HELP Gravitational force and spheres. (prob easy)

In summary, the conversation discusses how to prove that a sphere does not attract a small ball inside it gravitationally, regardless of the position of the ball. It also explores how this can be used to find the gravitational force acting on a body inside a planet with uniform density. The conclusion is that the resulting force is zero, as the opposite forces exerted by small masses on the spherical shell cancel each other out. This applies both inside and outside the sphere, and can be calculated using integration.
  • #1
physicsanyone
2
0
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.
 
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  • #2
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.
 
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  • #3
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?
 
  • #4
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
 

What is the relationship between gravitational force and spheres?

The relationship between gravitational force and spheres is that the force of gravity is directly proportional to the mass of the spheres and inversely proportional to the square of the distance between them.

How does the mass of a sphere affect the gravitational force?

The mass of a sphere directly affects the gravitational force, meaning that as the mass increases, the force of gravity also increases. This is because the greater the mass, the greater the pull due to gravity.

How does the distance between spheres affect the gravitational force?

The distance between spheres has an inverse relationship with the gravitational force, meaning that as the distance increases, the force of gravity decreases. This is because the farther the distance, the weaker the pull due to gravity.

What is the formula for calculating gravitational force between two spheres?

The formula for calculating gravitational force between two spheres is F = (G * m1 * m2) / r^2, where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two spheres, and r is the distance between them.

How does the gravitational force between spheres compare to other forces?

The gravitational force between spheres is a relatively weak force compared to other fundamental forces, such as the electromagnetic force. However, it is still a significant force that governs the motion of planets, stars, and other celestial bodies in the universe.

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