Math 307: Gravity and the earth

I may as well restate the problem:
Imagine a train which goes in a straight line through a tunnel between two points on the surface of the earth (for example, between Seattle and Rio de Janeiro). Suppose that there is no friction, and the train just operates under gravity, so if you start it at one end of the tunnel, at rest, it will fall into the tunnel, accelerate until it reaches the midpoint of its trip, decelerate as it nears the other end, stop at the other end, and then return. Show that the time required for a complete round trip is the same for all such tunnels (it doesn't matter whether it ends at Rio de Janeiro or Beijing or Baltimore), and estimate its value.

sketch of earth

Facts about gravity:


Questions or comments? E-mail me at

Back to Math 307 home page.

Go to John Palmieri's home page.

Last modified: Wed Nov 13 14:48:17 PST 2002