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Re: [Phys-L] gravity + tunneling to the antipodes



Sorry about that - my mistake. I wasn't correctly linking the dash vs.
dot titles with the appropriate dash vs. dot curves.

Robert A. Cohen, Department of Physics, East Stroudsburg University
570.422.3428 rcohen@esu.edu http://www.esu.edu/~bbq


-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of John
Clement
Sent: Thursday, January 03, 2013 2:39 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] gravity + tunneling to the antipodes

No they are correct. The linear density line has low density at the
surface and high density at the center. The density appears to be
fairly constant for the core as shown by the straight line for the
gravitational force. If you do the math you find that a constant
density Earth results in a straight line for the gravitational force vs
distance from the center. I created a simulation of the gravitational
force on an object which shows exactly that when the object is inside
the constant density planet. After all it is just proportional
reasoning. The force goes as mass inside the sphere/radius^2.
But the mass inside is proportional to r^3, so the force is proportional
to r. Calculus is not needed here.

John M. Clement
Houston, TX



It seems to me that the "linear density" line and the "constant
density"
line should be switched. What am I missing?

P.S. Here's a question: how fast does the Earth have to spin such that

the dropped object doesn't make it through the tunnel but instead pops

back up out the hole?

Robert A. Cohen, Department of Physics, East Stroudsburg University
570.422.3428 rcohen@esu.edu http://www.esu.edu/~bbq


...
This is a helpful depiction..
http://en.wikipedia.org/wiki/File%3aEarthGravityPREM.jpg



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