

A new method could help realize dreams of a space elevator










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RE: A bit misleading
By masher2 (blog) on 1/7/2009 10:25:35 AM , Rating: 3
I don't really understand wiki's article on it, and my likely erroneous guess is that the equation would be F=d/dt(mv), which is complicated by the decay of F as the object gets further away from the gravitational effect of the earth.
You need a bit of basic calculus to do the equation. You combine an expression for the mass of the cable at any point (which would be a constant for a linear cable, but in reality would taper at both ends) with the expression for gravitity at a given point (GM/r^2), and the term for centripedal acceleration

Then, you integrate over the range from altitude 6,000 (earth's surface) to 42,000 (geosynch), and equate that to whatever range of integral gives you the same value from 42,000 to x, x being the length of your cable past geosynch.

You can do it in a single step by just requiring the total force on the cable to be zero, and finding the appropriate rnage of integration, but it may be a little easier to understand in the two-step process I outlined above.

To be truly accurate, you need to take in additional terms such as atmospheric drag, the fact the earth is actually an oblate spheroid, etc, etc.


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