# How would shell theorem act in a hollow sphere?

1. Apr 30, 2013

### Joseph King

What I understand is this: Shell theorem states that the force of gravity is focused at the center of an object. But, say that there is a large planet with a gravitational force equal to that of earth's. It is perfectly round… and hollow. Since it is hollow, how large would it be to have earth's gravity? Stranger yet, what would the effects be inside and outside of the sphere?

2. Apr 30, 2013

### Staff: Mentor

To have earth gravity what would be its mass?

What is the gravity inside any shell of a given mass?

How large the planet is depends on the size of the shell and the density of mass composing it, right?

3. Apr 30, 2013

### Joseph King

Exactly. And what effects would it have on other objects inside the sphere.

4. Apr 30, 2013

### Staff: Mentor

There are two shell theorems that describe the field from a spherically symmetry shell of mass. One describes the field outside the shell, the other describes the field inside the shell. Are you familiar with both of those?

5. Apr 30, 2013

### Joseph King

I only know of the one focused inward.

6. Apr 30, 2013

### Staff: Mentor

And what does that theorem say? (In post #1 you mentioned the theorem that deals with the field outside the shell.)

7. Apr 30, 2013

### Joseph King

Well, basically, it states that if you have an object (ie earth) then the force of gravity is focused at the center. So, if you are underground, the mass above you does not have any gravitational effect on you.

8. Apr 30, 2013

### Staff: Mentor

Here's how I would put the two theorems:

(1) Outside the shell, the field is that of a point mass equal to the mass of the shell and located at the center of the shell.

(2) Inside the shell, the field is everywhere zero.

9. Apr 30, 2013

### Joseph King

That makes sense, thanks!