Physics problem with the space elevator?

I'm cross-posting the following to sci.space.science; it'll probably
get much better responses there.

Galen Musbach wrote:
On Tue, 20 Dec 2005 23:12:32 -0600, "Jorge R. Frank"
wrote:

Galen Musbach wrote in
:

Up is the direction away from the center of the Earth.
Objects moving up the cable will be initally moving at
ground speed, and must eventually reach orbital speed.
Altitude alone is not sufficient, the cable must also pull
the materials forward as they proceed upwards. Which
will have the effect of pulling the cable backwards. Since
the far end is hanging free, that's a problem.

Fortunately, there is a simple solution to this problem. Either extend the
cable beyond twice geostationary height, or put a counterweight on the
upper end. Or some combination of both, such that the center of mass of
the cable is above geostationary height (most recent space elevator designs
are 100,000 km long, compared to the 70,000 km minimum required to reach
twice geostationary height). This provides tension in the cable to counter
the forces exerted by climbers.

The maximum climber weight will be a function of the cable tension, which
in turn is a function of just how far beyond twice geostationary the cable
is extended, or how massive the counterweight. The space elevator must be
designed to a particular maximum climber weight, and then must be operated
within those limits.
That does not solve the problem. Suppose the counterweight masses
100,000 lbs; 100 lifts of 1000 pound loads means that 100,000 lbs of
mass has been accelerated from 25,000 miles per day to 90,000 miles
per day, thereby exerting a drag force against the counterweight that
will have reduced the velocity by 55,000 miles per day. No matter
how massive the counterweight, without some way of bringing it back
up to speed, it will eventually slow below orbital velocity and fall.

-Galen

As space elevator problems go, this is a relatively trivial one compared to
the strength-of-materials problem, and the solution is fairly well
understood. (There's been quite a bit of discussion on sci.space.* about
it).

I'm repeating what has already been said elsewhere (google) on this....
anyway...

This slow down problem does not exist in pratice. Lets assume that
payloads only ever go up, then the conterweight is slowed only a tiny
bit. Its still going far faster than obital velcity for that altitude.
As the counterweight lags behind the tension in the cable pulls it
faster untill everything ends up in some kinda equilibrim. (it could
cause resonate waves etc.. but these are easy to avoid). The angle of
the cable is still tiny. But then so is the mass of the payloads
compared to the cable and counterweight.

The real problems are IMHO:

1) strong material-carbon nano tubes mite solve this, but they havn't
yet.

2) debris. This is a tough one.

3) politics.

Out of these 1 is the hardest. But we don't need to do anything about
this one. A composite this strong is so usfull for so many things it
will be devopled anyway. Once you have a composite that strong rockets
gets much easier. So will it be worth it. Maybee, but only if there is
allready a huge amount of orbital traffic in the first place.

I leave solutions to 2 and 3 to the reader .

greg