## Variation of the Gravitational Field Inside the Earth

The Earth's gravitational field is nowhere uniform. It varies over the surface of the Earth and decreases asoutside the Earth. Inside the Earth the gravitational field is very non uniform. If the Earth had uniform density, the gravitational field strengthat a pointfrom the centre of the Earth would bewhereis the mass inside the sphere of radiusFor an Earth of uniform density, the mass outside this sphere has no effect.

For a sphere of radiusand densityso

This means that the gravitational field inside a sphere of uniform density is directly proportional to the radius. In fact the Earth is not uniform – it is denser at the center, so near the center the acceleration of density increases more rapidly than if the Earth had uniform density, as shown below.