Why Is There No Gravitational Force Inside a Solid Sphere?

[Fallen Seraph]

I'm trying to understand why there is no gravitational force on a mass inside a solid sphere. It's clear why the only force could be toward the centre of gravity, but my problem is this:

Consider a point of mass halfway between the centre of the sphere and the outside (as in the diagram). It seems to me that the force due to the two lengths of mass of length r/2 will cancel each other out, leaving a net force due to the other radius.. any explanation?

Thanks.

 

[ObsessiveMathsFreak]

I'm trying to understand why there is no gravitational force on a mass inside a solid sphere.

Looks like a misunderstanding here. There's no gravitational force inside a hollow sphere. That is, a sphere which is just an empty shell, and no mass inside.

For a solid sphere, i.e. a solid ball, there is in fact an overall gravitational force on the inside. If memory serves correctly, the overall force pulls towards the center and is directly proportional to the distance from the center. In other words the force grows linearly as you move towards the surface.

 

[Fallen Seraph]

but can't you consider the solid sphere to just be a collection of hollow spheres? So if there's no force on the hollow ones, there should be no force on a solid one?

 

[neutrino]

but can't you consider the solid sphere to just be a collection of hollow spheres? So if there's no force on the hollow ones, there should be no force on a solid one?

There is NO force INSIDE a hollow sphere but it will exert once you are outside.

Okay, let's say that you're between two "hollow spheres" withing the original sphere. There's no effect due to the one enclosing you and the spheres within, but the ones that are inside will have an effect, right? This is a very crude example, but I hope you get the point. And as ObsessiveMathsFreak noted, the force is linear.

 

[ranger]

I'm trying to understand why there is no gravitational force on a mass inside a solid sphere.

How can there be a mass inside a sphere that is completely solid? That sounds kind of confusing to me. In any case, there is a discussion about the hollow sphere from a few days back floating around somewhere. And here is an extra resource:
https://www.physicsforums.com/showthread.php?t=121120

 

[Fallen Seraph]

Ah. There we go. Thanks a lot for that help.

 

[misnoma]

Looks like a misunderstanding here. There's no gravitational force inside a hollow sphere. That is, a sphere which is just an empty shell, and no mass inside.

For a solid sphere, i.e. a solid ball, there is in fact an overall gravitational force on the inside. If memory serves correctly, the overall force pulls towards the center and is directly proportional to the distance from the center. In other words the force grows linearly as you move towards the surface.

F if proportional to 1/d^2

 

[misnoma]

There is NO force INSIDE a hollow sphere but it will exert once you are outside.

Okay, let's say that you're between two "hollow spheres" withing the original sphere. There's no effect due to the one enclosing you and the spheres within, but the ones that are inside will have an effect, right? This is a very crude example, but I hope you get the point. And as ObsessiveMathsFreak noted, the force is linear.

look up gravitational potential well and it should become clear.

 

[Hootenanny]

F if proportional to 1/d^2

Not inside the earth, or a solid sphere. Inside the Earth $F\propto r$ as ObsessiveMathsFreak says.

P.S. It's nice to see another Brit posting on the Forums

 

[misnoma]

Not inside the earth, or a solid sphere. Inside the Earth $F\propto r$ as ObsessiveMathsFreak says.

P.S. It's nice to see another Brit posting on the Forums

Yes- inside - but not outside. was there some mis understanding here?

 

[misnoma]

Yes- inside - but not outside. was there some mis understanding here?

Thanks fellow brit

 

[misnoma]

Not inside the earth, or a solid sphere. Inside the Earth $F\propto r$ as ObsessiveMathsFreak says.

P.S. It's nice to see another Brit posting on the Forums

"In other words the force grows linearly as you move towards the surface."

I picked up on this and made the assumption that it was moving towards the surface from the outside. (incorrect assumption). which is why I mentioned 1/d^2

 

[Hootenanny]

"In other words the force grows linearly as you move towards the surface."

I picked up on this and made the assumption that it was moving towards the surface from the outside. (incorrect assumption). which is why I mentioned 1/d^2

No problem, easily done. Have a good new year.