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The sun at its equator rotates on its axis once every 25.4 days and every 36 days at its poles. This is why you see sunspots moving across the surface in time lapsed films. It also orbits around the center of the Milky way Galaxy. The galactic year for our sun is about 250 million years.
The dynamics of this galactic orbit of the sun is a bit different than our orbit around the sun. Earth is orbiting a gravitational point in space caused by the sun, whereas the sun orbits a collective center of mass of billions of suns which each individually have virtually no gravitational influence on our sun.
The sun also oscillates up and down relative to the galactic plane about 2.7 times per orbit which gives the path a wave pattern around the galactic center.