Inertia and density distribution

[SWiTCHRiDE]

Assuming I have the mass, radius and moment of inertia of the earth, is it possible to determine the unique density distribution of the earth? The assumtion is the Earth is composed of N shells with constant density and thickness.

I think so, because that's how geophysists do itbut I am not sure why

edit: all i do know is I=(2/5)*M*r^2 and I= (integral) r^2 dm

but i don't know how to equate that to prove that the Earth is denser in the middle.

thanks

 

[Astronuc]

Without knowing the precise structure of a solid, particularly a sphere or oblate spheroid, which is the shape of the earth, it is not possible AFAIK to determine the mass/density distribution.

The integral which describes the moment of inertia gives one a more or less average value, so one gets an effective density.

On the other hand, knowing the total mass, and consequently an average (uniform), by virtue of the Earth's orbit around the sun, one probably could develop a mass distribution (M(r), in polynomial form) and calculate the Moment of Inertia and compare it to a calculation with a uniform density.

A nice reference on Moment of Inertia concepts - http://hyperphysics.phy-astr.gsu.edu/Hbase/mi.html#mi

 

[SWiTCHRiDE]

im still confused. i have read that section on inertia at hyperphysics. so if one knows radius, mass and orbital radius it IS possible to determine the mass distribution. (assuming the Earth is spherical)

 

[SWiTCHRiDE]

bump...please can somebody help, its the last question of my homework and its due in 1 hour from the time of this post. i don't have a lot of time to pound through a physics book as I am struggling to get MATLAB to display a plot of Newtonian potential for the earth.

thanks.