Inertia and Density question help

[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 don't think so, but I am not sure why or how...other than the uniform density can be calculated.

thanks

 

[actionintegral]

I don't think the solution is unique. There may be many radial density distributions with identical moments of intertia

 

[arildno]

Well, you have 2N densities&thicknesses, and three equations as far as I can see:
1. The sum of the shell's masses equals the known mass
2. The sum of the thicknesses equals the radius
3. the sum of the moments of inertae equals the Earth's moment of inertia.

looks like a typical lack of equations to me, even for N=2!

 

[cesiumfrog]

Assuming I have the mass, radius and moment of inertia of the earth

Hmm.. the radius of the Earth has long been measured, and its mass can be determined in a laboratory, but I thought the composition of the Earth was inferred from seismology - and moment of inertia perhaps from that. Of course, I wouldn't be wondering this is you wanted to calculate the density distribution of a golf ball, but is there a method of directly measuring the Earth's moment of inertia? Can you get it from simple observations of the moon and the lengthening day?