Explain the variation of g with altitude from the Earth's surface.

1.	Explain the variation of g with altitude from the Earth's surface.
Answer» Solution :Consider an object of MASS m at a height h from the surface of the EARTH. Acceleration experienced by the object due to Earth is `g.(GM)/((R_(E)+h)^(2)) , g. = (GM)/(R_(e)^(2) (1+h/(R_(e)))^(2))` `g. = (GM)/(R_(e)^(2)) (1+h/(R_(e)))^(-2)` If `h lt lt R_(e)`: We can use Binomial expension. Taking the terms up to first order `(1+x)^(n)=1+nx ` `[1+h/(R_(e))]^(-2) = [ 1-2 (h/(R_(e)))] ` Replacing this value and we get `g. = (GM)/(R_(e)^(2)) [ 1- (2h)/(R_(e))] ` ` g . = g (1-2 h/(R_(e)))` We find that `g. < g`. This means that as altitude h increase the acceleration due to GRAVITY g decreases.

Discussion