Assume that a satellite(mass m) is orbiting the Earth(mass M) at radius R and speed V (the orbit is circular). The satellite is in a position such that the force of gravity exerted on it by the planet is not enough to keep it in orbit. Therefore, the satellite has an engine, which always points at the centre of Earth. The rocket, when ignited, exerts an additional force on the satellite, enough to keep it in orbit with the help of Earth's gravity. Now the work done by the rocket is zero because it always points perpendicular to the trajectory and the total energy of the system stays constant. However, the rocket eventually runs out of fuel, meaning that some energy has been put in the rocket-satellite system. That energy goes into keeping the satellite in orbit, but is there a way to calculate it in terms of V,R,M and m?