Homework Help: Inertia and density distribution

1. Oct 3, 2006

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 thats how geophysists do itbut im not sure why

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

but i dont know how to equate that to prove that the earth is denser in the middle.

thanks

Last edited: Oct 3, 2006
2. Oct 4, 2006

Astronuc

Staff Emeritus
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

3. Oct 4, 2006

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)

4. Oct 4, 2006

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 dont have a lot of time to pound through a physics book as im struggling to get MATLAB to display a plot of newtonian potential for the earth.

thanks.