Use Newton?s law to compute the gravitational acceleration g(r) as a function of radius r within a sphere of total mass M that is uniformly distributed through the volume. Compute g(r) in a simple model of Earth with a core of radius 3500 km with density 1.2 ? 10⁴ kg/m^3?surrounded by a mantle of depth 3000 km with density 5 ? 10³ kg/m³. Graph this function and compare with Figure 32.3(b)

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350 10 300 | gravity 8 250 200 150 pressure 100 50 inner | outer core mantle Ey core 1000 2000 3000 4000 5000 6000 (b) radius [km] gravity [m/s ] 2. pressure [GPa]