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

["John Clement" <clement@hal-pc.org>]

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