The gravitational potential energy required to raise a satellite of mass ' m ' to height ' h ' above the earth's surface is ' E₁ '. Let the energy required to put this satellite into the orbit at the same height be ' E₂ '. If M and R are the mass and radius of the earth respectively then E₁: E₂ is

Step-by-step solution

Energy required to raise a satellite upto a height h , E ₁= U = mgh 1+ h R ...(i) Energy required to put satellite into orbit, E ₂= 1 2 mv ₀^2= 1 2 ~m ( GM r ) as v ₀ is orbital speed = 1 2 m ( GM R + h ) Dividing numerator and denominator by R ^2 , aligned E₂ & = 1 2 m ( G M R^2 R+h R 1 R ) & = 1 2 m ( g 1+ h R ) R E₂ & = m g R 2 (1+ h R ) ( g= G M R^2 ) E₁ E₂ & = 2 h R aligned [ From(i) and (ii) ]