Newton's Shell Theorem:

1. A uniform shell attracts an external particle as if all mass were at the centre.
2. A uniform shell exerts zero net force on any internal particle.

Inside a Solid Sphere (uniform density):

• Only the enclosed mass (radius r from centre) contributes
• g(r) = (GM/$R^3$)r = $\frac{4}{3}$piGrho*r (proportional to r)
• At centre: g = 0

Potential inside a solid sphere: V(r) = -($\frac{GM}{2R^3}$)(3$R^2$ - $r^2$) At centre: V = -$\frac{3}{2}$GM/R = -$\frac{3}{2}$gR (more negative than surface) At surface: V = -GM/R = -gR

The potential is minimum (most negative) at the centre, even though the field is zero there.