[Elmorshedy]

I'm really confused I have learned at school that the satellite remains in it's orbit because it's in an equilibrium state due to Centripetal force and the gravitational force but how?
Doesn't the centripetal force and the gravitational force both of them act toward the earth? And what is the role of the centrifugal force?

[Aurora2000]

It can be interpreted as "gravitation force acting as centripetal force".

Remember that a satellite in orbit around Earth must have variations for its velocity vector (in this case its direction must vary), and to change any element of velocity vector you need acceleration, thus force.

If you have no force acting on the satellite, it would go away from the Earth (as it has non zero velocity relative to Earth, it would go in the direction of velocity), thus you need a force that "pulls" the satellite, and this is the centripetal force which makes satellite's velocity change direction.

If the satellite has velocity , mass and distance from Earth,
then a centripetal force is required to "pull" the satellite. The only force acting between Earth and satellite is gravitational attraction, thus

gravitational force= centripetal force=

is required.

[ebaines]

Good explanation by Aurora, though I would add one clarification. The original question included: "Doesn't the centripetal force and the gravitational force both of them act toward the the earth?"

The answer to this is yes - the satellite does indeed accelerate towards the earth. You know from that a force toward the earth is required for the satellite to accelerate toward the earth, and that force of course is gravity, acting toward the earth. In essence the satellite is continually falling toward the earth as it moves in orbit, and the rate at which it falls exactly equals the rate of acceleration needed to travel in a circle. Astronauts in the space station are in continual free fall - the so-called "weightlessness" they experience is exactly the same as what you would experience if you were in an elevator car whose hoist cable snapped and put you in free fall - but without ever hitting bottom! Hope this helps.