1 · The race of two Earths
The start: two fallers, one tunnel
Both start from rest at the surface. Nothing slows them: no air, no friction, no rotation. The only difference is the Earth beneath them.
Gravity · The real Earth · The model race
The tunnel through the Earth: how long the fall through the planet's centre takes
Drill a tunnel through the planet's centre and jump in. The textbook says you come out on the other side after a fixed time — but its maths assumes the Earth has the same density everywhere. Find your town, see where your tunnel comes out, and start the race: the textbook Earth versus the real Earth.
Find your town Skip to the race
Drawing: Earth cross-section · numbers: the PREM model · 12 sources at the end
Where does the tunnel from your town come out?
Pick a town. The page computes its antipode — the exactly opposite point on the globe — and tells you whether your tunnel comes out on land or in the ocean. Guess first: no cheating, look at the map only after.
Is your town's antipode on land or in the ocean?
The tunnel from Bucharest comes out at 44.43° S, 153.90° W — in the ocean. Nearest land: the Chatham Islands, about 1,800 km away.
The point is the antipode of the chosen seat, not of your address. The drawn map omits small islands; the land/ocean verdict is computed on the detailed shore.
Only 13% of the planet's land has land at its antipode — the rest faces ocean. That is why almost any tunnel from Romania comes out in the South Pacific.
What the map shows
- The red dot: the chosen town. The blue dot: its antipode.
- The map is the whole world stretched on a rectangle: parallels and meridians are straight lines.
- Small islands are missing from the drawing, but the verdict counts them.
The race of two Earths
Two fallers jump at the same time down the same tunnel. One falls through a uniform Earth, as in the textbook; the other, through the real Earth, with its dense iron core. Each step below moves the race clock. Guess the winner before you start.
Who wins the race?
Choose before you start the race. The answer appears at the finish, times included.
2 · The race of two Earths
Halfway: top speed
At the centre each reaches top speed — 9.9 kilometres per second through the real Earth, 7.9 through the textbook — then starts slowing towards the exit.
3 · The race of two Earths
The finish: the winner
One of them comes out first. Check the margin in the table below, computed from the PREM model.
The race times
| Model | Time | Top speed |
|---|---|---|
| Uniform Earth (textbook) | ? | ? |
| Real Earth (PREM) | ? | ? |
Ideal free fall down the diameter tunnel: no air, no friction, no rotation.
?
Why does the real Earth win?
In the uniform Earth, gravity falls linearly towards the centre. In the real Earth, the dense interior pulls hard all the way through the mantle — gravity climbs to 10.69 m/s², 8.8% above the surface value — so the second faller accelerates earlier and can never be caught. (At the centre, gravity is zero in both models — which is why speed peaks there.)
The speed curves
The straight tunnel between two towns
Not every tunnel goes through the centre. Pick two towns and the page digs the chord between them — the straight tunnel through the interior — and tells you how long the fall takes. In the textbook every chord takes the same time; in the real Earth it does not.
The chord Bucharest–Sydney: 11,855 km of tunnel, maximum depth 4,035 km, the fall takes 38:49. In the textbook it would take 42:10.
The real fall time is interpolated from the PREM angle table (verified error under 0.3 s); length and depth are computed exactly for a sphere with a 6,371 km radius.
Some chords
| Route | Length | Depth | Time (PREM) |
|---|---|---|---|
| Bucharest–Constanța | 203 km | 1 km | 42:10 |
| Bucharest–Vienna | 856 km | 14 km | 42:09 |
| Bucharest–London | 2,082 km | 86 km | 42:04 |
| Bucharest–New York | 7,199 km | 1,114 km | 41:05 |
| Bucharest–Beijing | 6,704 km | 953 km | 41:13 |
| Bucharest–Sydney | 11,855 km | 4,035 km | 38:49 |
| Madrid–Wellington | 12,741 km | 6,291 km | 38:11 |
| Bucharest–Wellington | 12,485 km | 5,099 km | 38:22 |
The longer the chord, the closer its time gets to the real diameter's.
Bucharest–Wellington, the longest chord from Bucharest, takes 38:22 — almost as long as the real diameter.
Madrid and Wellington are near-antipodes: Madrid's antipode falls on land in New Zealand, 160 km from Wellington — which is why their chord takes almost as long as the diameter.
Why nobody digs the tunnel
Three walls of physics stand between us and the tunnel: spin, heat and pressure. Each comes with its computed number.
The planet spins
Our tunnel stands still only on paper. In reality, rotational inertia drives the faller into the wall of a straight tunnel; a dedicated analysis shows only a specially shaped tunnel would keep the ride weightless. Only a pole-to-pole tunnel would escape the deflection.
Isermann 2019
Heat that melts iron
Pure iron's estimated melting point, extrapolated to the inner-core boundary: 6,230 ± 500 K.
Anzellini et al. 2013
Millions of atmospheres
The pressure at the centre, integrated from the PREM model, reaches 364.1 GPa — about 3.6 million times the air pressure at the surface.
this page's computation, from PREM
How deep we actually got
The deepest vertical borehole in history, Kola SG-3, stopped at 12,262 m, in rock at about 180 °C — nearly twice as hot as the engineers expected. Earth's diameter is about 1,040 times the Kola hole.
Scientific American 2020
Scale: the Kola hole (12,262 m) beside Earth's diameter (12,742 km).
How much of the tunnel stuck?
Six questions from the page. The answers are above, sources included.
1 How long does the fall through the centre take in the real Earth?
2 Who wins the race of the two Earths?
3 Where does the tunnel dug from Bucharest come out?
4 How long does a short chord take, say Bucharest–Constanța?
5 How deep did the Kola borehole get?
6 What does the time calculation ignore?
The method, briefly
The ideal case: free fall with no air, no friction and no rotation, down an evacuated tunnel, inside a spherical Earth with a radius of 6,371 km. Any friction — air included — steals energy, so the far exit is never reached.
The real Earth is represented by the PREM model (Dziewonski & Anderson 1981), a one-dimensional model of the planet: depth-wise density comes from the prem.nd table (ObsPy), and gravity, speeds and pressure are integrated numerically from it. The uniform Earth uses the same total mass and radius, with simple harmonic motion — which is why it gives 42 minutes 10 seconds rather than Klotz's 42:12, which matches the g = 9.81 convention.
Chords are integrated in PREM for every whole-degree central angle; the page interpolates linearly between them (verified maximum error: under 0.3 s). Antipodes are the exact formula; the land/ocean verdict and distances use the Natural Earth 50m shore, the drawn map the 110m shore.
Times round to the second, speeds to whole km/h, distances to the kilometre. Romanian town coordinates are seats (the seats gazetteer, from Wikidata and GeoNames); the 12 world cities were verified through Nominatim on 3 October 2026.
What the page does not do: shortest-time curved paths (brachistochrones), tunnels with air, the Moon's or Sun's pull. The question's history and the step-by-step journey through the layers live in the neighbouring chapter.
Sources
Tunnel physics
The real Earth
The borehole and the places
The neighbouring chapter, with the step-by-step journey through the layers: fall-through-the-earth.
All links were checked at publication.
Questions and answers
How long does the fall through the Earth's centre take?
In the real Earth, 38 minutes 11 seconds; in the textbook uniform Earth, 42 minutes 10 seconds. Both assume ideal free fall: no air, no friction, no rotation.
Why does the real Earth win?
The dense interior pulls hard all the way through the mantle, so the second faller accelerates earlier. In figures: gravity climbs to 10.69 m/s² in the real Earth instead of falling linearly to zero as in the textbook.
Where do I come out if I dig from Bucharest?
In the South Pacific, at 44.43° S, 153.90° W — about 1,800 km from the Chatham Islands, the nearest land. Almost any tunnel from Romania comes out in the ocean.
Does every straight tunnel take the same time?
Only in the textbook. In the real Earth, short chords take almost as long as the uniform diameter (42 minutes 10 seconds), and long ones drop towards 38 minutes 11 seconds.
Why can't the tunnel be dug?
Three walls: the spin pins you to the wall, pure iron's estimated melting point, extrapolated to the core, is 6,230 ± 500 K, and the pressure at the centre is about 3.6 million atmospheres. The deepest vertical borehole, Kola, stopped at 12,262 m.
What does the calculation assume?
An evacuated tunnel, no friction, a spherical, non-rotating Earth. Air alone would stop the fall long before the centre — so the times are a thought experiment, not a project.