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In the tunnel through the Earth thought experiment, how does total energy of a particle vary when it goes from surface of the Earth to its center?
In the typical tunnel through the center of the Earth thought experiment, a particle at the surface would oscillate between the two diametrically opposite points ignoring the rotation of the Earth. ...
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Two expressions for potential energy in the gravitational field of the earth
Let $M$ be the mass of the earth, considered as a point mass, then the potential energy of a point with distance $r$ away from the center (assume $r > \textrm{radius of earth})$ is
$$
U(r) = -\...
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