Consider a vertical mine shaft drilled straight down from the Earth’s surface.
(a) Derive an expression for the acceleration due to gravity at a depth d inside the shaft in terms of the Earth’s radius R and the surface value g.
(b) At what depth will the acceleration due to gravity be reduced to 60% of its surface value?
(c) Sketch qualitatively on the same set of axes the variation of g with (i) altitude up to 2R above the surface and (ii) depth up to R below the surface. Indicate the key features of both curves.
(d) From your sketch, discuss briefly whether the decrease of g with altitude is symmetrical with its decrease with depth and state the physical reason for any asymmetry.