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When we say 'Andromeda galaxy is 2 500 000 light years away from us do we mean 'now' or in a far past and can this past be calculated easily?

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    $\begingroup$ As "is" implies that it still exists, that's not necessarily the case for astronomical objects, rather than whatever photons they 've emitted that are reaching us now. I very much doubt that that's the case for Andromeda, but there are several subtleties involved, which vary between cosmological models. In a preprint at arxiv.org/abs/astro-ph/0310808al, Lineweaver & Davis go into great detail about this, which, if you can get thru all their footnotes, can save you a lot of confusion between Special & General Relativity. $\endgroup$
    – Edouard
    Jan 20 at 5:03
  • $\begingroup$ There is no meaningful way of differentiating "nowness" of lightcone events. It is as now as can be. $\endgroup$ Jan 20 at 6:39
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    $\begingroup$ Answers might want to comment on how the answer would change if we were talking about a very distant galaxy. (As opposed to Andromeda, which is next door and not moving rapidly relative to us.) $\endgroup$
    – N. Virgo
    Jan 20 at 7:18
  • $\begingroup$ Do we remember something about the acceptance of an answer as the best one ??? $\endgroup$
    – Frobenius
    Jan 20 at 10:11
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    $\begingroup$ @Frobenius Let me study the answers.... Sorry. $\endgroup$ Jan 20 at 14:22

5 Answers 5

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The light that we see from the Andromeda galaxy was emitted 2.5 million years ago. During those 2.5 million years the Andromeda galaxy may have moved one or two thousand light years closer to us. However, the uncertainty in the 2.5 million light year distance estimate is of the order of 100 thousand light years (just because measuring the distance to other galaxies is hard) and the diameter of the Andromeda galaxy itself is about 200 thousand light years. So one or two thousand light years does not make a significant difference.

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    $\begingroup$ It might not make a significant difference in the age of Andromeda, but the notion that the uncertainty you've mentioned is not significant might be a little misleading concerning, for instance, spatial curvature, which, in turn, has implications for such existential issues as Poincare recurrence: Curvature has left the lambda-CDM "standard model" much more controversial than it was before 2019. See, for example, the paper at wizdom.ai/publication/10.1088/1361-6382/AC086D/title/… , which includes over 1,000 references. $\endgroup$
    – Edouard
    Jan 20 at 18:56
  • $\begingroup$ At arxiv.org/abs/2103.01183 , a preprint is available which might make the scope of the aforementioned paper more evident. $\endgroup$
    – Edouard
    Jan 20 at 21:38
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This is a more complicated question than you might think because in relativity there is no unique definition of time and therefore no unique definition of now. You have probably heard of time dilation, and this arises because different observers will in general define time in different ways.

However there is a natural choice for the time coordinate known as comoving time (aka cosmic time). This is the time since the Big Bang as measured by observers who are stationary relative to the cosmic microwave background. Unless specified otherwise the term time in cosmology usually means this comoving time. So now for the Andromeda galaxy would 13.7 billion years since the Big Bang, just as now for us humans means 13.7 billion years since the Big Bang.

Other answers have pointed out that Andromeda is relatively close to us and moving relatively slowly, so lets use the example of the distant galaxy GN-z11 instead. When you see the term distance used in popular science articles it generally means the apparent distance. So for example you might read that the distance to GN-z11 is 13.4 billion light years. But this means GN-z11 was 13.4 billion light years away when the light we are seeing today was emitted. Since GN-z11 is moving away from us it has increased the separation from us in that 13.4 billion years and if using comoving time as discussed above it is now about 32 billion light years away.

To avoid this confusion cosmologists will normally use the terms proper distance, or just refer to the distance using the red shift. So the answer to your question is: "It depends". If you are reading a popular science article the word distance almost certainly means "The distance from us when the light we are seeing today was emitted". If you are talking to a cosmologist they will probably say proper distance or red shift, and by that they mean the distance now where now refers to comoving time.

You ask whether we can easily calculate the proper distance, and the answer is that we can though it is only easy for people who understand general relativity. We describe the expansion of the universe using a scale factor usually written as $a(t)$. If we know the way the scale factor changes with time we can use this to calculate the proper distance to galaxies like GN-z11, and indeed that's how the figure of 32 billion light years mentioned above was obtained. We have a pretty good idea of how the scale factor has changed with time, though we have been surprised before when dark energy was discovered and there is no guarantee we won't be surprised again in the future.

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  • $\begingroup$ What is the receding velocity of GN-z11 now if the receding velocity as I understood before 13.4 BY was very close to c from the present Earth position (in no sense the Earth position 13.4 BY ago) ? It is now only visible from a place very distant from us which cosmological event horizon can contain GN-z11... $\endgroup$ Jan 20 at 15:04
  • $\begingroup$ @KrešimirBradvica for the first half of the universe's history the recession velocities decreased with time as the combined mass of the universe slowed the expansion. Recently dark energy has started to accelerate the expansion again and the recession velocities are now increasing with time. Offhand I don't know what the recession velocity of GN-z11 is now (comoving "now"). $\endgroup$ Jan 20 at 15:37
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When we look at the Andromeda galaxy, we see it as it was $2.5 \times 10^6$ years in the past, because the light from there was emitted $2.5 \times 10^6$ years ago. In that time, the galaxy may have changed its distance, but probably not by a significant amount.

Distances to cosmic objects are obtained by astronomers using the cosmic distance ladder methods. Plural “methods” because there is not one particular way of making these measurements, but a ladder of methods:

The ladder analogy arises because no single technique can measure distances at all ranges encountered in astronomy. Instead, one method can be used to measure nearby distances, a second can be used to measure nearby to intermediate distances, and so on. Each rung of the ladder provides information that can be used to determine the distances at the next higher rung.

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Since the relative speed between the Miliky Way and the Andromeda system is much smaller than the speed of light the difference is in this relatively very small.

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We generally mean "is now", because the word "is" means present.

The problem is that where we see it now, is where it really was 2.5 million years ago, because the light from Andromeda which we are seeing now, has taken 2.5 million years to reach us.

So Andromeda has of course moved since then.

But the galaxy moves much slower than the speed of light, so it really doesn't matter.

It might be that instead of 2500000 light years as we see it, its now in fact 2499000 light years from us in reality, but we can't yet see it in that location for another 2.499 million years. But its going to look virtually identical for all practical purposes, as far as we can tell.

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