. . . Space Elevator
The following comments were provided by Dr. Desmond Penny of Southern Utah University, 11 Dec 2002:
Dear Roice:
I was intrigued by your quote from Arthur C. Clarke, re the hanging
cable from a geosynchronous satellite, so I was impelled last night to
sit down and look at the equations. Attached are the 11 pages of my
notes: Page 1;
Page 2;
Page 3;
Page 4;
Page 5;
Page 6;
Page 7;
Page 8;
Page 9;
Page 10;
Page 11.
It was quite an interesting problem. Initially, as you will see from
my notes, I was convinced that there was a theoretical reason why this
was impossible. However, during the calculations I changed my mind and
discovered a way for it to be possible.
My overall conclusions were:
- In order for a cable to hang from a geosynchronous satellite at a
height of 22,000 miles, the satellite would have to fire its engines
radially away from the earth. These engines would need to provide a
continuous thrust equal to 5.57% of the weight of the cable at the
earth's surface.
- There IS a way to make the system work without an engine: Locate
the satellite at a height of 44,000 miles! At this height the cable
would float around with the earth, hanging vertically, every part of the
cable and the satellite would be in geosynchronous orbit ! The
satellite would have a speed of 5681 m/s. This speed is significantly
greater than the speed of a normal geosynchronous satellite 3073 m/s at
the 22,000 mile normal orbit.
- I have shown that there would be large tensile forces in the cable.
The tensile force would start at zero near the earth's surface,
increase to a maximum value near the middle of the cable, and decrease
to zero again near the satellite. The max tensile force would equal
5.57% of the weight of half of the cable at the earth's surface (i.e.
2.79% of the entire weight of the cable at the earth's surface.)
Whether the concept is practically feasible is doubtful. Further
calculations would throw more light on this aspect. For instance, it
would be possible to consider a real material and determine the max
diameter of the cable at the middle. You could then determine the
overall mass of the cable made from this material. Such calculations
would illuminate the practical feasibility of the concept. If you are
interested I could perform this calculation with a specific material in
mind. (If this is an exotic material, please supply me with the yield
point and youngs modulus).
There are a few approximations in my calculations, which I am confident
do not materially alter my conclusions. I did not check my
calculations, however, I am satisfied that my conclusions are
conceptually correct, even if there are errors.
Enjoy browsing through the attached pages :-).
Cheers,
Des
<![CDATA[Delivered-To: rnelson@walden3d.com
Date: Fri, 13 Dec 2002 09:34:43 -0700
From: "Des Penny" <Penny@suu.edu>
To: <rnelson@walden3d.com>
Subject: Clarke's Hypothesis
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Dear Roice:
One further thought:
The only requirement for geosynchronous orbit is that the center of
gravity (point G) of the space station and the hanging rope, must be
located at the 22,000 mile height. Thus, the more massive the space
station, the closer it can be to the earth! The station could be
brought down to a more reasonable height, say 30,000 miles. Obviously,
the 22,000 mile height is an absolute limit.
The precise positioning of the space station depends on:
1. Mass of the space station.
2. Mass and mass distribution of the cable.
Cheers,
Des]]>
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