Gravity on the surface of hollow spheres

[Watson768]

TL;DR

Gravity on hollow spheres of different sizes, same mass but different thicknesses of shells.

Can anyone tell me if gravity is greatest for someone standing on the surface of a hollow small sphere or a hollow larger sphere when the spheres are of equivalent mass, and the thickness of the shell is greater on the smaller sphere than the larger sphere (in order to maintain equivalent mass). Thank you.

 

[jbriggs444]

Summary: Gravity on hollow spheres of different sizes, same mass but different thicknesses of shells.

Can anyone tell me if gravity is greatest for someone standing on the surface of a hollow small sphere or a hollow larger sphere when the spheres are of equivalent mass, and the thickness of the shell is greater on the smaller sphere than the larger sphere (in order to maintain equivalent mass). Thank you.

Are you aware of the Spherical Shell Theorem?

 

[gleem]

Consider a solid sphere. The force at a distance from the center of the sphere is GmM/r² where G is a constant m is the mass being acted on , M the mass of the sphere and r the distance from the center of the sphere to m.

For a hollow sphere you can show using above that the force at a distance r is GmM/r² also for and thickness of the shell. So as long as the mass M is the same then you can conclude what?

 

[Nugatory]

Can anyone tell me if gravity is greatest for someone standing on the surface of a hollow small sphere or a hollow larger sphere when the spheres are of equivalent mass, and the thickness of the shell is greater on the smaller sphere than the larger sphere (in order to maintain equivalent mass).

As long as it is a sphere and you are on or above the surface, gravity behaves as if all the mass is concentrated at the center. If the masses are the same, the only thing that matters is the distance from the center; the greater the distance, the less the force by the inverse-square law.

 

[Watson768]

Consider a solid sphere. The force at a distance from the center of the sphere is GmM/r² where G is a constant m is the mass being acted on , M the mass of the sphere and r the distance from the center of the sphere to m.

For a hollow sphere you can show using above that the force at a distance r is GmM/r² also for and thickness of the shell. So as long as the mass M is the same then you can conclude what?

Force would be less for the larger sphere, assuming the mass of both spheres are equal and despite different thicknesses of the shells.