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Q & A: falling through earth

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Most recent answer: 10/13/2009
Q:
Suppose someone dug a hole through the center of the earth and you walked by and fell in. In detail, what would happen to you?
- Maddi (age 16)
Thibodaux, LA, United States
A:
I assume you mean in an idealized situation, where we ignore that the hole would collapse, that the earth is very hot inside, etc.
The interesting thing is that the gravitational force on you decreases proportional to the distance from the center. Of course it changes sign on the other side of the center. (The proportionality isn't exact, because the density isn't uniform.) That looks very much like the force from a spring. So you'd just bounce back and forth from one side of the earth to the other, as if you were a ball bouncing on a spring.  The time for a complete oscillation would be about 84 minutes, which is the same time a near earth satellite takes to circle the earth.  There is a nice web site that gives the gory details of the calculation:
http://hyperphysics.phy-astr.gsu.edu/HBASE/Mechanicsearthole.html 

Mike W.


(published on 10/13/2009)

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