Gravitation Part 1

Given that, radius of Earth =RE
Height above Earth’s surface, h = r
Depth below Earth surface, d = r
We know that, acceleration due to gravity at height (r) and depth (r) is (for r<RE)
gh=g(

RE

RE+h

)2=g(

RE

RE+r

)2 ...(i)
andgd=g(

RE−d

RE

)=g(

RE−r

RE

) ...(ii)
∴

gd

gh

=

g( RE−r RE )

g( RE RE+r )2

[from Eqs. (i) and (ii)] 1+

r

RE

−

r2

RE2

−

r3

RE3