JoshuaZ comments on Open thread, Oct. 12 - Oct. 18, 2015 - Less Wrong Discussion
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Good analysis! A few remarks:
In practice even for a planet with as thin an atmosphere as Earth, getting past the atmosphere is more difficult than actually reaching escape velocity. One of the most common times for a rocket to break up is near Max Q which is where maximum aerodynamic stress occurs. This is generally in the range of about 10 km to 20 km up.
Getting enough mass up there to build a space elevator is itself a very tough problem.
Whether gravity is stronger or weaker on top of a mountain is surprisingly complicated and depends a lot on the individual planet's makeup. However, at least on Earth-like planets it is weaker. See here. Note though that if a planet is really massive it is less likely to have large mountains. You can more easily get large mountains when a planet is small. (e.g. Olympus Mons on Mars).
This would require everyone on the planet to take this same attitude. This seems unlikely to be common.
You got me curious, and I read a bit more, and found this on Wikipedia:
In lay terms, I guess this means that, unlike a cannon ball, which only gets one initial "push", a rocket is being "pushed" continually and thus doesn't need to worry about escape velocity.
So first they get the rocket high enough to be safe from the air, and then they speed it up.