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Physics: Calculate a Planet's Interior Gravity Field

Assume a spherical, uniform planet with mass M and a radius R.

a) Develop a relationship which will the give the gravity field of a planet at any point beneath its surface which is distance r from the center.

b) Use the mass and radius of the earth to find the earth's field at a point halfway to the surface.

Solution Preview

a)
Recall that for points exterior to a planet we can write: (1) g= G M/r^2.
A point on the surface of a sphere is exterior to that sphere, and in that case, r in (1) would be the radius of the sphere. On the surface of the planet described above, for example, the field would be g= GM/R^2.

For additional information, refer to posting number #5948, for its derivation of the fact that the gravity field of a spherical shell ...

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