# Gravitational field

1. Oct 27, 2009

### songoku

1. The problem statement, all variables and given/known data

I found this statement from my book :
For points outside a uniform sphere of mass M, the gravitational fields is the same as that of a point mass M at the center of the sphere.
My question : what is the meaning of it?

2. Relevant equations
$$g=G\frac{M}{r^2}$$

3. The attempt at a solution
I don't think it will be the same.
At the center of the sphere, r = 0 and g will be infinite ??
And for point outside a uniform sphere, for a certain value of r, the point will have certain value of g, so how can they be the same?

Thanks

2. Oct 27, 2009

### Staff: Mentor

They are talking about outside a uniform sphere of mass M. What's that got to do with r = 0? (At r=0, M=0 also. So the division will be undefined.)
Why don't you figure it out and see? What's the value of g immediately above the surface of that uniform sphere of mass M and radius R. What's the g value at a distance R from a point mass M?

3. Oct 31, 2009

### songoku

Hi Doc Al
I interpret the statement is about comparison between gravitational field of point outside the sphere and the point at center of the sphere, that's why I tried to find g at r = 0. Maybe I am wrong but I keep thinking like that based on the question I read. Am I wong?

The value of immediately above the surface of that uniform sphere of mass M and radius R :

$$g=G\frac{M}{R^2}$$

The g value at a distance R from a point mass M is the same as above.

But outside the sphere can be the point located 2R from the mass M, so the value of g will be different.

Thanks

4. Oct 31, 2009

### Gear300

Usually in physics we deal with point particles. What they're saying is that if you're taking into account a gravitational field from a body of mass, such as Earth's, you're taking into account a bunch of point masses...so the question is what is Earth's gravitational field? For uniform spheres of mass, it turns out that it is the same as a point particle (except in cases when you're inside the sphere). The Earth isn't a uniform sphere, but this perspective in general does help.

Last edited: Oct 31, 2009
5. Oct 31, 2009

### Staff: Mentor

Yes, I'd say you are interpreting it incorrectly. They are comparing the field at a distance r from the center of a uniform sphere of mass M (as long as r > radius of the sphere) with the field at a distance r from a point mass M. The field is the same for both. At no point are you comparing anything at r = 0.

Exactly.

6. Nov 1, 2009

### songoku

Hi Doc Al and Gear300

Ahh, I see what you mean, Doc Al. And now I can also see what the statement really means.

Thanks a lot !!