A satellite of mass m is going around the earth in a circular orbital at a height `(R)/(2)` from the surface of the earth. The satellite has lived its life and a rocket, on board, is fired to ake it leave the gravity of the earth. The rocket remains active for a very small interval of time and imparts an impulse in the direction of motion of the satellite. Neglect any hange in mass due to firing of the rocket. Find the minimum impulse imparted by the rocket to the satellite. Find the minimum work done by the rocket engine. Mass of the earth = M, Radius of the earth = R

Answer

(a) `(sqrt(2)-1) m sqrt((2GM)/(3R))`
(b) `(GMm)/(3R)`