[extropy-chat] Re: Space Elevators

[Hal Finney]

I'm going to be speaking off the cuff here as I don't know that much
about orbital mechanics, just basic physics.

The question is, why does a cable stay oriented towards the earth as
you feed it out, rather than going into some other configuration.

Imagine that you have an orbital station (doesn't have to be
geosynchronous) that has some cable out that is pointing towards
the earth.  We'll ignore how it got that way, but we'll look at what
happens next.

First, the current situation is stable.  It is the lowest energy
configuration.  Also, the cable is in tension.  The bottom end of
the cable is moving at slower than orbital velocity, so it has a net
gravitational pull on it.

Now we feed out an incremental bit of cable.  What will happen is that
the lower end of the cable will tend to swing forward in the orbit.
You can see this as either a Coriolis force, in the rotating frame,
or the effect of it retaining its velocity while moving into a smaller
orbit, in the stationary frame.

However this is not a stable position, because it is not the lowest
energy configuration.  The cable will swing back towards vertical, like
a pendulum, back and forth.  It was hanging vertically originally, and
you gave it some energy that swung it forward, but it won't stay there,
it will oscillate around the low energy position.

If there are dissipative effects, such as friction with high altitude
gas molecules, or heat dissipation within the cable itself due to flexing
and motion, then this oscillation will die down and the cable will once
again be hanging straight towards the earth.

The net result, it seems to me, is that you can stably feed out cable as
long as you do it slowly enough that the motion due to Coriolis effects
gets dissipated.  If you do it too quickly the bottom end of the cable
will curve forward, and I'm not sure what shape it would end up in.

Hal