Centripetal Force = (mv^2)/r
The centripetal force must always act towards the centre of the circle in which the satellite is travelling. Therefore it is a attractive force from the Earth and hence gravitational attraction that provides the centripetal force.
From the above equation we can see that the centripetal force relies on three things:
m = the mass of the satellite
v = the velocity at which the satellite is travelling
r = radius of the orbit (the distance between the satellite and the earth)
So these are the factors affecting the centripetal force.