<P> g at depth d is given by g' = g (1 - d / R) where g is acceleration due to gravity on surface of the earth, d is depth and R is radius of Earth . If the density decreased linearly with increasing radius from a density ρ at the center to ρ at the surface, then ρ (r) = ρ − (ρ − ρ) r / r, and the dependence would be </P> <Dl> <Dd> g (r) = 4 π 3 G ρ 0 r − 4 π 3 G (ρ 0 − ρ 1) r 2 r e . (\ displaystyle g (r) = (\ frac (4 \ pi) (3)) G \ rho _ (0) r - (\ frac (4 \ pi) (3)) G \ left (\ rho _ (0) - \ rho _ (1) \ right) (\ frac (r ^ (2)) (r_ (\ mathrm (e)))).) </Dd> </Dl> <Dd> g (r) = 4 π 3 G ρ 0 r − 4 π 3 G (ρ 0 − ρ 1) r 2 r e . (\ displaystyle g (r) = (\ frac (4 \ pi) (3)) G \ rho _ (0) r - (\ frac (4 \ pi) (3)) G \ left (\ rho _ (0) - \ rho _ (1) \ right) (\ frac (r ^ (2)) (r_ (\ mathrm (e)))).) </Dd> <P> The actual depth dependence of density and gravity, inferred from seismic travel times (see Adams--Williamson equation), is shown in the graphs below . </P>

What is the value of g in centre of earth