Satelites!

[Deceitful Wings]

Why aren't satellites falling towards earth?
how does the centripetal force cancel out the force of gravitation? aren't the centripetal force and gravitational forces acting in the same direction?

[Planck's constant]

Why aren't satellites falling towards earth?
how does the centripetal force cancel out the force of gravitation? aren't the centripetal force and gravitational forces acting in the same direction?

No mate, the centripetal force and the gravitational force are the one and the same thing in this case.
In fact most of the important results on this topic are obtained from the equation :

Gravitational Force = Centripetal Force

As for why the satellite does not fall 'down', it is because the centripetal force is used up to sustain the satellite's uniform circular motion (which is a form of acceleration)

[Aurelian]

Why aren't satellites falling towards earth?
how does the centripetal force cancel out the force of gravitation? aren't the centripetal force and gravitational forces acting in the same direction?

The best way to conceive of this situation is to envisage the satellite as constantly trying to escape its orbit around the Earth to head into outer space. However, as much as the satellite tries, the Earth's gravity keeps pulling the satellite directly towards itself, perpendicularly to the direction in which the satellite is trying to escape. The result of this "tug of war" is a circular orbit around the Earth.