A satellite revolving around the earth is

Explanation

Consider a satellite of mass m revolving round the Earth at a height h above the surface of the Earth.
Let M be the mass and R be the radius of the Earth. The satellite is moving with velocity `v_(c)` and the radius of the circular orbit is `r = R + h`.
For necessary circular motion of satellite.
Centripetal force = Gravitational force
`:. (mv_(c)^(2))/(r ) = (GMm)/(r^(2))`
`:. v_(c)^(2) = (GM)/(r )`
`:. v_(c) = sqrt((GM)/(R + H))`
This is the expression for critical velocity of a satellite moving in a circular orbit around the Earth.
We know that,
`g_(h) = (GM)/((R + h)^(2))`
Where, `g_(h)` is acceleration due to gravity at height 'h' above the earth surface .
`:. GM = g_(h) (R +h)^(2)`
Substituting iin equation (i), we get
`v_(c ) = sqrt((g_(h)(R + h)^(2))/(R + h))`
`. v_(c) =sqrt(g_(h) (R + h))`