Hooke's calculations showed that if the technology could be developed to bore such holes through the Earth, a vehicle with sufficiently reduced friction could use such a tunnel to travel to another point anywhere on the on Earth within three quarters of an hour, regardless of distance. Even more amazingly, the vehicle would require negligible fuel. The concept is known as the Gravity Train, and though it seems inconceivably difficult to construct, it has received some serious scientific attention and research in the intervening centuries.
The basic concept behind the gravity train is straightforward: At each end of the tunnel, an observer looking into the hole would see a downhill slope. If a train at one end of the tunnel were to release its brakes, the force of gravity would immediately pull the train downhill and cause the train to accelerate much like a roller coaster. Steeper slopes would result in more speed, with the highest acceleration occurring in the straight-down tunnels which cross the Earth's center. The train would continue to accelerate until reaching the halfway point, at which time its inertia would be at odds with gravity and it would begin to decelerate. As Hooke's data indicates, if the train operated in a frictionless environment it would reach the surface on the opposite end of the tunnel at the exact moment that its speed reached zero. Naturally, a gravity train operating in a real-world environment would need to bring along enough horsepower to make up the friction loss.
One interesting property of the Gravity Express is that its transit time would always be very, very close to forty-two minutes regardless of the distance travelled. In fact, if the Earth were a perfect sphere, the trip time would always be exactly forty-two minutes and twelve seconds. Greater distances would be traversed in the same amount of time as short ones because the train's maximum speed would be increased enough to exactly make up the difference. Due to nature of gravity, this forty-two minute trip time would be consistent for any size of vehicle.
Consider a hypothetical Gravity Express station in Spain which connects to a sister station in New Zealand. The tunnel would be straight down because its route would intersect with the Earth's center, making for an interesting departure as the train entered sudden free-fall. The vehicle would accelerate to a maximum velocity of about 17,670 miles per hour before beginning to decelerate, and it would travel in a straight line for 7,920 miles-- a trip which would be 12,440 miles on the surface. Forty-two minutes after their stomach-turning departure, the train and its passengers would pull to a gentle stop at their destination on the other side of the world.
Though Robert Hooke and Isaac Newton corresponded on the subject of objects falling through the Earth, they did so merely as an intellectual exercise. The first serious suggestion to build a gravity train wasn't put forward until the 1800s, presented to the Paris Academy of Sciences by a group of scientific optimists. Unsurprisingly, the Academy opted to defer the ambitious suggestion. The concept was lost to obscurity until the 1960s, when physicist Paul Cooper published a paper in the American Journal of Physics suggesting that gravity trains be considered for a future transportation project. Though the article sparked some lively debate, the proposal was not taken very seriously.
Those who find sport in reflecting on such wild ideas have suggested that the tunnel could be evacuated of air to eliminate wind resistance, though such a feat would prove almost as challenging as the drilling itself. Some have also postulated that such a train could be magnetically levitated to eliminate friction in situations where the tunnel does not pass through the Earth's center; though if electromagnets were used, the amount of energy consumed by the apparatus would rise drastically. A more viable location for the gravity train would be on planets such as the moon which are not troubled by an atmosphere, plate tectonics, and magma. The concept would be the same, though a planet with a density different from that of Earth would also have a different standard trip length.
Though the Gravity Express may seem impossible-- or at best absurdly impractical-- it is appealing to consider the possibility of extremely rapid transit across the planet with very little expenditure of energy per trip. Certainly the creation and reinforcement of such tunnels is well beyond the reach of our current technology, but the future is full of surprises. Modern technology has sufficient momentum that it might eventually carry us through to the other side of the problem, provided that we can reduce creative friction by opening our minds.
Topic spotted on Reddit.