Calculate Earth's Mass Using Gauss Law & Density

[bananasplit]

Is it possible to find the mass of the Earth based on the Earth's volume mass density, roe = A-Br=R, where A = 1.42 x 10⁴ kg/m³, B = 1.16 x 10⁴ kg/m³, and Earth’s radius
R = 6.370 x 10⁶ m

I know that based on Gauss Law that (closed integral) g x da = -4Gmin, where g is the total electric field due to the inside and outside of the closed surface. I don't see how this is possible.

 

[Cantab Morgan]

Hi, bananasplit. Could you try to be a little clearer? I think you were trying to write an expression for the density of the Earth, \rho, as a function of distance from the center, r, but I can't read your expression. Does it have a spurious equals sign, or a missing / symbol?

If that's the case, then you have to do a volume integral, and I don't see any connection to Gauss's Law. Might you be confusing Gauss's Law with Gauss's Theorem?