Jeff, a 31 year old male from the Internet asks on May 12, 1999,How do astronomers know the true position of stars? When astronomers show us pictures of the Great Wall (or any celestial map for that matter), are they the 'true' position of those stars and galaxies? The light reaching earth may be several hundreds, thousands or millions of years old...the stars have travelled in that time. Do astronomers correct for the star's motion to show where they actually are now when drawing a map?
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In almost all cases in the astronomy literature, illustrations and maps are constructed representing objects as they appear to us now. There are several reasons for this. In our own galaxy, light travel time is fairly small (under a few thousand years for most telescopic objects, and under a few tens of thousands of years for the most distant things we can really image at all in our galaxy). I know this doesn't sound small, but it really is, comparatively speaking, with respect to the timescales on which significant changes tend to happen astronomically. Maps and diagrams of other galaxies, such as the "Great Wall" are also constructed as they currently appear. In the case of the "Great Wall" itself, this means that we are seeing things a few hundred million years old. To put this in perspective, galaxies moving about in a tight cluster go from side to side in a few billion years, and the stars inside a large spiral galaxy (like ours) orbit in about a quarter billion years. So pictures of "Great Wall" galaxies will show the galaxies not too far displaced from where they currently are, though their spiral arms have made a significant part of a revolution in the intervening ages. The primary reason that we can't do better is that we don't know where the galaxies in a cluster are to sufficient accuracy to map their movements beyond where we see them now. We know, of course, quite accurately how they appear to us in the sky, but the third dimension of distance is known to much less precision.
The velocities suffer an opposite problem: we can measure the speed at which galaxies are moving towards or away from us to high precision, but we cannot measure at all (with current technology) whether they are moving left or right, up or down, in a picture. So we can only make vague statements about the exact appearance of a galaxy cluster some billions of years down the line. What we know about the general evolution of galaxy clusters comes from studying many galaxy clusters of different ages and types. It would be nice if we could specifically correct for the motions: we'd learn a lot more about the dynamics of individual clusters. But for now we can't, and must make do with deductions based on the behavior of large samples of galaxy clusters. New technology in the next decade or so will start to give us a handle on galaxy motions, though, so science marches along.
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