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You see \(G\cos\theta \) is not balanced ... which will cause the satellite to fall along the \(G\cos\theta\)
You should not label \(C_f\) as there is no force pulling outward. Circular motion is NOT a case of balanced forces. The \(G\sin \theta\) is what makes the orbit happen. If it were cancelled out, the plane would not move in the horizontal circle. \(G \sin \theta\) IS the centripetal force. When we are in that reference frame, however it only may feel like we have a force going outward since we are not in fact in an inertia l reference frame. Your reasoning to actually answer the problem is correct, though.
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probably ... I am not quite sure about forces.
Trust me, there is no such thing as \(C_f\) as you indicated.
It's been a stereotyped concept in my mind that a path (rest or motion) followed by a particle or body will be the result of balance of force.
Well in this case force seems to be compensated with acceleration.
the body is moving in circle...so no velocity component is along radius of circular path..it is moving with constant speed or time period so no acceleration in the direction it is moving..but its direction is always changing so by definition an acceleration is there..so a net force must act on it and that too perpendicular to its tangential velocity(so as not to increase its speed)..
now assume that you are in place of the body..in "your" frame you are staying still.but you know that a force is always pulling you towards centre (from above reasoning)..so a force must be assumed to act opposite to the centripetal force to balance everything and newton's 2nd law to make sense..
hence in any accelerated frame we assume extra forces so as for newtons laws to make sense..this assumed forces are Pseudo forces or as here centrifugal force Cf ..so while we are looking from an external frame we dont need Cf..we assume it only when our frame itself is rotating or accelarating..