The Earth is layered, with the density changing as you go closer to the center
But in this case we're not only falling towards the center, but moving away from it as well. If we assume earth's layering to be similar in both halves, why aren't the effects you mentioned during the fall compensated for during the rise?
Mathematically it's an example of a degenerate orbit with one zero semi-axis, and the orbital period can be simply calculated from Kepler's laws.
Indeed. Never thought of it that way, interesting.
Their scenario should have started the person off at the south pole, not the north, for the extra altitude.
The problem with a vaccum tube, though, is that it is closed at both ends. As much as it sucks coming to an early stop below the surface, slamming into the airlock is going to hurt, at a speed which would otherwise get you up for another 4km
I tell them to turn to the study of mathematics, for it is only there that they might escape the lusts of the flesh. -- Thomas Mann, "The Magic Mountain"