Gravity at the centre of the earth

[caracasjim]

Is all the matter at the centre of the earth weightless?????

[Loosehead]

I suppose the bit in the actual centre is pulled in all directions at once so effectively yes. Imagine you could hollow out a small sphere in the exact centre, anything in that sphere would effectively be weightless.

[caracasjim]

So a tonne of coal dug up from a mile below the ground weighs more than a tonne when its winched to the surface.And the lower you go the less you weigh???. This must also apply to the higher you go as well. Hummmmm!

[Loosehead]

if you take a ton of coal from the surface down 1 mile and weighed down there, there would be a miniscule difference 1 mile of earth pulling up and the rest pulling down but it is neglegible. There is a much bigger variant between weighing you coal at the North Pole and weighing it at the equator.

[caracasjim]

Great tip for the wife when she complains about the extra weight. Go to the North Pole or climb Everest

[Loosehead]

It's lighter at the equator!

[steveb]

this exact question was asked in my a level physics class the other day, the answer loosehead gave was pretty much exactly what we were told

[Loosehead]

Yeah I was the teacher!

[steveb]

shoot, the above question was our homework, sorry sir.

[anthomson]

So would time up significantly speed up at the centre of the earth. (Since space time is distorted and slowed by gravity - relatively speaking)

[mibn2cweus]

I have speculated that since the earth is spinning, the angular momentum at the equator would counter the effect of gravity some but that this would effect the shape of the earth so as to equalize this difference.  Perhaps electromagnetic attraction does not allow the shape of the earth to completely compensate?  Why do things weight more at the poles?  How does this difference compare to the effects of tidal pull of the sun and moon?

[Peter Pedant]

yeah the a level students have to work out the field inside an arc of a  circle . And when the whole circle is considered, the atraction from the nearer arc is exactly counter balanced by the further greater arc.

obviously if it is true for a circle by doing a spinny sort of intergration, it will be true for a shell.

this is true for any inverse square law

and so der daaah... the electric field inside a hollow ball is zero and so is the magnetic field, as well as gravity.

a sort of good mornings work for an a level student

[stevie21]

Well, the earth would still be subject to the gravitational pull of the sun etc. so would anything really be weightless at the centre of the earth?
Wouldn't there be a tiny tiny difference in one direction?