The Gravity Tunnel in a Non-Uniform Earth

TL;DR

This study refines the understanding of gravity tunnel travel times through Earth by incorporating realistic Earth density data, showing shorter and more variable fall times than the uniform density model predicts.

Contribution

It introduces a numerical analysis of gravity tunnel dynamics using seismic Earth data, moving beyond the uniform density assumption to provide more accurate travel time estimates.

Findings

Fall time along Earth's diameter is approximately 38 minutes.

Travel time varies with distance, interpolating between 42 and 38 minutes.

The brachistochrone path is similar to the uniform density solution but more efficient.

Abstract

How long does it take to fall down a tunnel through the center of the Earth to the other side? Assuming a uniformly dense Earth, it would take 42 minutes, but this assumption has not been validated. This paper examines the gravity tunnel without this restriction, using the internal structure of the Earth as ascertained by seismic data, and the dynamics are solved numerically. The time taken to fall along the diameter is found to be 38 rather than 42 minutes. The time taken to fall along a straight line between any two points is no longer independent of distance, but interpolates between 42 minutes for short trips and 38 minutes for long trips. The brachistochrone path (minimizing the fall time between any two points) is similar to the uniform density solution, but tends to reach a greater maximum depth and takes less time to traverse. Although the assumption of uniform density works well in many cases, the simpler assumption of a constant gravitational field serves as a better approximation to the true results.