If I want to visit my parents, I currently have a trip of about three days ahead of me. From New Zealand to Spain (its antipodes), I inevitably have to take several planes with stopovers at airports in China or Dubai. However, 400 years ago, Isaac Newton along with Robert Hooke proposed that could do this trip in much less time, specifically in 42 minutes. Theory and practice, of course, do not always coincide.
British scientist and inventor Robert Hooke proposed in the 17th century an extremely fast method of traveling between different parts of the planet Earth. Although making it happen is currently impossible, it is an interesting theoretical exercise to better understand the mathematics behind gravity. Welcome aboard the gravity train.
The idea behind gravitational train it is relatively simple. It is about making tunnels in the Earth that connect different points. Completely straight tunnels and, if possible, vacuum tunnels to avoid air friction (hello Hyperloop). From there it’s a matter of letting gravity do its job, you wouldn’t even need fuel or other types of energy to move the train.
Considering that the Earth is a sphere, dropping an object (or train) down a straight tunnel, it will appear at the other end of the tunnel. The tunnel does not have to be the full diameter of the sphere/Earth (at the antipodes of a place) it can also be smaller pieces such as from Madrid to Berlin or Beijing.
42 minutes and 12 seconds
If the math of gravity is true, the object would accelerate by itself due to the attraction of the Earth, the same one that keeps us standing on the surface. But the interesting thing about this is that the object would not only accelerate by itself, but also it would also stop.Theoretically, the object accelerates until it reaches the point closest to the center of the Earth, then it would begin to slow down since it would no longer be attracted by the Earth’s gravity but instead would move due to the inertia of the previous acceleration, slowing down slowly. Technically it would slow down to a speed of 0 km/h at the exact point of the end of the tunnel, since it would be the same distance from the center of the Earth as the starting point of the tunnel.
The most interesting of all this is the travel time of the gravitational train. And it is that taking into account the mass and volume of the Earth, this time is always the same. About three quarters of an hour and if the Earth were a perfect sphere exactly 42 minutes and 12 seconds. Once again, it is a matter of the laws of gravity.
The further away the point you want to reach is, the steeper the tunnel will be and therefore the more the object will accelerate when falling. Otherwise there would be less slope and therefore the force of gravity would be less because it does not get so close to the center point of the Earth, thus reducing its maximum speed. That is why the trip would always take around 42 minutes.
With the given theory, let’s see it with an example. Suppose there is a gravitational train from my house in Auckland (New Zealand) to Valencia (Spain). Since they are the opposite sides of the Earth, the tunnel would have a distance of 12,742 kilometers and would pass through the very center of the Earth. The first 6,371 kilometers my train would be in free fall, accelerating without stopping until it reached about 28,400 km/h in the center of the Earth. From there, its speed would begin to slow down little by little during the second half of the route and it would arrive in Valencia at 0 km/h at the gravitational train station. Travel time? 42 minutes.
From the theory to the practice
The reality is not as pretty as the theories of Robert Hooke and Isaac Newton. Excavating a tunnel of such dimensions is currently impossible and the most we have managed to dig is barely 12.2 kilometers. The heat in these 12 kilometers of depth was already unbearable for the excavation machines, so it is better not to think about what it would be like another 6,000 kilometers below, where the core of the earth can reach 5,000 degrees Celsius.
We have built yet other tunnelsmore humble. From tunnels to cross rivers like the Thames to gigantic subway tunnels in China. We must not also forget about Elon Musk’s plan to fill the underground of cities with vacuum tunnels for Hyperloop. Elon Musk in fact also has another plan to travel anywhere in the world in less than an hour, but by air.
More information | GeoGebra and Keep Innovating
George is Digismak’s reported cum editor with 13 years of experience in Journalism