Can a motion that is periodic relative to one observer be non-periodic relative to another?
True
A body executes periodic motion about another body.
Particle A is going in a circle with fixed speed in the x-y plane. Can you think of a frame from where if looked the motion of A isn't periodic?
Let's assume I am also going in a circle of the same radius as A with the same speed, so I am always hovering over A.
To me A will look like as if it is at rest, and not doing a periodic motion.
So yes periodic motion is a relative term as is motion.