Initially a satellite of 100 kg is in a circular orbit of radius 1.5 R _ E . This satellite can be moved to a circular orbit of radius 3 R_ E by supplying 10⁶ ~J of energy. The value of is _ _ _ _ . (Take Radius of Earth R_ E =6 10⁶ ~m and g =10 ~m / s ² )

Step-by-step solution

Total energy of satellite in orbit: E = - GMm 2r = - gR_E^2 m 2r E₁ = - gR_E^2 m 2(1.5R_E) = - gR_E m 3 E₂ = - gR_E^2 m 2(3R_E) = - gR_E m 6 Energy supplied = E₂ - E₁ = - gR_E m 6 + gR_E m 3 = gR_E m 6 = 10 6 10^6 100 6 = 10^9 J = 1000 10^6 J = 1000