Variation of g with depth

Intermediate

Inside the Earth, g falls linearly toward the centre.

Key relationg' = g(1−d/R)

Inside a uniform Earth only the mass inside radius r attracts, so g' = g(1 − d/R), falling linearly to zero at the centre.

Worked example

At half the radius g' = 4.9 m/s².

Common mistake

Real Earth is denser at the core, so g first slightly increases.

In more detail

Inside a uniform Earth, g decreases linearly with depth, becoming zero at the centre. Only the mass below the point contributes to the pull there.

Mines are assessed for gravity changes as depth increases.
Gravimeters can detect underground voids by small changes in g.
Geophysicists use the variation of g with depth to infer the density structure of the Earth's interior.

Is g zero at the centre of the Earth?

Yes, in a uniform-density model, the mass pulling outward cancels the mass pulling inward.

Why does depth reduce g?

Because the mass outside the point at depth contributes nothing to the net pull.

Why does g fall inside the Earth?

Only the mass below you pulls on you, and that mass shrinks as you go deeper, so the net pull weakens.