<p>M31 is actually something like 141,000 light-years in diameter (there has been some variation in our understanding of its size, but 141K is good compromise).  M31 is 2.54 million light-years from us.  The rotational speed of stars near the edge of the galaxy's disk is in the vicinity of 200 km/sec. </p>

<p>Given all that, in one year a star in the vicinity of the outer edge of the galaxy's disk is going to traverse 6.3 x 10<sup>9</sup> km.  At 2.54 x 10<sup>6</sup> light-years away, the apparent movement of such a star in the course of a year is going to be about 1.5 x 10<sup>-8</sup> degrees, or 0.000054 arcseconds.</p>

<p>The Keck Telescopes in Hawaii, one of the most powerful telescopes in the world, has an angular resolution of 0.04 arcseconds.</p>

<p>As you can see, the best telescope in the world cannot distinguish any change of position of any star at that distance over the course of a year.  It would take about 740 years before such a star would move far enough for a telescope with the angular resolution of the Keck to distinguish any movement at all.</p>

<p>So, it isn't visible through an amateur telescope either.</p>

CC BY-SA 3.0
2014-01-14T08:18:02.637Z
I read the question slightly differently, but the answer is still in here. I thought it wasn't about resolving individual stars but the redshift differential between the part of the disk moving towards us and the part moving away from us. So that would be a difference of ~ 400 km/s, or 0.13% c if it was oriented flat towards us (which it isn't exactly, so the difference should be somewhat smaller). But would this redshift difference be observable, with one side of the disk shifting towards blue and the other towards red?
TildalWave
CC BY-SA 3.0
2014-01-14T09:15:11.840Z
I actually meant what he answered about, but the redshift perspective is also interesting. I suspect there would be a an increase in gravitational redshift closer to the center, and that the sides would have red- and blueshift but redshift would not be possible to see in an amateur telescope regardless (due to the wide spectrum of light coming from a star anyway). The angular movement of a star closer to the center would be much higher, but then the relative distance between them would also decrease.
frodeborli
CC BY-SA 3.0
2014-01-14T16:29:31.273Z
@TildalWave, I read "...the approximate real position of stars..." as dealing with images, not redshifts, and since he wrote about visibility of the effect through an amateur telescope, it seemed that visible light imaging was the subject of the question.  In fact, measuring red (and blue) shifting is how they measure the velocity of stars in the galaxy.
Cyberherbalist
CC BY-SA 3.0
2014-01-14T19:34:14.590Z
Hmm, good answer @Cyberherbalist, though I'm not convinced we can even resolve individual stars in M31 in the first place.
astromax
CC BY-SA 3.0
2014-01-14T21:58:14.573Z
Neither am I, @astromax, with the exception of supernovae that might occur there, but in any case, if we *could* resolve any individual stars, that would be the situation.
Cyberherbalist
CC BY-SA 3.0
2014-01-14T23:59:12.413Z
Well, the answer is wrong. The question is "where the stars are really located at present" (or did I misunderstand you too, @frodeborli). What the derivation shows is by how much do the stars move per year in Andromeda. The correct answer would estimate the time the light travels to us (done) and the motion of the stars during that time (not done). The resulting angle will be of order v/c, about 0.1% as said by TildalWave, which means that real stars are offset by about $(180*10^{-4}/\pi) \textrm{deg} \approx 20$ arcseconds, which is very accessible, but not so impressive visually on pictures.
Alexey Bobrick
CC BY-SA 3.0
2014-01-15T07:57:15.197Z
@AlexeyBobric That is relative to us? I'm thinking *most offset* compared to the *least offset* stars in M31.
frodeborli
CC BY-SA 3.0
2014-01-15T12:47:14.593Z
@frodeborli: That is, the stars are in reality 20 arcseconds off from where we see them, because we see how they were in the past and not now.
Alexey Bobrick
CC BY-SA 3.0
2014-01-15T14:33:51.193Z
Yes, but the most distant stars in M31 I assume will be something like 20.01 arcseconds off, while the least distant stars in M31 is something like 19.99 arcseconds off. I don't think that would be observable in amateur equipment.
frodeborli
CC BY-SA 3.0
2014-01-14T01:40:28.043Z
2014-01-14T21:59:23.830Z
2014-01-14T21:59:23.830Z
Cyberherbalist
<p>The Andromeda Galaxy is tens of thousands of light years in diameter. That suggests that the most distant stars in the Andromeda galaxy is up to tens of thousands of years "behind" in their orbit around the galaxy, compared to the closest stars. Have anybody generated pictures of the galaxy, which shows the approximate real position of stars? Is this effect visible when looking at the Andromeda galaxy through an amateur telescope?</p>

<telescope><light><rotation>
Pictures of large galaxies
frodeborli
# Pictures of large galaxies

(Asked by: username_0 on 2014-01-13)

The Andromeda Galaxy is tens of thousands of light years in diameter. That suggests that the most distant stars in the Andromeda galaxy is up to tens of thousands of years "behind" in their orbit around the galaxy, compared to the closest stars. Have anybody generated pictures of the galaxy, which shows the approximate real position of stars? Is this effect visible when looking at the Andromeda galaxy through an amateur telescope?

**Tags:** telescope, light, rotation

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## 1 answers

### Answer by username_1 on 2014-01-14. Score: 5 | Accepted answer

M31 is actually something like 141,000 light-years in diameter (there has been some variation in our understanding of its size, but 141K is good compromise). M31 is 2.54 million light-years from us. The rotational speed of stars near the edge of the galaxy's disk is in the vicinity of 200 km/sec.

Given all that, in one year a star in the vicinity of the outer edge of the galaxy's disk is going to traverse 6.3 x 109 km. At 2.54 x 106 light-years away, the apparent movement of such a star in the course of a year is going to be about 1.5 x 10-8 degrees, or 0.000054 arcseconds.

The Keck Telescopes in Hawaii, one of the most powerful telescopes in the world, has an angular resolution of 0.04 arcseconds.

As you can see, the best telescope in the world cannot distinguish any change of position of any star at that distance over the course of a year. It would take about 740 years before such a star would move far enough for a telescope with the angular resolution of the Keck to distinguish any movement at all.

So, it isn't visible through an amateur telescope either.

> **Comments:**
> **username_2**: I read the question slightly differently, but the answer is still in here. I thought it wasn't about resolving individual stars but the redshift differential between the part of the disk moving towards us and the part moving away from us. So that would be a difference of ~ 400 km/s, or 0.13% c if it was oriented flat towards us (which it isn't exactly, so the difference should be somewhat smaller). But would this redshift difference be observable, with one side of the disk shifting towards blue and the other towards red?  
> **username_0**: I actually meant what he answered about, but the redshift perspective is also interesting. I suspect there would be a an increase in gravitational redshift closer to the center, and that the sides would have red- and blueshift but redshift would not be possible to see in an amateur telescope regardless (due to the wide spectrum of light coming from a star anyway). The angular movement of a star closer to the center would be much higher, but then the relative distance between them would also decrease.  
> **username_1**: @TildalWave, I read "...the approximate real position of stars..." as dealing with images, not redshifts, and since he wrote about visibility of the effect through an amateur telescope, it seemed that visible light imaging was the subject of the question.  In fact, measuring red (and blue) shifting is how they measure the velocity of stars in the galaxy.  
> **username_3**: Hmm, good answer @Cyberherbalist, though I'm not convinced we can even resolve individual stars in M31 in the first place.  
> **username_1**: Neither am I, @astromax, with the exception of supernovae that might occur there, but in any case, if we *could* resolve any individual stars, that would be the situation.  
> **username_4**: Well, the answer is wrong. The question is "where the stars are really located at present" (or did I misunderstand you too, @frodeborli). What the derivation shows is by how much do the stars move per year in Andromeda. The correct answer would estimate the time the light travels to us (done) and the motion of the stars during that time (not done). The resulting angle will be of order v/c, about 0.1% as said by TildalWave, which means that real stars are offset by about $(180*10^{-4}/\pi) \textrm{deg} \approx 20$ arcseconds, which is very accessible, but not so impressive visually on pictures.  
> **username_0**: @AlexeyBobric That is relative to us? I'm thinking *most offset* compared to the *least offset* stars in M31.  
> **username_4**: @frodeborli: That is, the stars are in reality 20 arcseconds off from where we see them, because we see how they were in the past and not now.  
> **username_0**: Yes, but the most distant stars in M31 I assume will be something like 20.01 arcseconds off, while the least distant stars in M31 is something like 19.99 arcseconds off. I don't think that would be observable in amateur equipment.  

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