Rotate a moving object

I want to rotate a ball in a circle, and then move the ball into random places. So the circle it makes should remain the same size but the ball should still be able to move around.

I tried this

         transform.RotateAround(Vector3(transform.position.x,transform.position.y,transform.position.z+2),Vector3.up, 3 * Time.deltaTime);        

but that didn't work because as the ball moves the point of rotation also moves,

I just can't figure out how to do this

P.S. I want to do this without parenting, I know it can be done, in fact i was doing this with parenting for a while, but, it was causing me a lot of problems and i wish to avoid them

thanks!