Free Fall through the Earth

In the late 17^th century, British scientist Robert Hooke wrote to Isaac Newton and discussed the mathematics of a thought experiment—one where an object was dropped down a tunnel drilled through the earth. He was fascinated by the physics of it: For the first half of the journey, gravity would pull the object into free fall. It would accelerate until it reached the midway point, where it would decelerate because it would be climbing away from the centre of the earth—and yet in a completely frictionless environment, it would have exactly enough inertia to reach the opposite end of the tunnel before it stopped completely. If the earth was a perfect sphere and the tunnel was frictionless, the trip would always take exactly 42 minutes and 12 seconds no matter at what angle the tunnel was drilled. Of course, this perfect scenario doesn’t exist in the real world, but the thought experiment still presents a dazzling engineering prospect—an incredibly fast transportation system (say, a train). Building this “Gravity Train” was first proposed in the 1800s, but the Paris Academy of Sciences wisely declined the ambitious plan—and even now, the concept is seemingly out of reach. Billions of cubic metres of rock would have to be hauled away to even drill the tunnels, the extreme heat and pressure of the core and mantle would present a huge problem, and measures would have to be taken to minimise friction. Transporting cargo between continents seems like a more feasible outcome than transporting humans, but we can hope that some incarnation of this Gravity Train will come into the realms of possibility before another four hundred years has passed.

(Image Credit: 1, 2)