Problems with a Saturnian trans-atmospheric skyhook

Hello ladies and gents. I was wondering if you could help me figure
out some issues surrounding something that I'd like to put into a SF
computer adventure game that I'm working on.

Consider your run-of-the mill orbital skyhook. It extends up into
space perpendicular to the surface of the planet that it orbits.
Simple enough. Let's suppose that this skyhook is in orbit around
Saturn. Now, if we were to lower the orbit of the skyhook so that its
lower tip extends into the atmosphere of Saturn, it's going to
experience quite a bit of atmospheric drag. Eventually, its orbit will
decay and it will fall into the atmosphere, with the net result that
we've just thrown a very large amount of money into a gas giant. Not
good. The best solution is to keep the skyhook from ever entering the
atmosphere.

As it turns out, though, that's exactly what we want to do in order to
get at all the very useful He3 that you find in the atmosphere. So the
other option is to use some sort of propulsion system to counteract
the effects of the drag. Fortunately for us, Saturn has a rather
powerful magnetosphere, which we can use to our advantage. Since the
skyhook is nothing but a tether, it should be possible to use it as
its own electrodynamic tether propulsion system: you pump electricity
into it, and it raises itself out of the atmosphere. This should allow
it to offset the atmospheric drag and the loss of orbital velocity
caused by raising large amounts of He3 and other gases into orbit. And
where does the power for the electrodynamic propulsion come from? We
could burn some of that He3 in a fusion reactor, but we're looking to
sell that elsewhere. Instead, why not put a number of other tethers in
a higher orbit (not extending into the atmosphere) to generate
electricity by passing through the magnetosphere and then beam it to
our skyhook?

That's the plan, anyway. Here are the problems that I have:

First, I'm not sure that the electrodynamic propulsion system would
provide thrust in the proper direction to counteract atmospheric drag
and loss of momentum due to the constant pumping of gases up the
skyhook. As I understand it, to raise an orbit, you want to thrust in
the direction of your orbit; the tether propulsion system - again, as
I understand it - will thrust in the direction that the tether is
oriented. In this case, that would be perpendicular to the direction
of travel. Is this correct? And, if it is, would this be sufficient to
prevent orbital degradation or do I need to thrust in the direction of
travel?

Second, I'm not sure just how much drag and momentum loss we're
talking about, here. Would there be too much of either (or both) for
the propulsion system, assuming it works, to counteract? What would
the power requirements be? Would the electrodynamic power generation
tethers be up to the task?

Third, if everything else can be made to work, would the fact that the
drag on the skyhook is applied to one end only mean that the thing
would tip over? Would it just lean and then become stable at an angle?
If it would be a problem, is there anything that can be done to
counteract it?

Fourth, just what is a reasonable orbital period and speed for such a
setup? Ideally, the orbital period would match the rotation of Saturn
at the equator (about 614 minutes), but I'm not sure that such an
orbit is possible. If the orbital period is longer than the period of
Saturn's rotation, would that mean that the atmosphere is blowing in
the direction of the skyhook's travel? If so, how would this affect
its orbit?

And if you can think of any other problems with the setup, I'd
appreciate a heads-up.

Thanks a lot, guys.
.

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