Question

Derive an expression for orbital velocity of satellite of earth at height h​

Answer 1

Explanation:

Given :

• The expression for orbital velocity is √g( R+h) = √gr.

Solution :

The height from surface of the earth = h

Thus,

• r = R + h

Centripetal force for the movement of satellite - mv²/r

Orbital force between earth and satellite = GMm/r²

Therefore,

v² = Gm/r

v² = Gm/ R + h

v =  √Gm/r

v = √Gm/ R + h

g = - GM/ (R+h)²

gr = g (R+h)

Therefore orbital velocity = √g( R+h) = √gr