Reading a sci-fi book the author made a point that if your elevator car came detached from a space elevator before geosync orbit you would descend back to earth, if it detached after geosync orbit you would be flung out into interplanatary space.
My question is ‘is this correct?’. I would expect at a low enough level you would expect to hit the earth and at a high enough level you would escape earth’s gravity.
But in the middle it would seem you would enter a elliptical orbit around earth, below geosync you would you would be at apoapsis and above you would be at periapsis as you leave the ‘stalk’
Below the geosync orbit point (22,300 miles above the surface) you are going fast enough to circle the earth in 24 hours, at whatever radius you are at. Logically, you are too slow and you will fall.
There is a point (not up on my orbit calculations) where you are right. You are going fast enough that forward velocity carries you around the earth in an elliptical orbit. If the perigee is outside the atmosphere, then it’s relatively stable.
Whether you would be “flung out into interplanetary space” depends on the location of the top. In some scenarios, it is that high so the end is travelling at earth escape velocity to facilitate spacecraft launches; but it does not have to be that high/fast.
Both you and the author are correct. Below, you would enter an elliptical orbit with apogee at the detachment point and hence would start descending, and above you would enter an orbit (elliptical, parabolic, or hyperbolic depending on just how far above) with the detachment point at perigee and hence would start ascending. In many cases you would then start coming back to your original altitude after a time, but the initial behavior is as the author stated.
The geo-sync orbit is not a critical point.
And there are more results than those two.
The three situations are
Too low, orbit collides with earth (or degrades due to earths atmosphere), very quickly.
In between , can remain in orbit for long enough to be called an orbit. Suppose you became detached just 1km from the geo-sync level… that it almost geo-sync, which surely is a stable orbit of some sort.
Being flung out of the solar system ? Surely just 1km above geo-sync level is just another earth orbit that isn’t geosync ? And surely there are boundaries between leaving Earth’s orbit and leaving Sol’s orbit ?
But the author gets at two main results, either you crash to earth soon or you stay in space for a long time… well no, there is a third range which is ‘orbit but not stable, so the crash comes in a week or three…’
There isn’t really such a thing as an unstable orbit, in the two-body problem, unless you’re doing something like rubbing up against the upper atmosphere.
From my understanding of space elevators, if the upper terminal is in geosynchronous orbit:
If the car becomes detached any significant distance from the upper terminal its orbit will sooner or later decay and come crashing onto the Earth (or whatever planet this elevator is on).
I don’t understand how the car could end up higher than the upper terminal.
Yep. Earth has mascons too, but they aren’t a problem because they would only have a significant effect if you’re within the atmosphere, and obviously you can’t orbit within the atmosphere anyway. Of course, you could build a lunar space elevator…
The cable has to extend above geosync for balance. The center of mass of the whole thing is at geosync, so there has to be as much mass above that point as below. Since there’s 36,000 km worth of cable below, there has to be lots of mass above.
There’s no restriction on how this upper mass can be configured. You could put in a fairly short cable attached to a large mass or a very long cable attached to a very small mass, or even no mass at all, although most likely you’ll want something besides bare cable terminating it.
The first clause is correct, but the second is an oversimplification. Still, there certainly needs to be at least some mass, at least some distance above geosynchronous. Practically speaking, if we’re going to build one of these things, we might as well make it tall enough that you can hit escape speed (or more) from the top of it: That’d be a nice value-added feature, for a relatively small additional expenditure.
Oh, and you can’t build a lunar space elevator: It rotates too slowly. However, for an airless world like the Moon (or Mercury), you could build a different cheap-access-to-space device out of the same materials (call it a skyhook). The basic idea is that you have a long tether with a counterweight on one end and a hook on the other. Put it in a low (but not too low) orbit, and spin it around its center of mass. Spin it at the right rate, and make the cable the right length, and the hook will dip down to right next to the surface, momentarily be at rest, and pull back up again. Hook a payload on in that moment, and you lift it up (at the cost of some rotational energy of the device), and detach a payload at that moment, and you land it gently (paying back the energy). Between elevators and skyhooks, you can cheaply access any solid surface in the system, other than Venus (and really, who wants to go there?).
I tale it that the trip from the surface to the terminus will not be a straight line; with the trip up (or down) you will encounter side-loads.
Normally, orbital speeds are a function of distance from the surface; the farther away, the slower the orbit:: the nearer, the faster.
If you maintained a completely vertical trajectory…and thus constant angular velocity…you would have the opposite: closer to the surface, the slower the orbit:: the farther, the faster.
It depends on what you mean by a “straight line”. In the rotating reference frame of the Earth, you’re just going up, up, up, with no sideways motion at all, so in that sense it’s a straight line. In an inertial reference frame, though, where the Earth (and elevator and you) is rotating, your path will be a spiral.
And while you’re attached to the cable, you can’t really be said to be “in orbit”.
This was another point made by the author, but it this true? Yes the center of mass has to be at least geosycn, but can the center of mass be beyond geosync?
All I would think that would do is pull ‘up’ on the supports on earth, as long as it was strong enough it would be fine.
And for that matter if the CM was less then geosync the stalk would have to provide the additional support (as in a structural tower)
True, you’d want the center of mass to be slightly above geosynch, since a little extra tension on the base is tolerable, but slack is death, so you want to err on the side of tension. It would still be very close to geosynch, though.
It never struck me before, but the center of mass would change was a load went up or down. Would there then be a mass much larger than the load above geosynch?
I think a more pressing issue for the creation of a space elevator, once it because feasible, would be clearing the debris field surrounding the Earth so that the stationary, non maneuverable elevator wasn’t being hit by a constant rain of orbiting debris at every point along it’s length.
Yeah, the discussion of orbits after hopping off the elevator at various points made me realize that nearly every object orbiting below the end of the tether will collide with the elevator. However, compared to building a space elevator, a Giant Space Junk Deorbiting Laser seems almost trivial.
And once there is a space elevator, there won’t be much need for anything in LEO.
In the book the space elevator was on a mobile platform able to move on the surface (or at sea - the3re were several) to avoid tracked objects, for the smaller stuff that was not tracked the ribbon (stalk) was curved in a ‘(’ shape this way a small piece could not cut the entire thing, It was also self healing and also regularly repaired/strengthened by what they called ‘spiders’. The section that was at the greatest risk of debris was also strengthened and thicker then the rest.