A satellite is revolving around the earth in a circular orbit with kinetic energy of 1.69 10¹⁰ ~J . The additional kinetic energy required for just escaping into the outer space is

Step-by-step solution

For a satellite in a circular orbit of radius r around the earth of mass M , the gravitational potential energy is U = - GMm r and the kinetic energy is K = GMm 2r . The total mechanical energy of the satellite in the orbit is E = K + U = GMm 2r - GMm r = - GMm 2r = -K . Given K = 1.69 10¹⁰ J , the total energy is E = -1.69 10¹⁰ J . To escape into outer space, the final total energy of the satellite must be at least 0 . The required additional energy E is given by E_ final - E_ initial = 0 - E = -(-K) = K . Therefo