Why can I see the Andromeda Galaxy despite Milky Way's rotation?

Question

Okay ... so, I woke up from a dream last night wherein I was (apparently) attempting to devise a time-keeping system for interstellar travel (similar to the stardate system used in Star Trek). In the dream, I was attempting to correlate our current calendar, based on Earth's movements relative to the sun, with this fictitious calendar using the positions of intergalactic stellar bodies in comparison to Milky Way. (i.e., What if we could tell time based on the way other galaxies moved in relation to our own galaxy?)

So, in the dream, I was understanding that Milky Way is a spiral galaxy which rotates around a galactic center. That Earth is toward the middle-end of one arm of Milky Way's spirals. That almost every star we see in the night sky is inside Milky Way with us, and that the galaxy Andromeda is a great distance beyond Milky Way and can be seen in the night sky over Earth in the same location (between constellations Cassiopeia and Pegasus) every night since (at least) 10th century C.E.

Assuming Milky Way was graphed on a flat sheet of paper with the Galactic Center plotted at X=0,Y=0, and the arm which contains Earth was located at X=0,Y=-δ, and also assuming the galaxy Andromeda can be seen in earth's sky from this position ... why then, when Milky Way rotates around it's galactic center so that the arm which contains Earth is located at X=+δ,Y=0 (a rotation of 90°), or even X=0,Y=+δ (a rotation of 180°) is the galaxy Andromeda still visible in the same location in the sky?

Unless the galaxy Andromeda is in some sort of galactic-synchronous orbit with Milky Way (which seems unlikely since most of the posts referencing Andromeda here deal with the collision of the two galaxies), then, in the in either of the second rotational positions listed above, Andromeda should no longer be visible.

What am I missing? Why does Andromeda, which is not a part of Milky Way, only move in the night sky in relation to Earth's seasons and not in relation to any other galactic movement?

Answer 1

As barrycarter already pointed out, it is due to the huge time it takes for the milky way to rotate.

For once, as he pointed out, the stars in an orbit similar like the sun take about 250 million years for one full revolution around the center of the galaxy. If you put that in a relation to an earth year and take our civilization of roughy 6000 years of keeping records in comparison, we exist roughy 12 minutes of our galactic year. If you only take the last 150 years of the modern era, it's down to 18 seconds.

So if you compare that, how much does Earth move around the sun in 18 seconds? That is about how much Andromeda has apparently moved relative to the constellations in the night sky since we can capture visual images on film.

Answer 2

It is certainly true that the galactic orbit is very slow. Yet it should be noted that even if the Sun/Earth system orbited the galaxy once every century, the Andromeda galaxy would still be seen in essentially the "same part of the sky" at all times. This is because the only way objects appear to move in the sky, due to the motion of the Earth, is an effect called parallax, which depends on the ratio of how far the observer moves divided by how far away is the object. Andromeda is so far away that this ratio is 0.01, so that's not enough to make Andromeda move significantly to a different part of the sky.

Now, if the Sun orbited the galaxy every century, then all the stars in our galaxy would also be in rapid orbits at different orbital rates, so the stars and constellations would be scrambled over human history, so much more rapidly than they already are. But that really doesn't relate to where we would see Andromeda, only what background of stars we would see it against, so that doesn't seem to be the issue here.

The main point is, as objects go around in an orbit, one must avoid the tendency to imagine that the various axes of orientation rotate as well. This is a common mistake for understanding seasons, for the explanation would not work if the Earth's axis of rotation also re-aligned in synch with the Earth's position around the Sun, as if connected rigidly to the Earth-Sun line. So we should not think of an orbit as a global rotation, we should think of it as a circular translation of just the object and not any of its axes. It's true that we can go into an orbiting frame by using a rotation, but then we also have to rotate the distant objects in that frame, which is confusing if we want to understand where they will appear in the sky. Restricting to a circular translation shows that the only effect is parallax.

Also, we should constrast the general situation of how parallax alters location in the sky, with what happens in the special case of the Earth's orbit around the Sun over the seasons. As pointed out in the question, objects do appear to change locations in the sky in different seasons, even though the parallax is very small. But that's only because what is actually changing is the location of the Sun in the sky, not the other objects, and the parallax for the Sun is very large. Since the Sun is so bright, its location affects not the location of other things, but when we can see them, as its brightness blots out our view.