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I've already posted here on quora. But, I'm not totally sure if it's the most reasonable method.

Would anyone care to elaborate on how to find the average distance between stars in a given galaxy (For instance, let's take Milky way), somewhat efficiently and accurately - or at least clarify that my method is sufficiently efficient and accurate?

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Thanks for your input, but "best" is most often indicative of a subjectivity - for this reason I have reworded to use "efficient" and "accurate" instead, if this does not meet your criteria for the best method then please be more specific. –  Grant Thomas Aug 17 '11 at 22:22
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You seem to have an excellent grasp of how to go about solving the problem, but I wonder if it wouldn't be more useful to consider only far infrared luminosities to estimate the numbers of stars. As you know, most stars are cool red dwarfs and, in the visible, luminosity is dominated by either more massive main sequence stars (disks of galaxies) or evolved K giants (nuclear bulges of galaxies). Using far infrared also greatly reduces the effects of interstellar dust. –  Pete Jackson Aug 17 '11 at 23:57
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The answer may not be very useful, as the density of stars varies by orders of magnitude within most galaxies. For instance in the Milky Way, where the sun is, roughly within the galactic disk, but not in a spiral arm, it is several light years between stars on average. Within a spiral arm, the density is quite a bit higher, even more so in an active star forming region, like say the Orion Nebula. Then we have globular clusters, with a very high density of stars near the center. Then we have a very sparsely populated galactic halo region... –  Omega Centauri Aug 18 '11 at 18:35
    
Oh, very good points there - thanks! I'll try to add those points in when I have some time –  InquilineKea Aug 18 '11 at 19:44
    
How do you define "average distance"? The most straightforward definition is, I'm sure, not what you mean: the average distance between X and Y for each pair of stars X and Y in the galaxy. That would be some tens of thousands of light-years. Do you mean the average, over all stars in the galaxy, of the distance to that star's nearest neighbor (e.g., about 4.3 light-years for the Sun)? How do you handle multi-star systems? How do you define multi-star systems? How do you define "star"? And the core is going to skew the results quite a bit, as are clusters. –  Keith Thompson Nov 25 '11 at 20:36

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up vote 5 down vote accepted

As has been said, this is probably a very subjective question/answer. Not only that, but the composition of galaxies, and even regions within a galaxy, varies a great deal. Then there is the question of what constitutes as being part of the galaxy as opposed to perhaps a small orbiting dwarf galaxy. The answer you got from the Quora seems to be pretty comprehensive.

The volume of an area of interest, divided by the number of stars in that area seems to be the one that most people take as the approach. Which may not get a very accurate result, but smoothed out over said volume. Although, I will note that the first technique given on the quora site gives an answer that is close to the accepted "average" in the Milky Way, so at least there doesn't seem to be a large disagreement there. Of course, that assumes that the same initial starting conditions are used in both problems, which is highly unlikely since they aren't totally agreed upon anyway.

EDIT TO ADD: For more examples of similar math, here Dr. Plait calculates the number of habitable planets (where he shows the calculation for the volume of the galaxy). Making some assumptions of our own (like 200,000,000,000 stars which is LOW in my opinion), we come out to an average distance of about 5 light years. Doubling the number of stars gives an average of about 4 light years though, so again, we are not off by factors.

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