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Information Junky
Join Date: Mar 2001
Location: an island, upper left coast, USA
Posts: 73,167
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First, you would hit the sides. Coriolis - even if through the poles...
Gravity is an acceleration. F=ma or F=mg
When accelerations are balanced - like falling due to gravity that acceleration a=g (weightless, but not massless)
So, you reach terminal velocity on the way down that changes as the air gets thinner, fly back up the other side a ways, and oscillate about the center for a while dead from a lack of O2
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Everyone you meet knows something you don't. - - - and a whole bunch of crap that is wrong.
Disclaimer: the above was 2¢ worth.
More information is available as my professional opinion, which is provided for an exorbitant fee. 
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