What If You Fell Through the Earth? The Answer Isn't 42 Minutes
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What If You Fell Through the Earth? The Answer Isn't 42 Minutes
52 просмотра · 10 дн. назад
Alternaut
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52 просмотра · 10 дн. назад
Dig a tunnel straight through the middle of the Earth and jump in. The classic answer says you reach the other side in 42 minutes. The real Earth says about 38 minutes, and the reason is hiding in its core.
Then we ask why the real tunnel can never exist and where it would come out.
Chapters:
0:00 The 42-minute answer
1:06 Weightless from the first second
1:21 Passing the Kola borehole
1:59 Does gravity fade as you sink?
2:59 Gravity peaks at the core edge
3:57 Arriving at the centre
4:13 Zero gravity, top speed
5:23 38 minutes, not 42
6:06 London to New York
6:28 Why you can't dig it
8:16 Where the tunnel comes out
9:27 Your own tunnel
The thought experiment: a straight, empty (vacuum) tunnel through the centre of a non-rotating Earth, using the standard seismic Earth model (PREM), released from rest at the surface.
The measure behind every big claim:
About 38 minutes one way: 38 min 11 s in the published PREM result, 42 min 12 s for a planet of the same density everywhere. One way means from release to the far surface, through the centre.
You are weightless from the first second, not only at the centre, because nothing pushes back. The on-screen gauge shows the model's pull of gravity, which you do not feel in free fall.
The deepest hole humans have drilled straight down is the Kola borehole: 12,262 m of vertical depth (1989). Some sideways oil wells are longer by measured length. You pass that depth about 50 seconds after release, 0.19 percent of the way to the centre (of a 6,371 km radius).
In the model the pull of gravity rises to a peak of about 10.7 m/s2 at the core-mantle boundary, 2,891 km down, against about 9.8 m/s2 at the surface, and is still about 102 percent of the surface value halfway to the centre. "Strongest" means the highest value along the fall.
At the centre the pull of gravity is zero, but your speed is the highest of the trip: about 9.9 km/s (nearly 36,000 km/h). The same-density textbook model gives 7.9 km/s.
The temperature at the edge of the inner core is disputed: the estimates we cite run from about 5,500 K up to an upper bound of about 6,200 K, which brackets the Sun's surface (5,772 K).
The pressure at the centre in the model is about 364 GPa, roughly 3.6 million atmospheres.
Why the real tunnel is impossible: air caps your speed near 200 km/h and thickens until you hover, tens of kilometres down at the very least (ideal-gas estimate, no upper limit established); a bare tunnel in strong rock starts to fail at roughly 1.5 to 5 km down (simple stress estimate, details in the pinned comment); deeper down the squeeze on an open wall is many times the strength of strong rock (about 25 times at 100 km), so an open hole would be squeezed shut (no time given); the outer core is liquid metal, mostly iron; and at the equator the spin pushes you into the wall within about 16 seconds (tunnel 2 m wide, our assumption).
Where a tunnel comes out: more than four fifths of the world's land has ocean on the opposite side (our count from the ETOPO data below: 86 to 89 percent depending on the land mask; published about 85 percent). London's antipode is on the sea floor south-east of New Zealand, nearly 5 km down; New York's is in the southern Indian Ocean, about 4 km down.
Sources and data
Klotz, "The Gravity Tunnel in a Non-Uniform Earth", American Journal of Physics 83, 231 (2015): https://arxiv.org/abs/1308.1342
Dziewonski and Anderson, "Preliminary reference Earth model", Physics of the Earth and Planetary Interiors 25, 297-356 (1981).
Kola Superdeep Borehole: https://en.wikipedia.org/wiki/Kola_Su...
Inner core temperature: the ESRF highlight on Anzellini et al., Science 340 (2013); Balugani et al., Physical Review Letters 133, 254101 (2024), summarised in APS Physics 17, s139 (https://physics.aps.org/articles/v17/....
Antipodes: https://en.wikipedia.org/wiki/Antipodes
Full source list and our own calculations: first reply under the pinned comment.
Map data: NOAA NCEI, ETOPO 2022 (public domain, CC0-1.0). Earth model: PREM (Dziewonski and Anderson 1981).
The narration is a synthetic (AI) voice. The animation and sound effects were generated by us. Music: "Candlepower" by Chris Zabriskie | From the album Divider | Licensed under Creative Commons Attribution 4.0 | creativecommons.org/licenses/by/4.0/ | chriszabriskie.com . The music was edited for this video (looped, crossfaded, level-adjusted); no other changes.