The question is "The magnitude of the gravitational acceleration inside earth is given approximately by g(r) = g_0(r/R_E), where g_0 is the surface value, r is the distance from earth's center, and R_E 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. Evalueate and compare with the period of a satellite in a circular orbit not far above earth's surface." I am gettinng that T = 2(pi)*sqrt(R_E/g_0) How do I proceed from here? I am lost! I tried comparing and equations and think that R = RE, and their periods are exactly the same. is this correct?