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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.
New Horizons is traveling at about 15 km/s, 2 km/s slower than Voyager 1, and is still slowing down. When New Horizons reaches the same distance from the Sun as Voyager 1 is now, its speed will be about 13 km/s (8 mi/s).