[extropy-chat] Re: Space Elevators

[spike]

Damien!  This is such a cool thread, thanks.  {8-]

As it turns out, I did all the math on this as a result
of a story that youuuuu wrote, that sci-fi-ized children's
fairy tale about Jack and the beanstalk.  Good story!  Tell
the good proles how to get a copy please.  We will not consider
it spam.  {8^D

The math and physics on this is pretty simple.  In a round
orbit such as GEO, the R*omega^2 is equal to MG/R^2 where
M is the mass of the earth (about 6E24 if memory serves
correctly and G is 6.67E-11.)  Omega is 2 pi radians per
day.  

The reason the SE stays tidelocked is that the lower half
is closer to the earth, so R is smaller than GEO radius,
so MG/R^2 is greater than R*omega^2.  On the half that stretches
away from GEO, R is greater than GEO radius so MG/R^2 is
less than R*omega^2.  So if you parted the two halves at
GEO, the lower half would fall downward and the upper 
half would fall upward.  So it is stable pointing earthward.

If you take any long rigid pole, it will try to align itself
pointing earthward.  I think of it as kinda analogous to how
iron filings try to align themselves along the lines of magnetic
equipotential.

Nowthen, from your book, I realized that as the beanstalk 
is played out simultaneously upward and downward, it forms
kind of a giant integral symbol, since the total body wants
to conserve angular momentum, while gravity and centrifugal
force do what they do.  As the arms play outward, the moment
of inertia of the system increases.  Conservation of angular
momentum requires that I*omega is constant.  I is increasing.
So the trick is solved once you realize that angular momentum
is being transferred from the earth to the GEO object.

More later.

spike



> -----Original Message-----
> From: extropy-chat-bounces at lists.extropy.org [mailto:extropy-chat-
> bounces at lists.extropy.org] On Behalf Of Damien Broderick
> Sent: Wednesday, August 03, 2005 3:22 PM
> To: 'ExI chat list'
> Subject: Re: [extropy-chat] Re: Space Elevators
> 
> At 02:23 PM 8/3/2005 -0700, Adrian Tymes wrote:
> 
> >Rotation...assuming you adjust your angular velocity accordingly while
> >spooling out the cable (an easy trick to do, especially if you're
> >careful to spool out an exact same amount straight away from the
> >surface at the same time).
> 
> This don't make no lick o' sense to me, bubba.
> 
> Starting at the hind end -- I reckon you need to spool out a damned sight
> more from the farside spigot, on account o' the gravitational gradient
> weakening. Just a detail.
> 
> Now as for rotating -- what Mike called " tidally locked", although that's
> not what it is, just what it emulates -- obviously the station has to be
> spun so it rotates completely once a day, otherwise the cable would get
> wrapped around it. That is, you need to spin the station *before* you
> start
> feeding out the cable. But that doesn't explain (to me, anyway) how the
> cable sheds its five miles per second orbital velocity as it drops ever
> closer to the ground.
> 
> Damien Broderick
> [ probably making a complete fool of myself here ]
> 
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