If you drop an object through a hole in the Earth stretching from the North Pole to the South Pole, it would oscillate back and forth about 17 times per daypic.twitter.com/crCfBFK2qp
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Assumptions: •No air resistance •Earth is a perfect sphere w/ uniform mass density •Such a hole doesn't collapse under gravity
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Another neat fact is that the falling object and a satellite orbiting just above the Earth's surface will have the exact same oscillation period!pic.twitter.com/g7fgYSlmM6
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- object doesn't vaporize via temperature of the core
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i drilled it out ;)
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I agree with air resistance and no collapse. But, I think this would work in a rotationally symmetric planet around the hole with at least monotonically increasing density, but the timing would change. I have to think about that...
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Would the rotation of the earth around the sun change anything? I figure out it doesn't. Well, a little bit if you consider that the sun's gravity would have different direction at surface or at the center
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Here's a challenge to assumption 2. (Dark green show gravity below surface for uniform density) https://en.wikipedia.org/wiki/Gravity_of_Earth#Depth … https://commons.wikimedia.org/wiki/File:EarthGravityPREM.svg …pic.twitter.com/gqRc8jHSw5
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also, the exact value of the ocilation period under these assumptions is √(3π/Gρ), where G is Newton's gravitational constant and ρ is the density of the earth. figuring it out is a nice exercise on differential equations ;)
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*period value given in seconds
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- everything has been idealized
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*Spherical chicken in a vacuum
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