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While I have no doubt it would require an unreasonable amount of material and resources, so not doable... I wonder.... would a space-elevator made out of modern materials, but shapped like a pyramid with a broad base, be able to be made tall enough to extend into space. I figure if the base is wide enough and the materials at least as strong as solid rock, it should be possible... but without running the numbers I dunno... I do know there is a limit on the maximum size of a mountain so .... i dunno.
Internet has no answers.
@freemo If I gather correctly, you are thinking of a construction that is loaded ~only in compression. Am I right?
What's the order of magnitude of the size you're thinking about (it's not obvious, because it depends on the angle in the pyramid's tip)? Less than 1% of Earth's mass/more than that?
As I said in my post the height would be "outer space"... basically high enough that something slightly above it can maintain an orbit with low enough drag it is sustainable... basically the lower bounds of an LEO.
So LEO is ~1.2K miles
For relevance the GEO point is 22.2K miles... this is the height something needs to exceed and be fixed to earth in order to fell a force opposite to gravity at any point in its structure... The part beyond 22.2K would be pull out away from earth, and the part below pulled into earth. Since we only are discussing something of a height of about 1.2K then all of the stresses, as far as I know, should be compressive.
@robryk Keep in mind 1.2K is generous and puts you at the upper limit of LEO... if we want something more doable the lower limit of LEO is like 150 miles or so up, which would get you past the ISS.