Suppose a hole is drilled through the center of the Earth and a bowling ball of mass m i...

Suppose a hole is drilled through the center of the Earth and a bowling ball of mass m is dropped into the hole, as shown in Figure 1.3.21. Construct a mathematical model that describes the motion of the ball. At time t let r denote the distance from the center of the Earth to the mass m,Mdenote the mass of the Earth, M_r denote the mass of that portion of the Earth within a sphere of radius r, and denote the constant density of the Earth.