The gravitational force inside a hollow Earth is zero.
But our Earth is not hollow. If the Earth were of uniform density, then the force would vary linearly inside the Earth. It is zero at the center -- just from symmetry -- and reaches the value of the usual gravitational force at Earth's surface at Earth's surface! This linear force looks just like the linear force exerted by an ordinary spring. Indeed, this oscillatory motion is exactly like the motion of a mass attached to a spring.
This means the force inside the Earth is proportional the distance from the center -- just like the force of a spring is proportional to how far the spring has been stretched or compressed from equilibrium. A mass acted on by a spring moves back and forth is simple harmonic motion which we will study a little later. Since the force of gravity inside the Earth has the same form -- linearly proportional to a distance -- it will cause the same kind of simple harmonic motion.Therefore, . . .
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(C) 2003, Doug Davis; all rights reserved
