Rotate an Object from Point A to B

you should use quanternions to avoid gimbal lock.

you will probably need to store the initial hit location and the current hit location on the sphere, then subtract those from the center of the sphere to get vectors pointing at the center. then use cross product on those vectors to find a perpendicular vector, and use that as XYZ of a quanternion, and W would be based on the dot product of those hit vectors multiplied by 180, causing a rotation around that axis we found from the cross product… or something like that. good luck.