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## Homework Statement

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

P= density

I know what the answer is but I cannot get there!

ANSWER=

a= (-4/3)G(Pi)[((Pc-Pm)*Rc^3/R^2) + Pm*R]

## Homework Equations

.Gravitational Potential Equations

## The Attempt at a Solution

I have made 3 potential equations:

(R>Rc):

V= (-4(pi)GP/3R)*(R^3-Rc^3)

(Rp>R>Rc):

V= [(-4(Pi)GP/3R)*(R^3-Rc^3) + (-2(Pi)GP)*(Rp^3-R^3)]

(Rp>R):

V= -2(Pi)GP*(Rp^3-R^3)

I cannot get to the correct answer any help would be great!