Is Maximum Gravity at Earth's Core and Does it Decrease Linearly with Radius?

[paul-martin]

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?

 

[marlon]

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 $$U =- \frac{GmM}{R}$$

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

 

[Gokul43201]

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.

 

[paul-martin]

That put me on the rigth track, Thank you Marlon!

 

[marlon]

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

 

[Doc Al]

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.

 

[marlon]

thanks Doc Al, got it. I see where i misinterpreted some things here

marlon

 

[Werg22]

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.

 

[marlon]

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

 

[dextercioby]

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.

 

[Doc Al]

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!

 

[Werg22]

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 through 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.