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Pretty much awkward question though. I would like to ask how is the volume of a Galaxy X is measured? For example consider milky way, what are the techniques to measure the same? How accurate and precise are the obtained results? What instruments are used for the same? When was this techniques developed? What are he beneficial outcomes of determining the GALAXIES' volume?

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    $\begingroup$ Is there a particular example of the volume of a galaxy that you have seen, and provoked this question. I'm not sure if "volume" is well defined for galaxies. $\endgroup$ – James K Mar 5 '20 at 19:52
  • $\begingroup$ If you can't find an example of a galactic volume to support your question, you can change it to ask "How might the volume of a galaxy be defined?" But then people will ask how you plan on using it because you could use a gravitational definition or a density definition. $\endgroup$ – uhoh Mar 5 '20 at 22:29
  • $\begingroup$ People, I don't believe that there should be a edit in the question. However, I do have mentioned the questions concerned.... $\endgroup$ – Pranay Mar 6 '20 at 12:17
  • $\begingroup$ Thoughts: 1) consider the bounding box for 99% of the galaxy (ignoring stragglers), 2) assume the galaxy is a double frisbee-like structure and compute the volume of that, 3) draw a small sphere around each solar system and connect the spheres with very thin tunnels. (1) and (3) would be the extreme measures $\endgroup$ – user21 Mar 9 '20 at 3:19
  • $\begingroup$ To calculate the volume, you first need to define the boundary. Are you including outermost stars, or the gas envelope that extends much further out? What about the dark matter halo? $\endgroup$ – Chappo Hasn't Forgotten Monica Mar 9 '20 at 22:47
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The volume isn't well-defined, because the radius isn't. There are practical values for the radius such as scale length/height, half-light radius, $R_{200}$, etc. that are commonly used, depending on what you're interested in. But the densities never reach zero, so any value for the radius will be arbitrary. Moreover, you always only observe a 2D projection of a galaxy, so the third dimension is even more uncertain.

At any rate, I can't think of any use of the volume of a galaxy. Various scaling relations exist between the radius and quantities such as mass, concentration, rotation velocity, etc., and of course such scaling relations also correlate with volume, but since volume is more uncertain than radius, I don't see a reason for trying to estimate it.

Sometimes one is interested in the volume filling factor of various components of the galaxy, e.g. the volume fraction occupied by warm gas, hot gas, or molecular clouds. But in this case there's no need to define a precise volume of the total galaxy; one may just consider "a representative part" of it.

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