What is the relation between height h and depth d for the same change in g?

Explanation

Acceleration due to gravity at a height h above the Earth's surface,
`g_(h)=g(1-(2h)/(R))`
Acceleration due to gravity at a depth d below the Earth's surface.
`g_(d)=g(1-(d)/(R))`
For the same change in g, we have
`g_(h)=g_(d)`
`therefore1-(2h)/(R)=1-(d)/(R)"(or)"(2h)/(R)=(d)/(R)`
(or) d = 2h
Hence the acceleration due to gravity at a height h above the Earth's surface will be same as that of depth d = 2h, below the Earth's surface. But this fact holds only when `hltltR`.