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Using speed measurements of the gas at different distances from the Galactic center, the Sun appears to be cruising along at 200 kilometers per second and it takes 240 million years to complete the grand circuit around the Galaxy. This speed is an absolute speed.
It spins (rotates) at a speed of about 1,000 miles (1600 kilometers) per hour and orbits around the Sun at a speed of about 67,000 miles (107,000 kilometers) per hour. We do not feel any of this motion because these speeds are constant.