In uniform circular motion, (eg, a mass on the end of a string moving in a horizontal circle) centripetal force is the only thing causing acceleration. we have the kinematic relationship V=RW or velocity is proportional to radius. I.e a bigger radius means greater linear speed? For the motion of a satellite in earth orbit in uniform circular motion, we have centripetal force due to gravity alone. Equating the force of gravity to centripetal force we obtain V=square root of :(GM/R) i.e. speed is now INVERSELY proportional to orbital radius. I dont understand whats going on here. How can a centrally directed force, being the only thing causing acceleration, lead to two different relationships between V and R?