Explain the variation of 'g' with altitude.

Explanation

Variation of g with altitude:
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))`
`R_(E) to` Radius of Earth
`g' = (GM)/(R_(E)^(2)(1 + h/(R_E))^(2)) = (GM)/(R_E^2) (1 + h/(R_E))^(-2)`
If `h < < R_(E)`
We can use Binomial expansion. Taking the terms upto first order
`g' = (GM)/(R_E^2) (1-2h/(R_E)) = g(1-2 h/(R_E))`
We find tat `g' < g`. This means that as altitude h increases, the acceleration due to gravity g decreases.
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