How big would the Milky Way be if all the stars were emptied into one sphere? Neglecting the fact that this ball of gas would just collapse on itself - I'm curious if there's an agreed-upon measurement that takes into account the volume of all the ~100 billion stars to predict the diameter of a milky way where all the gas is in one orb. If not, is it safe to just use the volume of our Sun (which is an &quot;average&quot; star) and multiply by 100 billion or is there a more accurate data set to include in the calculation?
Asking for a 6-year-old :)
Obviously the answer depends on what the density of such a sphere was!
The only sensible way I can interpret this question is to ask what is the combined volume occupied by all of the galaxy's stars and then get a spherical radius from this.
A modal star in the galaxy has a mass of around 0.3 times the Sun and a radius of 0.3 times the Sun. Since the stellar mass distribution is quite peaked at that value, we could do worse than simply assume that we have about $10^{11}$ stars like this, since stars of higher and lower masses are less common.
In which case, the radius containing a similar total volume is just $0.3\times 10^{11/3}\ R_\odot= 1400R\odot$.
The problem with this calculation is that although the masses of stars are quite peaked, their radii are not. Some evolved stars individually have radii that are a significant fraction of the combined radius figure. Thus although the figure above might be good for the combined radius of all main sequence stars it certainly isn't a good number if you wanted to include all giant stars, with the densities they have now.