In sci.math message ,
Sun, 8 Jan 2012 02:11:06, K_h posted:


"Dr J R Stockton" wrote in message
. invalid...
In sci.math message
oglegroups.com, Sat, 31 Dec 2011 22:49:23, STJensen
posted:

Let us say that you had a 62,000-mile-long Earth-anchored space
elevator and let us say it has an electro-magnetic repulsion
accelerator along its entire length. If you were to accelerate a
human so that he experienced only 2g (twice the force of gravity)
during the entire length of the space elevator, what velocity would
that human be expelled from the space elevator and how long would it
take the human to travel the entire length?

Since the elevator cable cannot be infinitely rigid, and will in
practice be quite flexible, one will need to consider the effect of the
sideways forces on its shape - unless the mass of a shortish length of
the cable is large in comparison with that of your human and his
accessories.

Really good point. And the Earth is rotating so the cable must rotate
with the
same angular speed as the Earth. So, to do this calculation properly requires
consideration of tangent speeds, tangent acceleration (tangent to the
cable for
those) and so forth.


It should not be difficult for the rigid-cable case, where the cable is
kept under sufficient tension by having an adequate mass at its tip..


Perhaps the rigid case is best done in natural units, in which GSO is at
unit radius and the sidereal period at GSO is also unity. The variables
are then, in GSO units, the starting and finishing heights, and the
constant thrust, which ISTR was going to be twice of what is needed to
be felt to remain stationary at the starting point, a.k.a. ground level.

The acceleration outwards results from the combination of the thrust,
the inverse square gravity, and the linear centripetal pseudo-force.
Integrate once with respect to the time to get the outwards speed as a
function of time, and again to get the outwards distance as a function
of time. Then determine the time to release from the second integral,
and substitute in the first integral to get the release speed.
Unchecked.

--
(c) John Stockton, near London.
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