Obtain an expression for the acceleration due to gravity at a point above the surface of the Earth .

Explanation

Let `M_(E)` Be the mass of the Earth,
`R_(E)` Be the radius of the Earth.
Let 'm'be the mass of the body at 'h' above the surface of the Earth.
Acceleration due to gravity on the surface of the Earth (h = 0) , g (0) = `(GM_(E))/(R_(E)^(2)`
Acceleration due to gravity at an altitude 'h'
i.e., `g(h)=(GM_(E))/(R_(E)+h)^(2) " i.e., "(g(h))/(g(0))=(GM_(E))/((R_(E)+h))xx(R_(E)^(2))/(GM_(E))`
i.e., `g(h) = g (0) (R_(E)^(2))/(R_(E)^(2)(1+h/R_(E))^(2))`
For `h ltltR_(E),(1+(h)/(R_(E)))~~1-(2h)/(R_(E))`
Hence `g(h) =g(0)(1+(h)/(R_(E)))^(-2)`