Gravity and the earth's geometry

Hi all,
I was just wondering if the earth had a flat shape, then what could we say about the gravity? In other words how would the shape of the earth affect its gravity? Would the gravity increase, decrease, be constant, or are there other factors that we should take into consideration?

thnx in advance!
 

ZapperZ

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Hi all,
I was just wondering if the earth had a flat shape, then what could we say about the gravity? In other words how would the shape of the earth affect its gravity? Would the gravity increase, decrease, be constant, or are there other factors that we should take into consideration?

thnx in advance!
Do a Gauss's Law equivalent to find the gravitational field the same way one would find the electric field of an infinite plane of charge, and you get the answer.

Besides, for us on earth, the earth is large enough that we can accurately approximate it as being flat (do you see the earth curving from where you're standing on the ground?). That's why you can use "g" as being a constant in most cases! So you are already using a "flat earth" result.

Zz.
 
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A charged metal plate of infinite dimensions (and infinitesimal width) creates an electrical field that does not depend on the distance from it. As I recall this is the case for finite plates for short distances. Since gravity and the electric force dwindle similarly with distance I'd conclude the same for a flat earth. So, if you take a round earth and flatten it out to a thin enough layer, you would get a constant gravitational pull with distance.

As for the strength of the pull compared to that of a sphere (as measured by a man on it's surface), my guess was that it would be reduced. But I looked at the equations and am not so sure now. Since one would stand on the surface of the flat earth, it would be possible to let the layer of the earth be thicker to allow an undifferential pull for a few kilometers (say 5 km for as high as a scientist would climb to measure gravity). With a thicker surface, the "facial" mass density of the flat earth would increase. When the whole mass would fill a surface of R^2 (R is the radius of our spherical earth), the gravitational pull of the flat earth would be higher than ours. And 5 kilometers would seam near enough to allow a somewhat constant field. However, there won't be enough land to suffice the real estate in need, so maybe my guess would still stand for a flat earth of sufficient space. But since this place cannot ever exist due to human tendency for gluttony, I would conclude an increase in the gravitational pull of any reasonable flat earth.
 
(do you see the earth curving from where you're standing on the ground?)
Just to nitpick and be difficult: Yes you do. You can see the top of a ship sailing in from the ocean before you see the bottom parts. This is due to the curvature of the earth.

k
 

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