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What would be the effect of gravity on me if I were at the centre of the earth?

 

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Categories: Planet Earth.

Tags: Earth, gravity, Earthsgravity.

 

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Jon-Richfield says:

Mostly to squash you very, very small under the mass above you, but the gravitational field affecting you would be effectively cancelled out by the pull of material all around you. It goes further than that.  If you are partway down, the mass of matter further out from the centre than you are, cancels out, leavingyou under the net influence of only the matter beneath your feet. 

One consequence is that about halfway down you weigh MORE that you do at the surface. This is because the core of the planet is far denser than the crust and you then are closer to its centre of mass.  If you doubt me, do the arithmetic.

Go well,

 

Jon

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Tags: Earth, gravity, Earthsgravity.

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posted on 2010-03-18 15:39:19 | Report abuse


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neilbdm says:

assuming you're in a hollow super-insulated sphere... as soon as you moved from the centre, wouldn't you be splatted against the wall.. ending up as a thin symmetrical skin on the inside.. ? :-)

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posted on 2010-03-20 14:34:24 | Report abuse

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Jon-Richfield says:

No, it is a well-known effect in calculus that inside a hollow symmetrical sphere, the resulting gravitation cancels out to zero. Instead of getting splatted, you would be in free fall. You get similar resultant effects with other fields such as electric fields inside a hollow sphere. If you are a programmer without the necessary calculus, you can have some fun programming a finite-element simulation to demonstrate the effect; just regard the shell as a spherical (NOT circular!) cloud of particles, and use the formula for gravitational attraction as G*m1*m2/r/r. Remember to round off your results before making the comparison to allow for limited precision.

Piece of cake. Having done that, compare your results with the results for other shapes.

 

Good fun!

It also has a very important (or possibly very unimportant, cf  CHAPTER XII of Alice's Adventures in Wonderland: Alice's Evidence) implication: a solid, homogeneous, symmetrical sphere can be regarded as a nested set of hollow spheres, and at any level in the sphere, you only feel the gravity of the spheres below you. So at a depth of say 3000 km from the centre of the earth, you would be subjected to the same downward pull as if you were standing on a bare 3000 km-radius sphere.

And if you were at a distance of 0 km from the centre, your downward pull would be zero.

Got it?

Cheers,

 

Jon

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Tags: Earth, gravity, Earthsgravity, Nested-Spheres, Hollow-Spheres.

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posted on 2010-03-20 17:49:20 | Report abuse


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