Show that the magnitude of the gravitational acceleration inside Earth is given

Question

Show that the magnitude of the gravitational acceleration inside Earth is given approximately by g(r) = g0(r/RE). where g0 is the surface value, r is the distance from Earth's center, and RE is Earth's radius; the acceleration is directed toward Earth's center. Suppose a narrow hole were drilled straight through the center of Earth and out the other side. Neglecting air resistance, show that an object dropped into this hole executes simple harmonic motion, and find an expression for the period. Evaluate and compare with the period of a satellite in a circular orbit not far above Earth's surface.

Explanation / Answer

You might find the following link helpful, as it discusses the same problem: http://www.physicsforums.com/showthread.php?t=228840 I hope this is of help.

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