Earth is orbiting the sun at about 60,000 mph. Galactic rotation is a big part of the sun's true motion. We go around the core about every 200 million years at a distance of however far we are from the core. Somebody [preferably a 1st year engineering student] should cruch the numbers and tell us the result in feet or miles. They say the Andromeda galaxy is approaching us, but we might be approaching the Andromeda galaxy, so that speed might be added in.
Too complicated. I regard myself as a privileged frame of reference, and everything is (or is not) in motion relative to me. From my point of view, here on earth, the sun isn't really going anywhere.
Fair enough. So relative to its old position, the Sun will have moved some significant, measurable distance in 8.3 minutes.
This brings up the really interesting question: is the Earth orbiting around the position of the Sun 8.3 minutes ago, as it would if Gravity travels as slow as the Speed of Light, or is the earth orbiting around the Sun at some point closer to the Sun's actual position at this moment, which would indicate that Gravity travels some measurable amount faster than Light.
I am not a 1st year engineering student, but will I do?
Distance of the Earth to the center of the galaxy: about 30,000 light years
Total distance traveled for one rotation = Pi x D = 188,400 light years
Speed of light = 299,792,458 meters per second
There are 86400 seconds in one day with approximately 365.25 days per year giving us approximately 31,557,600 seconds/year.
So the distance of one light year is around 9.46 x 1015meters.
This gives us a total distance travel for one rotation of 1.78 x 1021meters.
Rotational period of the galaxy: 2.25 x 108 years.
This gives us about 8 x 1012meters traveled per year.
8 x 1012 divided by 365.24 = approximately 2.2 x 1010 meters/day or 912,600 kilometers per hour.
This then is approximately 565,837 miles per hour or 157 miles per second.