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From my understanding, a practical space elevator would require a large center 'station' in geostationary orbit that the cable is attached to, and some form of counterweight on the other side, possibly in the form of extending a cable the same distance in that direction. Since, at that station, you're travelling approximately 3 km/s, being the speed of the rotation of the earth, and as you go further away, your speed increases, while the velocity needed to orbit decreases.

If a space elevator had a cable extending 36000km into space past the station as a counterweight, could you move the elevator up it and 'let go', and get flung onto an escape trajectory as soon as the centripetal force is removed? Furthermore, I understand that the orbital planes don't line up, as a space elevator would have to be on the equator, but would it be possible to use a space elevator to slingshot you on a path to the moon and do a burn to adjust your inclination during the transfer for a much less Delta V intensive lunar transfer? Since all you need to do is change inclination and perform a capture burn.

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  • $\begingroup$ Just a note that goes along with any Space Elevator plan - Material Science has not yet come up with anything that can withstand the forces necessary to construct a useful Space Elevator, and it's unclear if there will ever be such a material. The forces involved would be considerable... to say the least. $\endgroup$
    – SnakeDoc
    Nov 18, 2022 at 20:25
  • $\begingroup$ @SnakeDoc even if we had magic materials for tensile stregth I don't think it would be feasible. We have plenty of satellites in LEO, including uncontrollable trash... the space elevator cannot move, so it will hit significant masses at km/s speeds, i.e. it will break in a matter of decades at most. And once you destroy a space elevator that's probably going to produce enough trash to prevent any space launches for a while. Also, given the risks involving the whole of Earth, it would require Earth-wide consensus to pull off... and terrorists could easily wreak havoc on the world... $\endgroup$
    – Bakuriu
    Nov 19, 2022 at 13:07
  • $\begingroup$ Isn't that backwards? Isn't the sole point that a space elevator should be able to launch a payload to solar orbit? Else, what would be the point? $\endgroup$ Nov 19, 2022 at 19:29

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Yes. If you could build the elevator, it could be used to launch satellites into prograde orbits with the same inclination as the Earth's equator. This includes solar orbits.

Changing orbital inclination is very expensive in terms of delta-v.

In your lunar scenario, you could release from the elevator when the elevator is aligned with one lunar orbital node, do a Hohman transfer and arrive at the moon (at the other node) 180 degrees later. This would avoid the delta-v cost of an inclination burn.

enter image description here

The satellite is released when the elevator is aligned with Node 1. Blue line is the Hohmann transfer in the Earth's equatorial plane. Purple line is the Moon's trajectory during the same period.

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  • $\begingroup$ Thank you for your answer! I'm not quite sure what you mean with the last part of your answer, is there a point in orbit where the trajectory you'd leave on from the equator overlaps where the moon will be at one of the two points it crosses the equatorial plane? Or is there some more complicated orbital mechanics at play? $\endgroup$
    – EriKana
    Nov 18, 2022 at 22:23
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    $\begingroup$ @EriKana ... easiest with a diagram. I'm on the road but I'll edit in a sketch next week . From your comment it sounds like you have it figured out $\endgroup$
    – Woody
    Nov 18, 2022 at 23:55
  • $\begingroup$ @EriKana Yes, when the moon crosses the plane of Earth's orbit a payload slung from an elevator can reach it. The relative velocity from the plane change is minimal at that point. $\endgroup$ Nov 19, 2022 at 2:42
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    $\begingroup$ @LorenPechtel.... I think you should have written "when the moon crosses the plane of Earth's EQUATOR ..." since the plane of the transfer orbit is coplanar with the equator, not Earth's orbit around the Sun. $\endgroup$
    – Woody
    Nov 19, 2022 at 2:53
  • $\begingroup$ @EriKana ... did the sketch explain the orbital mechanics involved? $\endgroup$
    – Woody
    Dec 4, 2022 at 5:02
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Technically yes, but there is an issue you will encounter.

That is, when you accelerate your space ship against the counterweight wire, that wire won't have as big inertial mass as the entire space elevator, so it will start to collapse towards the space station in a very complicated manner, considering that any wire that long is flexible and stretchable instead of being rigid and reliable position wise. Therefore, a single launch to a solar orbit via space elevator can render it useless, or at least would require an indeterminate amount of time to stabilize the counterweight for the second launch.

In order to successfully launch something using space elevator as accelerator, your best action would be stop accelerating against it as soon as the bulk of the elevator's mass is below the accelerating device, meaning that even if your counterweight is a wire stretching 36000 km into space, you should NOT use it to apply force, or else the counterweight would be accelerated towards Earth many times stronger than below the station. Also, after you launch, you'll have to accelerate the space elevator itself in order to maintain its orbit, because its structure and orbital parameters are all balanced around having its mass center in relatively the same location, but here you have a free momentum towards Earth for the space elevator that you have to compensate somehow.

This means that if your space elevator has a station at its middle, you cannot effectively use its counterweight to accelerate space ships. Better make your elevator's station, where the bulk of its mass is located, positioned at its very end, a tad above geostationary orbit, yet have its orbital speed in sync with the planet, this way the station would act as both the hub for whatever orbital activities and the counterweight for the wire down to the surface. Such construction might have an opening in the center to allow accelerated cabins to slide off the wire into the open space, although whatever mechanism used to keep the wire attached would need to account for such use, implementing devices to allow detaching from the wire prior to reaching the station. But, speaking of theories, what you ask for is possible with a certain aftermath you'll have to deal with.

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    $\begingroup$ I don't get it. The counterweight is held up by centrifugal force, it naturally falls "up" away from the earth. There can be flex issues as the cable imparts horizontal acceleration to the elevator car, but this seems to suggest there is a danger of pulling the entire space elevator down, but that shouldn't be the case with a big enough counterweight. $\endgroup$ Nov 18, 2022 at 15:31
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    $\begingroup$ ""when you accelerate your space ship against the counterweight wire": The acceleration could be quite low. It presumably doesn't matter if we take weeks to get to the counterweight end of the cable, if that is required to lower the effects on the cable's stability. $\endgroup$ Nov 18, 2022 at 16:22
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    $\begingroup$ The more I read this, the less sense it makes. You'd never accelerate a climber up the cable with so much acceleration or mass that it pulls the counterweight down (otherwise you haven't made a big enough or high enough counterweight). A space elevator doesn't need to accelerate to maintain its orbit, it naturally wants to move into a bigger orbit but is held down by the cable. The Coriolis force makes the counterweight swing like a pendulum as the climber ascends, but none of those forces make the space elevator fall down. I can't make heads or tails of what the problem is supposed to be. $\endgroup$ Nov 18, 2022 at 18:19
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    $\begingroup$ Put another way, the elevator will settle toward an equilibrium with the elevator straight out. A payload ascending will perturb it, causing it to swing to one side, but you can just slow the ascent to keep this to a degree that the elevator can tolerate. $\endgroup$ Nov 18, 2022 at 18:41
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    $\begingroup$ You don't accelerate the payload past the synchronous orbit. Rather, at that point you use it's motors as generators, extracting energy as it moves outward until it reaches the desired release point. $\endgroup$ Nov 19, 2022 at 2:45

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