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Please help my twisted mind resolve this. Thanks!

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- Thread starter StoneWaz
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- #1

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Please help my twisted mind resolve this. Thanks!

- #2

Mark44

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Yes and yes. At the top of the whole, all of the earth's mass is pulling on you (and you on it). As you get farther down in the hole, there is less mass below you, and more above you. At the exact center, all gravitation forces would essentially cancel.At some point the direction of gravity would have to shift, right? And that would occur at the exact mid-point, right?

Decreases to zero, and then begins increasing again. When you pop out the other side, gravity will be the same as at the "top" of the hole.But does gravity increase or decrease as I go further down and what, exactly, happens at the center

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Amazing stuff to think about. Thanks for the help!

- #5

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Here's a graph comparing how gravity would change with depth according to three different models for its interior: constant density, Density that increases linearly as you move towards the center, and Our estimate of what is is for the real Earth (Preliminary Reference Earth Model,or PREM)

- #6

Chandra Prayaga

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- #7

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That would work in any spherically symmetric Earth regardless of the radial density distribution, in fact. Gravitational potential is equal at all points on the surface, so conservation of energy means you come to a stop at the same radius you started at (neglecting friction). So it would probably work in more general cases than the spherically symmetric Earth, too.In the idealized earth mentioned in post #3, you dont need rungs to climb down and then up on the other side. If you let go of the rungs, you will oscillate back and forth from one end of the tunnel to the other, and back again, like a ball attached to a spring.

- #8

jbriggs444

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Works best if the hole is evacuated and runs from north pole to south pole, of course.

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- #10

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You'd be in free fall the whole way and the tidal gradient wouldn't be anything to worry about. As long as you don't hit a wall on the way through (at the center you'd be moving at better than 7.9 km/sec), you'd be fine.

- #11

jbriggs444

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As long as the walls of the tube are strong enough to withstand the pressure (i.e. they are made of unobtainium), as long as the tube is evacuated and as long as one ignores Coriolis, falling through the tube would be like being weightless. There would be no stresses worth worrying about.

Edit: Nosed out by @Janus

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If we we assume a spherical Earth of constant density, and using a radius of 6378 km for the Earth, then the round trip would take 84 min 28 sec, or 42 min 14 sec one way.

If we drill our hole such that it doesn't pass through the center, but at some other angle so that it comes out at a point other than the exact opposite point of the Earth, an object dropped down that hole (we will have to assume friction-less sides here) will also take 42 min 14 sec to reach the other end.

So for instance, if you were to drill a straight hole through the Earth from LA to New York, put a ball in it and let it "roll" from one end to the other (again ignoring friction, the earth's rotation, etc. ), it would take 42 min 14 sec to travel from LA to New York. This is the idea behind the theoretical concept known as a gravity train:

https://en.wikipedia.org/wiki/Gravity_train

The time for the round trip is equal to the time it would take for a satellite to complete one orbit of the Earth at its surface.

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Thanks again for the enlightenment. I love this stuff!

- #14

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Rolling involves energy being stored as rotational KE in addition to translation KE.

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