Why the motion of earth around the sun is periodic motion but is not vibratory.

When a body rotates about a particular point or a line, keeping the distance of the particles of the body unchanged, it is called circular motion. Earth revolves around sun as it crosses a specific point at specific time that is why earth's motion is circular motion. 

Again, Periodic Motion If the motion of a moving object is such that it passes repeteadly through a definite point in the same direction in the same manner is called a periodic motion. However, earth revolves around sun at same direction. Therefore, it is not a periodic motion.

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