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Our weight is more at the pole than at the equator (because it is closer to the center).

Does that mean if we go down into the earth (some kind of bore), will our weight increase further?

I remember reading somewhere that this is not the case. Is that true?

Qmechanic
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Atul Anand
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    Related: https://physics.stackexchange.com/q/18446/ – AFG Mar 07 '21 at 15:25
  • Another duplicate: https://physics.stackexchange.com/q/2481/2451 – Qmechanic Mar 07 '21 at 16:10
  • Here's why boring down is not the same as going to the North Pole: When you go to the Pole, you get closer to the center of the earth, so you are pulled down harder. End of story. When you bore down, you get closer to the center of the Earth, so you expect to be pulled down harder. But you ALSO suddenly have part of the earth ABOVE you, which pulls you in the opposite direction. Nothing like that happens when you go to the Pole. – WillO Mar 07 '21 at 16:15

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NO!

An approximate value for gravity at a distance $r$ from the center of the Earth can be obtained by assuming that the Earth's density is spherically symmetric. The dependence of gravity of earth on depth given by $$g(r)=\frac{4\pi}{3}G\rho r$$ $$g'=g\left( 1-\frac{d}{R}\right)$$ It's clear from here that the gravity goes to zero as $d\rightarrow R$. Note $d$ represents the depth from the surface.

Young Kindaichi
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