The sun and the solar system appear to be moving at 200 kilometers per second, or at an average speed of 448,000 mph (720,000 km/h). Even at this rapid speed, the solar system would take about 230 million years to travel all the way around the Milky Way.
"Note that the path of the Sun is tilted relative to the horizon. That means that, as the Sun moves from the civil twilight line to the horizon, it is travelling MORE than 6 degrees along its golden path. The purely vertical distance in this diagram between those two lines is 6 degrees, yes, but the Sun travels along a slanted line between them. If you work out the geometry, you will find that the actual distance the Sun travels along its path is about 8.5 degrees: 6 degrees vertically and about 6 degrees horizontally. If it takes the Sun 34 minutes to travel 8.5 degrees along its path, then the Sun is moving at an angular speed of (8.5 degrees) / (34 minutes) = 0.25 degrees per minute. At that rate, the Sun will travel (0.25 degrees per minute) * (1440 minutes) = 360 degrees in a single day (just as you would expect)."
Explanation:
(credit to the site for answer, this is not my work)