If you are in a rotating system newton's law do not work .Adding a frictious force can make the law work. If an orbiting object is in constant freefall under gravity . Even elliptical planet orbits are examples of freefall under gravity. The force F which the planet feels; this force can be resolved into two components, centripetal force F_C and tangential force F_T.
The tangential force causes an acceleration(newton's second law) which decreases the speed and the centripetal force causes the velocity to turn. In there is circular orbit of radius R, F_T=0 and the centripetal force is F_C=Mv^2/R;
The centrifugal force would be a vector with magnitude Mv^2/R( same as that of centripetal) pointing away from the sun but it does not really exist.
