External gravity field independent of mass distribution?

[JP O'Donnell]

Hi.

Gauss' law applied to gravity states that the gravitational flux through a given surface is proportional to the total enclosed mass.

Considering a gaussian surface which encloses a continuous mass distribution, an arbitrary re-distribution of the total mass must yield the same value for the gravitational flux over the same surface. And since the surface integration element has not changed this means that gravity has not changed over the surface.

This is just the nonuniqueness of causative source distributions in potential field theory.

Are there any errors in the above argument?

Basically all I want to confirm is that a redistribution of mass within a given equipotential surface does not alter gravity on that surface.

Thanks.

 

[Doc Al]

Considering a gaussian surface which encloses a continuous mass distribution, an arbitrary re-distribution of the total mass must yield the same value for the gravitational flux over the same surface.

The total flux through the closed surface doesn't change.

And since the surface integration element has not changed this means that gravity has not changed over the surface.

But the flux/field through any particular section of the surface can certainly change.

 

[JP O'Donnell]

thanks. Appreciate your help.