The ratio of the energy required to raise a satellite upto a height h above the earth to the kinetic energy of the satellite into the orbit is

Step-by-step solution

Energy required to raise a satellite upto a height h , E₁= U= m g h 1+ h R ...(i) E₂= energy required to put in orbit aligned & = 1 2 m v₀^2 & = 1 2 m ( G M r ) as v₀= orbital speed & = 1 2 m ( G M R+h )= 1 2 m ( G M R^2 ) R 1+ h R aligned ...(ii) E₂= m g R 2 (1+ h R ) From Eqs. (i) and (ii), we get E₁ E₂ = 2 h R