[xpe]

More (interesting!) flaws of the 42 minute calculation are shown here: https://www.livescience.com/50312-how-long-to-fall-through-e...

This approximation accounts for non-uniform density of the earth:

> Klotz based his calculations on the internal structure of the planet as determined from seismic data. While the Earth's crust has a density less than about 187 lbs. per cubic foot (3 grams per cubic centimeter), Earth's center has a density of about 811 lbs. per cubic foot (13 grams per cubic centimeter). The density of the planet does not rise in a straightforward manner the farther down one goes — there is a sharp 50 percent increase in density at the boundary of the planet's mantle and its outer core about 1,800 miles (2,900 km) below Earth's surface.

> Now, using a more realistic model of the Earth, Klotz finds the fall would take only about 38 minutes and 11 seconds, about 4 minutes faster than thought.