So imagine a tennis ball (or other object) attached to a string and spun in perfectly horizontal circular motion at a constant velocity. The two forces acting on the ball would be the force of tension (pulling the ball towards the center aka centripetal force) and the force of gravity (pulling the ball downwards aka weight).
In order for the ball to not succumb to gravity, its centripetal force must be greater, right?
So therefore, would the centripetal force have to be equivalent (or greater) than the force of gravity on the ball? Is the weight of the ball always going to be the minimal centripetal force required to keep the ball in motion?
On one level this seems almost intuitive (you want to balance the forces) but on the other I feel like gravity shouldn't even play a part in horizontal motion.
Any help in clearing up my befuddled brain is greatly appreciated.