All aboard the gravity train!

Have you heard of a gravity tunnel? What are they and do gravity trains exist? We wanted to know more on this subject and asked UNSW Canberra PhD student Aleksander Simonič all about it.

What is a gravity tunnel?

A gravity tunnel is a frictionless subterranean passage between two positions on the surface of a massive physical body, the Earth for instance. The vehicle used for traveling is called the gravity train and its motion is solely due to the body's gravitational field. The most common and easiest example is a straight gravity tunnel, when the fall is through a chord path, but other paths, e.g., free fall trajectories, have been also intensively studied.

The most interesting examples of gravity tunnels are those which are traversable, that is the gravity train, initially at rest, will reach its destination in both directions. The main purpose of my research was to obtain conditions on the position of the tunnel's endpoints as well as on the gravitational field in order to have traversability of a straight gravity tunnel through a rotating body with a spherically symmetric gravitational field.

How quick and fast could something travel through a gravity tunnel if one ran from one side of the Earth to the other?

This depends on the position of a straight gravity tunnel and of the model of Earth's gravitational field. Popular choices for the latter are linear and constant gravitational fields, and also the more realistic Preliminary Reference Earth Model (PREM). For these fields our condition on traversability is satisfied, so we are left with the restriction on tunnel's endpoints, that is the absolute values of the endpoints' latitudes must be the same. Such gravity tunnels are traversable, and fall-through times range between 38 minutes to 42.3 minutes, while the maximum velocities are around 9 kps, comparable to the reentry speeds of spacecrafts. For linear and constant gravitational fields there even exist exact formulas for calculating the fall-through times, but for the PREM we need to use numerical methods. As a particular example, consider a straight gravity tunnel between Heraklion (Crete, Greece) and Canberra, thus connecting Europe with Australia. The PREM gives that our journey will take 38.9 minutes with the maximum velocity 8.8 kps while passing the center of the Earth at a distance of 2434 km.

Do gravity trains exist/could they exist? What would a gravity tunnel be used for?

People have always pursued faster and faster travel around the world. In theory, gravity tunnels provide quick journeys between continents, and moreover, gravity trains don't need extra energy for locomotion. Although this is a very tempting idea, building such a tunnel is currently out of the question due to our limitations of engineering.

In the case of a typical gravity tunnel, not only would we need to drill through Earth's mantle, where temperatures range between 500 K to 4000 K and pressure is up to 139 GPa, we also need to ensure that such a tunnel is in a vacuum and is equiped with some magnetic levitation system in order to reduce friction.

So, this subject is for now only in domain of science fiction!

How did this research come about? What got you interested in this area?

I'm a pure mathematician, currently doing PhD in analytic number theory at UNSW Canberra, so this topic is obviously not on the top of my list. Although I like reading physics literature, I came across of this kind of research completely by coincidence two years ago while checking on Wikipedia for novels related to The Hitchhiker's Guide to the Galaxy by Douglas Adams. Because 42 is a prominent number in this sci-fi series, I was soon redirected to the page about appearances of this number in mathematics and science, where Cooper's paper is mentioned. I immediately got interest in gravity tunnels and soon started with reading newer research and »experimenting« on my own, which eventually led to the present paper.