Is time taken into account by astronomers when creating and using maps of the universe?

Question

There's really two questions I'm asking.

Firstly, when maps are produced of stars and galaxies, are they just produced as we see them now from our viewpoint? Or are they based on the motion of those bodies? Eg Galaxy X is 1 million light years away and we know it's moving at Y speed, so it's real position now is actually 1 million years worth of movement along that trajectory.

Secondly, are those things taken into account when doing other studies of things like dark matter? Ie things are actually further apart than what we see because we're seeing them as they were Z million years ago. I would expect that would affect calculations for things like how much 'missing' matter there was.

To try to further clarify this second question, simplifying things to 3 points on a triangle... if we're at A and we observe points B and C which are X billion light years apart, then the effect of gravity on the speed of B and C moving apart would have been greater in the past when they were closer together and furthermore the effects of the current gravitational force will take more than X billion years to reach the other object. As far as I understand, dark matter is a way to account for observed gravitational effects that can't be accounted for in other ways. When astronomers do these calculations, can I assume that they have taken into account the time delay in the effects of gravity between galaxies? Or have I in my naivety, stumbled on some profound insight! (I doubt it.)

Answer 1

For the first part of your question, @userLTK has already provided a very good explanation, and I believe that by introducing redshift, the second part of your question is also partially answered. I will try to expand a little on it, hoping that I have understood your question correctly. To start off, I'm going to go ahead and quote my own thesis (not yet published);

[W]hen moving to celestial distances we quickly realise that time measurement ambiguity also arises. To combat this we tend to not describe distances to objects directly, but relate these properties to an object’s relative line-of-sight velocity with respect to us.

This is why, when NASA earlier this year announced the Hubble Space Telescope having observed the most distant galaxy yet, the distance to the galaxy was never mentioned. The distance is not a direct observable, and has to be calculated based on certain assumptions. One direct observable we do have, is the line-of-sight velocity, which we express in terms of redshift. By describing objects in terms of redshift, we simultaneously have a "distance" measurement to the objects, as well as knowing how fast they move away from us.

When we make observations and try to learn more about things like the energy content of the universe (radiation, regular matter, dark matter, dark energy), the redshifts of the objects we observe are crucial. We consider various models of the universe, and see how they compare with what we observe on different redshifts. I very quickly found back to a paper written by my supervisor some years back; figure 7 in there shows you that kind of comparison.

Personally, I am working on something which I hope will lead to us being able to see whether dark energy evolves over time. In doing that, knowing the redshifts of the objects are crucial to my work, and I constantly need to keep in mind the implications of the distant objects' movement away from us. It is simply a factor I need to multiply or divide by in my calculations, to make sure I am comparing the correct things with each other.

Answer 2

For any local map of galaxies, the relative velocity is slow enough as to be irrelevant. Andromeda and the Milky way are roughly 2.5 million light years apart and they are moving towards each other currently at about 1 light year every 2,270 years (based on 402,000 km/h). In the 2.5 million years that it takes for Andromeda's light to reach us, it's moved less than 0.05% closer to us, so any adjustment on the maps to account for Andromeda's distance relative to our galaxy would be very small and not worth adjusting unless you're actually plotting it's movement in great detail. For most maps, what we see, even 2.5 million years old, is close enough and that's true for all local galaxies. That said, your intuition is correct, the light we see and the pictures made of Andromeda are where it was 2.5 million years ago. The more interesting movement is that it's rotated a handful of degrees in that time.

For maps over a billion light years across or of the known universe, then it's a little different because the relative movement is sufficient to measurably have changed the map in the time it took the light to reach us. That said, calculating where galaxies would be now vs where they were when the light left them is rather a lot of work. What's commonly done, rather than show distance for maps of that size is that they're usually coded with a redshift percentage instead of the more familiar distance ratio key.

Redshift(V_H/c)

See here, lower right corner.

I realize I've not answered your 2nd question on missing matter. I'm not sure what you're asking.