HELP Gravitational force and spheres. (prob easy)

[physicsanyone]

So I'm completely lost...here's the problem.

There's a small ball inside an empty sphere. How can I prove this sphere doesn't attract the small ball gravitationally, independently of the position of the ball inside the sphere??

Also, how can I use the result from above to find the gravity force acting on some body of mass (m) inside a planet of radius (R) and mass (M) if this body is at distance r<R from the center of the planet. (The density of the planet is uniform).

Thanks ahead of time.

 

[rl.bhat]

When you want to find the gravitational effect of a spherically distributed mass on a particle of mass m outside it, we divide the whole spherical shell into small parts of equal mass and find the force on external particle. The forces are of different magnitude and direction. So we find the vector sum of all the forces. For that we use intregration. The resultant force which we get shows that a uniformly dense spherical shell attract an external mass point as if all its mass were concentrated at its center. A small mass inside the spherical shell is attracted by the opposite forces due to the small masses on the spherical shell and resultant force is zero. This explains both part of your question.

 

[physicsanyone]

Thanks. I'm still a little confused by...

A small mass inside the spherical shell is attracted by the opposite forces due to the small masses on the spherical shell and resultant force is zero.

Which opposite forces exactly? are these the same forces that attract something outside the sphere? and why doesn't the balls position inside the sphere matter? is there some proof/formula for this?

 

[rl.bhat]

Yes.these are the same forces that attract something outside the sphere. If you draw a straight line through the small mass in side the sperical shell, it meets the shell at two points. Small masses of the shell at these points exert opposite forces ( not equal ) on the inner mass. IF you take the vector sum of all these pair of forces , the sum is zero. When you want find the gravitaional force on a body in side a planet, Calculate mass of the planet of radius r in terms of M amd R