A question concerning gravity.

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In summary, at the center of the Earth, the gravitational field is zero due to the balanced attractions in every direction. However, as you move away from the center, the gravitational field and force increase linearly with the radial distance until reaching the maximum at the surface. The gravitational potential energy is not linear with the radius and can be calculated using the universal gravitational constant and the masses of the objects. If one were to be at the center of the Earth, they would not experience any weight, but would still be under immense pressure and compression due to the weight of the Earth above them.
  • #1
paul-martin
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My question is concerning the gravity, is the maximum gravity at the middle of the Earth and are it decreaseing linear as a function of the radius? Second question does anyone know how big the gravity is in the middle of the earth?
 
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  • #2
paul-martin said:
My question is concerning the gravity, is the maximum gravity at the middle of the Earth and are it decreaseing linear as a function of the radius? Second question does anyone know how big the gravity is in the middle of the earth?

If you put a mass at the center of the Earth it will feel ZERO gravitational interaction. When you're at the center of the earth, gravity is balanced in every direction, so there is zero field there. In other words, the same amount of matter is above your head as below your feet, so their attractions cancel.


This is an approximation because we look at the Earth as being a sphere, which is not really the case. However it is a very good approximation.

Secondly, the gravitational potential energy is NOT linear wtr to the radius. This energy is equal to [tex]U =- \frac{GmM}{R}[/tex]

G is the universal gravitational constant (which can be determined experimentally by the torsion balance of cavendish)

m and M are the two masses that interact through gravity

R is the distance between those two masses.

the equipotential surfaces (where the potential is the same) are shells of the sphere.

marlon
 
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  • #3
The gravitational field (and hence force on an object) however, increases linearly with the radial distance from the center of the Earth (where it is zero), till you reach the surface (where it is maximum). Then it falls off as the inverse square.
 
  • #4
That put me on the rigth track, Thank you Marlon!
 
  • #5
Gokul43201 said:
The gravitational field (and hence force on an object) however, increases linearly with the radial distance from the center of the Earth (where it is zero), till you reach the surface (where it is maximum). Then it falls off as the inverse square.

I am not sure i follow you Gokul. If we put one mass at the Earth's center and we move away from it, there is no linear evolution in both E, F and U. So what am i missing here ?

marlon
 
  • #6
marlon said:
If we put one mass at the Earth's center and we move away from it, there is no linear evolution in both E, F and U. So what am i missing here ?
At the Earth's center, the gravitational field is zero. As your distance from the center increases, the mass beneath you (which is all that counts) increases as the distance cubed (assuming the Earth is a sphere of uniform density). So the net effect is that the gravitational field strength within the Earth increases linearly with distance from the center, from zero at the center to g at the surface.
 
  • #7
thanks Doc Al, got it. I see where i misinterpreted some things here

marlon
 
  • #8
If you where at the middle of the Earth you would be compressed and reduced (if you weren't burned). In fact all the weight on Earth would be forcing on you.
 
  • #9
Werg22 said:
If you where at the middle of the Earth you would be compressed and reduced

No, not at all. haven't you read the answer to the original question in this thread ?

marlon
 
  • #10
I think he meant

What would be the pressure on an iron sphere (of neglijable width) whose content would be filled with air (aand a man to breath it),if the sphere had been concentrical with a spherical isothermal (to 300K) uniformy densed Earth.The radius of Earth would be its avg radius from now,and the iron sphere would be 3m in diameter...

Daniel.
 
  • #11
Werg22 said:
If you where at the middle of the Earth you would be compressed and reduced (if you weren't burned). In fact all the weight on Earth would be forcing on you.
This is true. But your weight would still be zero!
 
  • #12
marlon said:
No, not at all. haven't you read the answer to the original question in this thread ?

marlon

You think the forces will just cancel out passing throught you? If two walls collides and someone is in between, do you think the forces of the walls will cancel out and the person will remain safe? You awnser.
 

Related to A question concerning gravity.

1. What is gravity?

Gravity is a fundamental force that exists between two objects with mass. It is responsible for the attraction between objects and is essential for the formation and maintenance of the universe.

2. Who discovered gravity?

Sir Isaac Newton is credited with discovering the concept of gravity in the 17th century. He formulated the law of universal gravitation, which describes the force of gravity between two objects.

3. How does gravity work?

Gravity works by exerting a force between two objects with mass. The force of gravity is directly proportional to the mass of the objects and inversely proportional to the square of the distance between them.

4. What is the difference between gravity and weight?

Gravity and weight are often used interchangeably, but they are not the same. Gravity is a force that exists between two objects, while weight is a measure of the force of gravity on an object. Weight can change depending on the strength of the gravitational force acting on an object, while gravity remains constant.

5. Can gravity be manipulated or controlled?

Currently, there is no known way to manipulate or control gravity. However, scientists are constantly researching and studying the properties of gravity to better understand its nature and potential applications in the future.

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