# Gravity and the earth's geometry

• sutupidmath
In summary, the conversation discusses the concept of a flat Earth and its potential effects on gravity. Some suggest that the Earth can be approximated as flat for practical purposes, while others argue that there may be differences in the gravitational pull depending on the shape of the Earth. Ultimately, it is concluded that a flat Earth with a thicker surface may have a higher gravitational pull, but it is not a feasible concept due to the Earth's limited land space.
sutupidmath
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?

sutupidmath said:
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?

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.

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.

ZapperZ said:
(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

## 1. How does gravity affect the shape of the Earth?

The Earth is not a perfect sphere, and gravity plays a significant role in shaping its form. Gravity pulls matter towards the center of mass, creating a force that compresses the Earth's shape into an oblate spheroid. This means that the Earth is slightly flattened at the poles and bulging at the equator.

## 2. Why is gravity stronger at the Earth's surface than in space?

The strength of gravity is inversely proportional to the square of the distance between two objects. As we move away from the Earth's surface, the distance between us and the center of the Earth increases, resulting in a weaker gravitational force. In space, the distance between objects is much greater, and therefore, the force of gravity is significantly weaker.

## 3. How does the Earth's geometry affect the gravitational pull?

The Earth's geometry plays a crucial role in determining the strength of the gravitational pull. The Earth's mass and its distribution are directly related to the gravitational pull it exerts. The closer an object is to the center of the Earth, the stronger the gravitational pull will be.

## 4. Can gravity affect the Earth's rotation?

Yes, gravity can affect the Earth's rotation. As the Earth rotates, the centrifugal force generated by its rotation acts in the opposite direction of gravity, pushing the Earth's equator outwards. This results in a slight bulging at the equator, which affects the Earth's rotation and slows it down over time.

## 5. How does the Earth's gravity affect other objects in space?

All objects with mass have gravitational pull, and the Earth is no exception. The Earth's gravity affects other objects in space by pulling them towards its center of mass. This is why the Moon orbits around the Earth and why objects thrown into space eventually fall back to Earth. The strength of the Earth's gravity also determines the trajectory and speed of objects in space.

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