On 2020-06-10 15:27, David Spain wrote:
I haven't done any research in this area. Does anyone know of any
studies of micro-gravity inside the cab of a space elevator?

Remember to work, the entire system has to be under elastic tension. The
designs I've seen discussed use a big counter-mass at the far space end
of the cable to hold the system in place above the anchorpoint on
Earth's equator.

The trivial case is when the cab is down on the Earth side. Obviously
we're at 1G on the surface. I've presumed as the cab rises the effect of
Earth's gravity goes down as inverse square (Universal Gravitation):

Yes, but you also have to take into account that as the cab rises, it
gains "orbital" velocity, which counteracts the gravity. The effect of
the "orbital" velocity increases until it exactly balances gravity when
the cab reaches the geosynchronous altitude.

Are objects inside the cab of the space elevator near the "space" end
undergoing any form of microgravity?

Yes, see above.

The system really isn't in free fall because of the counter-mass
suspended above it and the cable running below.
Irrelevant. The entire elevator is rotating at the geosynchronous
period. Below the geosynchronous point, this rotation is slower than
free-fall orbital velocity, so the cab will feel a residual
gravitational attraction towards Earth. Above the geosynchronous point,
this rotation is faster than free-fall orbital velocity, so the cab will
feel a "centrifugal" force out from Earth.

Does the tensive forces provide any form of microgravity
inside the cabin or are the occupants fully in 'free fall'?

Below the geosynchronous altitude, the elevator is holding the car up,
so there is an attraction towards the Earth and the floor of the cab.

Free fall comes when the cab is at the geosynchronous altitude.

If you were to suspend a cabin above the
counter-mass would you end up with an artificial gravity in the vector
direction of 180 degrees opposite the Earth's surface? i.e. the 'floor'
of the cabin becomes the surface of the cabin opposite the Earth,
alongside empty space?

Yes.

This discussion assumes that the cab is moving slowly along the
elevator. If the cab is moving fast, there are sideways forces and
accelerations that tilt the apparent gravity in the cab.

--
Niklas Holsti

niklas holsti tidorum fi
. @ .