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 = (4/3)piGrho*r (proportional to r)
• At centre: g = 0

Potential inside a solid sphere: V(r) = -(GM/(2R^3))(3R^2 - r^2) At centre: V = -(3/2)GM/R = -(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.