How do we go up and increase lateral speed without bending the cable into a big "C" shape?
A little basic physics. A point on the outside of a tire moves faster that a point toward the rim. The speed increases linearly with the radius distance from the point of rotation.
w=vr Angular (rotational velocity) is velocity time radius
You put the termination point at geostationary orbit where the speed needed to maintain orbit is equal to the rotation of the earth.
I agree. Obviously, it must.
My question is, what causes the speed to increase? Yes, as the elevator rises, angular speed increases, but the elevator is "rubbing" against one side of the cable on the way up.
Let me put it this way. Think of a space launch. We don't fire the rockets straight up. They'd just fall right back down.
At a certain altitude, the rocket pitches to pick up that angular speed.
By definition, a geostationary orbit is at 21,000 miles over the equator, moving at 6550 mph.
So, I take back what I said before -- if you took the elevator to exactly this height and stepped out the door you'd stay in orbit.
But any lower, you'd fall to Earth. Any higher, you'd fly away.