Once a satelite has entered a stable orbit round earth why does it not need fuel?

For the same reason that the Earth doesn't need any fuel to keep

orbiting the sun, and the moon doesn't need any fuel to keep

orbiting the Earth ...

Here's something to think а bout: A satellite in a perfectly circular

orbit always stays at the same distance from the Earth, so it never

moves in the direction of the gravitational force. The work that

gravity does on it is (force) x (distance) = zero, so the satellite's

energy never changes.