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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.
Standing anywhere on earth you are traveling around the sun at about 65,000 MPH. Standing anywhere within our solar system you are traveling around Sagittarius A at about 640,000 MPH. But the entire galaxy is moving through space at about 1,000,000 MPH. The speed of light is 669,600,000 MPH.