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Galaxies are organized systems a few hundred to hundreds of thousands of light years across made of thousands to trillions of stars sometimes mixed with gas and dust all held together by their mutual gravity and the gravity of dark matter. There is not some unfortunate astronomer counting up all the stars in the galaxies. You can quickly get an estimate of the number of stars in a galaxy by dividing the total luminosity of the galaxy by a typical star's luminosity. A more accurate value would result if you use the galaxy's luminosity function (a table of the proportion of stars of a given luminosity). Or you could divide the total mass of the galaxy by a typical star's mass (or use the mass function to get the proportions right) but one must also consider the dark matter that makes up at least 90% of the mass of galaxies. The presence of such a large proportion of dark matter is one of the defining feature of a galaxy that distinguishes it from an open or globular cluster: galaxies are 90% to 99.99% dark matter while star clusters have very little to zero dark matter. Star clusters are also composed of stars with the same composition and age while stars in a galaxy usually have a range of compositions and ages.
The distances between galaxies are large and are often measured in megaparsecs. A megaparsec is one million parsecs (or about 3.3 million light years). For instance, the distance between the Milky Way and the closest large galaxy, the Andromeda Galaxy, is about 0.899 megaparsecs. There was a big controversy in the 1910s and early 1920s over whether the nebulae called galaxies were outside the Milky Way or were part of it. There was so much controversy that the National Academy of Sciences held a debate between the opposing sides in 1920. Those favoring a large Milky Way with the spiral nebulae inside it were represented by Harlow Shapley. Those favoring the spiral nebulae as separate groups of stars outside the Milky Way were represented by Heber Curtis. The Shapley-Curtis debate did not decide much beyond the fact that both sides had powerful evidence for their views.
Edwin Hubble and Milton Humason set out to resolve the debate by using the largest telescope at the time, the 100-inch telescope on Mount Wilson, to study the large spiral nebula in the Andromeda constellation. Because of its large mirror, the telescope had sufficient resolving power and light-gathering power to spot individual stars in the Andromeda Galaxy. In the mid-1920s they discovered Cepheid variables in the galaxy and used the period-luminosity relation to find that the distance to the galaxy was very much greater than even the largest estimates for the size of the Milky Way. Galaxies are definitely outside the Milky Way and our galaxy is just one of billions of galaxies in the universe. Their discovery continued the process started by discovered Copernicus long ago of moving us from the center of the universe.
It is ironic that the person who moved the Sun from the center, Harlow Shapley, would be the one to hold fast to our galaxy being the center of the universe. Scientists are humans with all of the greatness and foibles that comes with being human. Despite our prejudices, nature and experiments will always ultimately show us the truth about the physical universe.
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last updated: June 28, 2022