Question

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

Answer 1

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 about:  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.