Gravity tunnel
~42.2 min
Frictionless fall through a straight chord of Earth. Uniform-density model versus PREM.
A generated cutaway with a layered interior. The entry is the textbook tunnel through an even Earth.
ImageGROK IMAGINEGenerated
A uniform Earth gives about 42 minutes 12 seconds, the same for any straight hole. A PREM Earth, denser at the core, gives 38 minutes 11 seconds for a diameter. The 42 is the textbook model, not the present geophysical value.
What it supports
Simple harmonic motion in a uniform sphere: t = π √(R/g) ≈ 42.2 min, independent of chord. Same ω as a grazing orbit, half-period. Klotz 2015, using PREM, prints 38 min 11 s for a diametric fall. Short chords stay near 42. Long chords near 38. Culture remembers the superseded model. That is why the card stays labeled.
What it does not
Not a measured transit. Not 42 minutes on the real Earth. Mariner 2’s 42 minutes is a mission dwell, a different object.
Calculation
Uniform: t = π √(R/g) ≈ 42 min 12 s. PREM diameter: 38 min 11 s.
Simple harmonic motion in a uniform sphere. PREM density profile for the geophysical line.
ExactnessApproximate
Form42 as duration
Unitmin
Strengthhard