Journey To The Center Of The Earth
In the Vernian adventure, A Journey to the Center of the Earth , Professor Lidenbrock finds a vast underground cavern several miles below the surface of the Earth.
Where does the Professor weigh more: in the underground cavern, or on the surface of the Earth?
Assumptions and Details
- The Earth has a uniform density.
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We can treat Earth as a uniform solid sphere, made of many concentric shells. By Gauss' Law, the gravitational field at any point inside a uniform shell is zero.
When the professor stands on the surface of Earth, he experiences gravitational force due to all concentric shells.
When he descends to the cavern, only the concentric shells between him and the center of the Earth exert a force on him. The shells that are above him do not exert force on him, by Gauss' Law.
Thus, he weighs more on the surface of the Earth. □