Gravity - Effective distance of center of earth

In summary, when calculating the force of gravity from a distant body, we assume it is a point mass and use its effective distance. Similarly, on Earth, we use the radius of the Earth as the effective distance. However, this assumption may not be valid when considering the effect of a cubic mile of Earth at different depths. Newton's shell theorem states that a uniform spherical shell of mass produces the same gravitational field as a point mass at the center of the sphere, but the distance between the near and far sides of the Earth's shell can greatly affect this assumption.
  • #1
John Davis
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To calculate the force of gravity from a distant body we assume the body is a point mass and it is therefore relatively easy to determine its effective distance. On the surface of the earth, the same formula is used and we use the radius of the Earth as the effective distance, thus we assume the Earth is a point mass at a distance of about 4000 miles.
But a cubic mile of Earth that is only 1 mile below the surface has a much greater effect than a cubic mile of Earth that is nearly 8000 miles below the surface. So how is it valid to assume the Earth is a point mass when we are so close to it?
 
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  • #2
its because given uniform density you get cancelation of the affect on either side of the line of symmetry.

this is a proof of using Newtons law of gravity as a point mass for the Earth from my mechanics lectures

http://members.iinet.net.au/~housewrk/pointmass.jpg [Broken]
 
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  • #3
John Davis said:
But a cubic mile of Earth that is only 1 mile below the surface has a much greater effect than a cubic mile of Earth that is nearly 8000 miles below the surface. So how is it valid to assume the Earth is a point mass when we are so close to it?
Realize that a uniform spherical shell of mass m produces the same gravitational field as a point mass of mass m located at the center of the sphere. (This is one of Newton's shell theorems.) But that shell of Earth 1 mile below the surface is only one mile away from you at the near side--the other side is about 8000 miles away.
 
  • #4
yeh he's right, sorry i should have mentioned that :P
clever mr mentor :)
 

1. What is the effective distance of the center of the earth?

The effective distance of the center of the earth is approximately 6,371 kilometers. This is the average distance from the surface of the earth to its center.

2. How does the effective distance of the center of the earth affect gravity?

The effective distance of the center of the earth is a key factor in determining the strength of gravity. As objects get closer to the center of the earth, the force of gravity becomes stronger. This is why we feel more gravity at the surface of the earth compared to in outer space.

3. Is the effective distance of the center of the earth constant?

No, the effective distance of the center of the earth is not constant. It varies slightly depending on the location on the earth's surface. This is due to the earth's shape, which is not a perfect sphere.

4. How does the effective distance of the center of the earth affect the weight of an object?

The effective distance of the center of the earth is directly related to an object's weight. As an object gets closer to the center of the earth, its weight increases due to the stronger force of gravity. This is why objects weigh less at higher altitudes.

5. Can the effective distance of the center of the earth be changed?

No, the effective distance of the center of the earth cannot be changed. It is a fundamental characteristic of the earth's structure and cannot be altered. However, the strength of gravity can be affected by other factors such as altitude and the mass of nearby objects.

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