Home / Topics / Oscillations & SHM
Tunnel through the Earth
Advanced
A mass falling through a tunnel executes SHM with a period of about 84 minutes.
Inside a uniform Earth, g ∝ r, so a body falling through a tunnel executes SHM with T = 2π√(R/g) ≈ 84 minutes, the same as a low orbit.
Travel through the planet in 42 minutes.
Neglects friction and Earth's rotation.
In more detail
A hypothetical tunnel through the Earth, with no friction, would give an object SHM with a period of about 84 minutes. The restoring force is proportional to distance from the centre, as in a uniform sphere.
Real-world uses
- The tunnel is a classic textbook problem in gravitation and oscillation.
- It shows how SHM arises from gravity inside a uniform planet.
- A classic thought experiment shows that a train through a straight tunnel through the Earth would take about 84 minutes for a round trip.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
Why is the period independent of the tunnel?
Because the force inside a uniform sphere depends only on distance from the centre, giving SHM whatever the path.
Would it really work?
Not in practice, since the tunnel and the planet are not uniform and friction would matter.
Why does the object not need to fly around the Earth?
Gravity inside the Earth is proportional to distance from the centre, so the motion is simple harmonic and needs no energy from outside.
Related topics in Oscillations & SHM
Parametric resonance · Oscillation of a floating body · Liquid in a U-tube · Molecular vibrations · Quantum harmonic oscillator