The Gravity Express

Gravity Train

Ever heard of a gravity train? the concept is a solid one and has been around for almost 400 years.
Imagine a supertrain zooming through underground tunnels at tremendous speeds. 

This train could be left to accelerate using just the force of gravity, since, during the first half of the trip (from the point of departure until the middle), the downwards pull towards the center of gravity would pull it towards the destination. During the second half of the trip, the acceleration would be in the opposite direction relative to the trajectory, but (ignoring the effects of friction) the speed acquired before would be enough to cancel this deceleration exactly (so that the train would reach its destination with speed equal to zero).