I understand that a space elevator should be at least as long as a geosynchronous orbit (22,236 mi), because only beyond that is the centrifugal force from the Earth's rotation is greater than the effects of its gravity.
At the same time, astronauts in a space station in low Earth orbit experience weightlessness even though gravity is about 90% of the strength as on the surface. I understand that this is because they are in free-fall, but remain in orbit due to the high speed in which the space station was initially placed.
Let's say you have a 40,000 mi space elevator at the equator, and it has a climber wherein occupants are strapped into chairs. If I understand correctly, if you were to stop the climber and hold it there or apply the brakes, then at...
4,000 mi (roughly the Earth's radius), the occupants would feel about 1/4 of the effects of Earth's gravity. So if they were holding an object and let go, it would fall, but more slowly than on Earth.
22,236 mi (GEO), the occupants would feel weightless. If they were holding an object and let go, it would float (in theory).
Greater than 22,236 mi, the occupants would feel drawn toward the ceiling. If they let go of an object, it would rise and hit the ceiling, at some speed proportional to how much greater than GEO they are stopped at.
Do I have this correct?