Is there a specific starting point and direction where the ball will travel in a circle or ellipse and perhaps never cross the equator? Presumably the ball keeps moving indefinitely, so what would these path's look like? Obviously without the force, any perpetually moving ball across the surface would move in a great circle, inevitably crossing the equator or riding perfectly along the equator, but with the Coriolis effect the path gets more complicated.
I imagine the path would be dependent on velocity, direction and starting place, so it might be a lot to explain or diagram. The Coriolis force increases with velocity too from what I've read.
I'm keeping this to velocities that would keep the ball on the surface of the Earth. No escape velocity or orbital velocity paths please. Also, lets ignore any spin from the ball (Friction-less Earth should cover that).
Thanks. An answer with pictures and logical explanation would be preferred over pure math, which would probably be over my head.