I like the model of an insulated tunnel bored through the Earth from the north to the south pole and filled with a vacuum (technologically implausible, yes). If

I like the model of an insulated tunnel bored through the Earth from the north to the south pole and filled with a vacuum (technologically implausible, yes). If we drop a steel ball into the tunnel at the north pole, what forces does it experience? From Newton's perspective, F = ma and the ball accelerates towards the center of the Earth. The value of g diminishes to zero at the center, the ball is at its maximum velocity, and then enters the negative acceleration regime until it just reaches the surface of the Earth at the south pole. This will continue indefinitely in harmonic motion. It's not a perpetual motion machine because machines do work and we're not doing any work on the ball; it's similar to an orbiting sphere. (ChatGPT-o1 claims the period is 84.4 minutes, assuming uniform density) The general relativity perspective seems to be the ball is just rolling up and down a bowl of spacetime, without any friction or drag, which isn't all that satisfying a picture, since it implies a restorative force being involved to keep the ball from escaping the bowl. It helps to consider the state of the ball right before it is kicked into the tunnel - it is being prevented from following its natural geodesic trajectory by the electromagnetic forces of the rocks of the Earth's crust upon which it is being held up - that's the only relevant force in this picture.