Find the acceleration of gravity within the mantle (at some radius R) of a planet that has a core and a mantle, each with different constant density.
Rp= radius of planet
Rc= radius of core
Pm= density of the mantle
Pc= density of the core
I know what the answer is but I cannot get there!
a= (-4/3)G(Pi)[((Pc-Pm)*Rc^3/R^2) + Pm*R]
Gravitational Potential Equations
The Attempt at a Solution
I have made 3 potential equations:
V= [(-4(Pi)GP/3R)*(R^3-Rc^3) + (-2(Pi)GP)*(Rp^3-R^3)]
I cannot get to the correct answer any help would be great!