How does value of acceleration due to gravity vary with altitude

Explanation

The acceleration due to gravity on the surface of earth is given by `g= (GM)/(R^(2))` ..(i)
Here M= mass of earth, R= radius of earth.
Consider a body of mass m, at a height h above the surface of earth. The acceleration due to gravity at height h is given by : `g_(h)= (GM)/((R+h)^(2))` ...(ii)
Dividing (ii) by (i), we get `(g_(h))/(g)= (R^(2))/((R+h)^(2))= (R^(2))/(R^(2) (1+ (h)/(R ))^(2))`
`g_(h)= g (1 + (h)/(R ))^(-2)`
Using binomial theorem and neglecting higher terms `(because h lt lt R)`
We get `(1+ (h)/(R ))^(2) ~~ 1- (2h)/(R )`
Hence, `g_(h)= g (1- (2h)/(R ))`
This shows that acceleration due to gravity decreases with altitude