N004 fall model: our own simulation (RK4, dt = 0.01 s, no air, no heat, no Earth spin) PREM density self-check vs IRIS PREM_1s.csv: 21/21 points match (tolerance 0.0002 g/cm^3) PREM total mass: 5.97318e+24 kg (NASA NSSDC: 5.9722e+24) -> ratio 1.00016 GM: PREM 3.986677e+14 vs NSSDC 3.986000e+14 m^3/s^2 (ratio 1.00017) Surface gravity: uniform/NSSDC 9.8202 m/s^2, PREM 9.8219 m/s^2 Uniform Earth, analytic: transit = pi*sqrt(R/g), max speed = sqrt(g*R) transit 2530.4 s = 42 min 10.4 s; to center 21 min 05.2 s; max speed 7909.8 m/s = 17694 mph = 28475 km/h grazing-orbit period 2*pi*sqrt(R^3/GM) = 84 min 20.8 s (half of it = the transit; Klotz: same period and peak speed as a surface orbit) Klotz's numbers with g = 9.81: uniform 42 min 11.7 s; constant-g 37 min 59.4 s == Uniform-density Earth (textbook) == Time to the center: 21 min 05.2 s speed there 7909.8 m/s = 17694 mph Total transit (stop at the far-side lip): 42 min 10.4 s (far-side stop at -0.000 km from the surface; ~0 = energy conserved) Round trip home if nobody grabs you: 84 min 20.8 s Max speed: 7909.8 m/s = 17694 mph = 28475 km/h, at radius 0.0 km Boundaries on the way down: Deepest mine shaft (3.891 km) t = 0 min 28.2 s v = 276.4 m/s = 618 mph g = 9.814 m/s^2 Depth of the ocean's deepest point (10.935 km) t = 0 min 47.2 s v = 463.2 m/s = 1036 mph g = 9.803 m/s^2 Kola Superdeep Borehole depth (12.262 km) t = 0 min 50.0 s v = 490.5 m/s = 1097 mph g = 9.801 m/s^2 Base of the crust in PREM (24.4 km) t = 1 min 10.5 s v = 691.6 m/s = 1547 mph g = 9.783 m/s^2 Upper/lower mantle boundary (670 km) t = 6 min 12.7 s v = 3530.9 m/s = 7898 mph g = 8.788 m/s^2 Core-mantle boundary: outer core starts (2,891 km) t = 13 min 19.8 s v = 6625.5 m/s = 14821 mph g = 5.364 m/s^2 Inner core starts (5,149.5 km) t = 18 min 29.8 s v = 7763.0 m/s = 17365 mph g = 1.883 m/s^2 == Layered Earth (PREM densities) == Time to the center: 19 min 05.3 s speed there 9918.8 m/s = 22188 mph Total transit (stop at the far-side lip): 38 min 10.7 s (far-side stop at -0.000 km from the surface; ~0 = energy conserved) Round trip home if nobody grabs you: 76 min 21.3 s Max speed: 9918.8 m/s = 22188 mph = 35708 km/h, at radius 0.0 km Boundaries on the way down: Deepest mine shaft (3.891 km) t = 0 min 28.1 s v = 276.5 m/s = 619 mph g = 9.829 m/s^2 Depth of the ocean's deepest point (10.935 km) t = 0 min 47.2 s v = 463.7 m/s = 1037 mph g = 9.836 m/s^2 Kola Superdeep Borehole depth (12.262 km) t = 0 min 50.0 s v = 491.0 m/s = 1098 mph g = 9.837 m/s^2 Base of the crust in PREM (24.4 km) t = 1 min 10.5 s v = 692.8 m/s = 1550 mph g = 9.846 m/s^2 Upper/lower mantle boundary (670 km) t = 6 min 08.4 s v = 3650.0 m/s = 8165 mph g = 10.021 m/s^2 Core-mantle boundary: outer core starts (2,891 km) t = 12 min 43.5 s v = 7622.7 m/s = 17051 mph g = 10.689 m/s^2 Inner core starts (5,149.5 km) t = 17 min 01.0 s v = 9641.8 m/s = 21568 mph g = 4.403 m/s^2 == Constant gravity (Klotz check only) == Time to the center: 18 min 59.1 s speed there 11186.1 m/s = 25023 mph Total transit (stop at the far-side lip): 37 min 58.2 s (far-side stop at -0.021 km from the surface; ~0 = energy conserved) Round trip home if nobody grabs you: 75 min 56.4 s Max speed: 11186.1 m/s = 25023 mph = 40270 km/h, at radius 0.0 km Boundaries on the way down: Deepest mine shaft (3.891 km) t = 0 min 28.2 s v = 276.4 m/s = 618 mph g = 9.820 m/s^2 Depth of the ocean's deepest point (10.935 km) t = 0 min 47.2 s v = 463.4 m/s = 1037 mph g = 9.820 m/s^2 Kola Superdeep Borehole depth (12.262 km) t = 0 min 50.0 s v = 490.7 m/s = 1098 mph g = 9.820 m/s^2 Base of the crust in PREM (24.4 km) t = 1 min 10.5 s v = 692.3 m/s = 1549 mph g = 9.820 m/s^2 Upper/lower mantle boundary (670 km) t = 6 min 09.4 s v = 3627.6 m/s = 8115 mph g = 9.820 m/s^2 Core-mantle boundary: outer core starts (2,891 km) t = 12 min 47.3 s v = 7535.3 m/s = 16856 mph g = 9.820 m/s^2 Inner core starts (5,149.5 km) t = 17 min 04.1 s v = 10056.8 m/s = 22496 mph g = 9.820 m/s^2 PREM: gravity peaks at 10.689 m/s^2 = 1.088 x surface gravity, at radius 3480.0 km (depth 2891.0 km). Klotz: "about 1.09 g". PREM: gravity at the center = 0 m/s^2 (mass inside r -> 0) Race: layered Earth beats uniform by 239.8 s (9.5% faster). Max speed ratio 1.254. Pressure by layer (our PREM calc; ESRF quotes 330 GPa = 3.3 million atm at the inner-core boundary): r = 6371 km (depth 0.0 km): 0.0 GPa = 0.00 million atm r = 6346.6 km (depth 24.4 km): 0.6 GPa = 0.01 million atm r = 5701 km (depth 670.0 km): 23.8 GPa = 0.24 million atm r = 3480 km (depth 2891.0 km): 135.8 GPa = 1.34 million atm r = 1221.5 km (depth 5149.5 km): 329.1 GPa = 3.25 million atm r = 0 km (depth 6371.0 km): 364.1 GPa = 3.59 million atm Scale of human digging (radius = 6371 km = 3958.8 mi; diameter 7918 mi): Analogy 1: Earth's radius = one football field, goal line to goal line (300 ft). Analogy 2: a 12-inch globe. Deepest mine shaft 0.0611% of radius | field: 2.20 in (0.06 yd) | 12-in globe: 0.093 mm Ocean's deepest point, Challenger Deep (below sea level) 0.1716% of radius | field: 6.18 in (0.17 yd) | 12-in globe: 0.262 mm Kola Superdeep Borehole 0.1925% of radius | field: 6.93 in (0.19 yd) | 12-in globe: 0.293 mm Average continental crust (USGS ~30 km) 0.4709% of radius | field: 16.95 in (0.47 yd) | 12-in globe: 0.718 mm Top of the core (PREM, 2,891 km) 45.3775% of radius | field: 1633.59 in (45.38 yd) | 12-in globe: 69.155 mm Top of the inner core (PREM, 5,149.5 km) 80.8272% of radius | field: 2909.78 in (80.83 yd) | 12-in globe: 123.181 mm Center of the Earth (6,371 km) 100.0000% of radius | field: 3600.00 in (100.00 yd) | 12-in globe: 152.400 mm At Kola's average pace over 19 years (0.645 km/yr): center in 9872 yr, all the way through in 19744 yr (our estimate, straight-line extrapolation) At Kola's average pace over 22 years (0.557 km/yr): center in 11431 yr, all the way through in 22861 yr (our estimate, straight-line extrapolation) Kola depth in feet: 40230 ft; in miles: 7.619 mi Bonus, gravity train New York -> Los Angeles: surface distance 3936 km (2446 mi), straight tunnel 3873 km, deepest point 302 km down Uniform-density Earth (textbook) trip 42 min 10.4 s, top speed 2405 m/s = 5379 mph Layered Earth (PREM densities) trip 41 min 50.6 s, top speed 2442 m/s = 5462 mph Wrote fall-sim-summary.csv, fall-sim-trace.csv, pressure-by-layer.csv, dig-scale.csv