Comment Re:What does that even mean (Score 3, Informative) 95
A mountain at 42,164bkm would have the peak in geosynchronous orbit
But not geostationary (unless the mountain were at the equator) so while you might not fall down, you'd be in a bit of an awkward orbit yourself, relative to that mountain. Quick, someone try it in Kerbal Space Program!
But if someone built a tower 384,000 km high, it would travel faster than the moon. And if you jumped off that tower, you'd also never reach the ground.
One of the problems with building a space elevator on Mars is that it would be higher then the (innermost) moon, which would come say "Hi!" every few hours, moving quite fast.