Derive the formula for critical velcoity `(V_(c))`.

Explanation

If a satellite of mass 'm' is revolving around the earth in an orbit of height 'h' with speed `V_(c)` then centripetal force ` F = (mv_(c)^(2))/(r)` will act on it .
Here, 'r' is the orbital radius of the satellite from the centre of the earth .
This centripetal force is provided by the gravitational force of the earth.
Therefore centripetal force = gravitational force between the Earth and the satellite .
`(mv_(c)^(2))//(R+h) = (GMm)/((R + h)^(2))`
`v_(c)^(2) = (GM)/(R+h)`
Taking square root on both sides, ltrgt ` v_(c) = sqrt((GM)/(R+h))`