shell theorem
A uniform spherical shell attracts an external particle as if all its mass were at the centre; it exerts zero net force on an internal particle.
Definition
Newton proved two remarkable results in Book I of the Principia. First, a uniform thin spherical shell attracts any external point mass exactly as if the shell's entire mass were concentrated at its centre. Second, the same shell exerts zero net gravitational force on any particle inside it — every inward pull is perfectly cancelled by a pull from the opposite side.
The shell theorem is the reason planets and stars can be treated as point masses when computing their gravitational influence on distant objects. It also explains why gravity inside a uniform hollow sphere is zero, and why the gravitational acceleration inside a solid uniform sphere grows linearly with distance from the centre (only the mass interior to your radius contributes). Newton reportedly delayed publication of the Principia by nearly twenty years because he could not initially prove this result with sufficient rigour.