zuz said:
When a photo of a nearly edge on galaxy, say Andromeda, is taken. Why are the stars on the far side of the galaxy so clear? The light from those stars took an additional 220,000 years to reach us. Those stars have moved quite a lot from their positions since the light from the foreground stars left them. Shouldn't the background be fuzzy?
As already pointed out, "fuzziness" would have to involve really long exposures during which the stars were moving. But this would effect both the near side and far side stars equally as they both would be moving during the exposure.
Perhaps, you are thinking more along the lines as to why the galaxy doesn't look "distorted". If we are seeing near side stars where they were at a time 220,000 years later than than where we are seeing the far side stars, shouldn't the galaxy look kind off "bunched up" on one side and stretched out on the other?
To answer this we need to compare the galactic rotation rate against that time delay. Our sun is about 27,000 light years away from the center of the Galaxy. Which puts its orbital diameter at ~ 54,000 ly. It also takes roughly 230 million years to complete 1 full orbit around the center. This means that in the 54,000 yrs it takes for light to cross its orbit, it will have only traveled 1/4259 of a complete orbit, or 1/12 of a degree. This is how much of a "shift" you would expect to see in stars on opposite sides of this orbit when viewed edge on.
If we are looking at a galaxy with a typical flat rotation curve, then looking across greater diameter of the galaxy won't make this visual angular shift larger. A flat rotation curve means that the orbital velocity of the star remains the same as you move outward. Moving outward means traveling in a larger circle. traveling a larger circle at the same speed takes more time. So at 110,000 ly from the center, or about twice the distance of the Earth from the center, a star would take about twice as long to complete a orbit, and the fact that it takes the light twice as long to cross the diameter results in us seeing the same 1/12 of degree shift.
1/12 of a degree is just too small a angle to cause any noticeable distortion in the image when seen by eye alone.
Another way to look at it is that if a star moves at ~ 200 km/sec then in 220,000 years it will have moved 1.4e15 km in 220,000 years. This is ~150 ly.
If we were looking at a photo of a galaxy 220,000 ly across, and and that photo has a resolution of 4000 pixels in width and the galaxy fills the image, each pixel in that photo represents 55 ly or a bit over 1/3 the distance moved by the star in the time it took light to cross the galaxy. This equates to less than 3 pixels worth of apparent shift in that 4000 pixel wide image.