Do you have to go all the way to the top of a space elevator? Would it be possible to stop say 200 KM above the surface and launch a low Earth orbit satellite from there? Would it have enough velocity to maintain an orbit, or would it just fall?
Anything let off the space elevator short of the top, 23k miles or so IIRC, would fall if it wasn’t given an additional boost to it’s orbital velocity. The additional boost would be less the closer you are to the top. Step out 99% of the way there and you’d probably be in a slowly decaying orbit, someone correct me on that if I’m out of line. Step out 1% of the way there and your fall will be much more vertical.
Would there be any advantage to lifting a rocket up to a certain height and then launching it from there?
It seems like the Clarke orbit is going to get awfully crowded once we build and elevator!
Probably a big advantage as you wont have to contend with aerodynamic drag getting out of the atmosphere.
The Clarke orbit is already pretty crowded. The issue isn’t so much things running into each other but them being so close together that ground based antennas have a hard time telling one from the next.
… and if you wait until the elevator’s almost to the top and then jump up, when the elevator stops you’ll have achieved escape velocity…
If you have enough space elevators constructed around the equator, you might as well just build a solid ring around the Earth at the Clarke Orbit.
That’s pretty much what they did in 3001.
You won’t even have to do that. Just ride in an open top car and don’t be strapped in when it stops.
Jumping from a ‘standing still’ position at a geostationary orbit height wouldn’t be escape velocity. If you’re not moving at the right speed perpendicular to the pull of gravity, you’ll fall all the same. You’re nowhere near being beyond the pull of Earth’s gravity.
Or does the space elevator ascend at a particularly high speed?
So, let me get this straight. The space station at the top of the elevator is moving at orbital speed, but no other part of the elevator is? A random section of cable 5,000 KM from the surface is NOT going to be moving fast enough to orbit on its own? The tauntness cable totally depends on the firmness of the connection to the ground and the top of the elevator?
I’m not trying to be dense here. I’ve known about the concept of the space elevator since I was a sci-fi reading pre-teen. I guess I just never gave enough thought to the physics behind it. Clearly, I did not understand it!
The elevator is moving at orbit speed, and its center of mass is at geostationary height. But if you jump off…
So if you get off at the Center of Mass, your are in a geostationary orbit, no problem. Above that point (which includes the top) you are moving faster than a circular orbit. You will have an elliptic orbit, your launch point being perigee. Below that, also elliptical, with launch point apogee. If that orbit’s perigee is too low, you’ll hit the atmosphere, etc.
BTW, the space elevator is widely considered a joke. It will never happen. Basic physics will tell you why. Ask yourself: “What is the exact configuration of the elevator 1 hour before final hookup?”
Well, the speed gets less and less as you go down … until it reaches zero at the ground, naturally. Presumably, you’re only building the elevator to orbital-speed altitude. I guess if you wanted to build it higher than that, you could … but it would cost more. Right?
Unless you have a pesky atmosphere to deal with, there’s no such thing as a decaying orbit. What you can get, though, is an elliptical orbit, and if it’s too eliptical, then it’ll intersect the Earth, and the satellite will crash after less than half an orbit.
The really interesting thing about a space elevator, though, is that it wouldn’t stop at geosynchronous orbit. Go up higher than geosynch, and you’ll actually “fall” away from the Earth. In fact, you could reach anywhere in the Universe this way, for only a little more energy cost than getting into orbit. You’re actually stealing some of the Earth’s rotational energy to do this, but there’s so much energy available there that it makes no difference whatsoever.
That’s not quite right. If you get off below geosynchronous height, you’ll fall on an elliptical orbit. For many lower positions on the elevator, your new orbit will intersect the atmosphere and/or ocean/crust of Earth. For higher positions, your elliptical orbit will not intersect the atmosphere, and will be as stable (non-decaying) as any orbit of the same altitude.
The orbit you fall into will have an apogee that is at the same altitude as you were when you got off the elevator, and the higher you go the closer perigee altitude will be to apogee altitude, until at geosynchronous altitude your orbit is circular (and you’ll just stay near the elevator station.)
The elevator must go far beyond geosynchronous, because the center of mass must be at geosynchronous. If you release from the elevator higher than geosynchronous, you have two options. Go high enough, and you are on a hyperbolic or open orbit, meaning you leave Earth and travel off in a Solar orbit (perhaps an open Solar orbit in the unlikely case that the elevator reaches high enough. I haven’t done the math but I doubt this is practical.) If you don’t go high enough, you’ll be on an elliptical orbit with perigee at the altitude you released from, and apogee higher. The higher you release from the elevator, the higher apogee will be above perigee, until at a certain critical height your orbit will be parabolic, and any higher will give you the hyperbolic orbit.
So, you can easily launch a satellite from the elevator. If you wish a circular orbit lower than geosynchronous, you can drop the satellite from high enough that it’s perigee is at the altitude you want, then fire a thruster at perigee to reduce velocity and circularize the orbit. You could also launch the satellite from lower on the elevator, using a thruster to accelerate to a circular orbit, or you could launch it from some intermediate height, accelerate, then at perigee decelerate. Without checking the math, I don’t know if all methods are equally efficient.
Finally, vibrotronica, the elevator extends straight up like a skyscraper. At any point on the lower elevator, jumping off is exactly like jumping out of a skyscraper or a stationary balloon. Go high enough, however, and coriolis force will move you noticeably to the east. Go higher still, and it will move you into an orbit that doesn’t intersect Earth.
Urg simulpost. Chronos also says in two short paragraphs what I muddle through in five. Brevity is the soul of something or other.
Dangit, I should have previewed after coming back from lunch. All this wasn’t here before.
What do you mean by “final hookup”? If you mean while the elevator is being built, and when it’s attached to the ground at the end of construction, the tension at ground level should be zero, or as close to it as tolerances allow. Even without a ground anchor, it’d be in equilibrium. An unstable equilibrium, to be sure, but we can compensate for that with station-keeping thrusters (which wouldn’t be necessary any more once the anchor was attached).
There is nothing in the laws of physics, basic or otherwise, which would make a space elevator impossible or impractical. The only remaining major engineering hurdle is making macroscopic quantities of nanofiber, and that has enough practical applications that we’d want to develop it even without a space elevator.
Thanks for the correction Chronos, I should have known that.
If we ignore that logistics and materials problems will keep a space elevator from ever being built I propose the following thought experiment for folks to shoot holes in.
Start with a satellite in Clarke orbit. Then send some guys up to attach a section of ladder hanging toward the earth and a ham radio mast pointing away to act as a counterbalance. Next flight adds a secton of ladder and a section of mast. Keep adding sections and maintain balance so the mass of the satellite stays in the Clarke orbit. Eventually the ladder will reach the ground.
Hmmm, as a layperson without any serious physics education, I find this conceptually interesting. I’d like to restate it a bit to make sure I’ve got it.
I go out to, say, a thousand miles above the equator, in a stationary position relative to the Earth (i.e. not in any sort of orbital trajectory), and I release a bowling ball. The bowling ball begins drifting, and gradually accelerating, toward the surface in basically a straight line (not precisely, given that the Earth is moving laterally in its own orbit around the Sun, but close enough). Would it be technically correct to say that the bowling ball is in an orbit that is so elliptical it’s essentially indistinguishable from a straight line?
I ask for clarification because, as I understand it, the gravitational pull of any body can be simplified to a point. In other words, an object the size of a Flintstones vitamin with the same mass as the Earth will behave gravitationally as an Earth surrogate for purposes of calculating the Moon’s orbit, and so on.
Which means, then, that if I release my bowling ball to fall in its “straight line,” but nudge it just slightly to one side, its highly elliptical orbit could conceivably miss the Flintstones vitamin and whip back out the other side in, again, almost a straight line, before it slows, stops, and rubber-bands back to pass on the other side of the vitamin?
Sorry if this is all basic stuff, but like I said, I’m just a fascinated layperson.
Yes, this is how the ladder would have to be built, sorta. The ladder doesn’t have to extend as far above the clarke orbit as far as it hangs below, merely have enough mass above as to counteract the weight of the ladder hanging down to earth. While the free end hanging out into space would be usefull for launching things out of earth orbit, it would be very difficult to stabilize. With nothing to really achor it ( the bottom has the earth, the middle has the asteroid), the top end would tend to whip around everytime it was disturbed. Think Verazano Narrows bridge, only worse, this would have less anchorage.
So as far as I can see, the best configuration would be for the ladder to end at the clark orbit, with the asteroid just above the clark orbit acting as the counterweight. This asteroid would have to be fairly large, the space ladder would be extremely massive even with nanofibers. I beleive that it would have to be about 22,000 miles long, and have to support the weight of things going up it, in addition to its own weight. If you have cargo containers scheduled to have one going up while another was coming down ( on seperate cables obviously), the cost savings for getting stuff into orbit would be even greater.
Whatever equatorial country it is located in would have a huge boost to its economy, I could see wars being fought over the placement site.
One hour before you have 1 continuous thread of something from Earth to beyond geosynch. Note that the base will be a mountain sized bundle of wonder nanotube-kevlar-transparent aluminum stuff. It isn’t attached to the Earth is it? (If not, then why do you need it at all. That should cause an “oh my gosh” gasp right there.) Add in tidal pulls, instabilities, the Earth’s atmosphere trying to whip the low end around. Good grief.
Your ladders will do two things: flex and break from the strain. Real materials differ from the ideal considerably.