Low cost access to space via tethers

I tried to post this to sci.space.tech with no success. Our moderator
must be asleep because the last post there is over 5 days old.

I have made some basic calculations of a tether scheme to put a
payload into orbit from Earth.

Say we build a rocket that takes our payload to a 100 km apogee with a
zero or small horizontal velocity. From this point the payload docks
with the substation that is tethered to a heavy space station and is
spinning around in order to cancel out the orbital motion. The
substation and the tether accelerate the payload and raise it higher
to an orbital or faster velocity. This slows the space station down.
The space station uses ion engines to restore its orbital velocity.
This could be done with solar panels or a nuclear reactor. The ion
engines having a high specific impulse will use very little propellant
mass to keep the station's orbit. The space station would have to be
heavy enough to make sure it does not reenter when boosting a payload
to orbit.

The numbers I got are the following:

Rotational period 13 minutes.
Radius 1000 km (diameter 2000 km)
Gravity load 6.4 g

Such a scheme is probably cheaper than the beanstalk. Depending on the
masses of the space station and the substation the tether would have
to be 1000 km to 2000 km long. This scheme could be built up
incrementally, gradually adding mass to the space station and more
tethers.

Zoltan