From: spike66 (spike66@attbi.com)
Date: Mon Aug 26 2002 - 21:57:30 MDT
>
>
>On Mon, 26 Aug 2002, Rafal Smigrodzki wrote:
>
>>Now, this *is* smart - almost all the benefits of the space elevator, and no
>>need for miracles, either.
>>
On the other hand, it is not clear to me what it would be good for.
OK, so you climb to the top of a 100 km tower with a payload.
Now what? You are about 3% of the way to orbit.
I found a paper I wrote in 93 about a space cable, so I have
the formulae I derived back then. Given the following:
A = cross sectional area of the cable at the ground
M = mass of the earth (6E24 kg)
G = gravitational constant (6.67E-11 Nm^2kg^-2)
R = equatorial radius of the earth (6.4E6 M)
w = earth's sidereal rotation rate (7.3E-5 rad/sec)
p = density of the cable
S = maximum stress per unit area
h = height above ground
The formula I derived for the mass of the cable is
Mass = A*p*exp{(p/s)*(GM/R+w^2*R^2/2)} *
integral [exp{(p/S)(-GM/(R+h)-w^2(R+h)^2/2}] dh
where the integral is from 0 to whatever height you want
before attaching a large enough counterweight to put the
CG of the assembly at GEO.
If you put the above formula in a spreadsheet with increments
of about a km, it makes for an interesting education in how
much mass a space cable would require.
spike
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