper getting written?
      • Libration, that's where the moon takes a swig of wine every time it orbits the Earth, right?
      • by suutar ( 1860506 )

        Can the flex required for libration be spread over the length of the cable enough to not be a problem? Or are we looking at a cosmic crack-the-whip game here?

  • by Crashmarik ( 635988 ) on Wednesday September 18, 2019 @02:39PM (#59209904)

    Is to get in and out of Earth's gravity well more efficiently. Once you're at geo synchronous orbit, it's pretty easy to get to the moon.

    Think of the size of the Saturn V and compare that to the size of the command module, and lander.

    • it's pretty easy to get to the moon.

      Only if you’re not in a hurry. The bus schedules are *completely* unreliable.

      • The bus schedules are *completely* unreliable.

        Says the guy who calls himself 93 Escort Wagon [youtube.com].

        • by Curunir_wolf ( 588405 ) on Wednesday September 18, 2019 @03:08PM (#59210044) Homepage Journal

          The bus schedules are *completely* unreliable.

          Says the guy who calls himself 93 Escort Wagon [youtube.com].

          What a WHINER! He should feel lucky to have a car that nice, he's just complaining about a bunch of minor little issues. "Oh, noes, I have to hand-crank the window!" BAH! At least it has windows AND they move up and down. Whiner.

          I've driven MUCH worse cars, and I was glad to have that got me around!

          • I've driven MUCH worse cars, and I was glad to have that got me around!

            And I bet you had to drive them uphill both ways, both coming and going - right?

      • it's pretty easy to get to the moon.

        Only if you’re not in a hurry. The bus schedules are *completely* unreliable.

        I drove my old RAV4 to the Moon, 253,000 miles. I did it in 18 years.

    • You got it backwards.

      It's easy to get to Geo synchronous orbit, it's really really hard to land on the moon (ask India and Israel) . This would make the latter much safer.

    • by ceoyoyo ( 59147 )

      Yes. So the point of a lunar space elevator is to get to and from the moon's surface. Getting partway to/from the Earth is just a side benefit, which you would probably only use if you were cargo, because it would likely take a looooong time.

  • Obligatory xkcd (Score:5, Informative)

    by itsme1234 ( 199680 ) on Wednesday September 18, 2019 @02:46PM (#59209942)
  • Remember the episode with the 5th doctor where the politicians were wired into electric chairs, and people voted via the TV? The losers were fried, slowly.
  • If you have a cable running from the Moon to the geostationary orbit, don't you still have the end of the cable whipping through that orbit once a day? That's not as fast as LEO orbit, but it's not exactly slow either. The Concorde used to race the terminator, so I'm thinking it'd be roughly that speed that you'd have to catch. How do you even catch something that fast without boosting yourself out of orbit? I'm thinking such a rendezvous would require more fuel than is typical, and controlling things i

    • You are correct that it's not stationary. The end of the cable whips through geosynchronous orbit at a relative speed of about 3 km/second: much faster than the Concorde.

    • by ceoyoyo ( 59147 )

      The end of the cable whips around the Earth about once a month. *YOU* on the other hand, whip around once a day. So you'd have to slow down to catch it. You'd launch in a suborbital trajectory that goes up retrograde and intercepts the cable at it's apogee. To come down, you could accelerate a bit, nowhere near orbital velocity, and come down going west to east, or, if you were careful, you might be able to drop off, accelerate a bit more retrograde, do some aerobraking, then land E-W. Or have some awesome

  • The OP seems seriously confused between an Earth Elevator and a Moon Elevator, which never the 'twain shall meet. 8-)

    Previous talk was about an Earth elevator, this proposal is a Moon Elevator which has much lower loads and material requirements. I think they are saying that the "Unobtainium" might not be needed!

    • If "unobtainium may not be needed", exactly what materials will suffice? It doesn't matters if 'the numbers work', reality has to as well.

      Reminds me of the physicist that insisted travel backwards through time was possible. You simply have to take a large disk of infinite mass, rotate it at the speed (or near) of light and travel around it the opposite direction at the same speed.

      In other words, no, you cannot go backwards in time. This is much the same.
      • by ceoyoyo ( 59147 )

        Kevlar or carbon fibre are more than twice the required strength, so they have a nice practical safety margin. The paper estimates you'd need about an SLS cargo launch worth of cable.

  • Geostationary orbit means the dangling end of the cable will be above the same spot on the earth's surface.

    The other end is attached to the moon.

    And the moon orbits around the earth (disregard lunar libration for the moment which is a decidedly secondary effect to my concern).

    So won't one end of the cable want to be in a fixed location relative to the surface of the earth, and the other end want to be going round-and-round? Those two constraints seem to be incompatible.

    What am I missing?

    • What am I missing?

      Nothing, you are just smarter than the paper's authors.

    • The end of the cable is at the Earth-relative height of geostationary orbit, but is not in geostationary orbit, because it goes around the Earth once per Moon orbit, rather than once per Earth 'day'.

      So, yes, this means that if you launch up to geostationary orbit you then have to find a whole bunch of other delta-v in order to dock with this thing, all the while having to maintain your Earth-height without being in an orbit that easily allows for that (you're going too slow, so would tend to fall down).

      • by suutar ( 1860506 )

        you do have to find some lateral delta v, but less than it takes to get into actual geostationary orbit.

      • The end of the cable is at the Earth-relative height of geostationary orbit, but is not in geostationary orbit

        Which makes the whole endeavour of this paper pointless.

        It's like building an elevator to the 200th floor that only starts at 150 so you have to walk up 150 flights first.

    • Tis a bit confusing they way they word it.
      One cable end anchored to the moon. Fixed point. That means that the other end is moving around the earth at the same speed as the moon, zipping around the earth about once daily. It just so happens that the free end is about the height that geo-stationary satellites already occupy.

      Yes, the free end of the cable would likely hit existing satellites, doing bad and expensive things to whatever is in the way.

      • *zipping around the earth once daily, relative to the surface of the earth. This is also relative to existing geostationary satellites.

        Technically, the moon orbits earth about once every, oh about a month, but that's less relevant to orbital debris creation.

  • we find that farting our way to space is easy and inexpensive!

  • They actually cited wikipedia in the article for strength and density information. Really, you guys couldn't find that anywhere else?

  • by WindBourne ( 631190 ) on Wednesday September 18, 2019 @03:25PM (#59210154) Journal
    Cool thing is that terrorists could not easily target it .
  • I have to believe that the costs associated with launching all the materials (as well as the people, living quarters, etc.) needed to build this to the moon (at least, initially) to be darned (to put it mildly) expensive. Build it using raw materials found on the moon? Still have to build lunar manufacturing facilities---not exactly inexpensive. Plus, if it's not technically feasible to construct such a structure anchored to the Earth's surface, do we know how to build something anchored on the moon that wi

  • by Required Snark ( 1702878 ) on Wednesday September 18, 2019 @03:50PM (#59210288)
    "the strength of existing materials, such as Kevlar and Dyneema, is more than sufficient to construct a spaceline"

    The article intends to show current technology can build this structure. It makes a convincing case. They derive a profile for the cross section of the material to minimize the weight and how much stress it must withstand. That is why they conclude it is feasible.

    Besides making access to the moon's surface easier, the other major benefit is being able to build a space station at the L1 Lagrange point. [wikipedia.org]

    The Lagrange point base camp - The last item on this list is the thing we believe to be most impor-tant and influential for the early use of the space-line (and for human space exploration in general). The spaceline makes the Earth Moon Lagrange point effectively stable. In this gravity free environment we can construct habitats and equipment of arbitrary mass. It is a pristine and gravity free environment, with no great hindrance to developing space constructions on a scale that would seem impossible otherwise.

    If I understand correctly it would be possible to build a shorter structure to the L1 point by giving up synchronous orbit access.

    • If I understand correctly it would be possible to build a shorter structure to the L1 point by giving up synchronous orbit access.

      While L1 has no net gravity, it's unstable. You would need a counterweight on the other side of L1 to stabilize it unless you made the elevator out of some sort of rigid material.

  • If it could work, it would be a way to make Earth-based elevators less expensive to build:

    Build lunar "space line" to make it easier to land on the moon.
    Set up mining/manufacturing to build components for the rest of the "elevator network".
    Use space line to lift materials into earth orbit, above geostationary level.
    Build platforms to drop space lines to earth, and launch them to geostationary orbits.

    Less energy needed to get material to orbit, assuming the materials needed can be found/processed on the moon

  • you can build a usable space launch system in under 20km, if the asteroid is rotating fast enough. ( https://www.researchgate.net/p... [researchgate.net] ) Plenty of known sizable rocks for tethers of less than a few hundred km. 0km - if it's rotating too fast to hold itself together.
  • by tomhath ( 637240 ) on Wednesday September 18, 2019 @05:05PM (#59210630)
    It seems to me that a "climb up the cable all the way up to the moon" and then a deceleration upon arrival would take just as much energy with or without the cable. Yeah, I get that you could attach to the cable and pull yourself along it, but the amount of work to accelerate and decelerate doesn't change. And please don't suggest that the last few miles of the elevator could be strong enough to use as a brake, it can't be that strong.
  • I suspect that the original source for the article was referring to a lunar elevator that could carry materials between the moon's surface and a space station at either the L1 or L2 point of the Earth and Moon. There are no stable synchronous orbits around the moon, and you really couldn't have an elevator (certainly not a practical one) that reached all the way to Earth or to Earth geosynchronous orbit.

    As I recall there has been some research showing that such an elevator is feasible now, using Kevlar or o

  • by Solandri ( 704621 ) on Wednesday September 18, 2019 @05:45PM (#59210754)

    These won't be problems for the moon because the lunar gravitational pull is significantly smaller and the moon's orbit is tidally locked, meaning that the moon keeps the same face turned toward Earth during its orbit, therefore no relative motion of the anchor point.

    That's not quite true. In addition to the moon's orbit not being perfectly circular, the moon undergoes libration [wikipedia.org]. It's not perfectly tidally locked, and oscillates back and forth a bit. About 7 degrees in the north-south axis, about 8 degrees in the east-west direction. What effect this would have on a moon-mounted tether I don't know. It might simply be a matter of putting a pivot at the tether's anchor point so it can wobble a few degrees. Or it may cause the whole thing to snap due to shear forces from the tether being forced to move back and forth to try to remain intersecting the L1 Lagrange point.

  • 1) observer.com is basically calling two astronomy students submitting a paper about creating a lunar space elevator, scientists and researchers. There are no degreed scientists or researchers actually advocating to do this, because there is near zero utility in building such a structure.

    2) observer.com is equating a lunar space elevator to an earth tethered space elevator. How can there be any energy benefit getting materials from earth to GEO, when the tether starts 22K miles from the earth's surface?

  • by viperidaenz ( 2515578 ) on Thursday September 19, 2019 @01:22AM (#59211634)

    One you're up in geo orbit, you'll need to bleed of a few km/s of velocity to slow down to the speed of the elevator, without losing altitude. That means burning lots of fuel.
    The biggest use of fuel is getting out of the atmosphere in the first place. This won't solve that problem.
    That big velocity difference means Earth's gravity will still be pulling on the elevator. Without pulling out a calculator, probably about 0.4g. it's still going to have to be a very strong cable.

Every nonzero finite dimensional inner product space has an orthonormal basis. It makes sense, when you don't think about it.

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