On Jun/14/2020 at 01:43, JF Mezei wrote :
On 2020-06-13 12:01, Alain Fournier wrote:

What happens is a complex issue. I wouldn't trust it to gently lay
itself on the ground. If the cable breaks, I would get out of its path.

Following assumes a cut just below geosynchronous altitude and a tether
of equal mass from sea level to cut.


The way I see it, a mass exerts upward force when its orbital speed is
higher than needed at that altitude and it isn't allowed to rise.

With the 0 point being geosyncrhonous altitude, when the cut happens,
the position of cable at -1m is pretty close to having orbital speed. So
it weights less than the same lenght of cable at sea level, not only
because gravity is less, but also because it is nearly at orbital speed
where its weight (strict definition) would be near 0.

So with cable at sea level wanting to accelerate down at 9.8m/s2, the
portion at the top wants to go down at only 0.1 m/s2 (pr whatever low
value). The lower end wanting to accelerate more than the top would
create tension in cable, keeping it straight.


So far correct?

Not really. At very first, yes that is what will happen. The bottom part
will pull the cable down under some tension. This will cause parts
higher up to go eastward. Pieces higher up will start going eastward
slower than pieces in the middle, but with time the pieces higher up
will get more eastward speed than those in the middle. You get a chaotic
result, the cable breaks at multiple places.

Since the tip of cable had enough energy to almost be in orbit, as it is
pulled down, it will reach an altitude where its energy is above what is
necessary to be in orbit, below which, the cable will have upward force
and want to slow down the fall.

So, when the tip of cable is pulled down, its orbital instinct will be
to try to increase its forward speed. Won't that result in part of the
force pulling upwards since the cable will end up diagonal? Won't that
also slow down the fall?

Yes it will, but this phenomenon will happen all along the cable with
different intensities and different speeds at different heights.

Big picture, will the cable trying to move eastward during its fall give
back to the planet the eastward spin that the planet gave up when it
accelerated the cable?

The cable will give some negligeable amount of eastward spin to the
planet when it falls. I'm not quite sure what you mean by "the spin the
planet gave up when it accelerated the cable". When the cable is put in
place, it is put there at orbital speed at geosynchronous orbit. The
planet does not lose angular momentum when you anchor the cable to the
ground. The planet does lose some momentum when a payload goes up the
elevator. The amount of angular momentum the cable will give the planet
uppon falling to the ground has nothing to do with the amount the planet
lost while payloads were going up.

More imkportantly, will a 36,000km cable end up almostly circling the
equator (40,000) as it falls, or will there be significant amounts of
cable that will be piulot onto itself, greatly reducing the distance
covered as the cable falls back down?

Sorry, I can't parse piulot.

Now, changing cable to "structure". If it breaks at geostationary AND
ground levels, are there scenarios where distribution of mass and energy
might result in the structure going horizontal and at half geostationary
orbit ? (aka: top part lowering from geo to half and bottom part dragged
up to half geo?

No. A cable in orbit will always take a vertical orientation because of
tidal forces. The cable might break up in several pieces and some pieces
might go kind of horizontal momentarily (while spinning). But the pieces
that stay in orbit will stabilize in a vertical orientation.


Alain Fournier