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Old October 8 2012, 03:35 PM   #70
Christopher
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Re: About planetary gravity

Missed this before:

The Borgified Corpse wrote: View Post
Do you have an equation for that "any freefall trip through the Earth would take only 42 minutes" thing? My dad kept insisting that the Fall couldn't work by freefall because the fastest speed you could possibly reach would be 150 miles per hour, which would mean the trip would take about 53 hours.
Gardner didn't offer any specific equations in his article, I'm afraid. But your father must've been thinking of terminal velocity, the maximum allowed by air friction. The scenario Martin Gardner described in his essay assumed the tube was in vacuum and the train/elevator was magnetically suspended apart from the walls, so there was no friction and no terminal velocity limit.

Also, terminal velocity would be different depending on the density and surface area of the object and the density of the air it falls through (which is why a sheet of paper falls faster when crumpled than when flat). The 150 mph figure is terminal velocity for a human adult falling under 1g acceleration through the lower atmosphere of Earth, not a large elevator car. So if the car in the Fall wasn't in vacuum, there would be a terminal velocity, but we don't know what the actual value of it would be.
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