42 Minutes

When you think Robert Hooke and Issac Newton, you think of great strides in the human understanding of the natural world. What you perhaps don’t think of is mass transportation systems that can ferry you to any point on the planet in 42 minutes.

Yet, these two veritable giants of 17th century science, in letters, discussed this very idea. Hooke wrote to Newton sometime in the late 17th century, mathematically describing how an object falling through a planet would wind up at its destination point in a fraction over 42 minutes.

What Hooke had mathematically shown was, if it was technically possible to bore a large enough hole through a planet, any object dropped down that hole would accelerate under gravity (assuming the object and the hole were somehow made frictionless) until it reached the halfway point where, as the object reached its terminal velocity, it would begin to slow, thanks to its own inertia fighting the force of gravity wanting to pull it back towards the centre, and finally reach the other end of the hole with zero momentum. Total travel time would be approximately 42 minutes and 20 seconds.

What Hooke discovered was that, no matter what the distance between the two points, whether they be direct polar opposites, or closer together, the forces of gravity would conspire to always make the total travel time just over 42 minutes. A trip from the north pole to the south pole would take almost exactly the same amount of time as a journey from London to New York.

I say almost exactly, because, as we all know, the Earth is not a perfect sphere. Hooke’s equations calculated that for a perfect sphere, the travel time would always be 42 minutes and 12 seconds. Since the Earth is pretty much an oblate spheroid (a sphere that is fatter than it is tall), the travel time would vary depending on the direction of travel, but always be somewhere a shade over 42 minutes. Due to how gravity operates on bodies, this time would remain constant if you dropped a marble or a blue whale down the hole.

Assuming you were a passenger aboard a north to south pole “Gravity Train”, you would achieve a speed of around 17,500 miles per hour by the time the train reached the centre of the Earth, before beginning to decelerate. The total distance you would travel would be 7,900 miles, shaving just over 4,500 miles off a trip along the surface of the Earth. It would be like the most exhilarating roller coaster you had ever ridden, and would get you there in under three quarters of an hour.

Whilst Hooke and Newton only thought of this as a completely theoretical method of traversing a planet, the idea was put forward to the Paris Academy of Sciences in the 1800’s as a consideration for an ambitious engineering project. Although the idea was shelved as wildly impractical and beyond the technology of the 1800’s, the idea was again proposed by Paul Cooper in the 1960’s in a paper submitted to the American Journal of Physics, however, as we now know, there are no transport systems that utilise this method, we can assume the idea was never taken seriously then either.

A Gravity Train would be a massive technical undertaking - not only the fact that friction would play a huge role in slowing the train down, ensuring that it would never actually reach its destination, the sheer logistics of drilling a hole through the Earth, somehow lining it with pressure and heat resistant materials would prove beyond even 21st century technology. Not to mention the billions of tons of material that would be excavated has to be put somewhere. Perhaps we could create the world’s first artificial mountain range?

Not only that, but the lining would have to be made out of some form of frictionless material and the entire tube would have to be as close to a perfect vacuum as possible, in order to negate air resistance on the way down and up. Assuming such a material existed, one that was not only a perfect heat and pressure resistor, but also air tight and frictionless, and we had enough of it to line a hole bored right through the planet, there is still one seemingly insurmountable obstacle that must be overcome - one that Hooke and Newton had no knowledge of, the Paris Academy of Sciences were ignorant of and Paul Cooper was probably only relatively familiar with: plate tectonics. The continents on Earth move, so any tunnel bored between landmasses on Earth would also have to be able to stretch, contract and flex as the continents shifted. This fact alone makes such a transit system on Earth a near impossibility, let alone the near impossibility of our hypothetical lining material.

Assuming we can find a material that only supports one of our needs - friction, there is nothing stopping us (aside from cost, engineering know how and equipment) from building such a transit system on another body in the solar system, unencumbered by molten rock, plate tectonics and air resistance. Imagine future human colonies on the moon, they could benefit from such a system - the vacuum needed is provided for by nature, all we would have to do is figure out how to turn the moon into a swiss cheese.