Mention the effect of altitude and depth on the value of acceleration due to gravity. Give the corresponding mathematical relation.
g=GMR2
or, GM=gR2 −(1)
Now for R→R+h [h→ height]
gh=GM(R+h)2
or GM=(R+h)2gh −(2)
From (1) and (2)
(R+h)2gh=gR2
or, gh=g(1+2hR)
Similarly for R=R−d [d→ depth]
gd=GM(R−d)2
or GM=(R−d)2gd −(3)
From (1) and (3)
gR2=(R−d)2gd
or gd=g(1−dR)