4 ms·
>If you are inside or at the inner surface of a spherical shell, then the gravity from all the atoms in the shell is pulling at you in all directions. Now it so
by VladRussian 15y ago
>If you are inside or at the inner surface of a spherical shell, then the gravity from all the atoms in the shell is pulling at you in all directions. Now it so happens that all these little pulls exactly cancel each other out. This can be shown with Gauss' law. [Does anybody know an intuitive proof of this?]
imagine rays through you position that form narrow cones to the closest and the farthest point of the shell - if you're 2 times closer to one side than to another, they'd cut 4 times less (proportional to distance squared) of the shell on the closer side than on the farthest.
The gravitational pull (reverse of the distance squared) per unit mass is 4 times stronger from the pieces on the closer side. Thus 4 times stronger pull per unit mass from 4 times less mass - the same.
(for complete mathematical correctness now make the cones infinitesimally narrow, slice the shell into infinitesimally thin shells and integrate over the 2 angles [pie x pie] to cover the surface of the shell and over the thickness of the shell to cover all the layers - each such infinitesimal would be 0 as described above and integrating 0 would produce 0 in this case. For a general Gauss law it is based on the same distance squared proportionality of the surface element size and reverse distance squared proportionality of the field gradient value (ie. it works only for such fields) )