# How do you prove it for a general point inside the earth?

1. May 20, 2007

### Ahmed Abdullah

As we go inside the bulk of the earth our effective weights decrease gradually and eventually turn to a 'nought' as we reach the graviational center of the earth.
It is understandable why there is no weight at the center of the earth. There are equal number of masses in every direction around the center point. So there is no net force toward any direction.

How do you prove it for a general point inside the earth?

2. May 20, 2007

### maverick280857

What is the force per unit mass (the gravitational field strength) inside a sphere of radius R? Outside, it falls off as inverse square, but inside it varies linearly with the radial coordinate...so for r = 0, the field strength is zero too.

3. May 20, 2007

### Ahmed Abdullah

Can you explain why?

4. May 20, 2007

### Ahmed Abdullah

I read somewhere that this is related with Gauss' Theorem. Gauss' Theorem is out of my scope. Can it be explained reasonablely without Gauss' Theorem?

5. May 20, 2007

### neu

The reasonable explanation is what you said. The quantative explanation is Gauss' Theorum

6. May 20, 2007

### Ahmed Abdullah

Can't it be explained in simple way? Gauss' theorem is something I haven't learned before, so I am trying to avoid it. But if it is simple enough then please state the essense of Gauss' theorem in basic terms. I am an O level student.

7. May 20, 2007

### Staff: Mentor

Last edited by a moderator: Apr 22, 2017
8. May 20, 2007

### Ahmed Abdullah

9. May 20, 2007

### DaveC426913

A refination:

(1a) The gravitational field anywhere inside a uniform spherical shell (i.e. hollow) of mass is zero.

(1b) The gravitational field anywhere inside a uniform solid sphere is equivalent to standing on a sphere of that (smaller) radius (i.e If one were 100km from the centre of the Earth, one would experience a gravitational pull as if one were standing at the surface of a sphere only 100km in radius - all mass outside 100km is exactly equivalent to a hollow sphere as in 1a, and thus contributes zero.)

(3) The gravitational field anywhere outside a uniform spherical shell of mass is as if the shell's mass were concentrated at the center.

I think it's actually (1b) that the poster is looking for.

Last edited: May 20, 2007
10. May 20, 2007

### Staff: Mentor

Your 1b follows immediately from Newton's shell theorems (my 1 and 2).