What provides the centripetal force on a satellite and what are the factors that determine the size of the centripetal force on the satellite

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.