  How long does it take to fall down a tunnel through the center of the Earth
to the other side? Assuming a uniformly dense Earth, it would take 42 minutes,
but this assumption has not been validated. This paper examines the gravity
tunnel without this restriction, using the internal structure of the Earth as
ascertained by seismic data, and the dynamics are solved numerically. The time
taken to fall along the diameter is found to be 38 rather than 42 minutes. The
time taken to fall along a straight line between any two points is no longer
independent of distance, but interpolates between 42 minutes for short trips
and 38 minutes for long trips. The brachistochrone path (minimizing the fall
time between any two points) is similar to the uniform density solution, but
tends to reach a greater maximum depth and takes less time to traverse.
Although the assumption of uniform density works well in many cases, the
simpler assumption of a constant gravitational field serves as a better
approximation to the true results.
