For small displacements from Earth’s surface, the change in the acceleration due to gravity depends on whether the displacement is upward (altitude) or downward (depth).
Answer the following questions about this statement.
(i) State the approximate fractional change in g when a body is taken to a height h above Earth’s surface, where h≪R (Earth’s radius).
(ii) State the approximate fractional change in g when the body is taken to a depth d below Earth’s surface, where d≪R.
(iii) Using your answers to (i) and (ii), explain why a given small altitude produces roughly twice the percentage decrease in weight as the same numerical value of depth.
(iv) Comment on what this result implies for designing experiments that compare variations of weight above and below the surface.