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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.
The linear speed of Earth in its orbit around the Sun is approximately 107,300 kilometers per hour, or about 67,062 miles per hour. That speed is equivalent to 29.78 kilometers per second or 18.5 miles per second.