Derive an expression for the variation of acceleration due to gravity
above.

Explanation

Variation of accleration due to gravity above the surface of earth: We know 'g' on planet, `g=(GM)/(R^2)`. But on earth 'g' value changes with height above the ground 'h'.
Variation of 'g' with altitude : For a point 'h' above the earth total mass of earth seems to be concentrated at centre of earth. Now distance form centre of earth is (R+h).
Acceleration due to gravity at 'h'=g(h)=`(GM_E)/((R_E+h)^2)`
For small values of 'h' i.e., `h lt ltR` then `g(h)=g(1-(2h)/(R_E))`
Prof: `g(h)=(GM)/((R+h)^2)=(GM)/(R^2(1+(h)/(R))^2)` or
`g(h)=(GM)/(R^2)(1+(h)/(R))^(-2) " or "g(h)=g(1+(h)/(R))^(-2)` on Binomial expansion `g(h)=g(1-(2h)/(R)+(4h^2)/(R^2)".........."" etc ")`.
By neglecting higher order terms, `g(h)=g(1-(2h)/(R))`.