Re: Space Elevator by 2019?

From: Joann Evans (bondage_at_frontiernet.net)
Date: 06/28/04 

Date: Mon, 28 Jun 2004 01:17:52 GMT

Peter Fairbrother wrote:
>
> Joann Evans wrote:
>
> > Peter Fairbrother wrote:
> >>
> >> The thing I don't understand about a space elevator is how they are going to
> >> get the first thread in place.
> >>
> >> I read somewhere that they wanted to start at GSO and unreel it both
> >> downwards and upwards simultaneously, but that won't work - the bits will
> >> move sideways. Does anyone know?
> >
> > No. I agree the engineering is far off, but there's no physical
> > reason one could not do exactly as you say. Space elevators are
> > essentially long, thin orbiting objects that happen to be long enough to
> > reach the surface.
>
> Consider an element at the Earthward end of the rope. It is moving
> horizontally at a velocity v, and is kept in a circular path by the forces
> of gravity and tension which give it a resultant vertical acceleration in
> the direction of Earth.
>
> Now decrease the tension, in order to extend the rope, and the acceleration
> increases. The horizontal velocity component remains the same though, and as
> the length of the element's orbit decreases, the period decreases too,
> causing the rope to bend.
>
> Another way to look at it is to consider the half-extended rope. It is
> rotating at one revolution per second. Extend it and it slows like a
> spinning ballerina opening her arms unless some extra angular momentum can
> be gotten from somewhere.
>
> As far as I can tell that cannot come from the interaction with the earth's
> gravity, and certainly not sufficiently evenly over the entire length of the
> rope to keep it straight, but perhaps I missed something?
>
> I expect the people who fly tethers know a bit about doing this sort of
> thing, but I haven't heard how the Elevator people plan to do it.
>
> >> Another is, why do they want to put it on the equator? It can touch down
> >> anywhere on Earth. Near-space above the equator should be reserved for
> >> orbits.
> >

> > Because, just like the big satcoms, that's the only place you can be
> > stationary with respect to Earth's surface.
>
> I do not understand. Surely once it reaches equilibrium the rope does not
> move relative to the spinning Earth, no matter the latitude at which the end
> is attached?

   I't important to remember that it's an orbiting object, whose center
is at orbital altitude. That which hangs down is closer to Earth, and
being part of a solid object, is moving at something less that orbital
velocity for that altitude. The more distant parts are moving at
something greater than orbital velocity for those altitudes. That's what
keeps it taut. This is referred to as 'gravity gradient stabilization'
or 'tidal forces.'

   Even as you stand on Earth's surface, gravity is slightly stronger at
your feet than your head, as the latter is slightly farther from Earth's
center.
 
> It would certainly be possible to arrange for the rope to pass through the
> GEO circle, with the Earth end attached at say 20 degrees North.

   You could, but it wouldn't stay there long. 'Down' is toward Earth's
center. This is why the Leaning Tower of Pisa could eventually fall,
left to itself. It's under stresses in a direction that it it wasn't
designed for. Space tethers 'want,' if you will, to point toward Earth's
center.
 
> Think of a dangling chain. It goes almost vertically at the top, but may go
> at an angle at the bottom.

   Again, it would be like a leaning building. Its center isn't
'anchored' in orbit. Forces in other directions would pull it down.
Others may be able to give a more explicit numerical explanation, but I
know, generally, there are no other options.
 
> > Any other inclination (at
> > the same altitude) will trace out a figure-8 pattern on the ground.
>
> Why would that be important?

   You want to get aboard it from the ground, right? Imagine (if it
could still hang straight down) trying to grab a rope lowered from a
supersonic aircraft. An object orbiting at 22,500 miles will stay
*approxamately* at the same longitude, but if its orbital plane doesn't
also match the plane of Earth's equator, it won't be truly
geostationary, and will have a north-south component.
 
> > Lower orbits will be even messier. You don't want to drag the end of
> > this thing through the atmosphere.
>
> I'm afraid I cannot make head nor tail of that.

   In that case, an orbiting object doesn't even stay on the same
lattitude, either.

   Visualize any object in a lower orbit. Or better yet, find any
freeware or shareware satellite tracking program. (STSPlus and Traksat
are my favorites. They'll illustrate the matter better than I can.)

  A tether extending down from, and out from it will make a line
constantly pointing toward Earth's center. If the orbit is, say, 200
miles up, the tether must extent 200 miles down to Earth's surface, and
200 miles out from Earth. Ignoring atmospheric effects, the tip of this
thing is tracing out the orbital path on the surface below. Anyone with
satellite TV is pointing their antenna along the sort of line you
describe, but you couldn't build a structure down from orbit in that
direction. ('Slant range' it's called, as opposed to the sat's height
straight down. They're the same only if and when a satellite is directly
above you. Above/below the lattitude of 81.3 degrees north/south, you
can't see sats in geostationary orbit at all.)

   Again, how do you get aboard the thing? and there's the matter of
terrain changes.....

   Of course there is an atmosphere, and drag will eventually slow the
whole thing, causing it to de-orbit.

   If you use a satellite tracking program, and have the Kepllerian
two-line elements for a geostationary satellite, the program will show
it staying at one point above the equator, indefinitely. (and even then,
those sats need occasional tweaking, due to perturbations from Solar and
Lunar gravity) 

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