newtonian mechanics - Weightlessness in Satellites

The following is written in my textbook as the reason for weightlessness felt in satellites:

The gravitational pull is counterbalanced by the centripetal force.

This introduces two problems:

1. 
   

   For satellites orbiting around Earth, gravity is, in fact, the centripetal force.

   
   


2. 
   

   If the gravitational pull and centripetal force on a satellite are both in the same direction, then how do they cancel each other out?

   
   

Answer

The statement:

The Gravitational Pull is counterbalanced by the Centripetal Force

is rubbish.

The satellite undergoes a centripetal acceleration because it is acted on by the gravitation force. Some people call the force which causes a centripetal acceleration the centripetal force. So in such a case the gravitational force and the centripetal force are one and the same thing. This is your statement 1.

The reason for thinking that you are weightless when in an orbiting satellite is that the satellite and your good self would be accelerating towards the Earth at exactly the same rate. So there is no normal reaction between you and the satellite.
You must have a force acting on you because otherwise you would not accelerate and hence not be in orbit.