this topic has been covered in the Thinkers Cult and here was my response.
if you jumped down into your shaft to china, you would be dead before
you reached the center of the earth. the reason for this, due to the
coriolis effect, the earth is still spinning while you are suspended in
air which means your body will be deflected to the right and you will
slam into the side of the shaft. then friction will take its toll.
this will be repeated thousands of times before you even reached the
center.
when you are in the norther hemisphere everything deflects to the right
or clockwise. over, this deflection is not as dramatic if you are say,
15 degrees N of the equator, reason for this being, is that the earth
is actually moving more slowly at this point then say if you were at 70
degrees north. so, if you jumped into a shaft in the NH but closer to
the equator, you would not bounce of the walls as much as you would if
you did it in the 70 degrees north latitudes. although, this concept
has been proven by Newton in 1803 when he dropped 29 iron pebbles into
a 90 meter deep mineshaft. they record the average deflection to be
8.8mm. so if you were falling down a mineshaft that could actually
make it to china, you would have about 6440km to go, depending on where
you dropped from. (assuming the point where you dropped the crust is
at its thickest, of 40 km versus 8 km, if you could drop from the crust
of the ocean which is impossible, so 6440 km in meters is 6,440,000m.
if the average deflection every 90meters was 8.8 mm then 6,440,000m
divided by 90m is 71,555, so that means you would be deflecting for a
total of 71,555 times for every 90m fallen. and if one deflects 8.8m or
0.0088m every 90m, then 71,555 times 0.0088m would give 629meters of
deflection before you hit the bottom, so you're gonna have to dig a
pretty wide hole..