What If You Fell Through a Hole in the Earth?

Dig a hole through the center of the Earth and jump in. How long does the fall take? About 42 minutes in a perfect world, about 38 in the real one, and you would pass the center at 17,700 mph (28,460 km/h), weightless. This film does the math on screen, step by step, and then shows why it all breaks in reality: the heat, the pressure, the air and the spin of the Earth. Questions answered: How deep is deep (Kola, the deepest hole ever drilled)? Why does gravity fade as you fall? How fast, and how soon? What happens at the center? Why does every straight tunnel, even New York to Los Angeles, take the same 42 minutes in the simple model? How hot is it? Where would you come out? (Jump in from New York and you land in the Indian Ocean.) CHAPTERS 0:00 Dig a hole and jump in 0:27 1. The Fall 2:35 2. Why Every Tunnel Takes 42 Minutes 4:20 3. Reality, and Where You Come Out 6:37 Your question OUR MATH (simple model: sphere, same density everywhere, no air, no spin; R = 3,959 mi (6,371 km), g = 9.81 m/s²) g(r) = g · r/R, so r(t) = R cos(ωt) with ω = √(g/R) = 0.001241 per second Fall time to the other side: T = π√(R/g) = 2,532 s = 42.2 minutes (round trip 84.4 minutes) Top speed at the center: v = ωR = 7.9 km/s = 17,700 mph (28,460 km/h) Any straight tunnel (chord) has the same ω and the same T; only the depth and top speed scale with the half length L/2: x(t) = (L/2)·cos(ωt), v_max = ω·L/2 50 s: 7.6 mi (12.26 km), 1,100 mph (1,760 km/h); 1 min: 11 mi (18 km), 1,300 mph (2,100 km/h); 5 min: 270 mi (436 km), 6,400 mph (10,350 km/h); 10 min: 1,050 mi (1,690 km), 12,000 mph (19,300 km/h) New York to Los Angeles: 2,446 mi (3,936 km) along the surface, 187 mi (301 km) deep, top speed about 5,400 mph (8,650 km/h); a 100-mile tunnel: 0.32 mi deep, top speed 223 mph All numbers were recomputed by code. SOURCES Klotz, A. R. (2015), "The gravity tunnel in a non-uniform Earth", American Journal of Physics 83, 231 (arXiv:1308.1342): about 38 minutes through the center with real density; chords between 38 and 42 minutes Gravity train, Wikipedia: https://en.wikipedia.org/wiki/Gravity... (uniform model 42.2 min; all straight-line gravity trains on a planet take the same time) Kola Superdeep Borehole, Wikipedia: https://en.wikipedia.org/wiki/Kola_Su... (12,262 m / 40,230 ft in 1989; stopped at 180 °C / 356 °F) APS Physics (2024), inner core: https://physics.aps.org/articles/v17/... (about 330 GPa at the inner core boundary) Earth's inner core, Wikipedia: https://en.wikipedia.org/wiki/Earth%2... (about 5,700 K, about the temperature at the surface of the Sun) Speed skydiving, Wikipedia: https://en.wikipedia.org/wiki/Speed_s... (a belly-down skydiver falls at about 120 mph) Antipodes on Earth, Wikipedia: https://en.wikipedia.org/wiki/Antipod... (about 15% of land has land on the other side; Hawaii and Botswana) Antipode of New York City, geodatos: https://www.geodatos.net/en/antipodes... (about 40.71 °S, 106.01 °E, Indian Ocean) Our own calculations: equator speed 1,040 mph (1,674 km/h) = 2π · 6,378 km / 86,164 s; air-drag lower bound 66 hours = 7,918 mi / 120 mph; antipodes (−lat, lon ± 180°) of New York, Los Angeles, Chicago and Honolulu Our short film about Kola:    • HUMANS HAVE DRILLED ONLY 0.2% TO EARTH'S C...   ABOUT THIS FILM The voice is AI-generated (Kokoro). The math, the 3D globe and the video were made with code by an AI agent and checked against the sources above. Music: generated by us. Textures: Solar System Scope (solarsystemscope.com, CC BY 4.0), adapted. Font: Montserrat (SIL OFL). Where the film simplifies (uniform density, no air, no spin), it says so on screen. If you find an error or a newer study, tell us in the comments and we will correct it. #physics #earth #science #3D #gravity