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why does a satellite need no fuel to go around the earth

A satellite revolving around a planet is actually on a free-fall. That means it is freely falling under gravity. Now, the centrifugal force acting on the satellite radially outwards exactly balances the centripetal force radially inwards (provided by gravitational force). So, the satellite is in equilibrium in its orbit and hence it needs no fuel to keep moving.

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A satellite rotates around the earth by using earth's gravitational force as centripetal force. Also as there is no air in space, it does not have to work against air resistance. Hence it doesn't lose any energy while rotating. So it does not require fuel to rotate around the earth.

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every object tries to maintain its velocity. but on earth there is friction force and air resistance so object slows down.

but in space there is no atmosphere and no friction so the satelite maintains its velocity. while its direction (orbiting the earth) is due to centripetal force due to gravity.

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