At a particular location, the acceleration due to gravity has the same value at a depth d below the surface as it does at a height h above the surface. Treat both d and h as small compared with the Earth’s radius R.
(i) Starting from the standard approximate expressions for gd and gh, derive a relation connecting h and d.
(ii) If the value of g at a depth of 16km equals that at some altitude h, calculate this altitude.
(iii) Discuss briefly why the altitude required is not equal in magnitude to the depth, even though the values of g are the same.