Ron, I'm very confused... You wrote
:
:The big thing to remember is that this altitude/velocity combination is
:*inviolate*. Increase your velocity, and you climb into an elliptical
rbit with a higher average altitude or even shoot away, free of the
:Earth's gravity. Decrease the velocity, and you drop into an elliptical
rbit with a lower average altitude...too much lower, of course, and you
:impact the Earth.

OK, I think I understand. If you're in LEO and you want to go to a
higher orbit, you have to add not just altitude, but velocity. So you
point your self forward and up, light the rocket and climb and
accelerate.
:
:Left to their own devices, the Main Station would require an orbital
:velocity of about 10,000 FPS, and the Way Station about 25,000 FPS. The
:Main station would float in stately grace, fixed above a spot on the
:equator. In truth, though, it doesn't care about what's below it...all it
:knows is that it orbits the Earth once every day. The fact that the Earth
:turns to keep the same point underneath it is trivial. At the same time,
:the Way Station whizzes past underneath, 13 orbits per day.

And that's where I'm confused. Isn't 10,000 fps at GEO a lot less
than the 25,000 FPS at LEO?

I understand that the actual distance, the circumference, of the orbit
at GEO is a lot bigger than at LEO, and I'd always thought that
accounted for lower satellites going "faster" around the earth in
radians or orbits per day.

It's the spinning ice skater/angular velocity thing that has me
confused. Pull in the arms, you spin faster, but drag slows you down.
Put out your arms, you go slower - your hands are going the same speed
in FPS as before, but they're going around a bigger circle.

Why is it that in going from LEO to GEO you're getting rid of speed?

Maybe this will do it. Say I'm in a nice, stable, circular orbit at
GEO. I want to drop to a nice, stable, circular orbit 100 miles
lower. I don't care about the orbital period, I just want to do it.
Which way do I point my nose before I light my rocket?