A gravity train is a theoretical means of transportation intended to go between two points on the surface of a sphere, following a straight tunnel that goes directly from one point to the other through the interior of the sphere.It's idea was given about four hundred years ago– sometime in the latter half of the 17th century– when Isaac Newton received a letter from the brilliant British scientist and inventor Robert Hooke. In this letter, Hooke outlined the mathematics governing how objects might fall if dropped through hypothetical tunnels drilled through the Earth at varying angles. Though it seems that Hooke was mostly interested in the physics of the thought experiment, an improbable yet intriguing idea fell out of the data: a dizzyingly fast transportation system, a 42 min train route from new york to hawaii.
The basic concept behind the train is quite simple: At each end of the tunnel, an observer looking into the hole would see a downward slope. If a train at one end of the tunnel were to release its brakes, the force of gravity would immediately pull the train down the slope and cause the train to accelerate much like a roller coaster. Steeper slopes would result in higher speed, with the highest acceleration occurring in the straight-down tunnels which cross the center of the Earth. The train would continue to accelerate until reaching the halfway point, at which time its inertia would be at odds with the gravity and it would begin to decelerate. As Hooke’s data showed, if the train operated in a frictionless environment it would reach the surface on the other end of the tunnel at the exact moment that its speed reached zero.
In reality, there are two reasons gravity trains do not exist. The transit would pierce the Earth's mantle and traverse a region where rock is more fluid than solid. No materials are known that would withstand the tremendous heat and pressure. Secondly, friction losses would be significant. Rolling friction losses could be reduced by using a magnetically levitated train. However, unless all air is evacuated from the tunnel, friction losses due to air resistance would rise with the square of the velocity. Evacuating the atmosphere to make it a vactrain and eliminate drag would require additional power. Such objections would not apply for solid planets and moons that don't have an atmosphere.The idea is still intriguing enough that it is a food for thought for many futuristic thinkers.