[extropy-chat] Re: Space Elevators

[spike]

> bounces at lists.extropy.org] On Behalf Of Damien Broderick
> Subject: [extropy-chat] Re: Space Elevators
> 
...
> 
> ... suggestion by Clarke and others that the cable might be able to avoid
> satellites by harmonic twanging. I believe Spike had objections to this...
> 
> Damien Broderick


Ja, Clarke used the first resonance trick in Songs of
Distant Earth to explain how the low orbit junk didn't 
hit the cable.  I worked out the equations and realized 
that this trick might help some but it wouldn't solve 
the problem.

To estimate the probability of a collision for a GEO space
cable, recall that every low orbit item must cross the equatorial 
plane twice each orbit.  If we make some educated guesses
on how much stuff is up there and its size, we can
get a pretty good single digit estimate of the probability
of a collision.  OK there are the Iridium satellites,
66 of those I think, and they are about two meter class,
so lumping the Hubble and the other biggie stuff together
with that, say about 100 objects in the 2 meter class,
about 1000 objects in the 10 cm class, 1E4 objects in
the 1 cm class, and I don't even know how much stuff
the commies launched, then neglect the rest, thats a 
cumulative cross section of about 400 meters of stuff in 
orbit below GEO, and 15 orbits per day is close enough,
so thats 30 crossings, and then you divide by the
sine of the angle of inclination, and we know that
a bunch of stuff is at 27 degrees (the latitude of
Cape Canaveral) some higher but some of the stuff
unfortunately was launched from Guiana which is
down around 5 degrees, so lets just say about 20
degrees is a typical average orbit inclination, and the
total equatorial plane length at a typical LEO
altitude is 2*pi*7Mm, or close enough to 4E7 meters,
and i get about a 30 percent chance of a collision
per year for Earth.

Nowthen, Clarke suggested a first mode resonance swinging
motion of the cable, but you might be better off simply 
placing the center of mass a couple degrees off the equator, 
and it would accomplish the same thing: nada.  Swinging the 
cable helps a little for stuff orbiting very near the equator, 
but doesn't really help for everything else.  (Too bad: Songs 
of Distant Earth is a good story which is kinda ruined by the 
space cable fumbles.  I was thinking of praying to Clarke 
about it but I'm pretty sure I need an intercessor of
some kind for my prayer to be heard, as I am a lowly 
sinner.  Someone would need to play Jesus for me: take 
my humble supplication to Arthur the Father, thru Damien 
the Son.)  

The first mode resonance trick also ignores the fact that 
the cable is not uniform in diameter all the way up, so 
that first mode wouldn't be stable anyway.

If you have a copy of Songs of Distant Earth, read it
over and see that Clarke actually made a more serious
error, which isn't hard to spot for space cable fans.  I
will post it here after a couple days so you get a chance
to think it over.

spike