The ratio of energy required to raise a satellite to a height ' h ' above the earth's surface to that required to put it into the orbit at the same height is ( R = radius of earth)

Step-by-step solution

The formula for the energy required to raise a satellite to height h is E ₁= U = mgh 1+ h R = mghR R + h The formula for the energy required to set the satellite in orbit is E ₂= - GMm 2( R + h ) + GMm R = mgR [1- 1 2 (1+ h R ) ] ( GM = gR ^2 ) aligned E₂ & = m g R ( 2 h R +1 ) 2 (1+ h R ) E₁ E₂ & = m g h 1+ h R 2 (1+ h R ) m g R & = 2 h R ( h R 1+ 2 h R 0 ) aligned