What is the work done by the force of gravity on a satellite moving round the earth?

When a satellite revolves around the earth in a circular orbit, the earth applies a gravitational force on the satellite in the direction towards the center of the earth but the satellite moves in the tangential direction to the orbit. Therefore, the force of gravity and displacement are perpendicular to each other. Since W=Fscosθ, if θ=90°, then W=0. Hence, the work done by the force of gravity on the satellite is zero. W=0