Here's a thought experiment that hopefully never happens: Imagine that a hole suddenly appeared under your feet that stretched all the way through to the opposite side of the Earth. How long would it take you to fall through? Would you even fall all the way to the other side, or would you hover in Earth's gravity somewhere in the center?
Though it sounds like an absurd scenario, this is a common question asked of physics students to get them to stretch their minds around a problem. The generally accepted answer is that it would take 42 minutes. And yes, you would fall straight through to the other side, not get lost in the center. The speed attained during the descent on the first half of the journey would be significant enough to cause you to continue moving against gravity through the other half, right up to the surface. (Hopefully you'd catch the ledge — you wouldn't want to fall all the way back through again!)
But according to Alexander Klotz, a particularly astute student at McGill University in Canada, the generally accepted answer to this problem is all wrong. He has put together a new, more sophisticated calculation to the problem, and he claims that it would actually take only 38 minutes, reports Phys.org.
What makes Klotz's calculation different is that he takes into consideration the varied densities of the Earth's layers. The planet is much denser at the center than it is at the crust, for instance, and this effects the pull of gravity. So Klotz gathered the best available seismic data he could find, and began factoring in the different densities at different depths.
This allowed him to generate the most accurate answer to the falling man question to date: 38 minutes and 11 seconds, to be exact.
Interestingly, Klotz also noted that if gravity were to be assumed to be at a surface level constant throughout the duration of the trip, it would also take just 38 minutes. So perhaps 38 is the magic number then, not 42.
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