The discussion revolves around the gravitational effects experienced by individuals standing on the surfaces of hollow spheres of different sizes but equivalent mass. The spheres have varying shell thicknesses, with the smaller sphere having a thicker shell than the larger one. Participants explore the implications of the Spherical Shell Theorem and the inverse-square law of gravitation in this context.
Participants express differing views on the gravitational effects of the hollow spheres, with no consensus reached on whether gravity is greater on the smaller or larger sphere.
Participants do not fully resolve the implications of shell thickness on gravitational force, and assumptions regarding the uniformity of mass distribution are not explicitly stated.
Are you aware of the Spherical Shell Theorem?Watson768 said: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.
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 said: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).
gleem said: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?