Explain the variation of 'g' with altitude.

Explanation

Let us 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 `hltltR_(e)`
Using Binomial expansion and taking the terms upto first order.
`g'=(GM)/(R_(e)^(2))(1-2(h)/(R_e))`
`g'=g(1-2(h)/(R_e))`
We find that `g'ltg`. This means that as altitude h increases the acceleration due to gravity g decreases.